%% Papers Published
@article{fds349577,
Author = {Orizaga, S and Riahi, DN and Soto, JR},
Title = {Drug delivery in catheterized arterial blood flow with
atherosclerosis},
Journal = {Results in Applied Mathematics},
Volume = {7},
Pages = {100117-100117},
Publisher = {Elsevier BV},
Year = {2020},
Month = {August},
url = {http://dx.doi.org/10.1016/j.rinam.2020.100117},
Abstract = {© 2020 The Author(s) We study the problem of drug delivery
in a catheterized artery in the presence of atherosclerosis.
The problem is modeled in the context of a two-phase flow
system which consists of red blood cells and blood plasma.
The coupled differential equations for fluid (plasma) and
particles (red cells) are solved for the relevant quantities
in the reasonable limits. The drug delivery problem is
modeled with a partial differential equation that is
developed in terms of the drug concentration, blood plasma
velocity, hematocrit value and the diffusion coefficient of
the drug/fluid. A conservative-implicit finite difference
scheme is develop in order to numerically solve the drug
concentration model with an atherosclerosis region. We find
that the evolution of the drug concentration varies in
magnitude depending on the roles played by the convection
and diffusion effects. For the cases where the diffusion
coefficient is not too small, then convection effect is not
strong enough and drug was delivered mostly in the central
part of the blood flow region and could not reach
effectively the atherosclerosis zone. However, for
sufficiently small values of the diffusion coefficient, the
convective effect dominates over the diffusion effect and
the drug was delivered effectively over the blood flow
region and on the atherosclerosis zone.},
Doi = {10.1016/j.rinam.2020.100117},
Key = {fds349577}
}
@article{fds335544,
Author = {Glasner, K and Orizaga, S},
Title = {Multidimensional equilibria and their stability in
copolymer–solvent mixtures},
Journal = {Physica D: Nonlinear Phenomena},
Volume = {373},
Pages = {1-12},
Publisher = {Elsevier BV},
Year = {2018},
Month = {June},
url = {http://dx.doi.org/10.1016/j.physd.2018.02.001},
Abstract = {© 2018 Elsevier B.V. This paper discusses localized
equilibria which arise in copolymer–solvent mixtures. A
free boundary problem associated with the sharp-interface
limit of a density functional model is used to identify both
lamellar and concentric domain patterns composed of a finite
number of layers. Stability of these morphologies is studied
through explicit linearization of the free boundary
evolution. For the multilayered lamellar configuration,
transverse instability is observed for sufficiently small
dimensionless interfacial energies. Additionally, a
crossover between small and large wavelength instabilities
is observed depending on whether solvent–polymer or
monomer–monomer interfacial energy is dominant. Concentric
domain patterns resembling multilayered micelles and
vesicles exhibit bifurcations wherein they only exist for
sufficiently small dimensionless interfacial energies. The
bifurcation of large radii vesicle solutions is studied
analytically, and a crossover from a supercritical case with
only one solution branch to a subcritical case with two is
observed. Linearized stability of these configurations shows
that azimuthal perturbation may lead to instabilities as
interfacial energy is decreased.},
Doi = {10.1016/j.physd.2018.02.001},
Key = {fds335544}
}
@article{fds329007,
Author = {Orizaga, S and Riahi, DN},
Title = {Triad resonant wave interactions in electrically charged
jets},
Journal = {Applied Mathematics and Mechanics},
Volume = {38},
Number = {8},
Pages = {1127-1148},
Year = {2017},
Month = {August},
url = {http://dx.doi.org/10.1007/s10483-017-2229-9},
Abstract = {© 2017, Shanghai University and Springer-Verlag GmbH
Germany. Nonlinear instability in electrically charged jets
is studied using the governing electro-hydrodynamic
equations describing stretching and thinning of a liquid
jet. A jet flow system subject to both space and time
evolving disturbances is considered. At the linear stage,
the Rayleigh and conducting jet flow instability modes are
uncovered. Nonlinear instability in the flow is explored via
triad resonant waves which uncover fa- vorable operating
modes not previously detected in the linear study of the
problem. In particular, the jet radius is significantly
reduced, and the electric field of the jet is properly
oriented under the nonlinear study. It is found that taking
into account the resonance triad modes provides a better
mathematical description of a jet that stretches and thins
due to tangential electric field effects. Both linear and
nonlinear instability results in the jet flow system are
presented and discussed.},
Doi = {10.1007/s10483-017-2229-9},
Key = {fds329007}
}
@article{fds329008,
Author = {Glasner, K and Orizaga, S},
Title = {Improving the accuracy of convexity splitting methods for
gradient flow equations},
Journal = {Journal of Computational Physics},
Volume = {315},
Pages = {52-64},
Publisher = {Elsevier BV},
Year = {2016},
Month = {June},
url = {http://dx.doi.org/10.1016/j.jcp.2016.03.042},
Abstract = {© 2016 Elsevier Inc. This paper introduces numerical time
discretization methods which significantly improve the
accuracy of the convexity-splitting approach of Eyre (1998)
[7], while retaining the same numerical cost and stability
properties.A first order method is constructed by iteration
of a semi-implicit method based upon decomposing the energy
into convex and concave parts. A second order method is also
presented based on backwards differentiation formulas.
Several extrapolation procedures for iteration
initialization are proposed. We show that, under broad
circumstances, these methods have an energy decreasing
property, leading to good numerical stability.The new
schemes are tested using two evolution equations commonly
used in materials science: the Cahn-Hilliard equation and
the phase field crystal equation. We find that our methods
can increase accuracy by many orders of magnitude in
comparison to the original convexity-splitting algorithm. In
addition, the optimal methods require little or no
iteration, making their computation cost similar to the
original algorithm.},
Doi = {10.1016/j.jcp.2016.03.042},
Key = {fds329008}
}
@article{fds329009,
Author = {Orizaga, S and Glasner, K},
Title = {Instability and reorientation of block copolymer
microstructure by imposed electric fields.},
Journal = {Physical Review. E},
Volume = {93},
Number = {5},
Pages = {052504},
Year = {2016},
Month = {May},
url = {http://dx.doi.org/10.1103/physreve.93.052504},
Abstract = {The influence of electric fields on lamellar block copolymer
microstructure is studied in the context of a density
functional model and its sharp interface limit. A free
boundary problem for domain interfaces of strongly
segregated polymers is derived, which includes coupling of
interface and electric field orientation. The linearized
dynamics of lamellar configurations is computed in this
context, leading to quantitative criteria for instability as
a function of pattern wavelength, field magnitude, and
orientation. Numerical simulations of the full model in two
and three dimensions are used to study the nonlinear
development of instabilities. In three dimensions,
sufficiently large electric field magnitude always leads to
instability. In two dimensions, the field has either
stabilizing or destabilizing effects depending on the
misorientation of the field and pattern. Even when linear
instabilities are present, the dynamics can lead to stable
corrugated domain interfaces which do not align with the
electric field. Sufficiently high field strengths, on the
other hand, produce topological rearrangement which may lead
to alignment.},
Doi = {10.1103/physreve.93.052504},
Key = {fds329009}
}
@article{fds329010,
Author = {Orizaga, S and Riahi, DN},
Title = {On nonlinear spatio-temporal instability regime for
electrically forced viscous jets [Errata
corrige]},
Journal = {International Journal of Non Linear Mechanics},
Volume = {74},
Pages = {38-39},
Publisher = {Elsevier BV},
Year = {2015},
Month = {September},
url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2015.04.001},
Abstract = {© 2015 Elsevier Ltd. The authors have found errors in the
published paper, Nonlinear spatio-temporal instability
regime for electrically forced viscous jets, Int. J.
Nonlinear Mech. 67 (2014), 218-230. The errors and the
corrections provided here do not affect the abstract, main
findings and conclusions of the original
paper.},
Doi = {10.1016/j.ijnonlinmec.2015.04.001},
Key = {fds329010}
}
@article{fds329011,
Author = {Orizaga, S and Riahi, DN and Steven Hou and L},
Title = {Nonlinear spatio-temporal instability regime for
electrically forced viscous jets},
Journal = {International Journal of Non Linear Mechanics},
Volume = {67},
Pages = {218-230},
Publisher = {Elsevier BV},
Year = {2014},
Month = {January},
url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2014.09.001},
Abstract = {© 2014 Elsevier Ltd. This paper considers the problem of
nonlinear instability in electrically driven viscous
axisymmetric jets with respect to spatial and temporal
growing disturbances in the presence of a uniform or
non-uniform applied electric field. The mathematical
modeling for the jets, which uses the original
electrohydrodynamics equations (Melcher and Taylor, 1969)
[8], is based on the nonlinear mechanics that govern the
liquid jet due to tangential electric field effects. At the
linear stage, we found that a particular jet of fluid could
exhibit the Rayleigh and Conducting flow Instabilities for
the spatial and temporal evolution of the disturbance. For
the nonlinear regime of the problem, we studied the resonant
instability and nonlinear wave interactions of certain modes
that satisfy the dyad resonant condition. The nonlinear wave
interactions in the jet provided a significant change in the
fluid flow properties that extend notably the available
understanding of the problem at the linear stage. It was
found that the nonlinear resonant instability provides an
amplifying effect on the magnitude of the disturbances which
evolves the jet to reduce significantly its radius at a
shorter axial location. For the case of higher viscosity
fluid, the electric field in the jet was found to be
increasing spatially and temporally when nonlinear wave
interactions were taken into account during the resonant
instability. The resulting nonlinear solutions for the jet
thickness, jet's electric field, jet's surface charge and
jet velocity are presented and discussed.},
Doi = {10.1016/j.ijnonlinmec.2014.09.001},
Key = {fds329011}
}
@article{fds329012,
Author = {Orizaga, S and Riahi, DN},
Title = {On combined spatial and temporal instabilities of
electrically driven jets with constant or variable applied
field},
Journal = {Journal of Theoretical and Applied Mechanics},
Volume = {50},
Number = {1},
Pages = {301-319},
Year = {2012},
Month = {January},
Abstract = {We investigate the problem of combined spatial and temporal
instabilities of electrically driven viscous jets with
finite electrical conductivity in the presence of either
constant or variable applied electric field. A mathematical
model leads to a lengthy equation for the unknown spatial
growth rate and temporal growth rate of the disturbances.
This equation is solved numerically using Newton's method.
We investigated two cases of water jets and glycerol jets.
For water jets and in the case of either constant or
variable applied field, we found two new modes of
instabilities which grow simultaneously in time and space
and lead to significant reduction in the jet radius.
However, in the case of glycerol jets, we found two new
modes of instabilities in the presence of constant applied
field but only one mode of instability in the presence of
variable applied field. For the glycerol jets, the combined
temporal and spatial instabilities are less stronger and
lead to an increase in the jet radius. The instabilities for
both types of water and glycerol jets were found to be
restricted to particular domain in their wavelength and were
enhanced with the strength of the electric
field.},
Key = {fds329012}
}
@article{fds329013,
Author = {Orizaga, S and Riahi, DN},
Title = {Resonant instability and nonlinear wave interactions in
electrically forced jets},
Journal = {Nonlinear Analysis: Real World Applications},
Volume = {12},
Number = {2},
Pages = {1300-1313},
Publisher = {Elsevier BV},
Year = {2011},
Month = {April},
url = {http://dx.doi.org/10.1016/j.nonrwa.2010.09.027},
Abstract = {We investigate the problem of linear temporal instability of
the modes that satisfy the dyad resonance conditions and the
associated nonlinear wave interactions in jets driven by
either a constant or a variable external electric field. A
mathematical model, which is developed and used for the
temporally growing modes with resonance and their nonlinear
wave interactions in electrically driven jet flows, leads to
equations for the unknown amplitudes of such waves. These
equations are solved for both water and glycerol jet cases,
and the expressions for the dependent variables of the
corresponding modes are determined. The results of the
generated data for these dependent variables versus time
indicate, in particular, that the instability resulted from
the nonlinear interactions of such modes is mostly quite
strong but can also lead to significant reduction in the jet
radius. © 2010 Elsevier Ltd. All rights
reserved.},
Doi = {10.1016/j.nonrwa.2010.09.027},
Key = {fds329013}
}
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Mathematics Department