12,178 research outputs found
Newtonian limit of Maxwell fluid flows
In this paper, we revise Maxwell's constitutive relation and formulate a
system of first-order partial differential equations with two parameters for
compressible viscoelastic fluid flows. The system is shown to possess a nice
conservation-dissipation (relaxation) structure and therefore is symmetrizable
hyperbolic. Moreover, for smooth flows we rigorously verify that the revised
Maxwell's constitutive relations are compatible with Newton's law of viscosity.Comment: 11 page
Mean-field backward stochastic differential equations on Markov chains
In this paper, we deal with a class of mean-field backward stochastic
differential equations (BSDEs) related to finite state, continuous time Markov
chains. We obtain the existence and uniqueness theorem and a comparison theorem
for solutions of one-dimensional mean-field BSDEs under Lipschitz condition
Stability of Steady Solutions to Reaction-Hyperbolic Systems for Axonal Transport
This paper is concerned with the stability of steady solutions to
initial-boundary-value problems of reaction-hyperbolic systems for axonal
transport. Under proper structural assumptions, we clarify the relaxation
structure of the reaction-hyperbolic systems and show the time-asymptotic
stability of steady solutions or relaxation boundary-layers
Relaxation-rate formula for the entropic lattice Boltzmann method
An elegant and uniform relaxation-rate formula is presented for the entropic
lattice Boltzmann method (ELBM). The formula not only guarantees the discrete
time H-theorem at numerical level but also gives full consideration to the
consistency with hydrodynamics. With this novel formula, the computational cost
of the ELBM is significantly reduced and the method now can be efficiently used
for a broad range of hydrodynamics applications including high Renolds number
flows. Moreover, we demonstrate that the grid points where flow fields change
drastically are effectively marked by the formula
Stability analysis of the Biot/squirt models for wave propagation in saturated porous media
This work is concerned with the Biot/squirt (BISQ) models for wave
propagation in saturated porous media. We show that the models allow
exponentially exploding solutions, as time goes to infinity, when the
characteristic squirt-flow coefficient is negative or has a non-zero imaginary
part. We also show that the squirt-flow coefficient does have non-zero
imaginary parts for some experimental parameters. Because the models are
linear, the existence of such exploding solutions indicates instability of the
BISQ models. This result calls on a reconsideration of the widely used BISQ
theory. Furthermore, we demonstrate that the 3D isotropic BISQ model is stable
when the squirt-flow coefficient is positive. In particular, the original Biot
model is unconditionally stable where the squirt-flow coefficient is 1.Comment: 19 page
Weak entropy solutions of nonlinear reaction-hyperbolic systems for axonal transport
This paper is concerned with a class of nonlinear reaction-hyperbolic systems
as models for axonal transport in neuroscience. We show the global existence of
entropy-satisfying BV-solutions to the initial-value problems by using
hyperbolic-type methods. Moreover, we rigorously justify the limit as the
biochemical processes are much faster than the transport ones
On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials
We report the bright solitons of the generalized Gross-Pitaevskii (GP)
equation with some types of physically relevant parity-time-(PT-) and
non-PT-symmetric potentials. We find that the constant momentum coefficient can
modulate the linear stability and complicated transverse power-flows (not
always from the gain toward loss) of nonlinear modes. However, the varying
momentum coefficient Gamma(x) can modulate both unbroken linear PT-symmetric
phases and stability of nonlinear modes. Particularly, the nonlinearity can
excite the unstable linear mode (i.e., broken linear PT-symmetric phase) to
stable nonlinear modes. Moreover, we also find stable bright solitons in the
presence of non-PT-symmetric harmonic-Gaussian potential. The interactions of
two bright solitons are also illustrated in PT-symmetric potentials. Finally,
we consider nonlinear modes and transverse power-flows in the three-dimensional
(3D) GP equation with the generalized PT-symmetric Scarf-II potentialComment: 16 pages, 23 figure
Partial equilibrium approximations in Apoptosis
Apoptosis is one of the most basic biological processes. In apoptosis, tens
of species are involved in many biochemical reactions with times scales of
widely differing orders of magnitude. By the law of mass action, the process is
mathematically described with a large and stiff system of ODEs (ordinary
differential equations). The goal of this work is to simplify such systems of
ODEs with the PEA (partial equilibrium approximation) method. In doing so, we
propose a general framework of the PEA method together with some conditions,
under which the PEA method can be justified rigorously. The main condition is
the principle of detailed balance for fast reactions as a whole. With the
justified method as a tool, we made many attempts via numerical tests to
simplify the Fas-signaling pathway model due to Hua et al. (2005) and found
that nine of reactions therein can be well regarded as relatively fast. This
paper reports our simplification of Hua at el.'s model with the PEA method
based on the fastness of the nine reactions, together with numerical results
which confirm the reliability of our simplified model.Comment: 22 pages, 12 figure
Multivalued backward doubly stochastic differential equations with time delayed coefficients
In this paper, we deal with a class of multivalued backward doubly stochastic
differential equations with time delayed coefficients. Based on a slight
extension of the existence and uniqueness of solutions for backward doubly
stochastic differential equations with time delayed coefficients, we establish
the existence and uniqueness of solutions for these equations by means of
Yosida approximation.Comment: 12 page
Mean-field backward stochastic differential equations with subdifferrential operator and its applications
In this paper, we deal with a class of mean-field backward stochastic
differential equations with subdifferrential operator corresponding to a lower
semi-continuous convex function. By means of Yosida approximation, the
existence and uniqueness of the solution is established. As an application, we
give a probability interpretation for the viscosity solutions of a class of
nonlocal parabolic variational inequalities
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