%% Papers Published @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 = {5-1}, 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 long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle θ of the rotating magnetic field. For a purely in-plane field, θ=90^{∘}, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles 50^{∘}≲θ≲55^{∘}, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.}, Doi = {10.1103/physreve.95.052607}, Key = {fds326695} } @article{fds325483, Author = {Oğuz, EC and Socolar, JES and Steinhardt, PJ and Torquato, S}, Title = {Hyperuniformity of quasicrystals}, Journal = {Physical Review B}, Volume = {95}, Number = {5}, Year = {2017}, Month = {February}, url = {http://dx.doi.org/10.1103/PhysRevB.95.054119}, 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 = {025003-025003}, Year = {2017}, Month = {February}, url = {http://dx.doi.org/10.1088/1367-2630/aa57bb}, Doi = {10.1088/1367-2630/aa57bb}, Key = {fds325482} } @article{fds323248, Author = {Rutkowski, DM and Marcoux, C and Socolar, JES and Hall, CK}, Title = {Formation of limit-periodic structures by quadrupole particles confined to a triangular lattice}, Journal = {Physical Review. E}, Volume = {95}, Number = {1}, Publisher = {American Physical Society}, Year = {2017}, Month = {January}, url = {http://dx.doi.org/10.1103/PhysRevE.95.012604}, Abstract = {We have performed Monte Carlo (MC) simulations on two-dimensional systems of quadrupole particles confined to a triangular lattice in order to determine the conditions that permit the formation of a limit-periodic phase. We have found that limit-periodic 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/6 rotations or continuous rotations are allowed. Order parameters signaling the formation of the limit-periodic structure and related structures are measured as a function of temperature. Our findings on the formation of the limit-periodic 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}, Year = {2016}, Month = {July}, url = {http://arxiv.org/abs/1604.02479v1}, Abstract = {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 long-range 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, face-to-face 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 limit-periodic structure}, Journal = {Physical Review. B, Condensed Matter}, Volume = {93}, Number = {17}, Publisher = {American Physical Society}, Year = {2016}, Month = {May}, ISSN = {0163-1829}, url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.174102}, Abstract = {Limit-periodic structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. We study a ball and spring model with a limit-periodic pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to limit-periodic 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 limit-periodic 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 = {2505-2514}, Year = {2016}, Month = {March}, ISSN = {1744-683X}, 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 Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (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 three-dimensional 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 limit-periodic order in tiling models [Phys. Rev. E 90 , 012136 (2014)]}, Journal = {Physical Review. E}, Volume = {93}, Number = {2}, Year = {2016}, Month = {February}, ISSN = {2470-0045}, 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 = {2404-2415}, Year = {2015}, Month = {March}, ISSN = {1744-683X}, 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 real-space characterization of phase transitions. Here, we study a quasi-two-dimensional, binary colloidal alloy that exhibits liquid-solid and solid-solid 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 = {80-92}, Year = {2014}, Month = {December}, ISSN = {0022-5193}, 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 continuous-time 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 two-node 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 hand--the formation of three latitudinal tissue bands from an initial state with only two distinct cell types. Analysis of an eight-gene model constructed from available experimental data reveals that it has a modular structure equivalent to the successful two-node 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{PhysRevE.90.012136, Author = {Marcoux, C and Byington, TW and Qian, Z and Charbonneau, P and Socolar, JES}, Title = {Emergence of limit-periodic 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 = {1539-3755}, url = {http://link.aps.org/doi/10.1103/PhysRevE.90.012136}, Abstract = {A two-dimensional (2D) lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar monotile is known to have a limit-periodic 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 next-nearest-neighbor interactions and introduce closely related 3D models with only nearest-neighbor interactions that exhibit limit-periodic phases. For models with no next-nearest-neighbor interactions of the Taylor-Socolar type, there is a large degenerate class of ground states, including crystalline patterns and limit-periodic ones, but a slow quench still yields the limit-periodic state. For the Taylor-Socolar 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 nearest-neighbor 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 = {147-157}, Year = {2014}, Month = {July}, ISSN = {0012-1606}, 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. Non-skeletogenic 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 figure-8 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 time-delay 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 well-studied 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 well-studied 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 limit-periodic 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 = {3682-3687}, 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{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 two-dimensional lattice model with nearest and next-nearest neighbor interactions is known to have a limit-periodic 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 pre-programmed 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 non-magnetic 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{fds248344, Author = {Socolar, JES and Taylor, JM}, Title = {Forcing Nonperiodicity with a Single Tile}, Journal = {The Mathematical Intelligencer}, Volume = {34}, Number = {1}, Pages = {18-28}, Year = {2012}, Month = {Spring}, ISSN = {0343-6993}, url = {http://dx.doi.org/10.1007/s00283-011-9255-y}, 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/s00283-011-9255-y}, Key = {fds248344} } @article{fds248332, Author = {Socolar, JES}, Title = {Local action, global impact: forcing nonperiodicity with a single structural unit.}, Journal = {Chaos}, 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 next-nearest 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 = {2207-2231}, Publisher = {Academic Press, Inc.}, Address = {Orlando, FL, USA}, Year = {2011}, Month = {November}, ISSN = {0097-3165}, 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 two-dimensional, hexagonal prototile with markings that enforce local matching rules is proven to be aperiodic by two independent methods. The space-filling 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 three-dimensional 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 = {495-513}, Year = {2010}, Month = {January}, ISSN = {1364-503X}, 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 logic-transition events circulating in the network per unit time grows as a power law. In an experiment, the non-ideal behaviour of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse 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 Boolean-like 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 test-bed for fundamental studies of real-world Boolean-like 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 cell-cycle oscillator.}, Journal = {Plos Computational Biology}, Volume = {6}, Number = {7}, Pages = {e1000842}, Year = {2010}, ISSN = {1553-7358}, 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 auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time 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 ultrawide-band 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 cell-cycle transcription by coupled CDK and network oscillators.}, Journal = {Nature}, Volume = {453}, Number = {7197}, Pages = {944-947}, 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 cell-cycle 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 cyclin-dependent kinases (CDKs). To determine the extent to which the global cell-cycle transcription programme is controlled by cyclin-CDK complexes, we examined genome-wide transcription dynamics in budding yeast mutant cells that do not express S-phase 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 cell-cycle 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 cell-cycle oscillator independently of, and in tandem with, the CDK oscillator.}, Doi = {10.1038/nature06955}, Key = {fds248339} } @article{fds248314, Author = {Socolar, JES}, Title = {Time-Delay Control for Discrete Maps}, Pages = {29-45}, 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 self-contained 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 Wiley-VCH 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 cell-cycle 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 = {1539-3755}, url = {http://www.ncbi.nlm.nih.gov/pubmed/18517366}, Abstract = {We study the nonlinear elastic response of a two-dimensional 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 ball-and-spring 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 Lloyd-Price, 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 = {1539-3755}, 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 = {Time-delay control for discrete maps}, Booktitle = {Handbook of Chaos Control}, Publisher = {Wiley-VCH Verlag GmbH}, Editor = {E. Scholl and H. G. Schuster}, Year = {2007}, Month = {December}, url = {http://www.wiley.com/WileyCDA/WileyTitle/productCd-3527406050,descCd-tableOfContents.html}, Abstract = {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 self-contained 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 = {1539-3755}, 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 self-input. 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 non-Boolean 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 time-delay autosynchronization.}, Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics}, Volume = {76}, Number = {4 Pt 1}, Pages = {041917}, Year = {2007}, Month = {October}, ISSN = {1539-3755}, url = {http://www.ncbi.nlm.nih.gov/pubmed/17995036}, Abstract = {Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop 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 time-delay 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{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 = {0031-9007}, 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 in-degree 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{fds248328, Author = {Socolar, JES}, Title = {Erratum: The hexagonal parquet tiling, k-isohedral monotiles with arbitrarily large k (The Mathematical Intelligencer 29:2 (33-38))}, Journal = {The Mathematical Intelligencer}, Volume = {29}, Number = {4}, Pages = {6-}, Year = {2007}, ISSN = {0343-6993}, url = {http://dx.doi.org/10.1007/BF02986167}, Doi = {10.1007/BF02986167}, Key = {fds248328} } @article{fds248350, Author = {Socolar, JES}, Title = {The hexagonal parquet tiling k-isohedral monotiles with arbitrarily large k}, Journal = {The Mathematical Intelligencer}, Volume = {29}, Number = {2}, Pages = {33-38}, Year = {2007}, ISSN = {0343-6993}, 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 space-filling; (4) allowing the tile to have a thickness in the third dimension.}, Doi = {10.1007/BF02986203}, Key = {fds248350} } @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 = {1539-3755}, 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 in-degree 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{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}, Year = {2006}, ISSN = {1539-3755}, 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 in-degree 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{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 = {1539-3755}, 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 single-contact 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{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 = {52-60}, Year = {2005}, ISSN = {1076-2787}, 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{fds248377, Author = {Harrington, I and Socolar, JES}, Title = {Design and robustness of delayed feedback controllers for discrete systems}, Journal = {Phys. Rev. E}, Volume = {69}, Number = {5 1}, Pages = {56207}, Year = {2004}, ISSN = {1539-3755}, Abstract = {A matrix form of time-delay feedback control in the context of discrete time maps of high dimension was studied. Time-delay feedback controllers containing only static elements can be designed to achieve identical linear stability properties, in almost all cases where standard proportional feedback control methods can achieve control. This control was a generalization of a method called 'extended time-delay autosynchronization' (ETDAS). Analysis of an example involving a ring of coupled maps that can be controlled at only two sites demonstrated that the time-delay controller equivalent to a standard optimal controller can be equally robust in the presence of noise.}, Key = {fds248377} } @article{fds248378, Author = {Hövel, P and Socolar, JES}, Title = {Stability domains for time-delay 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 = {1539-3755}, 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 time-delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored. We discuss the case of extended time-delay 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 = {0031-9007}, 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{fds318470, Author = {Hövel, P and Socolar, JES}, Title = {Stability domains for time-delay feedback control with latency}, Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter Physics}, Volume = {68}, Number = {3 2}, Pages = {362061-362067}, Year = {2003}, Abstract = {The stability of periodic orbits controlled by time-delay 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, J-P and Claudin, P and Socolar, JES}, Title = {Anisotropy in granular media: Classical elasticity and directed-force chain network}, Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter Physics}, Volume = {67}, Number = {3 1}, Pages = {031302/1-031302/24}, Year = {2003}, ISSN = {1063-651X}, url = {http://arxiv.org/abs/cond-mat/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 directed-force chain networks is presented. It is shown how the formalism applies to the example of a triangular ball-and-spring 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{fds248385, Author = {Socolar, JES}, Title = {Discrete models of force chain networks}, Journal = {Discrete and Continuous Dynamical Systems Series B}, Volume = {3}, Number = {4}, Pages = {601-618}, Year = {2003}, ISSN = {1531-3492}, url = {http://xxx.lanl.gov/abs/cond-mat/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 frame-work 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.}, Key = {fds248385} } @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 = {453-453}, Year = {2002}, Month = {July}, url = {http://dx.doi.org/10.1140/epje/i2002-10030-4}, Doi = {10.1140/epje/i2002-10030-4}, 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 = {353-370}, Year = {2002}, url = {http://xxx.lanl.gov/abs/cond-mat/0201242}, Abstract = {A theory of stress fields in two-dimensional 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 fixed-point 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{fds304614, Author = {Beck, O and Amann, A and Schöll, E and Socolar, JES and Just, W}, Title = {Comparison of time-delayed feedback schemes for spatiotemporal control of chaos in a reaction-diffusion system with global coupling}, Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics}, Volume = {66}, Number = {1}, Pages = {016213/1-016213/6}, Year = {2002}, ISSN = {1539-3755}, url = {http://dx.doi.org/10.1103/PhysRevE.66.016213}, Abstract = {Time-delayed feedback control for stabilizing time periodic spatial patterns is investigated in a generic reaction-diffusion system with global coupling. We focus on the case of low-dimensional 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{fds248383, Author = {Harrington, I and Socolar, JE}, Title = {Limitation on stabilizing plane waves via time-delay feedback.}, Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics}, Volume = {64}, Number = {5 Pt 2}, Pages = {056206}, Year = {2001}, Month = {November}, ISSN = {1539-3755}, url = {http://www.ncbi.nlm.nih.gov/pubmed/11736053}, Abstract = {Previous work has demonstrated the possibility of stabilizing plane wave solutions of one-dimensional systems using a spatially local form of time-delayed feedback. We show that the natural extension of this method to two-dimensional systems fails due to the presence of torsion-free unstable perturbations. Linear stability analysis of the complex Ginzburg-Landau equation reveals that long wavelength, transverse wave instabilities cannot be suppressed by the method of extended time-delay 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{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{fds248322, Author = {Socolar, JES and Richards, S and Wilson, WG}, 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 I}, Pages = {419081-419088}, Year = {2001}, Abstract = {A model that gave rise to inhomogenous population densities in a system of host individuals was studied. The model consisted of rules of reproduction, and natural death. Behavior observed in simulations of a one-dimensional system was accounted by a mean-field analysis, were the stable state corresponded to the solution of straightforward optimization problem.}, Key = {fds248322} } @article{fds248382, Author = {Bleich, ME and Socolar, JES}, Title = {Delayed feedback control of a paced excitable oscillator}, Journal = {International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}, Volume = {10}, Number = {3}, Pages = {603-609}, Year = {2000}, Abstract = {A simple numerical experiment on Fitzhugh-Nagumo equations demonstrates that time-delay 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.}, 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 = {2383-2388}, Year = {1999}, Month = {December}, ISSN = {0962-8452}, 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 'well-mixed' analytical model and spatially explicit individual-based 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 well-mixed 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 short-lived 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 = {1999-2008}, Year = {1999}, Month = {August}, ISSN = {1063-651X}, 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{fds248380, Author = {Socolar, JES and Gauthier, DJ}, Title = {Analysis and comparison of multiple-delay schemes for controlling unstable fixed points of discrete maps}, Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter Physics}, Volume = {57}, Number = {6}, Pages = {6589-6595}, Year = {1998}, Month = {June}, url = {http://dx.doi.org/10.1103/PhysRevE.57.6589}, Abstract = {We investigate theoretically the stabilization of a fixed point of a discrete one-dimensional 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 time-delay autosynchronization, which uses an infinite series of past iterates with weights that decay by a factor of R with each time step, and N-time-delay autosynchronization, which uses an average of N 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 R and N, and that N-time-delay autosynchronization tends to be less sensitive to noise.}, Doi = {10.1103/PhysRevE.57.6589}, Key = {fds248380} } @article{fds248379, Author = {Egolf, DA and Socolar, JES}, Title = {Failure of linear control in noisy coupled map lattices}, Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, Volume = {57}, Number = {5 SUPPL. A}, Pages = {5271-5275}, Year = {1998}, Abstract = {We study a one-dimensional 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.}, Key = {fds248379} } @article{fds248374, Author = {Sukow, DW and Bleich, ME and Gauthier, DJ and Socolar, JES}, Title = {Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis.}, Journal = {Chaos}, Volume = {7}, Number = {4}, Pages = {560-576}, 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 time-delay 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 all-optical 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 time-delay 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{fds248387, Author = {Gauthier, DJ and Socolar, JES}, Title = {Comment on ``Dynamic Control of Cardiac Alternans''}, Journal = {Physical Review Letters}, Volume = {79}, Number = {24}, Pages = {4938-4938}, Year = {1997}, Month = {December}, url = {http://dx.doi.org/10.1103/PhysRevLett.79.4938}, Doi = {10.1103/PhysRevLett.79.4938}, Key = {fds248387} } @article{fds303753, Author = {Socolar, JES}, Title = {Average stresses and force fluctuations in non-cohesive granular materials}, Volume = {57}, Pages = {3204}, Year = {1997}, Month = {October}, url = {http://arxiv.org/abs/cond-mat/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 q-model 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 q-model) without requiring the assumption of a constitutive relation. For a 2D system with periodic boundary conditions, the model generates single-grain force distributions similar to those obtained from the q-model with a singular distribution of q's.}, Doi = {10.1103/PhysRevE.57.3204}, Key = {fds303753} } @article{fds248375, Author = {Bleich, ME and Hochheiser, D and Moloney, JV and Socolar, JES}, Title = {Controlling extended systems with spatially filtered, time-delayed feedback}, Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, Volume = {55}, Number = {3 SUPPL. A}, Pages = {2119-2126}, Year = {1997}, Abstract = {We investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time-delay feedback. The scheme is naturally suited to real-time control of optical systems. We apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable, coherent traveling-wave 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.}, Key = {fds248375} } @article{fds248373, Author = {Bleich, ME and Socolar, JE}, Title = {Controlling spatiotemporal dynamics with time-delay feedback.}, Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter Physics}, Volume = {54}, Number = {1}, Pages = {R17-R20}, Year = {1996}, Month = {July}, ISSN = {1063-651X}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9965164}, Key = {fds248373} } @article{fds248372, Author = {Bleich, ME and Socolar, JES}, Title = {Stability of periodic orbits controlled by time-delay feedback}, Journal = {Physics Letters A}, Volume = {210}, Number = {1-2}, Pages = {87-94}, Year = {1996}, Month = {January}, url = {http://dx.doi.org/10.1016/0375-9601(95)00827-6}, Abstract = {Extended time-delay auto-synchronization (ETDAS) is a promising technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems. The technique involves continuous feedback of signals delayed by multiples of the orbit's period in a manner that is especially well-suited for fast systems and optical implementation. We show how to analyze the stability of a given implementation of ETDAS without explicit integration of time-delay equations. To illustrate the method and point out some nontrivial features of ETDAS, we obtain the domain of control for a period-one orbit of the driven, damped pendulum.}, Doi = {10.1016/0375-9601(95)00827-6}, 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 = {3245-3248}, Year = {1994}, Month = {October}, ISSN = {1063-651X}, 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 time-delay autosynchronization.}, Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter Physics}, Volume = {50}, Number = {3}, Pages = {2343-2346}, Year = {1994}, Month = {September}, ISSN = {1063-651X}, 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 = {R643-R646}, Year = {1993}, Month = {August}, ISSN = {1063-651X}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9960763}, Key = {fds248369} } @article{fds248368, Author = {Socolar, JE and Grinstein, G and Jayaprakash, C}, Title = {On self-organized criticality in nonconserving systems.}, Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter Physics}, Volume = {47}, Number = {4}, Pages = {2366-2376}, Year = {1993}, Month = {April}, ISSN = {1063-651X}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9960267}, Key = {fds248368} } @article{fds303752, Author = {Krug, J and Socolar, JE and Grinstein, G}, Title = {Surface fluctuations and criticality in a class of one-dimensional sandpile models.}, Journal = {Physical Review A}, Volume = {46}, Number = {8}, Pages = {R4479-R4482}, Year = {1992}, Month = {October}, ISSN = {1050-2947}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9908766}, Key = {fds303752} } @article{fds248366, Author = {Krug, J and Socolar, JE}, Title = {Comment on "Scalings of growing self-organized 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{fds248365, Author = {Socolar, JES}, Title = {Theory of Packings of Identical Hard Disks Generated by Ballistic Deposition}, Journal = {Europhys. Lett.}, Volume = {18}, Pages = {39}, Year = {1992}, Key = {fds248365} } @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{fds37539, Author = {J.E.S. Socolar}, Title = {The Alternation Condition and 2D Quasicrystals}, Volume = {93}, Series = {Springer Series in Solid-State Sciences}, Booktitle = {Quasicrystals}, Publisher = {Springer-Verlag, Berlin}, Editor = {T. Fujiwara and T. Ogawa}, Year = {1990}, Key = {fds37539} } @article{fds248364, Author = {Socolar, JES}, Title = {Weak matching rules for quasicrystals}, Journal = {Communications in Mathematical Physics}, Volume = {129}, Number = {3}, Pages = {599-619}, Year = {1990}, ISSN = {0010-3616}, url = {http://dx.doi.org/10.1007/BF02097107}, Abstract = {Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in "perp-space" are uniformly bounded. It is shown here that weak matching rules exist for N-fold 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 N-fold 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 Springer-Verlag.}, Doi = {10.1007/BF02097107}, Key = {fds248364} } @article{fds248363, Author = {Socolar, JE}, Title = {Simple octagonal and dodecagonal quasicrystals.}, Journal = {Physical Review. B, Condensed Matter}, Volume = {39}, Number = {15}, Pages = {10519-10551}, Year = {1989}, Month = {May}, ISSN = {0163-1829}, 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 = {2653-2656}, 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 = {221-224}, 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 = {1440-1443}, 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 = {3345-3360}, Year = {1986}, Month = {September}, ISSN = {0163-1829}, 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. Unit-cell configurations.}, Journal = {Physical Review. B, Condensed Matter}, Volume = {34}, Number = {2}, Pages = {617-647}, Year = {1986}, Month = {July}, ISSN = {0163-1829}, 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 = {217-227}, 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 = {5547-5550}, Year = {1985}, Month = {October}, ISSN = {0163-1829}, 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 = {18}, Series = {Quantum Chemistry Symposium}, Pages = {347-358}, Year = {1984}, ISSN = {0020-7608}, 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}, 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 = {321-333}, Year = {1980}, ISSN = {0022-4715}, 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 non-periodic 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} } %% Papers Submitted @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} }