arXiv subjects

David Jasnow

Publications and source records attributed to David Jasnow.

At least 19 recordsLinked to original sources

arXiv2022

The propagation of infection fronts in spatially distributed compartment models in epidemiology

Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of reaction-diffusion systems, which allow familiar techniques to be applied. The focus is largely on the appearance of soliton-like moving fronts that spread infection to previously uninfected regions. Near threshold dynamical critical behavior and a degree of universality are revealed. Extending two of the models to include a simple nonlinearity in the strength of the binary interaction between a susceptible individual and an infected one, we find the possibility of static coexistence between spatial regions with different levels of infection and an analogy with first-order transitions in thermodynamics.

physics.bio-ph↗

arXiv2019

Dynamics of relaxation and dressing of a quenched Bose polaron

We study the non-equilibrium dynamics of relaxation and dressing of a mobile impurity suddenly immersed--or quenched-- into a zero temperature homogeneous Bose Einstein condensate (BEC) with velocity $v$. A many body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depend crucially on the Mach number $β=v/c$, with $c$ the speed of sound of superfluid phonons and features many different time scales. Quantum Zeno behavior at early time is followed by relaxational and dressing dynamics determined by Cerenkov emission of long-wavelength phonons for $β>1$ with a decay rate $Γ_p \propto (β-1)^3$. The polaron dressing dynamics \emph{slows-down} as $β\rightarrow 1$ and is characterized by power laws $t^{-α}$ with different exponents for $β\lessgtr 1$. The asymptotic entanglement entropy features a sharp discontinuity and the residue features a cusp at $β=1$. These non-equilibrium features suggest \emph{universal} dynamical critical phenomena near $β\simeq 1$, and are a direct consequence of the linear dispersion relation of long wavelength superfluid phonons. We conjecture on the emergence of an asymptotic dynamical attractor with $β\leq 1$.

cond-mat.quant-gas↗

arXiv2017

Heisenberg-Langevin vs. quantum master equation

The quantum master equation is an important tool in the study of quantum open systems. It is often derived under a set of approximations, chief among them the Born (factorization) and Markov (neglect of memory effects) approximations. In this article we study the paradigmatic model of quantum Brownian motion of an harmonic oscillator coupled to a bath of oscillators with a Drude-Ohmic spectral density. We obtain analytically the \emph{exact} solution of the Heisenberg-Langevin equations, with which we study correlation functions in the asymptotic stationary state. We compare the \emph{exact} correlation functions to those obtained in the asymptotic long time limit with the quantum master equation in the Born approximation \emph{with and without} the Markov approximation. In the latter case we implement a systematic derivative expansion that yields the \emph{exact} asymptotic limit under the factorization approximation \emph{only}. We find discrepancies that could be significant when the bandwidth of the bath $Λ$ is much larger than the typical scales of the system. We study the \emph{exact} interaction energy as a \emph{proxy} for the correlations missed by the Born approximation and find that its dependence on $Λ$ is similar to the \emph{discrepancy} between the exact solution and that of the quantum master equation in the Born approximation. We quantify the regime of validity of the quantum master equation in the Born approximation with or without the Markov approximation in terms of the system's relaxation rate $γ$, its \emph{unrenormalized} natural frequency $Ω$ and $Λ$: $γ/Ω\ll 1$ and \emph{also} $γΛ/Ω^2 \ll 1$. The reliability of the Born approximation is discussed within the context of recent experimental settings and more general environments.

quant-ph↗

arXiv2017

Coherence and entanglement of mechanical oscillators mediated by coupling to different baths

We study the non-equilibrium dynamics of two coupled mechanical oscillators with general linear couplings to two uncorrelated thermal baths at temperatures $T_1$ and $T_2$, respectively. We obtain the complete solution of the Heisenberg-Langevin equations, which reveal a coherent mixing among the normal modes of the oscillators as a consequence of their off-diagonal couplings to the baths. Unique renormalization aspects resulting from this mixing are discussed. Diagonal and off-diagonal (coherence) correlation functions are obtained analytically in the case of strictly Ohmic baths with different couplings in the strong and weak coupling regimes. An asymptotic non-equilibrium stationary state emerges for which we obtain the complete expressions for the correlations and coherence. Remarkably the coherence survives in the high temperature, classical limit for $T_1 \neq T_2$. In the case of vanishing detuning between the oscillator normal modes both coupling to one and the same bath the coherence retains memory of the initial conditions at long time. A perturbative expansion of the early time evolution reveals that the emergence of coherence is a consequence of the entanglement between the normal modes of the oscillators \emph{mediated} by their couplings to the baths. This \emph{suggests} the survival of entanglement in the high temperature limit for different temperatures of the baths which is essentially a consequence of the non-equilibrium nature of the asymptotic stationary state. An out of equilibrium setup with small detuning and large $|T_1- T_2|$ produces non-vanishing steady-state coherence and entanglement in the high temperature limit of the baths.

quant-ph↗

arXiv2015

Protein viscoelastic dynamics: a model system

A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the model is a strongly over-damped oscillator described by a harmonic restoring force for small displacements that reversibly yields to stress under sufficiently large displacement. This simple dynamical system also reveals unexpectedly rich behavior, exhibiting a series of dynamical transitions and analogies with equilibrium thermodynamic phase transitions. The effects of noise and of inertia are briefly considered and described.

cond-mat.soft↗

arXiv2011

Morphological Control of Grafted Polymer Films by Nanoparticle Binding

Mixtures of nanoparticles and polymer-like objects are encountered in many nanotechnological applications and biological systems. We study the behavior of grafted polymer layers decorated by nanoparticles that are attracted to the polymers using lattice gas based mean field theory and accompanying coarse-grained Brownian dynamics simulations. We find that the presence of nanoparticles can induce large morphological transitions in the layer morphology. In particular, at moderate nanoparticle concentrations, the nanoparticles cause a reduction in the height of the polymer layer above the grafting surface, which occurs via a novel first-order phase transition for sufficiently strong attraction between the polymers and the nanoparticles and smoothly for weak attractions. The predictions of the theory qualitatively agree with the observed behavior of grafted natively unfolded protein strands upon binding of proteins. The results also inform ways of designing nanopolymer layer morphologies.

cond-mat.soft↗

arXiv2011

Event-driven simulations of a plastic, spiking neural network

We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing randomly with the same mean frequency. For low values of the plasticity parameter, the activities of the system are dominated by noise, while large values of the plasticity parameter lead to self-sustaining activity in the network. We perform event-driven simulations on finite-size networks with up to 128 neurons to find the stationary synaptic weight conformations for different values of the plasticity parameter. In both the low and high activity regimes, the synaptic weights are narrowly distributed around the plasticity parameter value consistent with the predictions of mean-field theory. However, the distribution broadens in the transition region between the two regimes, representing emergent network structures. Using a pseudophysical approach for visualization, we show that the emergent structures are of "path" or "hub" type, observed at different values of the plasticity parameter in the transition region.

q-bio.NC↗

arXiv2009

The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures

The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the technique is statistically exact for a wide class of Markovian and non-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple "resampling" in path space. Similar reasoning indicates that arbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid. Numerical examples confirm the claims, including the use of bins which can adaptively find the target state in a simple model.

physics.comp-ph↗

arXiv2009

Mean-field theory of a plastic network of integrate-and-fire neurons

We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity. Assuming Poisson firing statistics for the neurons, the plasticity dynamics of a synapse under the influence of the mean-field environment can be mapped to the dynamics of an asymmetric random walk in synaptic-weight space. Using a master-equation for small steps, we predict a narrow distribution of synaptic weights that scales with the square root of the plasticity rate for the stationary state of the system given plausible physiological parameter values describing neural transmission and plasticity. The dependence of the distribution on the synaptic weight of the mean-field environment allows us to determine the mean synaptic weight self-consistently. The effect of fluctuations in the total synaptic conductance and plasticity step sizes are also considered. Such fluctuations result in a smoothing of the first-order transition for low number of afferent synapses per neuron and a broadening of the synaptic weight distribution, respectively.

q-bio.NC↗

arXiv2009

Weighted Ensemble Path Sampling for Multiple Reaction Channels

Finding and sampling multiple reaction channels for molecular transitions remains an important challenge in physical chemistry. Here we show that the weighted ensemble (WE) path sampling method can readily sample multiple channels. In a first test, both the WE and transition path sampling methods are applied to two-dimensional model potentials. The comparison explains why the weighted ensemble approach will not be trapped in one channel. The WE approach is then used to sample the full transition path ensemble in implicitly solvated alanine dipeptide at two different temperatures. The ensembles are of sufficient quality to permit quantification of the fractional importance of each channel, even at T=300K when brute-force simulation is prohibitively expensive.

physics.bio-ph↗

arXiv2006

Transition-Event Durations in One Dimensional Activated Processes

Despite their importance in activated processes, transition-event durations -- which are much shorter than first passage times -- have not received a complete theoretical treatment. We therefore study the distribution of durations of transition events over a barrier in a one-dimensional system undergoing over-damped Langevin dynamics.

cond-mat.stat-mech↗

arXiv2003

Cohesive energy, stability and structural transitions in polyelectrolyte bundles

A lattice of uniformly charged, infinitesimally thin, rods decorated with an ordered array of counterions exhibits anomalous behavior as the spacing between the rods is varied. In particular, the counterion lattice undergoes a sequence of structural shearing, or "tilting," phase transformations as the spacing between the rods decreases. The potential implications of this behavior with respect to the packaging of biologically relevant polyelectrolytic molecules are commented upon.

cond-mat.soft↗

arXiv2003

Periodic Droplet Formation in Chemically Patterned Microchannels

Simulations show that when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give rise to the simultaneous, periodic formation of monodisperse droplets of A-in-B and B-in-A. The system bifurcates between time-independent behavior and different types of regular, non-decaying oscillations in the structural characteristics. The surprisingly complex behavior is observed even in the absence of hydrodynamic interactions and arises from the interplay between the fluid flow and patterned substrate, which introduces non-linearity into the dynamical system.

cond-mat.soft↗

arXiv2000

Shear instabilities of freely standing thermotropic smectic-A films

In this Letter we discuss theoretically the instabilities of thermotropic freely standing smectic-A films under shear flow\cite{re:wu}. We show that, in Couette geometry, the centrifugal force pushes the liquid crystal toward the outer boundary and induces smectic layer dilation close to the outer boundary. Under strong shear, this effect induces a layer buckling instability. The critical shear rate is proportional to $1/\sqrt{d}$, where $d$ is the thickness of the film.

cond-mat.soft↗

arXiv2000

Interface and contact line motion in a two phase fluid under shear flow

A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The fluid is set in motion by displacing two parallel, infinite solid boundaries along their own plane. Dissipative relaxation of the order parameter leads to interfacial slip at the contact line, even when no-slip boundary conditions for the fluid velocity are considered. This relaxation occurs within a characteristic length scale l that depends on the order parameter mobility, the equilibrium interfacial tension, the imposed wall velocity, the thermal correlation length, the equilibrium miscibility gap, and the mutual diffusion coefficient. Steady-state interface equations which describe the system on a length scale large compared to the correlation length are derived. Scaling forms which involve the ratio l/L, where L is the width of the fluid layer, and the capillary number follow from the interface equations. The scaling results are verified by direct numerical solution of the governing equations.

cond-mat.stat-mech↗

arXiv1999

Simulation of Hard Particles in a Phase-Separating Binary Mixture

We simulate the motion of spherical particles in a phase-separating binary mixture. By combining cell dynamical equations with Langevin dynamics for particles, we show that the addition of hard particles significantly changes both the speed and the morphology of the phase separation. At the late stage of the spinodal decomposition process, particles significantly slow down the domain growth, in qualitative agreement with earlier experimental data.

cond-mat.stat-mech↗

arXiv1999

Layer dynamics of a freely standing smectic-A film

We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for the system can be obtained from the response functions for the free surfaces. Permeation is included and its importance near the free surfaces is discussed. The hydrodynamic mode structure for the dynamics of the system is compared with that of bulk systems. We show that to describe the dynamic correlation functions for the system, in general, it is necessary to consider the smectic layer displacement $u$ and the velocity normal to the layers, $v_z$, together. Finally, our analysis also provides a basis for the theoretical study of the off-equilibrium dynamics of freely-standing smectic-A films.

cond-mat.soft↗

arXiv1998

The effective potential, critical point scaling and the renormalization group

The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order parameter in an equilibrium Ising system, when combined with low-order renormalization group results for an ordinary $ϕ^4$ system, can be used to extract the effective potential. All scaling features are included in the process.

cond-mat.stat-mech↗