22 research outputs found

### Hydrodynamics of fluid-solid coexistence in dense shear granular flow

We consider dense rapid shear flow of inelastically colliding hard disks.
Navier-Stokes granular hydrodynamics is applied accounting for the recent
finding \cite{Luding,Khain} that shear viscosity diverges at a lower density
than the rest of constitutive relations. New interpolation formulas for
constitutive relations between dilute and dense cases are proposed and
justified in molecular dynamics (MD) simulations. A linear stability analysis
of the uniform shear flow is performed and the full phase diagram is presented.
It is shown that when the inelasticity of particle collision becomes large
enough, the uniform sheared flow gives way to a two-phase flow, where a dense
"solid-like" striped cluster is surrounded by two fluid layers. The results of
the analysis are verified in event-driven MD simulations, and a good agreement
is observed

### Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?

We investigate shear-induced crystallization in a very dense flow of
mono-disperse inelastic hard spheres. We consider a steady plane Couette flow
under constant pressure and neglect gravity. We assume that the granular
density is greater than the melting point of the equilibrium phase diagram of
elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive
relations all of which (except the shear viscosity) diverge at the crystal
packing density, while the shear viscosity diverges at a smaller density. The
phase diagram of the steady flow is described by three parameters: an effective
Mach number, a scaled energy loss parameter, and an integer number m: the
number of half-oscillations in a mechanical analogy that appears in this
problem. In a steady shear flow the viscous heating is balanced by energy
dissipation via inelastic collisions. This balance can have different forms,
producing either a uniform shear flow or a variety of more complicated,
nonlinear density, velocity and temperature profiles. In particular, the model
predicts a variety of multi-layer two-phase steady shear flows with sharp
interphase boundaries. Such a flow may include a few zero-shear (solid-like)
layers, each of which moving as a whole, separated by fluid-like regions. As we
are dealing with a hard sphere model, the granulate is fluidized within the
"solid" layers: the granular temperature is non-zero there, and there is energy
flow through the boundaries of the "solid" layers. A linear stability analysis
of the uniform steady shear flow is performed, and a plausible bifurcation
diagram of the system, for a fixed m, is suggested. The problem of selection of
m remains open.Comment: 11 pages, 7 eps figures, to appear in PR

### Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations

The position of a reaction front, propagating into a metastable state,
fluctuates because of the shot noise of reactions and diffusion. A recent
theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147
(2011)] gave a closed analytic expression for the front diffusion coefficient
in the weak noise limit. Here we test this theory in stochastic simulations
involving reacting and diffusing particles on a one-dimensional lattice. We
also investigate a small noise-induced systematic shift of the front velocity
compared to the prediction from the spatially continuous deterministic
reaction-diffusion equation.Comment: 5 pages, 5 figure

### A stochastic model for wound healing

We present a discrete stochastic model which represents many of the salient
features of the biological process of wound healing. The model describes fronts
of cells invading a wound. We have numerical results in one and two dimensions.
In one dimension we can give analytic results for the front speed as a power
series expansion in a parameter, p, that gives the relative size of
proliferation and diffusion processes for the invading cells. In two dimensions
the model becomes the Eden model for p near 1. In both one and two dimensions
for small p, front propagation for this model should approach that of the
Fisher-Kolmogorov equation. However, as in other cases, this discrete model
approaches Fisher-Kolmogorov behavior slowly.Comment: 16 pages, 7 figure

### Path-dependent course of epidemic: are two phases of quarantine better than one?

The importance of a strict quarantine has been widely debated during the
COVID-19 epidemic even from the purely epidemiological point of view. One
argument against strict lockdown measures is that once the strict quarantine is
lifted, the epidemic comes back, and so the cumulative number of infected
individuals during the entire epidemic will stay the same. We consider an SIR
model on a network and follow the disease dynamics, modeling the phases of
quarantine by changing the node degree distribution. We show that the system
reaches different steady states based on the history: the outcome of the
epidemic is path-dependent despite the same final node degree distribution. The
results indicate that two-phase route to the final node degree distribution (a
strict phase followed by a soft phase) are always better than one phase (the
same soft one) unless all the individuals have the same number of connections
at the end (the same degree); in the latter case, the overall number of
infected is indeed history-independent. The modeling also suggests that the
optimal procedure of lifting the quarantine consists of releasing nodes in the
order of their degree - highest first.Comment: 6 pages, 4 figures, accepted to EPL (Europhysics Letters

### Dynamics and pattern formation in invasive tumor growth

In this work, we study the in-vitro dynamics of the most malignant form of
the primary brain tumor: Glioblastoma Multiforme. Typically, the growing tumor
consists of the inner dense proliferating zone and the outer less dense
invasive region. Experiments with different types of cells show qualitatively
different behavior. Wild-type cells invade a spherically symmetric manner, but
mutant cells are organized in tenuous branches. We formulate a model for this
sort of growth using two coupled reaction-diffusion equations for the cell and
nutrient concentrations. When the ratio of the nutrient and cell diffusion
coefficients exceeds some critical value, the plane propagating front becomes
unstable with respect to transversal perturbations. The instability threshold
and the full phase-plane diagram in the parameter space are determined. The
results are in a good agreement with experimental findings for the two types of
cells.Comment: 4 pages, 4 figure

### Minimizing the population extinction risk by migration

Many populations in nature are fragmented: they consist of local populations
occupying separate patches. A local population is prone to extinction due to
the shot noise of birth and death processes. A migrating population from
another patch can dramatically delay the extinction. What is the optimal
migration rate that minimizes the extinction risk of the whole population? Here
we answer this question for a connected network of model habitat patches with
different carrying capacities.Comment: 7 pages, 3 figures, accepted for publication in PRL, appendix
contains supplementary materia

### Fast migration and emergent population dynamics

We consider population dynamics on a network of patches, each of which has a
the same local dynamics, with different population scales (carrying
capacities). It is reasonable to assume that if the patches are coupled by very
fast migration the whole system will look like an individual patch with a large
effective carrying capacity. This is called a "well-mixed" system. We show
that, in general, it is not true that the well-mixed system has the same
dynamics as each local patch. Different global dynamics can emerge from
coupling, and usually must be figured out for each individual case. We give a
general condition which must be satisfied for well-mixed systems to have the
same dynamics as the constituent patches.Comment: 4 page