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Pavel M. Lushnikov

Publications and source records attributed to Pavel M. Lushnikov.

At least 37 records · Page 2Linked to original sources
arXiv2013

Beyond leading order logarithmic scaling in the catastrophic self-focusing (collapse) of a laser beam in Kerr media

We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order modification of loglog type $\propto (\ln|\ln(z_c-z)|)^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which determines the system self-focusing across a large range of solution amplitudes. Based on this equation we develop a perturbation theory for scaling modifications beyond the leading loglog. We show that for the initial pulse with the optical power moderately above ($\lesssim 1.2$) the critical power of self-focusing, the new scaling agrees with numerical simulations beginning with amplitudes around only three times above of the initial pulse.

nlin.PS↗
arXiv2013

Logarithmic scaling of the collapse in the critical Keller-Segel equation

A reduced Keller-Segel equation (RKSE) is a parabolic-elliptic system of partial differential equations which describes bacterial aggregation and the collapse of a self-gravitating gas of brownian particles. We consider RKSE in two dimensions, where solution has a critical collapse (blow-up) if the total number of bacteria exceeds a critical value. We study the self-similar solutions of RKSE near the blow-up point. Near the collapse time, $t=t_c$, the critical collapse is characterized by the $L\propto (t_c-t)^{1/2}$ scaling law with logarithmic modification, where $L$ is the spatial width of collapsing solution. We develop an asymptotic perturbation theory for these modifications and show that the resulting scaling agrees well with numerical simulations. The quantitative comparison of the theory and simulations requires to take into account several terms of the perturbation series.

nlin.PS↗
arXiv2011

Proof of concept implementation of the massively parallel algorithm for simulation of dispersion-managed WDM optical fiber systems

We perform a proof-of-concept implementation of the massively parallel algorithm (P.M. Lushnikov, Opt. Lett., v. 27, 939 (2002)) for simulation of dispersion-managed wavelength-division-multiplexed optical fiber systems. Linear scalability of the algorithm with the number of computer cores is demonstrated. Exact result on the accuracy of the implemented algorithm is found analytically and confirmed numerically as well as it is compared with to accuracy of the standard split-step algorithm.

physics.comp-ph↗
arXiv2011

Collective stimulated Brillouin scatter

We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. We identify two contributions to BSBS convective instability increment. The first is collective with intensity threshold independent of the laser correlation time and controlled by diffraction. The second is independent of diffraction, it grows with increase of the correlation time and does not have an intensity threshold. The instability threshold is inside the typical parameter region of National Ignition Facility (NIF). We also find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.

physics.plasm-ph↗
arXiv2011

Strong Collapse Turbulence in Quintic Nonlinear Schrödinger Equation

We consider the quintic one dimensional nonlinear Schrödinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time forming forced turbulence. Without dissipation each of these collapses produces finite time singularity but dissipative terms prevents actual formation of singularity. In statistical steady state of the developed turbulence the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly-Gaussian while the large amplitude tail of probability density function (PDF) is strongly non-Gaussian with power-like behavior. The small amplitude nearly-Gaussian fluctuations seed formation of large collapse events. The universal spatio-temporal form of these events together with the PDF for their maximum amplitudes define the power-like tail of PDF for large amplitude fluctuations, i.e., the intermittency of strong turbulence.

nlin.CD↗
arXiv2011

Learning the nonlinear interactions from particle trajectories

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a novel statistical analysis technique for learning the characteristics of the nonlinear potential from the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of the potential for the much lower temporal resolution compare with the mean square displacement analysis.

physics.bio-ph↗
arXiv2011

Macroscopic model of self-propelled bacteria swarming with regular reversals

Periodic reversals of the direction of motion in systems of self-propelled rod shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize their swarming rate. In this paper, a connection is found between a microscopic one dimensional cell-based stochastic model of reversing non-overlapping bacteria and a macroscopic non-linear diffusion equation describing dynamics of the cellular density. Boltzmann-Matano analysis is used to determine the nonlinear diffusion equation corresponding to the specific reversal frequency. Macroscopically (ensemble-vise) averaged stochastic dynamics is shown to be in a very good agreement with the numerical solutions of the nonlinear diffusion equation. Critical density $p_0$ is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities $p>p_0$. An analytical approximation of the pairwise collision time and semi-analytical fit for the total jam time per reversal period are also obtained. It is shown that cell populations with high reversal frequencies are able to spread out effectively at high densities. If the cells rarely reverse then they are able to spread out at lower densities but are less efficient at spreading out at at higher densities.

physics.bio-ph↗
arXiv2010

Non-Gaussian Statistics of Multiple Filamentation

We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves. These waves form a nearly-Gaussian random field which seeds new filaments. For small amplitudes the probability density function (PDF) of light amplitude is close to Gaussian, while for large amplitudes the PDF has a long power-like tail which corresponds to strong non-Gaussian fluctuations, i.e. intermittency of strong optical turbulence. This tail is determined by the universal form of near singular filaments and the PDF for the maximum amplitudes of the filaments.

nlin.CD↗
arXiv2010

Critical chemotactic collapse

A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between bacteria. If bacterial density exceeds a critical value then the density collapses (blows up) in a finite time which corresponds to bacterial aggregation. Collapse in the Keller-Segel model has striking qualitative similarities with a nonlinear Schrodinger equation including critical collapse in two dimensions and supercritical in three dimensions. A self-similar solution near blow up point is studied in the critical case and it has a form of a rescaled steady state solution which contains a critical number of bacteria. Time dependence of scaling of that solution has square root scaling law with logarithmic corrections.

nlin.PS↗
arXiv2010

Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to $1/r^b$ and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires number of particles to exceed critical value to allow collapse. Critical collapse in that case is strong one trapping into collapsing region a finite number of particles. Case $b>2$ is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For $b<2$ singularity at $r=0$ is not strong enough to allow collapse but attractive $1/r^b$ interaction admits stable self-trapping even in absence of external trapping potential.

nlin.PS↗
arXiv2008

Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact

A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.

physics.bio-ph↗
arXiv2007

Collective stimulated Brillouin backscatter

We develop the statistical theory of the stimulated Brillouin backscatter (BSBS) instability of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new regime of BSBS which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. Instability is collective because it does not depend on the dynamics of isolated speckles of laser intensity, but rather depends on averaged beam intensity. We identify convective and absolute instability regimes. Well above the incoherent threshold the coherent instability growth rate is recovered. The threshold of convective instability is inside the typical parameter region of National Ignition Facility (NIF) designs although current NIF bandwidth is not large enough to insure dominance of collective instability and suggests lower instability threshold due to speckle contribution. In contrast, we estimate that the bandwidth of KrF-laser-based fusion systems would be large enough.

physics.plasm-ph↗
arXiv2007

Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.

physics.bio-ph↗
arXiv2006

How much laser power can propagate through fusion plasma?

Propagation of intense laser beams is crucial for inertial confinement fusion, which requires precise beam control to achieve the compression and heating necessary to ignite the fusion reaction. The National Ignition Facility (NIF), where fusion will be attempted, is now under construction. Control of intense beam propagation may be ruined by laser beam self-focusing. We have identified the maximum laser beam power that can propagate through fusion plasma without significant self-focusing and have found excellent agreement with recent experimental data, and suggest a way to increase that maximum by appropriate choice of plasma composition with implication for NIF designs. Our theory also leads to the prediction of anti-correlation between beam spray and backscatter and suggests the indirect control of backscatter through manipulation of plasma ionization state or acoustic damping.

physics.plasm-ph↗
arXiv2006

Multiscale dynamics of biological cells with chemotactic interactions: from a discrete stochastic model to a continuous description

The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit of discrete one dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

physics.bio-ph↗
arXiv2004

Diffusion of optical pulses in dispersion-shifted randomly birefringent optical fibers

An effect of polarization-mode dispersion, nonlinearity and random variation of dispersion along an optical fiber on a pulse propagation in a randomly birefringent dispersion-shifted optical fiber with zero average dispersion is studied. An averaged pulse width is shown analytically to diffuse with propagation distance for arbitrary strong pulse amplitude. It is found that optical fiber nonlinearity can not change qualitatively a diffusion of pulse width but can only modify a diffusion law which means that a root mean square pulse width grows at least as a linear function of the propagation distance.

nlin.CD↗
arXiv2004

On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface

Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transform from original physical variables to new variables for which instability is absent.

nlin.PS↗