We simulate the response of a particle-stabilized emulsion droplet in an external force field, such as gravity, acting equally on all $N$ particles. We show that the field strength required for breakup (at fixed initial area fraction) decreases markedly with droplet size, because the forces act cumulatively, not individually, to detach the interfacial particles. The breakup mode involves the collective destabilization of a solidified particle raft occupying the lower part of the droplet, leading to a critical force per particle that scales approximately as $N^{-1/2}$.

Isolated populations ultimately go extinct because of the intrinsic noise of elementary processes. In multipopulation systems extinction of a population may occur via more than one route. We investigate this generic situation in a simple predator-prey (or infected-susceptible) model. The predator and prey populations may coexist for a long time, but ultimately both go extinct. In the first extinction route the predators go extinct first, whereas the prey thrive for a long time and then also go extinct. In the second route the prey go extinct first, causing a rapid extinction of the predators. Assuming large subpopulation sizes in the coexistence state, we compare the probabilities of each of the two extinction routes and predict the most likely path of the subpopulations to extinction. We also suggest an effective three-state master equation for the probabilities to observe the coexistence state, the predator-free state, and the empty state.

We study the nonconserved phase-ordering dynamics of the $d=2,3$ random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the $d=1$ system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.

We study the critical behavior of a quenched random-exchange Ising model with competing interactions on a bcc lattice. This model was introduced in the study of the magnetic behavior of Fe${}_{1-x}$Ru${}_x$ alloys for ruthenium concentrations $x=0\%$, $x=4\%$, $x=6\%$, and $x=8\%$. Our study is carried out within a Monte Carlo approach, with the aid of a re-weighting multiple histogram technique. By means of a finite-size scaling analysis of several thermodynamic quantities, taking into account up to the leading irrelevant scaling field term, we find estimates of the critical exponents $\alpha$, $\beta$, $\gamma$, and $\nu$, and of the critical temperatures of the model. Our results for $x=0\%$ are in excellent agreement with those for the three-dimensional pure Ising model in the literature. We also show that our critical exponent estimates for the disordered cases are consistent with those reported for the transition line between paramagnetic and ferromagnetic phases of both randomly dilute and $\pm J$ Ising models. We compare the behavior of the magnetization as a function of temperature with that obtained by Paduani and Branco (2008), qualitatively confirming the mean-field result. However, the comparison of the critical temperatures obtained in this work with experimental measurements suggest that the model (initially obtained in a mean-field approach) needs to be modified.

This article concludes a series of papers [Folk, Holovatch, and Moser, Phys. Rev. E78, 041124 (2008); Folk, Holovatch, and Moser, Phys. Rev. E78, 041125 (2008); Folk, Holovatch, and Moser, Phys. Rev. E79, 031109 (2009)] where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here we give the complete two-loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The nonasymptotic analysis of the dynamic flow equations shows that due to cancellation effects the critical behavior is described, in distances from the critical point accessible to experiments, by the critical behavior qualitatively found in one-loop order. Although one may conclude from the effective dynamic exponents (taking almost their one-loop values) that weak scaling for the order parameter components is valid, the flow of the time-scale ratios is quite different, and they do not reach their asymptotic values.

We study numerically thermal effects at the depinning transition of an elastic string driven in a two-dimensional uncorrelated disorder potential. The velocity of the string exactly at the sample critical force is shown to behave as $V\sim T^{\psi }$, with $\psi$ the thermal rounding exponent. We show that the computed value of the thermal rounding exponent, $\psi =0.15$, is robust and accounts for the different scaling properties of several observables both in the steady state and in the transient relaxation to the steady state. In particular, we show the compatibility of the thermal rounding exponent with the scaling properties of the steady-state structure factor, the universal short-time dynamics of the transient velocity at the sample critical force, and the velocity scaling function describing the joint dependence of the steady-state velocity on the external drive and temperature.

We provide analytical solutions for two types of random walk: generic random walk (GRW) and maximal-entropy random walk (MERW) on a Cayley tree with arbitrary branching number, root degree, and number of generations. For MERW, we obtain the stationary state given by the squared elements of the eigenvector associated with the largest eigenvalue ${\lambda }_0$ of the adjacency matrix. We discuss the dynamics, depending on the second largest eigenvalue ${\lambda }_1$, of the probability distribution approaching to the stationary state. We find different scaling of the relaxation time with the system size, which is generically shorter for MERW than for GRW. We also signal that depending on the initial conditions, there are relaxations associated with lower eigenvalues which are induced by symmetries of the tree. In general, we find that there are three regimes of a tree structure resulting in different statics and dynamics of MERW; these correspond to strongly, critically, and weakly branched roots.

The dynamic modulus $G^{*}$ of a viscoelastic medium is often measured by following the trajectory of a small bead subject to Brownian motion in a method called “passive microbead rheology.” This equivalence between the positional autocorrelation function of the tracer bead and $G^{*}$ is assumed via the generalized Stokes-Einstein relation (GSER). However, inertia of both bead and medium are neglected in the GSER so that the analysis based on the GSER is not valid at high frequency where inertia is important. In this paper we show how to treat both contributions to inertia properly in one-bead passive microrheological analysis. A Maxwell fluid is studied as the simplest example of a viscoelastic fluid to resolve some apparent paradoxes of eliminating inertia. In the original GSER, the mean-square displacement (MSD) of the tracer bead does not satisfy the correct initial condition. If bead inertia is considered, the proper initial condition is realized, thereby indicating an importance of including inertia, but the MSD oscillates at a time regime smaller than the relaxation time of the fluid. This behavior is rather different from the original result of the GSER and what is observed. What is more, the discrepancy from the GSER result becomes worse with decreasing bead mass, and there is an anomalous gap between the MSD derived by naïvely taking the zero-mass limit in the equation of motion and the MSD for finite bead mass as indicated by McKinley et al. [J. Rheol. 53, 1487 (2009)]. In this paper we show what is necessary to take the zero-mass limit of the bead safely and correctly without causing either the inertial oscillation or the anomalous gap, while obtaining the proper initial condition. The presence of a very small purely viscous element can be used to eliminate bead inertia safely once included in the GSER. We also show that if the medium contains relaxation times outside the window where the single-mode Maxwell behavior is observed, the oscillation can be attenuated inside the window. This attenuation is realized even in the absence of a purely viscous element. Finally, fluid inertia also affects the bead autocorrelation through the Basset force and the fluid dragged around with the bead. We show that the Basset force plays the same role as the purely viscous element in high-frequency regime, and the oscillation of MSD is suppressed if fluid density and bead density are comparable.

The theory of Kolmogorov-Johnson-Mehl-Avrami for phase transition kinetics is subjected to severe limitations concerning the functional form of the growth law. This paper is devoted to sidestepping this drawback through the use of the correlation function approach. Moreover, we put forward an easy-to-handle formula, written in terms of the experimentally accessible actual extended volume fraction, which is found to match several types of growths. Computer simulations have been performed for corroborating the theoretical approach.

The performance of a simple method [E. L. Sibert III, E. Vergini, R. M. Benito, and F. Borondo, New J. Phys. 10, 053016 (2008)] to efficiently compute scar functions along unstable periodic orbits with complicated trajectories in configuration space is discussed, using a classically chaotic two-dimensional quartic oscillator as an illustration.

Persson's multiscale contact mechanics theory combined with a multiscale Brillouin-Prandtl-Tomlinson model is used to show that on the basis of these models “dry friction” [i.e., kinetic friction that remains at exceedingly small velocities (but still above the creep range) close to its value at higher velocities] should almost always occur for self-affine surfaces when the dominant interaction between two surfaces in contact is due to interatomic hard core repulsion, except for extremely smooth surfaces (i.e., surfaces with a Hurst index very close to 1).

Shape is an important feature of physical systems, although very seldom is it addressed in the framework of a quantitative description approach. In this paper we propose to interpret the shape of things as a physical manifestation of the content of information associated with each thing and show that a change of shape in a physical system is necessarily connected with a change of its entropy and thus involves energy. We estimate the amount of energy dissipated during a shape change and propose experimental tests to be performed in nanoscale systems to verify this prediction by measuring the expected dissipation in a few simple cases. Relevant implications in the design of future zero-power logic switches are discussed.

By application of the field-cycling technique, we measure the dispersion of the ${}^1$H nuclear magnetic resonance (NMR) spin-lattice relaxation time $T_1$(ω) for a series of molecular liquids. We demonstrate that such NMR relaxometry studies can be used for determining diffusion coefficients. A broad frequency range of 10 kHz–20 MHz is covered. By scanning $T_1$(ω) one directly probes the spectral density of the diffusion processes. The value of the diffusion coefficient $D$ can be determined from a linear dependence of the ${}^1$H spin-lattice relaxation rate on the square root of the frequency at which it is measured. The power of this method lies in its simplicity, which allows one to determine $D$($T$) independently of the diffusive model. The results obtained are in very good agreement with those of field gradient NMR methods.

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Long-range interacting systems, while relaxing to equilibrium, often get trapped in long-lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system in a quasistationary state (QSS) responds to an external perturbation. We consider a long-range system that evolves under deterministic Hamilton dynamics. The perturbation is taken to couple to the canonical coordinates of the individual constituents. Our study is based on analyzing the Vlasov equation for the single-particle phase-space distribution. The QSS represents a stable stationary solution of the Vlasov equation in the absence of the external perturbation. In the presence of small perturbation, we linearize the perturbed Vlasov equation about the QSS to obtain a formal expression for the response observed in a single-particle dynamical quantity. For a QSS that is homogeneous in the coordinate, we obtain an explicit formula for the response. We apply our analysis to a paradigmatic model, the Hamiltonian mean-field model, which involves particles moving on a circle under Hamiltonian dynamics. Our prediction for the response of three representative QSSs in this model (the water-bag QSS, the Fermi-Dirac QSS, and the Gaussian QSS) is found to be in good agreement with $N$-particle simulations for large $N$. We also show the long-time relaxation of the water-bag QSS to the Boltzmann-Gibbs equilibrium state.

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method.

We study the dynamic evolution of geometric structures in a polydegenerate system represented by a $q$-state Potts model with nonconserved order parameter that is quenched from its disordered into its ordered phase. The numerical results obtained with Monte Carlo simulations show a strong relation between the statistical properties of hull perimeters in the initial state and during coarsening: The statistics and morphology of the structures that are larger than the averaged ones are those of the initial state, while the ones of small structures are determined by the curvature-driven dynamic process. We link the hull properties to the ones of the areas they enclose. We analyze the linear von Neumann-Mullins law, both for individual domains and on the average, concluding that its validity, for the later case, is limited to domains with number of sides around 6, while presenting stronger violations in the former case.

The diffusion of charged particles interacting through a repulsive Yukawa potential, $\exp (-r/\lambda )/r$, confined by a parabolic potential in the $y$ direction and subjected to a periodic substrate potential in the $x$ direction is investigated. Langevin dynamic simulations are used to investigate the effect of the particle density, the amplitude of the periodic substrate, and the range of the interparticle interaction potential on the diffusive behavior of the particles. We found that in general the diffusion is suppressed with increasing the amplitude of the periodic potential, but for specific values of the strength of the substrate potential a remarkable increase of the diffusion is found with increasing the periodic potential amplitude. In addition, we found a strong dependence of the diffusion on the specific arrangement of the particles, e.g., single-chain versus multichain configuration. For certain particle configurations, a reentrant behavior of the diffusion is found as a function of the substrate strength due to structural transitions in the ordering of the particles.

We propose a minimal model of locally activated diffusion, in which the diffusion coefficient of a one-dimensional Brownian particle is modified in a prescribed way—either increased or decreased—upon each crossing of the origin. Such a local mobility decrease arises in the formation of atherosclerotic plaques due to diffusing macrophage cells accumulating lipid particles. We show that spatially localized mobility perturbations have remarkable consequences on diffusion at all scales, such as the emergence of a non-Gaussian multipeaked probability distribution and a dynamical transition to an absorbing static state. In the context of atherosclerosis, this dynamical transition can be viewed as a minimal mechanism that causes macrophages to aggregate in lipid-enriched regions and thereby to the formation of atherosclerotic plaques.