We study the mechanical fluctuations of a micrometer sized silicon cantilever subjected to a strong heat flow, thus having a highly nonuniform local temperature. In this nonequilibrium steady state, we show that fluctuations are equivalent to the thermal noise of a cantilever at equilibrium around room temperature, while its mean local temperature is several hundred degrees higher. Changing the mechanical dissipation by adding a coating to the cantilever, we recover the expected rise of fluctuations with the mean temperature. Our work demonstrates that inhomogeneous dissipation mechanisms can decouple the amplitude of thermal fluctuations from the average temperature. This property could be useful to understand out-of-equilibrium fluctuating systems, or to engineer low noise instruments.

We study a quantum heat engine at strong coupling between the system and the thermal reservoirs. Exploiting a collective coordinate mapping, we incorporate system-reservoir correlations into a consistent thermodynamic analysis, thus circumventing the usual restriction to weak coupling and vanishing correlations. We apply our formalism to the example of a quantum Otto cycle, demonstrating that the performance of the engine is diminished in the strong coupling regime with respect to its weakly coupled counterpart, producing a reduced net work output and operating at a lower energy conversion efficiency. We identify costs imposed by sudden decoupling of the system and reservoirs around the cycle as being primarily responsible for the diminished performance, and we define an alternative operational procedure which can partially recover the work output and efficiency. More generally, the collective coordinate mapping holds considerable promise for wider studies of thermodynamic systems beyond weak reservoir coupling.

We extend a recently proposed approach to determine the absolute free energy of crystalline phases [Phys. Rev. E 92, 022103 (2015)] to systems with continuous and orientation-dependent potentials. The method is based on the Monte Carlo thermodynamic integration method, and it provides a general procedure to obtain a simple, analytical, and exact reference free energy, together with an easy and accurate thermodynamic coupling integral. The approach is free from the difficulties of the standard method based on the harmonic coupling potential. A comparative discussion of both approaches is provided.

Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubblelike and droplike structures due to local internal shape mode instabilities. We describe the formation of such structures on the basis of a one-dimensional theory of activation of internal modes of sine-Gordon solitons. An interpretation of the observed phenomena, in the context of phase transition theory, is given. Implications in Josephson junctions with a current dipole device are discussed.

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long-term behavior of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behavior, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long-term behavior of multispecies populations and, in certain circumstances, establish spatially varying species densities.

With the use of the “two-fluid model,” we discuss anomalous diffusion induced by active force dipoles in viscoelastic media. Active force dipoles, such as proteins and bacteria, generate nonthermal fluctuating flows that lead to a substantial increment of the diffusion. Using the partial Green's function of the two-fluid model, we first obtain passive (thermal) two-point correlation functions such as the displacement cross-correlation function between the two-point particles separated by a finite distance. We then calculate active (nonthermal) one-point and two-point correlation functions due to active force dipoles. The time correlation of a force dipole is assumed to decay exponentially with a characteristic time scale. We show that the active component of the displacement cross-correlation function exhibits various crossovers from super-diffusive to subdiffusive behaviors depending on the characteristic time scales and the particle separation. Our theoretical results are intimately related to the microrheology technique to detect fluctuations in nonequilibrium environment.

We study the electro-optic properties of subwavelength-pitch deformed-helix ferroelectric liquid crystals (DHFLC) illuminated with unpolarized light. In the experimental setup based on the Mach-Zehnder interferometer, it was observed that the reference and the sample beams being both unpolarized produce the interference pattern which is insensitive to rotation of in-plane optical axes of the DHFLC cell. We find that the field-induced shift of the interference fringes can be described in terms of the electrically dependent Pancharatnam relative phase determined by the averaged phase shift, whereas the visibility of the fringes is solely dictated by the phase retardation.

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, $\text{Re}$, finding good agreement with the asymptotic, infinite $\text{Re}$ inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

The robustness of spatial patterns against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigated, little is known about a general mechanism for achieving robustness in reaction-diffusion systems. Here, we propose a buffered reaction-diffusion system, in which active states of chemicals mediated by buffer molecules contribute to reactions, and demonstrate that robustness of the pattern wavelength is achieved by the dynamics of the buffer molecule. This robustness is analytically explained as a result of the scaling properties of the buffered system, which also lead to a reciprocal relationship between the wavelength's robustness and the plasticity of the spatial phase upon external perturbations. Finally, we explore the relevance of this reciprocity to biological systems.

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample-to-sample fluctuations that grow without bound with the system size. More relevant, however, for experiments are the conditions of stress control. In the present Rapid Communication we show that also under stress control the shear modulus exists, but higher-order moduli show unbounded sample-to-sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.

We study the evolution leading to (or regressing from) a large fluctuation in a statistical mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$ ($m=1,M$) evolving by means of a master equation. We show that the process producing a nontypical fluctuation with a value of $N={\sum }_{m=1}^M{n}_m$ well above the average $\langle N\rangle$ is slow. Such process is characterized by the power-law growth of the largest possible observable value of $N$ at a given time $t$. We find similar features also for the reverse process of the regression from a rare state with $N\gg \langle N\rangle$ to a typical one with $N\simeq \langle N\rangle$.

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary-driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also verified that the Kipnis-Marchioro-Presutti model exhibits no phase transitions in a range much larger than previously explored.

Many car-following models of traffic flow admit the possibility of absolute stability, a situation in which uniform traffic flow at any spacing is linearly stable. Near the threshold of absolute stability, these models can often be reduced to a modified Korteweg-deVries (mKdV) equation plus small corrections. The hyperbolic-tangent “kink” solutions of the mKdV equation are usually of particular interest, as they represent transition zones between regions of different traffic spacings. Solvability analysis is believed to show that only a single member of the one-parameter family of kink solutions is preserved by the correction terms, and this is interpreted as a kind of selection. We show, however, that the usual solvability calculation rests on an unstated, unjustified assumption, and that without this assumption it merely gives a first-order correction to the relation between the traffic spacings far behind and far ahead of the kink, rather than any kind of “selection” criterion for the family of kink solutions. On the other hand, we display a two-parameter family of traveling wave solutions of the mKdV equation, which describe regions of one traffic spacing embedded in traffic of a different spacing; this family includes the kink solutions as a limiting case. We carry out a multiple-time-scales calculation and find conditions under which the inclusions decay, conditions that lead to a selected inclusion, and conditions for which the inclusion evolves into a pair of kinks.

Dictyostelium discoideum (Dd) utilizes inhomogeneities in the distribution of cell-cell adhesion molecules on cell membranes for collective cell migration. A simple example of an inhomogeneity is a front-side (leading-edge) polarization in the distribution at the early streaming stage. Experiments have shown that the polarized cell-cell adhesion induces side-by-side contact between cells [Beug et al., Nature (London) 274, 445 (1978)]. This result is counterintuitive, as one would expect cells to align front to front in contact with each other on the basis of front-side polarization. In this work, we theoretically examine whether front-side polarization induces side-by-side contact in collective cell migration. We construct a model for expressing cells with this polarization based on the two-dimensional cellular Potts model. By a numerical simulation with this model, we find cell-cell alignment wherein cells form lateral arrays with side-by-side contacts as observed in the experiments.

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of yielding transitions and grain-size effects in polycrystalline solids. Calculations are based on the 1995 experimental results of Meyers, Andrade, and Chokshi [Metall. Mater. Trans. A 26, 2881 (1995)] for polycrystalline copper under strain-hardening conditions. The main assertion is that the well-known Hall-Petch effects are caused by enhanced strengths of dislocation sources at the edges of grains instead of the commonly assumed resistance to dislocation flow across grain boundaries. The theory describes rapid transitions between elastic and plastic deformation at yield points; thus it can be used to predict grain-size dependence of both yield stresses and flow stresses.

We investigate the influence of orientation on the evolution of small perturbations in compressible shear layers with inflection points. By using linear analysis, we demonstrate that perturbations along the shear plane are most affected by compressibility. The influence of compressibility gradually diminishes with increasing obliqueness of the perturbations with respect to the shear plane. It is demonstrated that the effective gradient Mach number is an appropriate compressibility parameter. We establish that spanwise perturbations, orthogonal to the shear plane, are impervious to compressibility effects. Direct numerical simulations of compressible mixing layers subject to the perturbations at various obliqueness angles verify the analytical findings.

Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how this formalism reduces the network's expansion to three rules, which respectively govern the velocity, the direction, and the nucleation of its growing branches. This framework allows us to establish the mathematical equivalence between three formulations of the direction rule, namely geodesic growth, growth that maintains local symmetry, and growth that maximizes flux into tips for a given amount of growth. Surprisingly, we find that this growth rule may result in a network different from the static configuration that optimizes flux into tips.

Sintering—or coalescence—of compacts of viscous droplets is driven by the interfacial tension between the droplets and the interstitial gas phase. The process, which occurs in a range of industrial and natural settings, such as the manufacture of ceramics and the welding of volcanic ash, causes the compact to densify, to become stronger, and to become less permeable. We investigate the role of droplet polydispersivity in sintering dynamics by conducting experiments in which populations of glass spheres with different size distributions are heated to temperatures above the glass transition interval. We quantify the progress of sintering by tracking changes in porosity with time. The sintering dynamics is modeled by treating the system as a random distribution of interstitial gas bubbles shrinking under the action of interfacial tension only. We identify the scaling between the polydispersivity of the initial droplets and the dynamics of bulk densification. The framework that we develop allows the sintering dynamics of arbitrary polydisperse populations of droplets to be predicted if the initial droplet (or particle) size distribution is known.

Large-eddy simulations (LES) are a powerful tool in understanding processes that are inaccessible by direct simulations due to their complexity, for example, in the highly turbulent regime. However, their accuracy and success depends on a proper subgrid-scale (SGS) model that accounts for the unresolved scales in the simulation. We evaluate the applicability of two traditional SGS models, namely the eddy-viscosity (EV) and the scale-similarity (SS) models, and one recently proposed nonlinear (NL) SGS model in the realm of compressible magnetohydrodynamic (MHD) turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach number $M_s\approx 3$) MHD turbulence with a shock-capturing scheme and varying resolution, SGS model, and filter, we analyze the ensemble statistics of kinetic and magnetic energy spectra and structure functions. Furthermore, we compare the temporal evolution of lower- and higher-order statistical moments of the spatial distributions of kinetic and magnetic energy, vorticity, current density, and dilatation magnitudes. We find no statistical influence on the evolution of the flow by any model if grid-scale quantities are used to calculate SGS contributions. In addition, the SS models, which employ an explicit filter, have no impact in general. On the contrary, both the EV and NL models change the statistics if an explicit filter is used. For example, they slightly increase the dissipation on the smallest scales. We demonstrate that the nonlinear model improves higher-order statistics already with a small explicit filter, i.e., a three-point stencil. The results of, e.g., the structure functions or the skewness and kurtosis of the current density distribution are closer to the ones obtained from simulations at higher resolution. In addition, no additional regularization to stabilize the model is required. We conclude that the nonlinear model with a small explicit filter is suitable for application in more complex scenarios when higher-order statistics are important.