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Pierre Illien, Charlotte De Blois, Yang Liu, Marjolein N Van Der Linden, Olivier Dauchot
Published: 1 April 2020
Physical Review E, Volume 101

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Published: 1 April 2020
Physical Review E, Volume 101

The publisher has not yet granted permission to display this abstract.
Tetsuya J Kobayashi
Published: 1 April 2020
Physical Review E, Volume 101

The publisher has not yet granted permission to display this abstract.
H. S. Sousa, M. S. S. Pereira, I. N. De Oliveira, J. Strečka, M. L. Lyra
Physical Review E, Volume 97

Kishan A Manani, Kim Christensen, Nicholas S Peters
Published: 4 October 2016
Physical Review E, Volume 94

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Emmanuel Lance Christopher Vi Medillo Plan, , Dario Vincenzi
Published: 3 August 2016
Physical Review E, Volume 94

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Elijah Roberts, Shay Be'Er, Chris Bohrer, Rati Sharma,
Published: 31 December 2015
Physical Review E, Volume 92, pp 062717-062717; https://doi.org/10.1103/physreve.92.062717

Abstract:
Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the biomolecular interaction networks. Most previous work has been focused on the intrinsic noise (IN) of these networks. Yet, especially for high-copy-number biomolecules, extrinsic or environmental noise (EN) has been experimentally shown to dominate the variation. Here, we develop an analytical formalism that allows for calculation of the effect of EN on gene-expression motifs. We introduce a method for modeling bounded EN as an auxiliary species in the master equation. The method is fully generic and is not limited to systems with small EN magnitudes. We focus our study on motifs that can be viewed as the building blocks of genetic switches: a nonregulated gene, a self-inhibiting gene, and a self-promoting gene. The role of the EN properties (magnitude, correlation time, and distribution) on the statistics of interest are systematically investigated, and the effect of fluctuations in different reaction rates is compared. Due to its analytical nature, our formalism can be used to quantify the effect of EN on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single-cell gene-expression experiments.
Published: 31 December 2015
Physical Review E, Volume 92, pp 063034-063034; https://doi.org/10.1103/physreve.92.063034

Abstract:
In microfluidics, two important factors responsible for the differences between the characteristics of the flow and heat transfer in microchannels and conventional channels are rarefaction and surface roughness which are studied in the present work. An incompressible gas flow in a microchannel is simulated two dimensionally using the lattice Boltzmann method. The flow is in the slip regime and surface roughness is modeled by both regular and Gaussian random distribution of rectangular modules. The effects of relative surface roughness height and Knudsen number on gaseous flow and heat transfer are studied. It was shown that as the relative roughness height increases, the Poiseuille number increases and the Nusselt number has a decreasing or increasing trend, depending on the degree of rarefaction. A comparison between the flow and heat transfer characteristics in regular and random distribution of surface roughness demonstrates that in regular roughness, circular flows are more pronounced; Poiseuille number is higher and Nusselt number is lower than that of its equivalent random roughness.
Peng Zhang, Sunghwan Jung, Aram Lee,
Published: 31 December 2015
Physical Review E, Volume 92, pp 063033-063033; https://doi.org/10.1103/physreve.92.063033

Abstract:
High quality (Q) factor whispering gallery modes (WGMs) can induce nonlinear effects in liquid droplets through mechanisms such as radiation pressure, Kerr nonlinearity, and thermal effects. However, such nonlinear effects, especially those due to radiation pressure, have yet to be thoroughly investigated and compared in the literature. In this study, we present an analytical approach that can exactly calculate the droplet deformation induced by the radiation pressure. The accuracy of the analytical approach is confirmed through numerical analyses based on the boundary element method. We show that the nonlinear optofluidic effect induced by the radiation pressure is stronger than the Kerr effect and the thermal effect under a large variety of realistic conditions. Using liquids with ultralow and experimentally attainable interfacial tension, we further confirm the prediction that it may only take a few photons to produce measurable WGM resonance shift through radiation-pressure-induced droplet deformation.
Mehran Ebrahimian, Mohammad Yekehzare,
Published: 31 December 2015
Physical Review E, Volume 92, pp 063035-063035; https://doi.org/10.1103/physreve.92.063035

Abstract:
To generalize simple bead-linker model of swimmers to higher dimensions and to demonstrate the chemotaxis ability of such swimmers, here we introduce a low-Reynolds predator, using a two-dimensional triangular bead-spring model. Two-state linkers as mechanochemical enzymes expand as a result of interaction with particular activator substances in the environment, causing the whole body to translate and rotate. The concentration of the chemical stimulator controls expansion versus the contraction rate of each arm and so affects the ability of the body for diffusive movements; also the variation of activator substance's concentration in the environment breaks the symmetry of linkers' preferred state, resulting in the drift of the random walker along the gradient of the density of activators. External food or danger sources may attract or repel the body by producing or consuming the chemical activators of the organism's enzymes, inducing chemotaxis behavior. Generalization of the model to three dimensions is straightforward.
Hui-Shun Kuan, Robert Blackwell, , Matthew A. Glaser,
Published: 31 December 2015
Physical Review E, Volume 92, pp 060501-060501; https://doi.org/10.1103/physreve.92.060501

Abstract:
Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.
, A. Link, , S. C. Wilks, T. Bartal, S. Chawla, C. D. Chen, , L. C. Jarrott, M. H. Key, et al.
Published: 31 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.063112

Abstract:
The consequences of small scale-length precursor plasmas on high-intensity laser-driven relativistic electrons are studied via experiments and simulations. Longer scale-length plasmas are shown to dramatically increase the efficiency of electron acceleration, yet, if too long, they reduce the coupling of these electrons into the solid target. Evidence for the existence of an optimal plasma scale-length is presented and estimated to be from 1 to 5μm. Experiments on the Trident laser (I=5×1019W/cm2) diagnosed via Kα emission from Cu wires attached to Au cones are quantitively reproduced using 2D particle-in-cell simulations that capture the full temporal and spatial scale of the nonlinear laser interaction and electron transport. The simulations indicate that 32%±8%(6.5%±2%) of the laser energy is coupled into electrons of all energies (1–3 MeV) reaching the inner cone tip and that, with an optimized scale-length, this could increase to 35% (9%).
Published: 31 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062150

Abstract:
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with p-body quenched disordered interaction, with p>2, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.
Published: 31 December 2015
Physical Review E, Volume 92, pp 062830-062830; https://doi.org/10.1103/physreve.92.062830

Abstract:
The two-dimensional optimal velocity model has potential applications to pedestrian dynamics and the collective motion of animals. In this paper, we extend the linear stability analysis presented in a previous paper [A Nakayama et al., Phys. Rev. E. 77, 016105 (2008)] and investigate the effects of particle configuration on the stability of several wave modes of collective oscillations of moving particles. We find that, when a particle moves without interacting with particles that are positioned in a diagonally forward or backward direction, the stable region of the particle flow is completely removed by the elliptically polarized mode.
Published: 31 December 2015
Physical Review E, Volume 92, pp 062930-062930; https://doi.org/10.1103/physreve.92.062930

Abstract:
A predator-prey model of dual populations with stochastic oscillators is presented. A linear cross-coupling between the two populations is introduced following the coupling between the motions of a Wilberforce pendulum in two dimensions: one in the longitudinal and the other in torsional plain. Within each population a Kuramoto-type competition between the phases is assumed. Thus, the synchronization state of the whole system is controlled by these two types of competitions. The results of the numerical simulations show that by adding the linear cross-coupling interactions predator-prey oscillations between the two populations appear, which results in self-regulation of the system by a transfer of synchrony between the two populations. The model represents several important features of the dynamical interplay between the drift wave and zonal flow turbulence in magnetically confined plasmas, and a novel interpretation of the coupled dynamics of drift wave-zonal flow turbulence using synchronization of stochastic oscillator is discussed.
Merzu Kebede Belete,
Published: 31 December 2015
Physical Review E, Volume 92, pp 062716-062716; https://doi.org/10.1103/physreve.92.062716

Abstract:
Stochastic switching between alternative phenotypic states is a common cellular survival strategy during unforeseen environmental fluctuations. Cells can switch between different subpopulations that proliferate at different rates in different environments. Optimal population growth is typically assumed to occur when phenotypic switching rates match environmental switching rates. However, it is not well understood how this optimum behaves as a function of the growth rates of phenotypically different cells. In this study, we use mathematical and computational models to test how the actual parameters associated with optimal population growth differ from those assumed to be optimal. We find that the predicted optimum is practically always valid if the environmental durations are long. However, the regime of validity narrows as environmental durations shorten, especially if subpopulation growth rate differences differ from each other (are asymmetric) in two environments. Furthermore, we study the fate of mutants with switching rates previously predicted to be optimal. We find that mutants which match their phenotypic switching rates with the environmental ones can only sweep the population if the assumed optimum is valid, but not otherwise.
, David R. Smith, Yaroslav A. Urzhumov
Published: 30 December 2015
Physical Review E, Volume 92, pp 063030-063030; https://doi.org/10.1103/physreve.92.063030

Abstract:
We explore the possibility of controlling the wake and drag of a spherical object independently of each other, using radial distributions of permeability in the Brinkman-Stokes formalism. By discretizing a graded-permeability shell into discrete, macroscopically homogeneous layers, we are able to sample the entire functional space of spherically-symmetric permeabilities and observe quick convergence to a certain manifold in the wake-drag coordinates. Monte Carlo samplings with 104–105 points have become possible thanks to our new algorithm, which is based on exact analytical solutions for the Stokes flow through an arbitrary multilayer porous sphere. The algorithm is not restricted to the Brinkman-Stokes equation and can be modified to account for other types of scattering problems for spherically-symmetric systems with arbitrary radial complexity. Our main practical finding for Stokes flow is that it is possible to reduce a certain measure of wake of a spherical object without any energy penalty and without active (power-consuming) force generation.
Sungchul Kwon,
Published: 30 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062149

Abstract:
For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the critical behavior for regular initial conditions in which activities are distributed at regular intervals on average. The FE Manna model conserves the density ρ of total particles and undergoes an absorbing phase transition at a critical ρc. For the regular initial conditions, we show via extensive simulations that the dynamical scaling behaviors differ from those of the random and the natural initial conditions. Off-critical scaling exponents β and ν⊥ are also measured and shown to agree well with the values of the directed percolation (DP) class as reported by Basu et al. [Phys. Rev. Lett. 109, 015702 (2012)]. Our results suggest that the dynamical scaling behaviors depend on the characteristics of initial conditions, but the off-critical scaling behaviors in the steady state are independent of initial conditions and belong to the DP class.
Published: 30 December 2015
Physical Review E, Volume 92, pp 062928-062928; https://doi.org/10.1103/physreve.92.062928

Abstract:
An approach to predicting critical transitions from time series is introduced. A nonstationary low-order stochastic dynamical model of appropriate complexity to capture the transition mechanism under consideration is estimated from data. In the simplest case, the model is a one-dimensional effective Langevin equation, but also higher-dimensional dynamical reconstructions based on time-delay embedding and local modeling are considered. Integrations with the nonstationary models are performed beyond the learning data window to predict the nature and timing of critical transitions. The technique is generic, not requiring detailed a priori knowledge about the underlying dynamics of the system. The method is demonstrated to successfully predict a fold and a Hopf bifurcation well beyond the learning data window.
Ao Wang, , Bingqiang Ji,
Published: 30 December 2015
Physical Review E, Volume 92, pp 063031-063031; https://doi.org/10.1103/physreve.92.063031

Abstract:
As a key mechanism of submicron particle capture in wet deposition and wet scrubbing processes, thermophoresis is influenced by the flow and temperature fields. Three-dimensional direct numerical simulations were conducted to quantify the characteristics of the flow and temperature fields around a droplet at three droplet Reynolds numbers (Re) that correspond to three typical boundary-layer-separation flows (steady axisymmetric, steady plane-symmetric, and unsteady plane-symmetric flows). The thermophoretic motion of submicron particles was simulated in these cases. Numerical results show that the motion of submicron particles around the droplet and the deposition distribution exhibit different characteristics under three typical flow forms. The motion patterns of particles are dependent on their initial positions in the upstream and flow forms. The patterns of particle motion and deposition are diversified as Re increases. The particle motion pattern, initial position of captured particles, and capture efficiency change periodically, especially during periodic vortex shedding. The key effects of flow forms on particle motion are the shape and stability of the wake behind the droplet. The drag force of fluid and the thermophoretic force in the wake contribute jointly to the deposition of submicron particles after the boundary-layer separation around a droplet.
Gabriel Ramos, , Jean-Christophe Géminard,
Published: 30 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062210

Abstract:
Gas invasion in liquid-saturated sands exhibits different morphologies and dynamics. For mobile beds, the repeated rise of gas through the layer leads to the growth of a fluidized zone, which reaches a stationary shape. Here, we present experimental results characterizing the evolution of the fluidized region as a function of the gas-flow rate and grain size. We introduce a new observable, the flow density, which quantifies the motion of the grains in the system. The growth of the fluidized zone is characterized by a spatiotemporal analysis, which provides the stabilization time, τs. In the stationary regime, we report two main contributions to motion in the fluidized region: the central gas rise and a convective granular motion. Interestingly, a static model with a fixed porous network accounts for the final shape of the invasion zone. We propose an explanation where the initial gas invasion weakens the system and fixes since the early stage the morphology of the fluidized zone.
Published: 30 December 2015
Physical Review E, Volume 92, pp 060103-060103; https://doi.org/10.1103/physreve.92.060103

Abstract:
Temperature gradients polarize water, a nonequilibrium effect that may result in significant electrostatic fields for strong thermal gradients. Using nonequilibrium molecular dynamics simulations, we show that the thermal polarization features a significant dependence with temperature that ultimately leads to an inversion phenomenon, whereby the polarization field reverses its sign at a specific temperature. Temperature inversion effects have been reported before in the Soret coefficient of aqueous solutions, where the solution changes from thermophobic to thermophilic at specific temperatures. We show that a similar inversion behavior is observed in pure water. Microscopically, the inversion is the result of a balance of dipolar and quadrupolar contributions and the strong temperature dependence of the quadrupolar contribution, which is determined by the thermal expansion of the liquid.
Published: 30 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.063032

Abstract:
We study nonisothermal diffusion transport of a weakly soluble substance in a liquid-saturated porous medium in contact with a reservoir of this substance. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In this system, zones of saturated solution and nondissolved phase coexist with ones of undersaturated solution. The effect is first considered for the case of annual oscillation of the surface temperature of water-saturated ground in contact with the atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to temperature oscillation. An analytical theory of the phenomenon is developed. Further, the treatment is extended to the case of higher frequency oscillations and the case of weakly soluble solids and liquids.
, Sanjib Sabhapandit,
Published: 30 December 2015
Physical Review E, Volume 92, pp 062148-062148; https://doi.org/10.1103/physreve.92.062148

Abstract:
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting, we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed.
Xiao F. Jiang,
Published: 30 December 2015
Physical Review E, Volume 92, pp 061003-061003; https://doi.org/10.1103/physreve.92.061003

Abstract:
The pinch off of heterogeneous ferrofluid drops at a nozzle in air was experimentally investigated with a magnetic field (downward or upward) and without a magnetic field. Compared to homogeneous drops, the self-similarity and universal scaling law were verified through modifying the initial conditions, such as the nozzle diameter, flow rate, and magnitude and direction of the magnetic fields. Two pinch-off points were observed, and the two consecutive pinch-off dynamics were characterized through scaling laws. Here our scaling exponent remains within the scope of (0.70–0.80) for the primary whereas it remains within the scope of (0.60–0.70) for the secondary pinch off, respectively, comparable to the classic range from 2/3 to 1 for homogeneous drops. The gravity-compensating and gravity-superimposing magnetic fields display a negligible effect on the exponent but determine the sequence of double pinch offs. The universal character of the self-similar pinch off is extended to a heterogeneous fluid.
Published: 30 December 2015
Physical Review E, Volume 92, pp 062929-062929; https://doi.org/10.1103/physreve.92.062929

Abstract:
We perform a numerical investigation of the Lyapunov spectra of chaotic dynamics in lattices of classical spins in the vicinity of second-order ferromagnetic and antiferromagnetic phase transitions. On the basis of this investigation, we identify a characteristic of the shape of the Lyapunov spectra, the “G-index,” which exhibits a sharp peak as a function of temperature at the phase transition, provided the order parameter is capable of sufficiently strong dynamic fluctuations. As part of this work, we also propose a general numerical algorithm for determining the temperature in many-particle systems, where kinetic energy is not defined.
Published: 29 December 2015
Physical Review E, Volume 92, pp 062408-062408; https://doi.org/10.1103/physreve.92.062408

Abstract:
Hydrofracturing to recover natural gas and oil relies on the creation of a fracture network with pressurized water. We analyze the creation of the network in two ways. First, we assemble a collection of analytical estimates for pressure-driven crack motion in simple geometries, including crack speed as a function of length, energy dissipated by fluid viscosity and used to break rock, and the conditions under which a second crack will initiate while a first is running. We develop a pseudo-three-dimensional numerical model that couples fluid motion with solid mechanics and can generate branching crack structures not specified in advance. One of our main conclusions is that the typical spacing between fractures must be on the order of a meter, and this conclusion arises in two separate ways. First, it arises from analysis of gas production rates, given the diffusion constants for gas in the rock. Second, it arises from the number of fractures that should be generated given the scale of the affected region and the amounts of water pumped into the rock.
J. Piili,
Published: 29 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062715

Abstract:
We examine the ejection of an initially strongly confined flexible polymer from a spherical capsid through a nanoscale pore. We use molecular dynamics for unprecedentedly high initial monomer densities. We show that the time for an individual monomer to eject grows exponentially with the number of ejected monomers. By measurements of the force at the pore we show this dependence to be a consequence of the excess free energy of the polymer due to confinement growing exponentially with the number of monomers initially inside the capsid. This growth relates closely to the divergence of mixing energy in the Flory-Huggins theory at large concentration. We show that the pressure inside the capsid driving the ejection dominates the process that is characterized by the ejection time growing linearly with the lengths of different polymers. Waiting time profiles would indicate that the superlinear dependence obtained for polymers amenable to computer simulations results from a finite-size effect due to the final retraction of polymers' tails from capsids.
João R. Medeiros,
Published: 29 December 2015
Physical Review E, Volume 92, pp 062145-062145; https://doi.org/10.1103/physreve.92.062145

Abstract:
We study the thermostatistics of a damped bimodal particle, i.e., a particle of mass m subject to a work reservoir that is analytically represented by the telegraph noise. Because of the colored nature of the noise, it does not fit the Lévy-Itô class of stochastic processes, making this system an instance of a nonequilibrium system in contact with a non-Gaussian external reservoir. We obtain the statistical description of the position and velocity, namely in the stationary state, as well as the (time-dependent) statistics of the energy fluxes in the system considering no constraints on the telegraph noise features. With that result we are able to give an account of the statistical properties of the large deviations of the injected and dissipated power that can change from sub-Gaussianity to super-Gaussianity depending on the color of the noise. By properly defining an effective temperature for this system, T, we are capable of obtaining an equivalent entropy production-exchange rate equal to the ratio between the dissipation of the medium, γ, and the mass of the particle, m, a relation that concurs with the case of a standard thermal reservoir at temperature, T=T.
, Zengwei Ma, Yu-Qiang Ma
Published: 29 December 2015
Physical Review E, Volume 92, pp 060303-060303; https://doi.org/10.1103/physreve.92.060303

Abstract:
We report charge inversion using Monte Carlo calculations for a negatively charged surface in aqueous solutions involving coions of different charges and monovalent counterions. It is shown that a rise in the valence of coions at moderate concentrations can substantially promote charge inversion for the surface charge values of biological relevance, regardless of the representation of surface charges but dependent in a nontrivial way on polarization effects resulting from dielectric discontinuity. These obtained characteristics challenge the traditional belief that the coions are generally considered to suppress charge inversion and expose the important role of coions of higher valence in tailoring the effective interactions of biomolecules with the cell membrane.
Published: 29 December 2015
Physical Review E, Volume 92, pp 062146-062146; https://doi.org/10.1103/physreve.92.062146

Abstract:
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
Evgeny M. Gromov, Boris A. Malomed
Published: 29 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062926

Abstract:
The dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency surface waves in the ocean, coupled to damped low-frequency internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, which is a spatial-domain counterpart of the SRS term, a well-known ingredient of the temporal-domain NLSE in optics. Analysis of the field-momentum balance and direct simulations demonstrates that wave-number downshift by the pseudo-SRS may be compensated by the upshift induced by the wind traction, thus maintaining robust bright solitons in both stationary and oscillatory forms; in particular, they are not destroyed by the underlying convective instability. Analytical soliton solutions are found in an approximate form and are verified by numerical simulations. Solutions for soliton pairs are obtained in the numerical form.
Published: 29 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062147

Abstract:
We numerically demonstrate the dynamic stabilization of a strongly interacting many-body bosonic system which can be realized by coupled ultracold atom-molecule gases. The system is initialized to an unstable equilibrium state corresponding to a saddle point in the classical phase space, where subsequent free evolution gives rise to atom-molecule conversion. To control and stabilize the system, periodic modulation is applied that suddenly shifts the relative phase between the atomic and the molecular modes and limits their further interconversion. The stability diagram for the range of modulation amplitudes and periods that stabilize the dynamics is given. The validity of the phase diagram obtained from the time-average calculation is discussed by using the orbit tracking method, and the difference in contrast with the maximum absolute deviation analysis is shown as well. A brief quantum analysis shows that quantum fluctuations can put serious limitations on the applicability of the mean-field results.
Tirth Shah, Rohitashwa Chattopadhyay, ,
Published: 29 December 2015
Physical Review E, Volume 92, pp 062927-062927; https://doi.org/10.1103/physreve.92.062927

Abstract:
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit-cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz., Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system—a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass an even wider range of nonconservative systems.
Published: 29 December 2015
Physical Review E, Volume 92, pp 063029-063029; https://doi.org/10.1103/physreve.92.063029

Abstract:
Hydrodynamic interactions between a pair of capsules in simple shear are numerically investigated using a front-tracking finite difference method. The membrane of the capsule is modeled using different hyperelastic constitutive relations. We also compare the pair interactions between drops to those between capsules. An increased viscosity ratio leads to a reduced net cross-stream separation between capsules as well as drops after collision. At low viscosity ratios, for the same capillary number drop-pairs show higher cross-stream separation than those for capsule-pairs, while substantially large viscosity ratios result in almost the same value for both cases. We investigate pair-collisions between two heterogeneous capsules C1 and C2 with two different capillary numbers. The maximum deformation of C1 was seen to increase with increasing stiffness (decreasing capillary number) of C2, even though the stiffness of C1 was kept fixed. The findings are similar for a drop-pair, however, with a smaller maximum deformation for the same combinations of capillary numbers. The final cross-stream drift of the trajectory of C1 decreases with the increasing stiffness of C2, but the relative trajectory between the capsules remains unchanged. The maximum deformation and the cross-stream drift of the trajectory of C1 are shown to approximately vary with power-law functions of the ratio of the capillary numbers of C1 and C2. An analytical explanation of the dependence on the two capillary numbers is offered. Different membrane constitutive laws result in similar deformation and drift in trajectory.
D. A. Padgett, A. P. Mazzoleni,
Published: 28 December 2015
Physical Review E, Volume 92, pp 062209-062209; https://doi.org/10.1103/physreve.92.062209

Abstract:
We show the effects of simulated supersonic granular flow made up of smooth particles passing over two prototypical bodies: a wedge and a disk. We describe a way of computationally identifying shock wave locations in granular flows and tabulate the shock wave locations for flow over wedges and disks. We quantify the shock structure in terms of oblique shock angle for wedge impediments and shock standoff distance for disk impediments. We vary granular flow parameters including upstream volume fraction, average upstream velocity, granular temperature, and the collision coefficient of restitution. Both wedges and disks have been used in the aerospace community as prototypical impediments to flowing air in order to investigate the fundamentally different shock structures emanating from sharp and blunt bodies, and we present these results in order to increase the understanding of the fundamental behavior of supersonic granular flow.
Published: 28 December 2015
Physical Review E, Volume 92, pp 062143-062143; https://doi.org/10.1103/physreve.92.062143

Abstract:
This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix ρ of the spin pair from the ground state |Ψ⟩ of a spin chain, and then identify the quantum correlation part ρq embedded in ρ. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ρq as W|Φ⟩⟨Φ| with the weight W ≤1, and quantify the fluctuation properties using the two-spin entangled state |Φ⟩. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.
Jens C. Pfeifer, Tobias Bischoff, Georg Ehlers, Bruno Eckhardt
Published: 28 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062208

Abstract:
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped two-dimensional system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single-particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.
, Peter Schlagheck
Published: 28 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062923

Abstract:
When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
Debjani Chatterjee,
Published: 28 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.063110

Abstract:
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term ∝P∫|ϕ(ξ′,τ)|2dξ′ϕ/(ξ−ξ′) [where P denotes the Cauchy principal value, ϕ is the small-amplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion 1/3
Published: 28 December 2015
Physical Review E, Volume 92, pp 061301-061301; https://doi.org/10.1103/physreve.92.061301

Abstract:
We present a lattice Boltzmann model (LBM) that covers the entire range of fluid flows, from low Mach weakly compressible to transonic and supersonic flows. One of the most restrictive limitations of the lattice Boltzmann method, the low Mach number limit, is overcome here by three fundamental changes to the LBM scheme: use of an appropriately chosen multispeed lattice, accurate evaluation of the equilibrium, and the entropic relaxation for the collision. The range of applications is demonstrated through the simulation of a bow shock in front of an airfoil and the simulation of decaying compressible turbulence with shocklets.
Deshpreet Singh Bedi, XiaoMing Mao
Published: 28 December 2015
Physical Review E, Volume 92, pp 062141-062141; https://doi.org/10.1103/physreve.92.062141

Abstract:
Thermal fluctuations can play an important role in the buckling of elastic objects at small scales, such as polymers or nanotubes. In this paper, we study the finite-temperature buckling transition of an extensible rod by analyzing fluctuation corrections to the elasticity of the rod. We find that, in both two and three dimensions, thermal fluctuations delay the buckling transition, and near the transition, there is a critical regime in which fluctuations are prominent and make a contribution to the effective force that is of order T. We verify our theoretical prediction of the phase diagram with Monte Carlo simulations.
, Andrei S. Burmistrov, Taisiya S. Shinyaeva, , Nikolai Vygornitskii,
Published: 28 December 2015
Physical Review E, Volume 92; https://doi.org/10.1103/physreve.92.062142

Abstract:
Using the Monte Carlo simulation, we study the percolation and jamming of oriented linear k-mers on a square lattice that contains defects. The point defects with a concentration d are placed randomly and uniformly on the substrate before deposition of the k-mers. The general case of unequal probabilities for orientation of depositing of k-mers along different directions of the lattice is analyzed. Two different relaxation models of deposition that preserve the predetermined order parameter s are used. In the relaxation random sequential adsorption (RRSA) model, the deposition of k-mers is distributed over different sites on the substrate. In the single-cluster relaxation (RSC) model, the single cluster grows by the random accumulation of k-mers on the boundary of the cluster (Eden-like model). For both models, a suppression of growth of the infinite (percolation) cluster at some critical concentration of defects dc is observed. In the zero-defect lattices, the jamming concentration pj (RRSA model) and the density of single clusters ps (RSC model) decrease with increasing length k-mers and with a decrease in the order parameter. For the RRSA model, the value of dc decreases for short k-mers (k<16) as the value of s increases. For k=16 and 32, the value of dc is almost independent of s. Moreover, for short k-mers, the percolation threshold is almost insensitive to the defect concentration for all values of s. For the RSC model, the growth of clusters with ellipselike shapes is observed for nonzero values of s. The density of the clusters ps at the critical concentration of defects dc depends in a complex manner on the values of s and k. An interesting finding for disordered systems (s=0) is that the value of ps tends towards zero in the limits of the very long k-mers, k→∞, and very small critical concentrations dc→0. In this case, the introduction of defects results in a suppression of k-mer stacking and in the formation of empty or loose clusters with very low density. On the other hand, denser clusters are formed for ordered systems with ps≈0.065 at s=0.5 and ps≈0.38 at s=1.0.
Published: 28 December 2015
Physical Review E, Volume 92, pp 062828-062828; https://doi.org/10.1103/physreve.92.062828

Abstract:
We study the performance of the euro–Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Target zones and exchange rate dynamics, Q. J. Econ. 106, 669 (1991)]. We present direct quantitative empirical evidence that Krugman's theoretical model provides an accurate description of the euro–Swiss franc target zone. Motivated by the insights from the economic model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.
Christian Knapp, , Antti Koskela, Alexander Ostermann
Published: 28 December 2015
Physical Review E, Volume 92, pp 063310-063310; https://doi.org/10.1103/physreve.92.063310

Abstract:
The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called ϕ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the method considered.
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