arXiv subjects

Leonid Ryzhik

Publications and source records attributed to Leonid Ryzhik.

12 recordsLinked to original sources

arXiv2004

Rapid electron trapping studied by pump-probe photoconductivity: kinetic analysis

The use of ultrafast pump-probe conductivity (PPC) for studies of photoelectron dynamics in nonpolar molecular liquids has been based upon the perturbation of geminate recombination dynamics of trapped electrons by their laser photoexcitation into the conduction band. Such a method is unsuitable for the studies of electron trapping dynamics of quasifree electrons per se. We demonstrate that the PPC method can be extended to study such dynamics, provided that the time resolution of the conductivity setup is better than the ratio mu[e_qf]tau[e_qf]/mu[e_trap] of the mobility-lifetime product for the quasifree electron and the mobility of the trapped electron. For some liquids (e.g., supercritical CO2) this time is sufficiently long (> 100 ns) and the standard conductivity equipment can be used. Even if the time resolution cannot be increased (due to the adverse effect on the sensitivity), the trapping dynamics can be studied provided that the trapping competes with cross recombination of quasifree electrons with holes in the solvent bulk. Since the mobility of these quasifree electrons is very large (10-10^3 cm^2/Vs), this recombination is facile even when the density of ionization events is fairly low (< 1 mM). Perturbation of the geminate electron-hole dynamics is not required for this method to work.

physics.chem-ph↗

arXiv2002

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.

physics.flu-dyn↗

arXiv2002

Statistical stability in time reversal

When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency, remote sensing regime, and show that, because of multiple scattering, in an inhomogeneous or random medium it can improve beyond the diffraction limit. We also show that the back-propagated signal from a spatially localized narrow-band source is self-averaging, or statistically stable, and relate this to the self-averaging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is self-averaging only for broad-band signals. The array of transducers operates in a remote-sensing regime so we analyze time reversal with the parabolic or paraxial wave equation.

cond-mat.dis-nn↗

arXiv2002

Self-averaging in time reversal for the parabolic wave equation

We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a priori $L^2$-bounds available in the time-reversal setting, we prove that the Wigner transform in the high frequency limit converges in probability to its deterministic limit, which is the solution of a transport equation.

nlin.CD↗

arXiv2002

Time Reversal for Waves in Random Media

In time reversal acoustics experiments, a signal is emitted from a localized source, recorded at an array of receivers-transducers, time reversed, and finally re-emitted into the medium. A celebrated feature of time reversal experiments is that the refocusing of the re-emitted signals at the location of the initial source is improved when the medium is heterogeneous. Contrary to intuition, multiple scattering enhances the spatial resolution of the refocused signal and allows one to beat the diffraction limit obtained in homogeneous media. This paper presents a quantitative explanation of time reversal and other more general refocusing phenomena for general classical waves in heterogeneous media. The theory is based on the asymptotic analysis of the Wigner transform of wave fields in the high frequency limit. Numerical experiments complement the theory.

nlin.CD↗

arXiv2001

Radiative transport limit for the random Schrödinger equation

We give a detailed mathematical analysis of the radiative transport limit for the average phase space density of solutions of the Schroedinger equation with time dependent random potential. Our derivation is based on the construction of an approximate martingale for the random Wigner distribution.

nlin.CD↗

arXiv2001

Time Reversal for Classical Waves in Random Media

We propose a mathematical theory for the refocusing properties observed in time-reversal experiments, where classical waves propagate through a medium, are recorded in time, then time-reversed and sent back into the medium. The salient feature of such experiments is that the refocusing quality of the time-reversed reemitted signals is greatly enhanced when the underlying medium is heterogeneous. Based on the Wigner transform formalism, we show that random media indeed greatly improve refocusing. We analyze two different types of random media, where in the limit of high frequencies, the Wigner transform satisfies a random Liouville equation or a linear transport equation.

cond-mat.mes-hall↗

arXiv2000

An upper bound for the bulk burning rate for systems

We consider a system of reaction-diffusion equations with passive advection term and Lewis number not equal to one. Such systems are used to describe chemical reactions in a flow in a situation where temperature and material diffusivities are not equal. It is expected that the fluid advection will distort the reaction front, increasing the area of reaction and thus speeding up the reaction process. While a variety of estimates on the influence of the flow on reaction are available for a single reaction-diffusion equation (corresponding to the case of Lewis number equal to one), the case of the system is largely open. We prove a general upper bound on the reaction rate in such systems in terms of the reaction rate for a single reaction-diffusion equation, showing that the long time average of reaction rate with $\Le \ne 1$ does not exceed the $\Le=1$ case. Thus the upper estimates derived for $\Le=1$ apply to the systems. Both front-like and compact initial data (hot blob) are considered.

nlin.CD↗

arXiv2000

Quenching of flames by fluid advection

We consider a simple scalar reaction-advection-diffusion equation with ignition-type nonlinearity and discuss the following question: What kinds of velocity profiles are capable of quenching any given flame, provided the velocity's amplitude is adequately large? Even for shear flows, the answer turns out to be surprisingly subtle. If the velocity profile changes in space so that it is nowhere identically constant, (or if it is identically constant only in a region of small measure) then the flow can quench any initial data. But if the velocity profile is identically constant in a sizable region, then the ensuing flow is incapable of quenching large enough flames, no matter how much larger is the amplitude of this velocity. The constancy region must be wider across than a couple of laminar propagating front-widths. The proof uses a linear PDE associated to the nonlinear problem and quenching follows when the PDE is hypoelliptic. The techniques used allow the derivation of new, nearly optimal bounds on the speed of traveling wave solutions.

nlin.CD↗

arXiv2000

Enhancement of the Traveling Front Speeds in Reaction-Diffusion Equations with Advection

We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main classes of flows. Percolating flows, which are characterized by the presence of long tubes of streamlines mixing hot and cold material, lead to strong speed-up of burning which is linear in the amplitude of the flow, $U$. On the other hand the cellular flows, which have closed streamlines, are shown to produce weaker increase in reaction. For such flows we get a lower bound which grows as $U^{1/5}$ for a large amplitude of the flow.

math.AP↗

arXiv1999

Bulk Burning Rate in Passive - Reactive Diffusion

We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a quantity, the bulk burning rate, that makes both mathematical and physical sense in general situations and extends the often ill-defined notion of front speed. We establish rigorous lower bounds for the bulk burning rate that are linear in the amplitude of the advecting velocity for a large class of flows. These "percolating" flows are characterized by the presence of tubes of streamlines connecting distant regions of burned and unburned material and generalize shear flows. The bound contains geometric information on the velocity streamlines and degenerates when these oscillate on scales that are finer than the width of the laminar burning region. We give also examples of very different kind of flows, cellular flows with closed streamlines, and rigorously prove that these can produce only sub-linear enhancement of the bulk burning rate.

math.AP↗

arXiv1999

Radiative Transport in a Periodic Structure

We derive radiative transport equations for solutions of a Schrödinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, while the scattering part by the random fluctuations.

cond-mat.stat-mech↗