
%%
@article{fds340470,
Author = {Oğuz, EC and Socolar, JES and Steinhardt, PJ and Torquato,
S},
Title = {Hyperuniformity and antihyperuniformity in onedimensional
substitution tilings.},
Journal = {Acta Crystallographica. Section A, Foundations and
Advances},
Volume = {75},
Number = {Pt 1},
Pages = {313},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1107/S2053273318015528},
Abstract = {This work considers the scaling properties characterizing
the hyperuniformity (or antihyperuniformity) of
longwavelength fluctuations in a broad class of
onedimensional substitution tilings. A simple argument is
presented which predicts the exponent α governing the
scaling of Fourier intensities at small wavenumbers, tilings
with α > 0 being hyperuniform, and numerical computations
confirm that the predictions are accurate for quasiperiodic
tilings, tilings with singular continuous spectra and
limitperiodic tilings. Quasiperiodic or singular continuous
cases can be constructed with α arbitrarily close to any
given value between 1 and 3. Limitperiodic tilings can be
constructed with α between 1 and 1 or with Fourier
intensities that approach zero faster than any power
law.},
Doi = {10.1107/S2053273318015528},
Key = {fds340470}
}
@article{fds342627,
Author = {Goshaw, A and Greenside, H and Socolar, J and Schaeffer,
D},
Title = {Robert Paul Behringer},
Journal = {Physics Today},
Volume = {71},
Number = {12},
Pages = {6060},
Publisher = {AIP Publishing},
Year = {2018},
Month = {December},
url = {http://dx.doi.org/10.1063/pt.3.4098},
Doi = {10.1063/pt.3.4098},
Key = {fds342627}
}
@article{fds326695,
Author = {Pham, AT and Zhuang, Y and Detwiler, P and Socolar, JES and Charbonneau,
P and Yellen, BB},
Title = {Phase diagram and aggregation dynamics of a monolayer of
paramagnetic colloids.},
Journal = {Physical Review. E},
Volume = {95},
Number = {51},
Pages = {052607},
Year = {2017},
Month = {May},
url = {http://dx.doi.org/10.1103/physreve.95.052607},
Abstract = {We have developed a tunable colloidal system and a
corresponding theoretical model for studying the phase
behavior of particles assembling under the influence of
longrange magnetic interactions. A monolayer of
paramagnetic particles is subjected to a spatially uniform
magnetic field with a static perpendicular component and a
rapidly rotating inplane component. The sign and strength
of the interactions vary with the tilt angle θ of the
rotating magnetic field. For a purely inplane field,
θ=90^{∘}, interactions are attractive and the
experimental results agree well with both equilibrium and
outofequilibrium predictions based on a twobody
interaction model. For tilt angles 50^{∘}≲θ≲55^{∘},
the twobody interaction gives a shortrange attractive and
longrange repulsive interaction, which predicts the
formation of equilibrium microphases. In experiments,
however, a different type of assembly is observed. Inclusion
of threebody (and higherorder) terms in the model does not
resolve the discrepancy. We further characterize the
anomalous regime by measuring the timedependent cluster
size distribution.},
Doi = {10.1103/physreve.95.052607},
Key = {fds326695}
}
@article{fds325483,
Author = {Oǧuz, EC and Socolar, JES and Steinhardt, PJ and Torquato,
S},
Title = {Hyperuniformity of quasicrystals},
Journal = {Physical Review B},
Volume = {95},
Number = {5},
Publisher = {American Physical Society (APS)},
Year = {2017},
Month = {February},
url = {http://dx.doi.org/10.1103/PhysRevB.95.054119},
Abstract = {© 2017 American Physical Society. Hyperuniform systems,
which include crystals, quasicrystals, and special
disordered systems, have attracted considerable recent
attention, but rigorous analyses of the hyperuniformity of
quasicrystals have been lacking because the support of the
spectral intensity is dense and discontinuous. We employ the
integrated spectral intensity Z(k) to quantitatively
characterize the hyperuniformity of quasicrystalline point
sets generated by projection methods. The scaling of Z(k) as
k tends to zero is computed for onedimensional
quasicrystals and shown to be consistent with independent
calculations of the variance, σ2(R), in the number of
points contained in an interval of length 2R. We find that
onedimensional quasicrystals produced by projection from a
twodimensional lattice onto a line of slope 1/τ fall into
distinct classes determined by the width of the projection
window. For a countable dense set of widths, Z(k)∼k4; for
all others, Z(k)∼k2. This distinction suggests that
measures of hyperuniformity define new classes of
quasicrystals in higher dimensions as well.},
Doi = {10.1103/PhysRevB.95.054119},
Key = {fds325483}
}
@article{fds325482,
Author = {Socolar, JES and Lubensky, TC and Kane, CL},
Title = {Mechanical graphene},
Journal = {New Journal of Physics},
Volume = {19},
Number = {2},
Pages = {025003025003},
Publisher = {IOP Publishing},
Year = {2017},
Month = {February},
url = {http://dx.doi.org/10.1088/13672630/aa57bb},
Doi = {10.1088/13672630/aa57bb},
Key = {fds325482}
}
@article{fds323248,
Author = {Rutkowski, DM and Marcoux, C and Socolar, JES and Hall,
CK},
Title = {Formation of limitperiodic structures by quadrupole
particles confined to a triangular lattice},
Journal = {Physical Review. E},
Volume = {95},
Number = {1},
Publisher = {American Physical Society (APS)},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.95.012604},
Abstract = {© 2017 American Physical Society. We have performed Monte
Carlo (MC) simulations on twodimensional systems of
quadrupole particles confined to a triangular lattice in
order to determine the conditions that permit the formation
of a limitperiodic phase. We have found that limitperiodic
structures form only when the rotations of the particles are
confined to a set of six orientations aligned with the
lattice directions. Related structures including striped and
unidirectional rattler phases form when π/π66 rotations or
continuous rotations are allowed. Order parameters signaling
the formation of the limitperiodic structure and related
structures are measured as a function of temperature. Our
findings on the formation of the limitperiodic structure
elucidate features relevant to the experimental creation of
such a structure, which is expected to have interesting
vibrational and electromagnetic modes.},
Doi = {10.1103/PhysRevE.95.012604},
Key = {fds323248}
}
@article{fds315560,
Author = {Hann, CT and Socolar, JES and Steinhardt, PJ},
Title = {Local growth of icosahedral quasicrystalline
tilings},
Journal = {Physical Review B},
Volume = {94},
Number = {1},
Publisher = {American Physical Society (APS)},
Year = {2016},
Month = {July},
url = {http://arxiv.org/abs/1604.02479v1},
Abstract = {© 2016 American Physical Society. Icosahedral quasicrystals
(IQCs) with extremely high degrees of translational order
have been produced in the laboratory and found in naturally
occurring minerals, yet questions remain about how IQCs
form. In particular, the fundamental question of how locally
determined additions to a growing cluster can lead to the
intricate longrange correlations in IQCs remains open. In
answer to this question, we have developed an algorithm that
is capable of producing a perfectly ordered IQC yet relies
exclusively on local rules for sequential, facetoface
addition of tiles to a cluster. When the algorithm is seeded
with a special type of cluster containing a defect, we find
that growth is forced to infinity with high probability and
that the resultant IQC has a vanishing density of defects.
The geometric features underlying this algorithm can inform
analyses of experimental systems and numerical models that
generate highly ordered quasicrystals.},
Doi = {10.1103/PhysRevB.94.014113},
Key = {fds315560}
}
@article{fds311986,
Author = {Marcoux, C and Socolar, JES},
Title = {Sparse phonon modes of a limitperiodic structure},
Journal = {Physical Review. B, Condensed Matter},
Volume = {93},
Number = {17},
Publisher = {American Physical Society},
Year = {2016},
Month = {May},
ISSN = {01631829},
url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.174102},
Abstract = {Limitperiodic structures are well ordered but nonperiodic,
and hence have nontrivial vibrational modes. We study a ball
and spring model with a limitperiodic pattern of spring
stiffnesses and identify a set of extended modes with
arbitrarily low participation ratios, a situation that
appears to be unique to limitperiodic systems. The balls
that oscillate with large amplitude in these modes live on
periodic nets with arbitrarily large lattice constants. By
studying periodic approximants to the limitperiodic
structure, we present numerical evidence for the existence
of such modes, and we give a heuristic explanation of their
structure.},
Doi = {10.1103/PhysRevB.93.174102},
Key = {fds311986}
}
@article{fds311987,
Author = {Fu, L and Steinhardt, W and Zhao, H and Socolar, JES and Charbonneau,
P},
Title = {Hard sphere packings within cylinders.},
Journal = {Soft Matter},
Volume = {12},
Number = {9},
Pages = {25052514},
Year = {2016},
Month = {March},
ISSN = {1744683X},
url = {http://dx.doi.org/10.1039/c5sm02875b},
Abstract = {Arrangements of identical hard spheres confined to a
cylinder with hard walls have been used to model
experimental systems, such as fullerenes in nanotubes and
colloidal wire assembly. Finding the densest configurations,
called close packings, of hard spheres of diameter σ in a
cylinder of diameter D is a purely geometric problem that
grows increasingly complex as D/σ increases, and little is
thus known about the regime for D > 2.873σ. In this work,
we extend the identification of close packings up to D =
4.00σ by adapting TorquatoJiao's adaptiveshrinkingcell
formulation and sequentiallinearprogramming (SLP)
technique. We identify 17 new structures, almost all of them
chiral. Beyond D ≈ 2.85σ, most of the structures consist
of an outer shell and an inner core that compete for being
close packed. In some cases, the shell adopts its own
maximum density configuration, and the stacking of core
spheres within it is quasiperiodic. In other cases, an
interplay between the two components is observed, which may
result in simple periodic structures. In yet other cases,
the very distinction between the core and shell vanishes,
resulting in more exotic packing geometries, including some
that are threedimensional extensions of structures obtained
from packing hard disks in a circle.},
Doi = {10.1039/c5sm02875b},
Key = {fds311987}
}
@article{fds312774,
Author = {Marcoux, C and Byington, TW and Qian, Z and Charbonneau, P and Socolar,
JES},
Title = {Erratum: Emergence of limitperiodic order in tiling models
(Physical Review E  Statistical, Nonlinear, and Soft Matter
Physics (2014) 90 (012136))},
Journal = {Physical Review. E},
Volume = {93},
Number = {2},
Publisher = {American Physical Society (APS)},
Year = {2016},
Month = {February},
ISSN = {24700045},
url = {http://dx.doi.org/10.1103/PhysRevE.93.029902},
Doi = {10.1103/PhysRevE.93.029902},
Key = {fds312774}
}
@article{fds248310,
Author = {Yang, Y and Fu, L and Marcoux, C and Socolar, JES and Charbonneau, P and Yellen, BB},
Title = {Phase transformations in binary colloidal
monolayers.},
Journal = {Soft Matter},
Volume = {11},
Number = {12},
Pages = {24042415},
Year = {2015},
Month = {March},
ISSN = {1744683X},
url = {http://dx.doi.org/10.1039/c5sm00009b},
Abstract = {Phase transformations can be difficult to characterize at
the microscopic level due to the inability to directly
observe individual atomic motions. Model colloidal systems,
by contrast, permit the direct observation of individual
particle dynamics and of collective rearrangements, which
allows for realspace characterization of phase transitions.
Here, we study a quasitwodimensional, binary colloidal
alloy that exhibits liquidsolid and solidsolid phase
transitions, focusing on the kinetics of a diffusionless
transformation between two crystal phases. Experiments are
conducted on a monolayer of magnetic and nonmagnetic spheres
suspended in a thin layer of ferrofluid and exposed to a
tunable magnetic field. A theoretical model of hard spheres
with point dipoles at their centers is used to guide the
choice of experimental parameters and characterize the
underlying materials physics. When the applied field is
normal to the fluid layer, a checkerboard crystal forms;
when the angle between the field and the normal is
sufficiently large, a striped crystal assembles. As the
field is slowly tilted away from the normal, we find that
the transformation pathway between the two phases depends
strongly on crystal orientation, field strength, and degree
of confinement of the monolayer. In some cases, the pathway
occurs by smooth magnetostrictive shear, while in others it
involves the sudden formation of martensitic
plates.},
Doi = {10.1039/c5sm00009b},
Key = {fds248310}
}
@article{fds248311,
Author = {Sun, M and Cheng, X and Socolar, JES},
Title = {Regulatory logic and pattern formation in the early sea
urchin embryo.},
Journal = {Journal of Theoretical Biology},
Volume = {363},
Pages = {8092},
Year = {2014},
Month = {December},
ISSN = {00225193},
url = {http://dx.doi.org/10.1016/j.jtbi.2014.07.023},
Abstract = {We model the endomesoderm tissue specification process in
the vegetal half of the early sea urchin embryo using
Boolean models with continuoustime updating to represent
the regulatory network that controls gene expression. Our
models assume that the network interaction rules remain
constant over time and the dynamics plays out on a
predetermined program of cell divisions. An exhaustive
search of twonode models, in which each node may represent
a module of several genes in the real regulatory network,
yields a unique network architecture that can accomplish the
pattern formation task at handthe formation of three
latitudinal tissue bands from an initial state with only two
distinct cell types. Analysis of an eightgene model
constructed from available experimental data reveals that it
has a modular structure equivalent to the successful
twonode case. Our results support the hypothesis that the
gene regulatory network provides sufficient instructions for
producing the correct pattern of tissue specification at
this stage of development (between the fourth and tenth
cleavages in the urchin embryo).},
Doi = {10.1016/j.jtbi.2014.07.023},
Key = {fds248311}
}
@article{fds225655,
Author = {Y. Yang and L. Fu and C. Marcoux and J. E. S. Socolar and P.
Charbonneau, B. B. Yellen},
Title = {Martensitic transformations in binary colloidal
monolayers},
Journal = {PNAS},
Year = {2014},
Month = {October},
Key = {fds225655}
}
@article{PhysRevE.90.012136,
Author = {Marcoux, C and Byington, TW and Qian, Z and Charbonneau, P and Socolar,
JES},
Title = {Emergence of limitperiodic order in tiling
models.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {90},
Number = {1},
Pages = {012136},
Publisher = {American Physical Society},
Year = {2014},
Month = {July},
ISSN = {15393755},
url = {http://link.aps.org/doi/10.1103/PhysRevE.90.012136},
Abstract = {A twodimensional (2D) lattice model defined on a triangular
lattice with nearest and nextnearestneighbor interactions
based on the TaylorSocolar monotile is known to have a
limitperiodic ground state. The system reaches that state
during a slow quench through an infinite sequence of phase
transitions. We study the model as a function of the
strength of the nextnearestneighbor interactions and
introduce closely related 3D models with only
nearestneighbor interactions that exhibit limitperiodic
phases. For models with no nextnearestneighbor
interactions of the TaylorSocolar type, there is a large
degenerate class of ground states, including crystalline
patterns and limitperiodic ones, but a slow quench still
yields the limitperiodic state. For the TaylorSocolar
lattic model, we present calculations of the diffraction
pattern for a particular decoration of the tile that permits
exact expressions for the amplitudes and identify domain
walls that slow the relaxation times in the ordered phases.
For one of the 3D models, we show that the phase transitions
are first order, with equilibrium structures that can be
more complex than in the 2D case, and we include a proof of
aperiodicity for a geometrically simple tile with only
nearestneighbor matching rules.},
Doi = {10.1103/physreve.90.012136},
Key = {PhysRevE.90.012136}
}
@article{fds248313,
Author = {Cheng, X and Lyons, DC and Socolar, JES and McClay,
DR},
Title = {Delayed transition to new cell fates during cellular
reprogramming.},
Journal = {Developmental Biology},
Volume = {391},
Number = {2},
Pages = {147157},
Year = {2014},
Month = {July},
ISSN = {00121606},
url = {http://www.sciencedirect.com/science/article/pii/S001216061400222X},
Abstract = {In many embryos specification toward one cell fate can be
diverted to a different cell fate through a reprogramming
process. Understanding how that process works will reveal
insights into the developmental regulatory logic that
emerged from evolution. In the sea urchin embryo, cells at
gastrulation were found to reprogram and replace missing
cell types after surgical dissections of the embryo.
Nonskeletogenic mesoderm (NSM) cells reprogrammed to
replace missing skeletogenic mesoderm cells and animal caps
reprogrammed to replace all endomesoderm. In both cases
evidence of reprogramming onset was first observed at the
early gastrula stage, even if the cells to be replaced were
removed earlier in development. Once started however, the
reprogramming occurred with compressed gene expression
dynamics. The NSM did not require early contact with the
skeletogenic cells to reprogram, but the animal cap cells
gained the ability to reprogram early in gastrulation only
after extended contact with the vegetal halves prior to that
time. If the entire vegetal half was removed at early
gastrula, the animal caps reprogrammed and replaced the
vegetal half endomesoderm. If the animal caps carried
morpholinos to either hox11/13b or foxA (endomesoderm
specification genes), the isolated animal caps failed to
reprogram. Together these data reveal that the emergence of
a reprogramming capability occurs at early gastrulation in
the sea urchin embryo and requires activation of early
specification components of the target tissues.},
Doi = {10.1016/j.ydbio.2014.04.015},
Key = {fds248313}
}
@article{fds248315,
Author = {Sun, M and Cheng, X and Socolar, JES},
Title = {Causal structure of oscillations in gene regulatory
networks: Boolean analysis of ordinary differential equation
attractors.},
Journal = {Chaos},
Volume = {23},
Number = {2},
Pages = {025104},
Year = {2013},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23822502},
Abstract = {A common approach to the modeling of gene regulatory
networks is to represent activating or repressing
interactions using ordinary differential equations for
target gene concentrations that include Hill function
dependences on regulator gene concentrations. An alternative
formulation represents the same interactions using Boolean
logic with time delays associated with each network link. We
consider the attractors that emerge from the two types of
models in the case of a simple but nontrivial network: a
figure8 network with one positive and one negative feedback
loop. We show that the different modeling approaches give
rise to the same qualitative set of attractors with the
exception of a possible fixed point in the ordinary
differential equation model in which concentrations sit at
intermediate values. The properties of the attractors are
most easily understood from the Boolean perspective,
suggesting that timedelay Boolean modeling is a useful tool
for understanding the logic of regulatory
networks.},
Doi = {10.1063/1.4807733},
Key = {fds248315}
}
@article{fds248346,
Author = {Cheng, X and Sun, M and Socolar, JES},
Title = {Autonomous Boolean modelling of developmental gene
regulatory networks},
Journal = {Journal of the Royal Society, Interface},
Volume = {10},
Number = {78},
Pages = {20120574},
Year = {2013},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23034351},
Abstract = {During early embryonic development, a network of regulatory
interactions among genes dynamically determines a pattern of
differentiated tissues. We show that important timing
information associated with the interactions can be
faithfully represented in autonomous Boolean models in which
binary variables representing expression levels are updated
in continuous time, and that such models can provide a
direct insight into features that are difficult to extract
from ordinary differential equation (ODE) models. As an
application, we model the experimentally wellstudied
network controlling fly body segmentation. The Boolean model
successfully generates the patterns formed in normal and
genetically perturbed fly embryos, permits the derivation of
constraints on the time delay parameters, clarifies the
logic associated with different ODE parameter sets and
provides a platform for studying connectivity and robustness
in parameter space. By elucidating the role of regulatory
time delays in pattern formation, the results suggest new
types of experimental measurements in early embryonic
development. © 2012 The Author(s) Published by the Royal
Society. All rights reserved.},
Doi = {10.1098/rsif.2012.0574},
Key = {fds248346}
}
@article{fds304616,
Author = {Cheng, X and Sun, M and Socolar, JES},
Title = {Autonomous Boolean modelling of developmental gene
regulatory networks.},
Journal = {Journal of the Royal Society, Interface},
Volume = {10},
Number = {78},
Pages = {20120574},
Year = {2013},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23034351},
Abstract = {During early embryonic development, a network of regulatory
interactions among genes dynamically determines a pattern of
differentiated tissues. We show that important timing
information associated with the interactions can be
faithfully represented in autonomous Boolean models in which
binary variables representing expression levels are updated
in continuous time, and that such models can provide a
direct insight into features that are difficult to extract
from ordinary differential equation (ODE) models. As an
application, we model the experimentally wellstudied
network controlling fly body segmentation. The Boolean model
successfully generates the patterns formed in normal and
genetically perturbed fly embryos, permits the derivation of
constraints on the time delay parameters, clarifies the
logic associated with different ODE parameter sets and
provides a platform for studying connectivity and robustness
in parameter space. By elucidating the role of regulatory
time delays in pattern formation, the results suggest new
types of experimental measurements in early embryonic
development.},
Doi = {10.1098/rsif.2012.0574},
Key = {fds304616}
}
@article{fds248342,
Author = {Byington, T and Socolar, JES},
Title = {Hierarchical freezing of limitperiodic structure},
Journal = {Physical Review E},
Year = {2012},
Month = {November},
Key = {fds248342}
}
@article{fds248340,
Author = {Gong, X and Socolar, JES},
Title = {Quantifying the complexity of random Boolean
networks.},
Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
Volume = {85},
Number = {6 Pt 2},
Pages = {066107},
Year = {2012},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23005162},
Abstract = {We study two measures of the complexity of heterogeneous
extended systems, taking random Boolean networks as
prototypical cases. A measure defined by Shalizi et al. for
cellular automata, based on a criterion for optimal
statistical prediction [Shalizi et al., Phys. Rev. Lett. 93,
118701 (2004)], does not distinguish between the spatial
inhomogeneity of the ordered phase and the dynamical
inhomogeneity of the disordered phase. A modification in
which complexities of individual nodes are calculated yields
vanishing complexity values for networks in the ordered and
critical regimes and for highly disordered networks, peaking
somewhere in the disordered regime. Individual nodes with
high complexity are the ones that pass the most information
from the past to the future, a quantity that depends in a
nontrivial way on both the Boolean function of a given node
and its location within the network.},
Doi = {10.1103/PhysRevE.85.066107},
Key = {fds248340}
}
@article{fds248341,
Author = {Durrett, R and Gleeson, JP and Lloyd, AL and Mucha, PJ and Shi, F and Sivakoff, D and Socolar, JES and Varghese, C},
Title = {Graph fission in an evolving voter model.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {109},
Number = {10},
Pages = {36823687},
Year = {2012},
Month = {March},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22355142},
Abstract = {We consider a simplified model of a social network in which
individuals have one of two opinions (called 0 and 1) and
their opinions and the network connections coevolve. Edges
are picked at random. If the two connected individuals hold
different opinions then, with probability 1  α, one
imitates the opinion of the other; otherwise (i.e., with
probability α), the link between them is broken and one of
them makes a new connection to an individual chosen at
random (i) from those with the same opinion or (ii) from the
network as a whole. The evolution of the system stops when
there are no longer any discordant edges connecting
individuals with different opinions. Letting ρ be the
fraction of voters holding the minority opinion after the
evolution stops, we are interested in how ρ depends on α
and the initial fraction u of voters with opinion 1. In case
(i), there is a critical value α(c) which does not depend
on u, with ρ ≈ u for α > α(c) and ρ ≈ 0 for
α < α(c). In case (ii), the transition point α(c)(u)
depends on the initial density u. For α > α(c)(u),
ρ ≈ u, but for α < α(c)(u), we have
ρ(α,u) = ρ(α,1/2). Using simulations and approximate
calculations, we explain why these two nearly identical
models have such dramatically different phase
transitions.},
Doi = {10.1073/pnas.1200709109},
Key = {fds248341}
}
@article{fds248344,
Author = {Socolar, JES and Taylor, JM},
Title = {Forcing Nonperiodicity with a Single Tile},
Journal = {The Mathematical Intelligencer},
Volume = {34},
Number = {1},
Pages = {1828},
Publisher = {Springer Nature},
Year = {2012},
Month = {Spring},
ISSN = {03436993},
url = {http://dx.doi.org/10.1007/s002830119255y},
Abstract = {An aperiodic prototile is a shape for which infinitely many
copies can be arranged to fill Euclidean space completely
with no overlaps, but not in a periodic pattern. Tiling
theorists refer to such a prototile as an "einstein" (a
German pun on "one stone"). The possible existence of an
einstein has been pondered ever since Berger's discovery of
large set of prototiles that in combination can tile the
plane only in a nonperiodic way. In this article we review
and clarify some features of a prototile we recently
introduced that is an einstein according to a reasonable
definition.},
Doi = {10.1007/s002830119255y},
Key = {fds248344}
}
@article{fds248343,
Author = {Byington, TW and Socolar, JES},
Title = {Hierarchical freezing in a lattice model.},
Journal = {Phys Rev Lett},
Volume = {108},
Number = {4},
Pages = {045701},
Year = {2012},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22400863},
Abstract = {A certain twodimensional lattice model with nearest and
nextnearest neighbor interactions is known to have a
limitperiodic ground state. We show that during a slow
quench from the high temperature, disordered phase, the
ground state emerges through an infinite sequence of phase
transitions. We define appropriate order parameters and show
that the transitions are related by renormalizations of the
temperature scale. As the temperature is decreased,
sublattices with increasingly large lattice constants become
ordered. A rapid quench results in a glasslike state due to
kinetic barriers created by simultaneous freezing on
sublattices with different lattice constants.},
Doi = {10.1103/PhysRevLett.108.045701},
Key = {fds248343}
}
@article{fds248347,
Author = {Khalil, KS and Sagastegui, A and Li, Y and Tahir, MA and Socolar, JES and Wiley, BJ and Yellen, BB},
Title = {Binary colloidal structures assembled through Ising
interactions.},
Journal = {Nature Communications},
Volume = {3},
Pages = {794},
Year = {2012},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22531179},
Abstract = {New methods for inducing microscopic particles to assemble
into useful macroscopic structures could open pathways for
fabricating complex materials that cannot be produced by
lithographic methods. Here we demonstrate a colloidal
assembly technique that uses two parameters to tune the
assembly of over 20 different preprogrammed structures,
including kagome, honeycomb and square lattices, as well as
various chain and ring configurations. We programme the
assembled structures by controlling the relative
concentrations and interaction strengths between spherical
magnetic and nonmagnetic beads, which behave as
paramagnetic or diamagnetic dipoles when immersed in a
ferrofluid. A comparison of our experimental observations
with potential energy calculations suggests that the lowest
energy configuration within binary mixtures is determined
entirely by the relative dipole strengths and their relative
concentrations.},
Doi = {10.1038/ncomms1798},
Key = {fds248347}
}
@article{fds248331,
Author = {Sun, M and Socolar, JES},
Title = {Comparison of autonomous Boolean network dynamics and ODE
models},
Journal = {Chaos},
Year = {2012},
Key = {fds248331}
}
@article{fds248332,
Author = {Socolar, JES},
Title = {Local action, global impact: forcing nonperiodicity with a
single structural unit.},
Journal = {Chaos (Woodbury, N.Y.)},
Volume = {21},
Number = {4},
Pages = {041106},
Year = {2011},
Month = {December},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22225336},
Abstract = {This is a presentation, with explanation, of an image of a
nonperiodic tiling whose structure is forced by local rules
governing how nearest and nextnearest neighbors can
align.},
Doi = {10.1063/1.3668192},
Key = {fds248332}
}
@article{Socolar:2011:AHT:2027468.2027502,
Author = {Socolar, JES and Taylor, JM},
Title = {An aperiodic hexagonal tile},
Journal = {Journal of Combinatorial Theory, Series A},
Volume = {118},
Number = {8},
Pages = {22072231},
Publisher = {Elsevier BV},
Address = {Orlando, FL, USA},
Year = {2011},
Month = {November},
ISSN = {00973165},
url = {http://dx.doi.org/10.1016/j.jcta.2011.05.001},
Keywords = {Aperiodic, Matching rules, Substitution,
Tiling},
Abstract = {We show that a single prototile can fill space uniformly but
not admit a periodic tiling. A twodimensional, hexagonal
prototile with markings that enforce local matching rules is
proven to be aperiodic by two independent methods. The
spacefilling tiling that can be built from copies of the
prototile has the structure of a union of honeycombs with
lattice constants of 2na, where a sets the scale of the most
dense lattice and n takes all positive integer values. There
are two local isomorphism classes consistent with the
matching rules and there is a nontrivial relation between
these tilings and a previous construction by Penrose.
Alternative forms of the prototile enforce the local
matching rules by shape alone, one using a prototile that is
not a connected region and the other using a
threedimensional prototile. © 2011 Elsevier
Inc.},
Doi = {10.1016/j.jcta.2011.05.001},
Key = {Socolar:2011:AHT:2027468.2027502}
}
@article{fds248334,
Author = {Cavalcante, HLDDS and Gauthier, DJ and Socolar, JES and Zhang,
R},
Title = {On the origin of chaos in autonomous Boolean
networks.},
Journal = {Philosophical Transactions. Series A, Mathematical,
Physical, and Engineering Sciences},
Volume = {368},
Number = {1911},
Pages = {495513},
Year = {2010},
Month = {January},
ISSN = {1364503X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20008414},
Abstract = {We undertake a systematic study of the dynamics of Boolean
networks to determine the origin of chaos observed in recent
experiments. Networks with nodes consisting of ideal logic
gates are known to display either steady states, periodic
behaviour or an ultraviolet catastrophe where the number of
logictransition events circulating in the network per unit
time grows as a power law. In an experiment, the nonideal
behaviour of the logic gates prevents the ultraviolet
catastrophe and may lead to deterministic chaos. We identify
certain nonideal features of real logic gates that enable
chaos in experimental networks. We find that shortpulse
rejection and asymmetry between the logic states tend to
engender periodic behaviour, at least for the simplest
networks. On the other hand, we find that a memory effect
termed 'degradation' can generate chaos. Our results
strongly suggest that deterministic chaos can be expected in
a large class of experimental Booleanlike networks. Such
devices may find application in a variety of technologies
requiring fast complex waveforms or flat power spectra, and
can be used as a testbed for fundamental studies of
realworld Booleanlike networks.},
Doi = {10.1098/rsta.2009.0235},
Key = {fds248334}
}
@article{fds248345,
Author = {Sevim, V and Gong, X and Socolar, JES},
Title = {Reliability of transcriptional cycles and the yeast
cellcycle oscillator.},
Journal = {Plos Computational Biology},
Volume = {6},
Number = {7},
Pages = {e1000842},
Year = {2010},
ISSN = {15537358},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20628620},
Abstract = {A recently published transcriptional oscillator associated
with the yeast cell cycle provides clues and raises
questions about the mechanisms underlying autonomous cyclic
processes in cells. Unlike other biological and synthetic
oscillatory networks in the literature, this one does not
seem to rely on a constitutive signal or positive
autoregulation, but rather to operate through stable
transmission of a pulse on a slow positive feedback loop
that determines its period. We construct a continuoustime
Boolean model of this network, which permits the modeling of
noise through small fluctuations in the timing of events,
and show that it can sustain stable oscillations. Analysis
of simpler network models shows how a few building blocks
can be arranged to provide stability against fluctuations.
Our findings suggest that the transcriptional oscillator in
yeast belongs to a new class of biological
oscillators.},
Doi = {10.1371/journal.pcbi.1000842},
Key = {fds248345}
}
@article{fds248335,
Author = {Zhang, R and de S Cavalcante and HLD and Gao, Z and Gauthier, DJ and Socolar, JES and Adams, MM and Lathrop, DP},
Title = {Boolean chaos.},
Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
Volume = {80},
Number = {4 Pt 2},
Pages = {045202},
Year = {2009},
Month = {October},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19905381},
Abstract = {We observe deterministic chaos in a simple network of
electronic logic gates that are not regulated by a clocking
signal. The resulting power spectrum is ultrawide band,
extending from dc to beyond 2 GHz. The observed behavior is
reproduced qualitatively using an autonomously updating
Boolean model with signal propagation times that depend on
the recent history of the gates and filtering of pulses of
short duration, whose presence is confirmed experimentally.
Electronic Boolean chaos may find application as an
ultrawideband source of radio waves.},
Doi = {10.1103/PhysRevE.80.045202},
Key = {fds248335}
}
@article{fds248336,
Author = {Norrell, J and Socolar, JE},
Title = {Boolean modeling of collective effects in complex
networks.},
Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
Volume = {79},
Number = {6},
Pages = {nihpa131303},
Year = {2009},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19649269},
Abstract = {Complex systems are often modeled as Boolean networks in
attempts to capture their logical structure and reveal its
dynamical consequences. Approximating the dynamics of
continuous variables by discrete values and Boolean logic
gates may, however, introduce dynamical possibilities that
are not accessible to the original system. We show that
large random networks of variables coupled through
continuous transfer functions often fail to exhibit the
complex dynamics of corresponding Boolean models in the
disordered (chaotic) regime, even when each individual
function appears to be a good candidate for Boolean
idealization. A suitably modified Boolean theory explains
the behavior of systems in which information does not
propagate faithfully down certain chains of nodes. Model
networks incorporating calculated or directly measured
transfer functions reported in the literature on
transcriptional regulation of genes are described by the
modified theory.},
Doi = {10.1103/PhysRevE.79.061908},
Key = {fds248336}
}
@article{fds248339,
Author = {Orlando, DA and Lin, CY and Bernard, A and Wang, JY and Socolar, JES and Iversen, ES and Hartemink, AJ and Haase, SB},
Title = {Global control of cellcycle transcription by coupled CDK
and network oscillators.},
Journal = {Nature},
Volume = {453},
Number = {7197},
Pages = {944947},
Year = {2008},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18463633},
Abstract = {A significant fraction of the Saccharomyces cerevisiae
genome is transcribed periodically during the cell division
cycle, indicating that properly timed gene expression is
important for regulating cellcycle events. Genomic analyses
of the localization and expression dynamics of transcription
factors suggest that a network of sequentially expressed
transcription factors could control the temporal programme
of transcription during the cell cycle. However, directed
studies interrogating small numbers of genes indicate that
their periodic transcription is governed by the activity of
cyclindependent kinases (CDKs). To determine the extent to
which the global cellcycle transcription programme is
controlled by cyclinCDK complexes, we examined genomewide
transcription dynamics in budding yeast mutant cells that do
not express Sphase and mitotic cyclins. Here we show that a
significant fraction of periodic genes are aberrantly
expressed in the cyclin mutant. Although cells lacking
cyclins are blocked at the G1/S border, nearly 70% of
periodic genes continued to be expressed periodically and on
schedule. Our findings reveal that although CDKs have a
function in the regulation of cellcycle transcription, they
are not solely responsible for establishing the global
periodic transcription programme. We propose that periodic
transcription is an emergent property of a transcription
factor network that can function as a cellcycle oscillator
independently of, and in tandem with, the CDK
oscillator.},
Doi = {10.1038/nature06955},
Key = {fds248339}
}
@article{fds248314,
Author = {Socolar, JES},
Title = {TimeDelay Control for Discrete Maps},
Pages = {2945},
Publisher = {WileyVCH Verlag GmbH & Co. KGaA},
Year = {2008},
Month = {May},
url = {http://dx.doi.org/10.1002/9783527622313.ch2},
Abstract = {This chapter is intended as a pedagogical introduction to
discrete time delayed feedback methods. It is neither a
comprehensive review, nor a presentation of dramatic new
results. It does, on the other hand, organize known results
in a selfcontained manner that emphasizes the conceptual
points that have proven to be important, where much of the
original literature focuses on historically important points
and rigorous mathematical proofs. The present work also
contains examples and one generalization that have not
appeared elsewhere. The goal is to provide a conceptual
foundation for readers who wonder whether discrete time
delay feedback methods are up to the task they have in mind.
Since the study of discrete methods foreshadows many (but
not all!) of the important questions that arise in studies
of continuous versions of delayed feedback control, the
present chapter may also serve as a useful prequel to
chapters on continuous methods. © 2008 WileyVCH Verlag
GmbH & Co. KGaA.},
Doi = {10.1002/9783527622313.ch2},
Key = {fds248314}
}
@article{fds145241,
Author = {D.A. Orlando and C.Y. Lin and A. Bernard and J.Y. Wang and J.E.S.
Socolar, E.S. Iversen and A.J. Hartemink and S.B.
Haase},
Title = {Global control of cellcycle transcription by coupled CDK
and network oscillators},
Journal = {Nature},
Year = {2008},
Month = {May},
url = {http://dx.doi.org/doi:10.1038/nature06955},
Doi = {doi:10.1038/nature06955},
Key = {fds145241}
}
@article{fds248337,
Author = {Tighe, BP and Socolar, JES},
Title = {Nonlinear elastic stress response in granular
packings.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {77},
Number = {3 Pt 1},
Pages = {031303},
Year = {2008},
Month = {March},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18517366},
Abstract = {We study the nonlinear elastic response of a twodimensional
material to a localized boundary force, with the particular
goal of understanding the differences observed between
isotropic granular materials and those with hexagonal
anisotropy. Corrections to the classical Boussinesq result
for the stresses in an infinite half space of a linear,
isotropic material are developed in a power series in
inverse distance from the point of application of the force.
The breakdown of continuum theory on scales of order of the
grain size is modeled with phenomenological parameters
characterizing the strengths of induced multipoles near the
point of application of the external force. We find that the
data of Geng [Phys. Rev. Lett. 87, 035506 (2001)] on
isotropic and hexagonal packings of photoelastic grains can
be fitted within this framework. Fitting the hexagonal
packings requires a choice of elastic coefficients with
hexagonal anisotropy stronger than that of a simple
ballandspring model. For both the isotropic and hexagonal
cases, induced dipole and quadrupole terms produce
propagation of stresses away from the vertical direction
over short distances. The scale over which such propagation
occurs is significantly enhanced by the nonlinearities that
generate hexagonal anisotropy.},
Doi = {10.1103/PhysRevE.77.031303},
Key = {fds248337}
}
@article{fds248338,
Author = {Ribeiro, AS and Kauffman, SA and LloydPrice, J and Samuelsson, B and Socolar, JES},
Title = {Mutual information in random Boolean models of regulatory
networks.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {77},
Number = {1 Pt 1},
Pages = {011901},
Year = {2008},
Month = {January},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18351870},
Abstract = {The amount of mutual information contained in the time
series of two elements gives a measure of how well their
activities are coordinated. In a large, complex network of
interacting elements, such as a genetic regulatory network
within a cell, the average of the mutual information over
all pairs, <I>, is a global measure of how well the system
can coordinate its internal dynamics. We study this average
pairwise mutual information in random Boolean networks
(RBNs) as a function of the distribution of Boolean rules
implemented at each element, assuming that the links in the
network are randomly placed. Efficient numerical methods for
calculating <I> show that as the number of network nodes, N,
approaches infinity, the quantity N<I> exhibits a
discontinuity at parameter values corresponding to critical
RBNs. For finite systems it peaks near the critical value,
but slightly in the disordered regime for typical parameter
variations. The source of high values of N<I> is the
indirect correlations between pairs of elements from
different long chains with a common starting point. The
contribution from pairs that are directly linked approaches
zero for critical networks and peaks deep in the disordered
regime.},
Doi = {10.1103/PhysRevE.77.011901},
Key = {fds248338}
}
@inbook{fds70496,
Author = {J.E.S. Socolar},
Title = {Timedelay control for discrete maps},
Booktitle = {Handbook of Chaos Control},
Publisher = {WileyVCH Verlag GmbH},
Editor = {E. Scholl and H. G. Schuster},
Year = {2007},
Month = {December},
url = {http://www.wiley.com/WileyCDA/WileyTitle/productCd3527406050,descCdtableOfContents.html},
Abstract = {A pedagogical introduction to discrete timedelayed feedback
methods. It is neither a comprehensive review, nor a
presentation of dramatic new results. It does, on the other
hand, organize known results in a selfcontained manner that
emphasizes the conceptual points that have proven to be
important, where much of the original literature focuses on
historically important points and rigorous mathematical
proofs. The present work also contains examples and one
generalization that have not appeared elsewhere.},
Key = {fds70496}
}
@article{fds248349,
Author = {Norrell, J and Samuelsson, B and Socolar, JES},
Title = {Attractors in continuous and Boolean networks.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {76},
Number = {4 Pt 2},
Pages = {046122},
Year = {2007},
Month = {October},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17995075},
Abstract = {We study the stable attractors of a class of continuous
dynamical systems that may be idealized as networks of
Boolean elements, with the goal of determining which Boolean
attractors, if any, are good approximations of the
attractors of generic continuous systems. We investigate the
dynamics in simple rings and rings with one additional
selfinput. An analysis of switching characteristics and
pulse propagation explains the relation between attractors
of the continuous systems and their Boolean approximations.
For simple rings, "reliable" Boolean attractors correspond
to stable continuous attractors. For networks with more
complex logic, the qualitative features of continuous
attractors are influenced by inherently nonBoolean
characteristics of switching events.},
Doi = {10.1103/PhysRevE.76.046122},
Key = {fds248349}
}
@article{fds248351,
Author = {Berger, CM and Cain, JW and Socolar, JES and Gauthier,
DJ},
Title = {Control of electrical alternans in simulations of paced
myocardium using extended timedelay autosynchronization.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {76},
Number = {4 Pt 1},
Pages = {041917},
Year = {2007},
Month = {October},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17995036},
Abstract = {Experimental studies have linked alternans, an abnormal
beattobeat alternation of cardiac action potential
duration, to the genesis of lethal arrhythmias such as
ventricular fibrillation. Prior studies have considered
various closedloop feedback control algorithms for
perturbing interstimulus intervals in such a way that
alternans is suppressed. However, some experimental cases
are restricted in that the controller's stimuli must preempt
those of the existing waves that are propagating in the
tissue, and therefore only shortening perturbations to the
underlying pacing are allowed. We present results
demonstrating that a technique known as extended timedelay
autosynchronization (ETDAS) can effectively control
alternans locally while operating within the above
constraints. We show that ETDAS, which has already been used
to control chaos in physical systems, has numerous
advantages over previously proposed alternans control
schemes.},
Doi = {10.1103/PhysRevE.76.041917},
Key = {fds248351}
}
@article{fds248328,
Author = {Socolar, JES},
Title = {Erratum: The hexagonal parquet tiling, kisohedral monotiles
with arbitrarily large k (The Mathematical Intelligencer
29:2 (3338))},
Journal = {The Mathematical Intelligencer},
Volume = {29},
Number = {4},
Pages = {6},
Publisher = {Springer Nature},
Year = {2007},
Month = {September},
ISSN = {03436993},
url = {http://dx.doi.org/10.1007/BF02986167},
Doi = {10.1007/BF02986167},
Key = {fds248328}
}
@article{fds248348,
Author = {Shreim, A and Grassberger, P and Nadler, W and Samuelsson, B and Socolar, JES and Paczuski, M},
Title = {Network analysis of the state space of discrete dynamical
systems.},
Journal = {Physical Review Letters},
Volume = {98},
Number = {19},
Pages = {198701},
Year = {2007},
Month = {May},
ISSN = {00319007},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17677672},
Abstract = {We study networks representing the dynamics of elementary 1D
cellular automata (CA) on finite lattices. We analyze
scaling behaviors of both local and global network
properties as a function of system size. The scaling of the
largest node indegree is obtained analytically for a
variety of CA including rules 22, 54, and 110. We further
define the path diversity as a global network measure. The
coappearance of nontrivial scaling in both the hub size and
the path diversity separates simple dynamics from the more
complex behaviors typically found in Wolfram's class IV and
some class III CA.},
Doi = {10.1103/PhysRevLett.98.198701},
Key = {fds248348}
}
@article{fds248350,
Author = {Socolar, JES},
Title = {The hexagonal parquet tiling kisohedral monotiles with
arbitrarily large k},
Journal = {The Mathematical Intelligencer},
Volume = {29},
Number = {2},
Pages = {3338},
Publisher = {Springer Nature},
Year = {2007},
Month = {March},
ISSN = {03436993},
url = {http://www.phy.duke.edu/~socolar/hexparquet.pdf},
Abstract = {The interplay between local constraints and global structure
of mathematical and physical systems is both subtle and
important. This paper shows how to construct a single tile
that can fill the Euclidean plane only with a tiling that
contains k distinct isohedral sets of tiles, where k can be
made arbitrarily large. It is shown that the construction
cannot work for a simply connected 2D tile with matching
rules for adjacent tiles enforced by shape alone. It is also
shown that any of the following modifications allows the
construction to work: (1) coloring the edges of the tiling
and imposing rules on which colors can touch; (2) allowing
the tile to be multiply connected; (3) requiring maximum
density rather than spacefilling; (4) allowing the tile to
have a thickness in the third dimension.},
Doi = {10.1007/BF02986203},
Key = {fds248350}
}
@article{fds248353,
Author = {Samuelsson, B and Socolar, JES},
Title = {Exhaustive percolation on random networks},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {74},
Number = {3},
Pages = {031912},
Publisher = {American Physical Society (APS)},
Year = {2006},
Month = {October},
ISSN = {15393755},
url = {http://link.aps.org/abstract/PRE/v74/e036113},
Abstract = {We consider propagation models that describe the spreading
of an attribute, called "damage," through the nodes of a
random network. In some systems, the average fraction of
nodes that remain undamaged vanishes in the large system
limit, a phenomenon we refer to as exhaustive percolation.
We derive scaling law exponents and exact results for the
distribution of the number of undamaged nodes, valid for a
broad class of random networks at the exhaustive percolation
transition and in the exhaustive percolation regime. This
class includes processes that determine the set of frozen
nodes in random Boolean networks with indegree
distributions that decay sufficiently rapidly with the
number of inputs. Connections between our calculational
methods and previous studies of percolation beginning from a
single initial node are also pointed out. Central to our
approach is the observation that key aspects of damage
spreading on a random network are fully characterized by a
single function, specifying the probability that a given
node will be damaged as a function of the fraction of
damaged nodes. In addition to our analytical investigations
of random networks, we present a numerical example of
exhaustive percolation on a directed lattice. © 2006 The
American Physical Society.},
Doi = {10.1103/PhysRevE.74.036113},
Key = {fds248353}
}
@article{fds248352,
Author = {Foster, DV and Kauffman, SA and Socolar, JES},
Title = {Network growth models and genetic regulatory
networks.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {73},
Number = {3 Pt 1},
Pages = {031912},
Year = {2006},
Month = {March},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16605563},
Abstract = {We study a class of growth algorithms for directed graphs
that are candidate models for the evolution of genetic
regulatory networks. The algorithms involve partial
duplication of nodes and their links, together with the
innovation of new links, allowing for the possibility that
input and output links from a newly created node may have
different probabilities of survival. We find some
counterintuitive trends as the parameters are varied,
including the broadening of the indegree distribution when
the probability for retaining input links is decreased. We
also find that both the scaling of transcription factors
with genome size and the measured degree distributions for
genes in yeast can be reproduced by the growth algorithm if
and only if a special seed is used to initiate the
process.},
Doi = {10.1103/PhysRevE.73.031912},
Key = {fds248352}
}
@inbook{fds26115,
Author = {J.E.S. Socolar},
Title = {Nonlinear Dynamical Systems},
Booktitle = {Complex Systems Science and Biomedicine},
Publisher = {Kluwer},
Editor = {Deisboeck and Kresh},
Year = {2006},
Month = {February},
Key = {fds26115}
}
@article{fds248354,
Author = {Dealy, S and Kauffman, S and Socolar, J},
Title = {Modeling pathways of differentiation in genetic regulatory
networks with Boolean networks},
Journal = {Complexity},
Volume = {11},
Number = {1},
Pages = {5260},
Publisher = {WILEY},
Year = {2005},
Month = {September},
ISSN = {10762787},
url = {http://dx.doi.org/10.1002/cplx.20100},
Abstract = {We have carried out the first examination of pathways of
cell differentiation in model genetic networks in which cell
types are assumed to be attractors of the nonlinear
dynamics, and differentiation corresponds to a transition of
the cell to a new basin of attraction, which may be induced
by a signal or noise perturbation. The associated flow along
a transient to a new attractor corresponds to a pathway of
differentiation. We have measured a variety of features of
such model pathways of differentiation, most of which should
be observable using gene array techniques. © 2005 Wiley
Periodicals, Inc.},
Doi = {10.1002/cplx.20100},
Key = {fds248354}
}
@article{fds248355,
Author = {Tighe, BP and Socolar, JES and Schaeffer, DG and Mitchener, WG and Huber, ML},
Title = {Force distributions in a triangular lattice of rigid
bars.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {72},
Number = {3 Pt 1},
Pages = {031306},
Year = {2005},
Month = {September},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16241425},
Abstract = {We study the uniformly weighted ensemble of force balanced
configurations on a triangular network of nontensile contact
forces. For periodic boundary conditions corresponding to
isotropic compressive stress, we find that the probability
distribution for singlecontact forces decays faster than
exponentially. This superexponential decay persists in
lattices diluted to the rigidity percolation threshold. On
the other hand, for anisotropic imposed stresses, a broader
tail emerges in the force distribution, becoming a pure
exponential in the limit of infinite lattice size and
infinitely strong anisotropy.},
Doi = {10.1103/PhysRevE.72.031306},
Key = {fds248355}
}
@article{fds248377,
Author = {Harrington, I and Socolar, JES},
Title = {Design and robustness of delayed feedback controllers for
discrete systems},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {69},
Number = {5},
Pages = {8},
Year = {2004},
Month = {January},
ISSN = {15393755},
url = {http://dx.doi.org/10.1103/PhysRevE.69.056207},
Abstract = {We study a matrix form of timedelay feedback control in the
context of discrete time maps of high dimension. In almost
all cases where standard proportional feedback control
methods can achieve control, timedelay feedback controllers
containing only static elements can be designed to achieve
identical linear stability properties. Analysis of an
example involving a ring of coupled maps that can be
controlled at only two sites demonstrates that the
timedelay controller equivalent to a standard optimal
controller can be equally robust in the presence of noise,
except at special points in parameter space where the
uncontrolled system has a mode with Floquet multiplier
exactly equal to 1. Numerical simulations confirm the
results of the analysis. © 2004 The American Physical
Society.},
Doi = {10.1103/PhysRevE.69.056207},
Key = {fds248377}
}
@article{fds248378,
Author = {Hövel, P and Socolar, JES},
Title = {Stability domains for timedelay feedback control with
latency.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {68},
Number = {3 Pt 2},
Pages = {036206},
Year = {2003},
Month = {September},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/14524867},
Abstract = {We generalize a known analytical method for determining the
stability of periodic orbits controlled by timedelay
feedback methods when latencies associated with the
generation and injection of the feedback signal cannot be
ignored. We discuss the case of extended timedelay
autosynchronization and show that nontrivial qualitative
features of the domain of control observed in experiments
can be explained by taking into account the effects of both
the unstable eigenmode and a single stable eigenmode in the
Floquet theory.},
Doi = {10.1103/PhysRevE.68.036206},
Key = {fds248378}
}
@article{fds248386,
Author = {Socolar, JES and Kauffman, SA},
Title = {Scaling in ordered and critical random boolean
networks.},
Journal = {Physical Review Letters},
Volume = {90},
Number = {6},
Pages = {068702},
Year = {2003},
Month = {February},
ISSN = {00319007},
url = {http://www.ncbi.nlm.nih.gov/pubmed/12633339},
Abstract = {Random Boolean networks, originally invented as models of
genetic regulatory networks, are simple models for a broad
class of complex systems that show rich dynamical
structures. From a biological perspective, the most
interesting networks lie at or near a critical point in
parameter space that divides "ordered" from "chaotic"
attractor dynamics. We study the scaling of the average
number of dynamically relevant nodes and the median number
of distinct attractors in such networks. Our calculations
indicate that the correct asymptotic scalings emerge only
for very large systems.},
Doi = {10.1103/PhysRevLett.90.068702},
Key = {fds248386}
}
@article{fds248385,
Author = {Socolar, JES},
Title = {Discrete models of force chain networks},
Journal = {Discrete and Continuous Dynamical Systems Series
B},
Volume = {3},
Number = {4},
Pages = {601618},
Publisher = {American Institute of Mathematical Sciences
(AIMS)},
Year = {2003},
Month = {January},
ISSN = {15313492},
url = {http://xxx.lanl.gov/abs/condmat/0212162},
Abstract = {A fundamental property of any material is its response to a
localized stress applied at a boundary. For granular
materials consisting of hard, cohesionless particles, not
even the general form of the stress response is known.
Directed force chain networks (DFCNs) provide a theoretical
framework for addressing this issue, and analysis of
simplified DFCN models reveal both rich mathematical
structure and surprising properties. We review some basic
elements of DFCN models and present a class of homogeneous
solutions for cases in which force chains are restricted to
lie on a discrete set of directions.},
Doi = {10.3934/dcdsb.2003.3.601},
Key = {fds248385}
}
@article{fds318470,
Author = {Hövel, P and Socolar, JES},
Title = {Stability domains for timedelay feedback control with
latency},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {68},
Number = {3 2},
Pages = {362061362067},
Year = {2003},
Abstract = {The stability of periodic orbits controlled by timedelay
feedback methods with latency was determined. Floquet theory
and first order theory were used to derive nonlinear shapes
from parametrized plane. It was found that Floquet modes,
that contributed significantly to the overall stability
picture, reduced the domain control substantially.},
Key = {fds318470}
}
@article{fds248326,
Author = {Otto, M and Bouchaud, JP and Claudin, P and Socolar,
JES},
Title = {Anisotropy in granular media: Classical elasticity and
directedforce chain network},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {67},
Number = {3 1},
Pages = {031302/1031302/24},
Year = {2003},
ISSN = {1063651X},
url = {http://arxiv.org/abs/condmat/0211015v2},
Abstract = {A general framework that covers both classical anisotropic
elasticity theory and a generally anisotropic
"pseudoelasticity" theory, that appears within a linearized
treatment of directedforce chain networks is presented. It
is shown how the formalism applies to the example of a
triangular ballandspring network, indicating how spring
stiffnesses must be chosen to access all possible regions of
the general parameter space.},
Doi = {10.1103/PhysRevE.67.031302},
Key = {fds248326}
}
@article{fds304614,
Author = {Beck, O and Amann, A and Schöll, E and Socolar, JES and Just,
W},
Title = {Comparison of timedelayed feedback schemes for
spatiotemporal control of chaos in a reactiondiffusion
system with global coupling},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {66},
Number = {1},
Pages = {016213/1016213/6},
Publisher = {American Physical Society (APS)},
Year = {2002},
Month = {July},
ISSN = {15393755},
url = {http://dx.doi.org/10.1103/PhysRevE.66.016213},
Abstract = {Timedelayed feedback control for stabilizing time periodic
spatial patterns is investigated in a generic
reactiondiffusion system with global coupling. We focus on
the case of lowdimensional chaos where unstable patterns
admit only a single unstable mode. Spatial degrees of
freedom are taken into account to define different control
schemes. The efficiency of these schemes is discussed, where
control forces are motivated by physical requirements as
well as by the possibility of obtaining analytically exact
results. We find that control schemes that contain the full
feedback of the inhibitor variable may finally destroy the
control performance. Thus schemes that omit the inhibitor
might be more efficient. Our numerical findings are
explained in terms of Floquet spectra and compared with
analytical solutions of particular coupling schemes. © 2002
The American Physical Society.},
Doi = {10.1103/PhysRevE.66.016213},
Key = {fds304614}
}
@article{fds324423,
Author = {Socolar, JES and Schaeffer, DG and Claudin, P},
Title = {Erratum to: Directed force chain networks and stress
response in static granular materials},
Journal = {The European Physical Journal. E, Soft Matter},
Volume = {8},
Number = {4},
Pages = {453453},
Publisher = {Springer Nature},
Year = {2002},
Month = {July},
url = {http://dx.doi.org/10.1140/epje/i2002100304},
Doi = {10.1140/epje/i2002100304},
Key = {fds324423}
}
@article{fds248389,
Author = {Socolar, JES and Schaeffer, DG and Claudin, P},
Title = {Directed force chain networks and stress response in static
granular materials},
Journal = {European Physical Journal E},
Volume = {7},
Number = {4},
Pages = {353370},
Year = {2002},
url = {http://xxx.lanl.gov/abs/condmat/0201242},
Abstract = {A theory of stress fields in twodimensional granular
materials based on directed force chain networks is
presented. A general Boltzmann equation for the densities of
force chains in different directions is proposed and a
complete solution is obtained for a special case in which
chains lie along a discrete set of directions. The analysis
and results demonstrate the necessity of including nonlinear
terms in the Boltzmann equation. A line of nontrivial
fixedpoint solutions is shown to govern the properties of
large systems. In the vicinity of a generic fixed point, the
response to a localized load shows a crossover from a
single, centered peak at intermediate depths to two
propagating peaks at large depths that broaden
diffusively.},
Key = {fds248389}
}
@article{fds248383,
Author = {Harrington, I and Socolar, JE},
Title = {Limitation on stabilizing plane waves via timedelay
feedback.},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {64},
Number = {5 Pt 2},
Pages = {056206},
Year = {2001},
Month = {November},
ISSN = {15393755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11736053},
Abstract = {Previous work has demonstrated the possibility of
stabilizing plane wave solutions of onedimensional systems
using a spatially local form of timedelayed feedback. We
show that the natural extension of this method to
twodimensional systems fails due to the presence of
torsionfree unstable perturbations. Linear stability
analysis of the complex GinzburgLandau equation reveals
that long wavelength, transverse wave instabilities cannot
be suppressed by the method of extended timedelay
autosynchronization. The conclusion follows from symmetry
considerations and therefore applies to a wide class of
models with simple plane wave solutions.},
Doi = {10.1103/PhysRevE.64.056206},
Key = {fds248383}
}
@article{fds248322,
Author = {Socolar, JES},
Title = {Evolution in a spatially structured population subject to
rare epidemics},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {63},
Number = {4},
Pages = {419081419088},
Year = {2001},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.63.041908},
Abstract = {We study a model that gives rise to spatially inhomogeneous
population densities in a system of host individuals subject
to rare, randomly distributed disease events. For stationary
hosts that disperse offspring over short distances,
evolutionary dynamics can lead to persistent populations
with a variety of spatial structures. A meanfield analysis
is shown to account for the behavior observed in simulations
of a onedimensional system, where the evolutionarily stable
state corresponds to the solution of a straightforward
optimization problem. In two dimensions, evolution drives
the system to a stable critical state that is less well
understood. © 2001 The American Physical
Society.},
Doi = {10.1103/PhysRevE.63.041908},
Key = {fds248322}
}
@article{fds3758,
Author = {J.E.S Socolar},
Title = {Chaos},
Series = {3rd Edition},
Booktitle = {Encyclopedia of Physical Science and Technology},
Publisher = {Academic Press},
Editor = {R. Meyers},
Year = {2001},
Key = {fds3758}
}
@article{fds248382,
Author = {BLEICH, MICHAELE and SOCOLAR, JOSHUAES},
Title = {DELAYED FEEDBACK CONTROL OF A PACED EXCITABLE
OSCILLATOR},
Journal = {International Journal of Bifurcation and
Chaos},
Volume = {10},
Number = {03},
Pages = {603609},
Publisher = {World Scientific Pub Co Pte Lt},
Year = {2000},
Month = {March},
url = {http://dx.doi.org/10.1142/s0218127400000414},
Abstract = {A simple numerical experiment on FitzhughNagumo equations
demonstrates that timedelay feedback methods can stabilize
regular behavior in a paced, excitable oscillator without
using large applied pulses. The method is robust against
slow variations in the pacing rate and can be used to track
an orbit into a parameter regime where it is unstable.
Moreover, the method requires no information about the
desired orbit other than period, which is determined
directly by the observation of the pacing signal. Results
are presented for feedback stabilization of a nonspiking
orbit in the rapid pacing regime.},
Doi = {10.1142/s0218127400000414},
Key = {fds248382}
}
@article{fds248388,
Author = {Richards, SA and Wilson, WG and Socolar, JE},
Title = {Selection for intermediate mortality and reproduction rates
in a spatially structured population.},
Journal = {Proceedings of the Royal Society B: Biological
Sciences},
Volume = {266},
Number = {1436},
Pages = {23832388},
Year = {1999},
Month = {December},
ISSN = {09628452},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10643082},
Abstract = {How local interactions influence both population and
evolutionary dynamics is currently a key topic in
theoretical ecology. We use a 'wellmixed' analytical model
and spatially explicit individualbased models to
investigate a system where a population is subject to rare
disturbance events. The disturbance can only propagate
through regions of the population where the density of
individuals is sufficiently high and individuals affected by
the disturbance die shortly after. We find that populations
where individuals are sessile often exhibit very different
dynamic behaviour when compared to populations where
individuals are mobile and spatially well mixed. When
mutations are allowed which affect either offspring birth
rates or mortality rates, the wellmixed populations always
evolve to a state where a single disturbance event leads to
extinction. Populations often persist substantially longer
if individuals are sessile and they disperse their offspring
locally. We also find that for sessile populations selection
may favour shortlived individuals with limited offspring
production. Population dynamics are found to be strongly
influenced by the host characters that are evolving and the
rate at which host variation is introduced into the
system.},
Doi = {10.1098/rspb.1999.0935},
Key = {fds248388}
}
@article{fds248381,
Author = {Sexton, MG and Socolar, JE and Schaeffer, DG},
Title = {Force distribution in a scalar model for noncohesive
granular material.},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {60},
Number = {2 Pt B},
Pages = {19992008},
Year = {1999},
Month = {August},
ISSN = {1063651X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11969992},
Abstract = {We study a scalar lattice model for intergrain forces in
static, noncohesive, granular materials, obtaining two
primary results: (i) The applied stress as a function of
overall strain shows a power law dependence with a
nontrivial exponent, which moreover varies with system
geometry; and (ii) probability distributions for forces on
individual grains appear Gaussian at all stages of
compression, showing no evidence of exponential tails. With
regard to both results, we identify correlations responsible
for deviations from previously suggested
theories.},
Key = {fds248381}
}
@article{fds303753,
Author = {Socolar, JES},
Title = {Average stresses and force fluctuations in noncohesive
granular materials},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {57},
Number = {3},
Pages = {32043215},
Publisher = {AMERICAN PHYSICAL SOC},
Year = {1998},
Month = {March},
url = {http://arxiv.org/abs/condmat/9710089v1},
Abstract = {A lattice model is presented for investigating the
fluctuations in static granular materials under
gravitationally induced stress. The model is similar in
spirit to the scalar qmodel of Coppersmith et al., but
ensures balance of all components of forces and torques at
each site. The geometric randomness in real granular
materials is modeled by choosing random variables at each
site, consistent with the assumption of cohesionless grains.
Configurations of the model can be generated rapidly,
allowing the statistical study of relatively large systems.
For a 2D system with rough walls, the model generates
configurations consistent with continuum theories for the
average stresses (unlike the qmodel) without requiring the
assumption of a constitutive relation. For a 2D system with
periodic boundary conditions, the model generates
singlegrain force distributions similar to those obtained
from the qmodel with a singular distribution of
q's.},
Doi = {10.1103/PhysRevE.57.3204},
Key = {fds303753}
}
@article{fds248379,
Author = {Egolf, DA and Socolar, JES},
Title = {Failure of linear control in noisy coupled map
lattices},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {57},
Number = {5},
Pages = {52715275},
Publisher = {American Physical Society (APS)},
Year = {1998},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.57.5271},
Abstract = {We study a onedimensional ring of diffusively coupled
logistic maps in the vicinity of an unstable, spatially
homogeneous fixed point. The failure of linear controllers
due to additive noise is discussed with the aim of
clarifying the failure mechanism. A criterion is suggested
for estimating the noise level that can be tolerated by the
given controller. The criterion implies the loss of control
for surprisingly low noise levels in certain cases of
interest, and accurately accounts for the results of
numerical experiments over a broad range of parameter
values. Previous results of Grigoriev et al. [Phys. Rev.
Lett. 79, 2795 (1997)] are reviewed and compared with our
numerical and analytic results.© 1998 The American Physical
Society.},
Doi = {10.1103/PhysRevE.57.5271},
Key = {fds248379}
}
@article{fds248380,
Author = {Socolar, JES and Gauthier, DJ},
Title = {Analysis and comparison of multipledelay schemes for
controlling unstable fixed points of discrete
maps},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {57},
Number = {6},
Pages = {65896595},
Publisher = {American Physical Society (APS)},
Year = {1998},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.57.6589},
Abstract = {We investigate theoretically the stabilization of a fixed
point of a discrete onedimensional nonlinear map by
applying small perturbations to an accessible system
parameter or variable. The size of the perturbations is
determined in real time using feedback schemes incorporating
only the dynamical state of the system and its state at
previous iterates without making a comparison to a reference
state. In particular, we compare and contrast two
algorithms: extended timedelay autosynchronization, which
uses an infinite series of past iterates with weights that
decay by a factor of [formula presented] with each time
step, and [formula presented]timedelay
autosynchronization, which uses an average of [formula
presented] past iterates with equal weights. The range of
feedback parameters that successfully stabilize the fixed
point and the robustness of the schemes to noise are
determined. It is found that the domain of control for the
two schemes is similar for appropriately matched values of
[formula presented] and [formula presented], and that
[formula presented]timedelay autosynchronization tends to
be less sensitive to noise. © 1998 The American Physical
Society.},
Doi = {10.1103/PhysRevE.57.6589},
Key = {fds248380}
}
@article{fds248387,
Author = {Gauthier, DJ and Socolar, JES},
Title = {Comment on “Dynamic Control of Cardiac
Alternans”},
Journal = {Physical Review Letters},
Volume = {79},
Number = {24},
Pages = {4938},
Publisher = {American Physical Society (APS)},
Year = {1997},
Month = {December},
url = {http://dx.doi.org/10.1103/PhysRevLett.79.4938},
Abstract = {A Comment on the Letter by Keven Hall, et al., Phys. Rev.
Lett. 78, 4518 (1997). © 1997 The American Physical
Society.},
Doi = {10.1103/PhysRevLett.79.4938},
Key = {fds248387}
}
@article{fds248374,
Author = {Sukow, DW and Bleich, ME and Gauthier, DJ and Socolar,
JES},
Title = {Controlling chaos in a fast diode resonator using extended
timedelay autosynchronization: Experimental observations
and theoretical analysis.},
Journal = {Chaos},
Volume = {7},
Number = {4},
Pages = {560576},
Year = {1997},
Month = {December},
url = {http://www.ncbi.nlm.nih.gov/pubmed/12779682},
Abstract = {We stabilize unstable periodic orbits of a fast diode
resonator driven at 10.1 MHz (corresponding to a drive
period under 100 ns) using extended timedelay
autosynchronization. Stabilization is achieved by feedback
of an error signal that is proportional to the difference
between the value of a state variable and an infinite series
of values of the state variable delayed in time by integral
multiples of the period of the orbit. The technique is easy
to implement electronically and it has an alloptical
counterpart that may be useful for stabilizing the dynamics
of fast chaotic lasers. We show that increasing the weights
given to temporally distant states enlarges the domain of
control and reduces the sensitivity of the domain of control
on the propagation delays in the feedback loop. We determine
the average time to obtain control as a function of the
feedback gain and identify the mechanisms that destabilize
the system at the boundaries of the domain of control. A
theoretical stability analysis of a model of the diode
resonator in the presence of timedelay feedback is in good
agreement with the experimental results for the size and
shape of the domain of control. (c) 1997 American Institute
of Physics.},
Doi = {10.1063/1.166256},
Key = {fds248374}
}
@article{fds248375,
Author = {Bleich, ME and Hochheiser, D and Moloney, JV and Socolar,
JES},
Title = {Controlling extended systems with spatially filtered,
timedelayed feedback},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {55},
Number = {3},
Pages = {21192126},
Publisher = {American Physical Society (APS)},
Year = {1997},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.55.2119},
Abstract = {We investigate a control technique for spatially extended
systems combining spatial filtering with a previously
studied form of timedelay feedback. The scheme is naturally
suited to realtime control of optical systems. We apply the
control scheme to a model of a transversely extended
semiconductor laser in which a desirable, coherent
travelingwave state exists, but is a member of a nowhere
stable family. Our scheme stabilizes this state and directs
the system towards it from realistic, distant, and noisy
initial conditions. As confirmed by numerical simulation, a
linear stability analysis about the controlled state
accurately predicts when the scheme is successful and
illustrates some key features of the control including the
individual merit of, and interplay between, the spatial and
temporal degrees of freedom in the control. © 1997 The
American Physical Society.},
Doi = {10.1103/PhysRevE.55.2119},
Key = {fds248375}
}
@article{fds248373,
Author = {Bleich, ME and Socolar, JES},
Title = {Controlling spatiotemporal dynamics with timedelay
feedback},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {54},
Number = {1},
Pages = {R17R20},
Publisher = {American Physical Society (APS)},
Year = {1996},
Month = {July},
ISSN = {1063651X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9965164},
Doi = {10.1103/physreve.54.r17},
Key = {fds248373}
}
@article{fds248372,
Author = {Bleich, ME and Socolar, JES},
Title = {Stability of periodic orbits controlled by timedelay
feedback},
Journal = {Physics Letters A},
Volume = {210},
Number = {12},
Pages = {8794},
Publisher = {Elsevier BV},
Year = {1996},
Month = {January},
url = {http://dx.doi.org/10.1016/03759601(95)008276},
Abstract = {Extended timedelay autosynchronization (ETDAS) is a
promising technique for stabilizing unstable periodic orbits
in lowdimensional dynamical systems. The technique involves
continuous feedback of signals delayed by multiples of the
orbit's period in a manner that is especially wellsuited
for fast systems and optical implementation. We show how to
analyze the stability of a given implementation of ETDAS
without explicit integration of timedelay equations. To
illustrate the method and point out some nontrivial features
of ETDAS, we obtain the domain of control for a periodone
orbit of the driven, damped pendulum.},
Doi = {10.1016/03759601(95)008276},
Key = {fds248372}
}
@article{fds248371,
Author = {Socolar, JE and Sukow, DW and Gauthier, DJ},
Title = {Stabilizing unstable periodic orbits in fast dynamical
systems.},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {50},
Number = {4},
Pages = {32453248},
Year = {1994},
Month = {October},
ISSN = {1063651X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9962372},
Doi = {10.1103/physreve.50.3245},
Key = {fds248371}
}
@article{fds248370,
Author = {Gauthier, DJ and Sukow, DW and Concannon, HM and Socolar,
JE},
Title = {Stabilizing unstable periodic orbits in a fast diode
resonator using continuous timedelay autosynchronization.},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {50},
Number = {3},
Pages = {23432346},
Year = {1994},
Month = {September},
ISSN = {1063651X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9962244},
Key = {fds248370}
}
@article{fds248369,
Author = {Grinstein, G and Jayaprakash, C and Socolar, JE},
Title = {Scale invariance of nonconserved quantities in driven
systems.},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {48},
Number = {2},
Pages = {R643R646},
Year = {1993},
Month = {August},
ISSN = {1063651X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9960763},
Key = {fds248369}
}
@article{fds248368,
Author = {SOCOLAR, JES and GRINSTEIN, G and JAYAPRAKASH,
C},
Title = {ON SELFORGANIZED CRITICALITY IN NONCONSERVING
SYSTEMS},
Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {47},
Number = {4},
Pages = {23662376},
Publisher = {AMERICAN PHYSICAL SOC},
Year = {1993},
Month = {April},
ISSN = {1063651X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9960267},
Doi = {10.1103/PhysRevE.47.2366},
Key = {fds248368}
}
@article{fds303752,
Author = {Krug, J and Socolar, JE and Grinstein, G},
Title = {Surface fluctuations and criticality in a class of
onedimensional sandpile models.},
Journal = {Physical Review A},
Volume = {46},
Number = {8},
Pages = {R4479R4482},
Year = {1992},
Month = {October},
ISSN = {10502947},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9908766},
Key = {fds303752}
}
@article{fds248365,
Author = {Socolar, JES},
Title = {Theory of Packings of Identical Hard Disks Generated by
Ballistic Deposition},
Journal = {Epl (Europhysics Letters)},
Volume = {18},
Number = {1},
Pages = {3944},
Publisher = {IOP Publishing},
Year = {1992},
Month = {February},
url = {http://dx.doi.org/10.1209/02955075/18/1/008},
Doi = {10.1209/02955075/18/1/008},
Key = {fds248365}
}
@article{fds248366,
Author = {Krug, J and Socolar, JE},
Title = {Comment on "Scalings of growing selforganized
surfaces"},
Journal = {Phys Rev Lett},
Volume = {68},
Number = {5},
Pages = {722},
Year = {1992},
Month = {February},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10045973},
Doi = {10.1103/PhysRevLett.68.722},
Key = {fds248366}
}
@article{fds37538,
Author = {J.E.S. Socolar},
Title = {Growth Rules for Quasicrystals},
Booktitle = {Quasicrystals: The State of the Art},
Publisher = {World Scientific, Singapore},
Editor = {D. DiVincenzo and P. Steinhardt},
Year = {1991},
Key = {fds37538}
}
@article{fds248364,
Author = {Socolar, JES},
Title = {Weak matching rules for quasicrystals},
Journal = {Communications in Mathematical Physics},
Volume = {129},
Number = {3},
Pages = {599619},
Publisher = {Springer Nature},
Year = {1990},
Month = {May},
ISSN = {00103616},
url = {http://dx.doi.org/10.1007/BF02097107},
Abstract = {Weak matching rules for a quasicrystalline tiling are local
rules that ensure that fluctuations in "perpspace" are
uniformly bounded. It is shown here that weak matching rules
exist for Nfold symmetric tilings, where N is any integer
not divisible by four. The result suggests that, contrary to
previous indications, quasicrystalline ground states are not
confined to those symmetries for which the incommensurate
ratios of wavevectors are quadratic irrationals. An explicit
method of constructing weak matching rules for Nfold
symmetric tilings in two dimensions is presented. It is
shown that the generalization of the construction yields
weak matching rules in the case of icosahedral symmetry as
well. © 1990 SpringerVerlag.},
Doi = {10.1007/BF02097107},
Key = {fds248364}
}
@article{fds37539,
Author = {J.E.S. Socolar},
Title = {The Alternation Condition and 2D Quasicrystals},
Volume = {93},
Series = {Springer Series in SolidState Sciences},
Booktitle = {Quasicrystals},
Publisher = {SpringerVerlag, Berlin},
Editor = {T. Fujiwara and T. Ogawa},
Year = {1990},
Key = {fds37539}
}
@article{fds248363,
Author = {Socolar, JE},
Title = {Simple octagonal and dodecagonal quasicrystals.},
Journal = {Physical Review. B, Condensed Matter},
Volume = {39},
Number = {15},
Pages = {1051910551},
Year = {1989},
Month = {May},
ISSN = {01631829},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9947860},
Key = {fds248363}
}
@article{fds303751,
Author = {Onoda, G and Steinhardt, PJ and DiVincenzo, D and Socolar,
JE},
Title = {Onoda etal. reply.},
Journal = {Phys Rev Lett},
Volume = {62},
Number = {10},
Pages = {1210},
Year = {1989},
Month = {March},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10039608},
Doi = {10.1103/PhysRevLett.62.1210},
Key = {fds303751}
}
@article{fds37541,
Author = {J.E.S. Socolar},
Title = {Locality Constraints and 2D Quasicrystals},
Booktitle = {Quasicrystals  Adriatico Anniversary Research
Conference},
Publisher = {World Scientific, Singapore},
Editor = {M.V. Jaric and S. Lundqvist},
Year = {1989},
Key = {fds37541}
}
@article{fds248361,
Author = {Onoda, GY and Steinhardt, PJ and DiVincenzo, DP and Socolar,
JE},
Title = {Growing perfect quasicrystals.},
Journal = {Phys Rev Lett},
Volume = {60},
Number = {25},
Pages = {26532656},
Year = {1988},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10038414},
Doi = {10.1103/PhysRevLett.60.2653},
Key = {fds248361}
}
@article{fds248360,
Author = {Socolar, JE and Wright, DC},
Title = {Explanation of peak shapes observed in diffraction from
icosahedral quasicrystals.},
Journal = {Phys Rev Lett},
Volume = {59},
Number = {2},
Pages = {221224},
Year = {1987},
Month = {July},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10035483},
Doi = {10.1103/PhysRevLett.59.221},
Key = {fds248360}
}
@article{fds248358,
Author = {Lubensky, TC and Socolar, JE and Steinhardt, PJ and Bancel, PA and Heiney, AP},
Title = {Distortion and peak broadening in quasicrystal diffraction
patterns.},
Journal = {Phys Rev Lett},
Volume = {57},
Number = {12},
Pages = {14401443},
Year = {1986},
Month = {September},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10033450},
Doi = {10.1103/PhysRevLett.57.1440},
Key = {fds248358}
}
@article{fds248357,
Author = {Socolar, JE and Lubensky, TC and Steinhardt, PJ},
Title = {Phonons, phasons, and dislocations in quasicrystals.},
Journal = {Physical Review. B, Condensed Matter},
Volume = {34},
Number = {5},
Pages = {33453360},
Year = {1986},
Month = {September},
ISSN = {01631829},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9940073},
Doi = {10.1103/physrevb.34.3345},
Key = {fds248357}
}
@article{fds248319,
Author = {Socolar, JE and Steinhardt, PJ},
Title = {Quasicrystals. II. Unitcell configurations.},
Journal = {Physical Review. B, Condensed Matter},
Volume = {34},
Number = {2},
Pages = {617647},
Year = {1986},
Month = {July},
ISSN = {01631829},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9939668},
Key = {fds248319}
}
@article{fds248359,
Author = {Socolar, JES},
Title = {Phason Strain in Quasicrystals},
Journal = {Journal de Physique},
Volume = {C3},
Pages = {217227},
Year = {1986},
Key = {fds248359}
}
@article{fds248318,
Author = {Socolar, JE and Steinhardt, PJ and Levine, D},
Title = {Quasicrystals with arbitrary orientational
symmetry.},
Journal = {Physical Review. B, Condensed Matter},
Volume = {32},
Series = {Rapid Communication},
Number = {8},
Pages = {55475550},
Year = {1985},
Month = {October},
ISSN = {01631829},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9937798},
Key = {fds248318}
}
@article{fds248316,
Author = {Mele, EJ and Socolar, J},
Title = {Numerical integration of the time evolution operator:
Excited‐state dynamics in conjugated molecules},
Journal = {International Journal of Quantum Chemistry},
Volume = {26},
Series = {Quantum Chemistry Symposium},
Number = {18 S},
Pages = {347358},
Publisher = {WILEY},
Year = {1984},
Month = {January},
ISSN = {00207608},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1984ACF7600031&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {Two simple and manageable schemes for integrating the time
evolution operator e−iHt are discussed and applied to
study vibronic effects in photoemission and optical
excitation of model conjugated molecules. Copyright © 1984
John Wiley & Sons, Inc.},
Doi = {10.1002/qua.560260832},
Key = {fds248316}
}
@booklet{Gollub80,
Author = {Gollub, JP and Romer, EJ and Socolar, JE},
Title = {Trajectory divergence for coupled relaxation oscillators:
Measurements and models},
Journal = {Journal of Statistical Physics},
Volume = {23},
Number = {3},
Pages = {321333},
Publisher = {Springer Nature},
Year = {1980},
Month = {September},
ISSN = {00224715},
url = {http://dx.doi.org/10.1007/BF01011372},
Abstract = {The exponential divergence of nearby phase space
trajectories is a hallmark of nonperiodic (chaotic) behavior
in dynamical systems. We present the first laboratory of
measurements of divergence rates (or characteristic
exponents), using a system of coupled tunnel diode
relaxation oscillators. This property of sensitive
dependence on initial conditions is reliably associated with
broadband spectra, and both methods are used to characterize
the motion as a function of the coupling strength and
natural frequency ratio of the two oscillators. A simple
piecewise linear model correctly predicts the major periodic
and nonperiodic regions of the parameter space, thus
confirming that the chaotic behavior involves only a few
degrees of freedom. © 1980 Plenum Publishing
Corporation.},
Doi = {10.1007/BF01011372},
Key = {Gollub80}
}
