We study the efficiency of quantum Monte Carlo (QMC) methods in computing space localized ground state properties (properties which do not depend on distant degrees of freedom) as a function of the system size $N$. We prove that for the commonly used correlated sampling with reweighting method, the statistical fluctuations ${\sigma }^2\left(N\right)$ do not obey the locality property. ${\sigma }^2\left(N\right)$ grow at least linearly with $N$ and with a slope that is related to the fluctuations of the reweighting factors. We provide numerical illustrations of these tendencies in the form of QMC calculations on linear chains of hydrogen atoms.

Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary, oscillations can be discerned in the survival probability. We show that these oscillations are due to complex-valued higher-order eigenvalues of the Fokker-Planck operator, which we compute explicitly in the limit of small noise. We also show that in this limit the period of the oscillations is the winding number of the activated stochastic process. These peak probability oscillations are not related to stochastic resonance and should be detectable in planar dynamical systems with the topology described here.

Three-dimensional fast magnetic reconnection driven by two ultraintense femtosecond laser pulses is investigated by relativistic particle-in-cell simulation, where the two paralleled incident laser beams are shot into a near-critical plasma layer to form a magnetic reconnection configuration in self-generated magnetic fields. A reconnection $X$ point and out-of-plane quadrupole field structures associated with magnetic reconnection are formed. The reconnection rate is found to be faster than that found in previous two-dimensional Hall magnetohydrodynamic simulations and electrostatic turbulence contribution to the reconnection electric field plays an essential role. Both in-plane and out-of-plane electron and ion accelerations up to a few MeV due to the magnetic reconnection process are also obtained.

A region of two-dimensional space has been filled randomly with a large number of growing circular disks allowing only a “slight” overlapping among them just before their growth stops. More specifically, each disk grows from a nucleation center that is selected at a random location within the uncovered region. The growth rate $\delta$ is a continuously tunable parameter of the problem which assumes a specific value while a particular pattern of disks is generated. When a growing disk overlaps for the first time with at least one other disk, its growth is stopped and is said to be frozen. In this paper we study the percolation properties of the set of frozen disks. Using numerical simulations we present evidence for the following: (i) The order parameter appears to jump discontinuously at a certain critical value of the area coverage; (ii) the width of the window of the area coverage needed to observe a macroscopic jump in the order parameter tends to vanish as $\delta \to 0$; and on the contrary (iii) the cluster size distribution has a power-law-decaying functional form. While the first two results are the signatures of a discontinuous transition, the third result is indicative of a continuous transition. Therefore we refer to this transition as a sharp but continuous transition similar to what has been observed in the recently introduced Achlioptas process of explosive percolation. It is also observed that in the limit of $\delta \to 0$, the critical area coverage at the transition point tends to unity, implying that the limiting pattern is space filling. In this limit, the fractal dimension of the pore space at the percolation point has been estimated to be $1.42\left(10\right)$ and the contact network of the disk assembly is found to be a scale-free network.

The motion of an adiabatic piston under dry friction is investigated to clarify the roles of dry friction in nonequilibrium steady states. We clarify that dry friction can reverse the direction of the piston motion and causes a discontinuity or a cusplike singularity for velocity distribution functions of the piston. We also show that the heat fluctuation relation is modified under dry friction.

The response of an electrolyte solution bounded between two blocking electrodes subjected to an ac voltage is considered. We focus on the pertinent thin-double-layer limit, where this response is governed by a reduced dynamic model [L. Højgaard Olesen, M. Z. Bazant, and H. Bruus, Phys. Rev. E 82, 011501 (2010)]. During a transient stage, the system is nonlinearly entrained towards periodic oscillations of the same frequency as that of the applied voltage. Employing a strained-coordinate perturbation scheme, valid for moderately large values of the applied voltage amplitude $V$, we obtain a closed-form asymptotic approximation for the periodic orbit which is in remarkable agreement with numerical computations. The analysis elucidates the nonlinear characteristics of the system, including a slow (logarithmic) growth of the zeta-potential amplitude with $V$ and a phase straining scaling as $V^{-1}lnV$. In addition, an asymptotic current-voltage relation is provided, capturing the numerically observed rapid temporal variations in the electric current.

The influence of surface anchoring in thin chiral ferroelectric liquid crystals on helical superstructures imposed onto smectic layers is studied by means of a simple model allowing surface anchoring through the self-depolarization effect. It is shown that, for narrow temperature ranges close to temperatures of tilting phase transitions, these interactions can destroy helices, leading to the emergence of complex, intertwined undulatory, and helical substructures with different, mainly short, pitches. Regions with both undulated and helical orderings are demonstrated to reveal different sizes and random distributions along the smectic layer normal. Assuming values of material model parameters, typical for liquid crystals being close to tilting phase transitions, the free energy of thin helical smectic liquid crystal systems is determined as a function of two variables. One of them specifies the helix period of the appropriate bulk system (unperturbed by surfaces), while the second describes the interplay between the surface anchoring and the liquid crystal elasticity. It is shown that the free energy exhibits a very complicated behavior within variable regions for which the regular helices or complex superstructures occur. The resulting sensitivity of the free energy on changes of these variables corresponds to the appearance of a large variety of complex superstructures with coexisting helices of different periods. This gives an explanation of the occurrence of intricate superstructures and provides new insight into the interplay between molecular and surface interactions near the tilting phase transitions.

We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the external flow and can be described with power laws with exponents $2.59\pm 0.28$ and $0.91\pm 0.05$, respectively. We develop a theoretical model to describe the deformation of squeezed drops based on the Darcy approximation for shallow geometries and the use of complex potentials. The model describes the steady-state deformation of the drops as a function of a nondimensional parameter $\text{Ca}{\delta }^2$, where $\text{Ca}$ is the capillary number (proportional to the strain rate and the drop size) and $\delta$ is a confinement parameter equal to the drop size divided by the channel height. For small deformations, the theoretical model predicts a linear relationship between the deformation of drops and this parameter, in good agreement with the experimental observations.

This study investigates the local flow characteristics near droplet-droplet collisions by means of direct numerical simulation of isotropic cloudlike turbulence. The key finding is that, generally, droplets do not collide where they preferentially concentrate. Preferential concentration is found to happen as expected in regions of low enstrophy (vorticity magnitude), but collisions tend to take place in regions with significantly higher dissipation rates (up to a factor of 2.5 for Stokes unity droplets). Investigation of the droplet history reveals that collisions are consistently preceded by dissipative events. Based on the droplet history data, the following physical picture of a collision can be constructed: Enstrophy makes droplets preferentially concentrate in quiescent flow regions, thereby increasing the droplet velocity coherence, i.e., decreasing relative velocities between droplets. Strongly clustered droplets thus have a low collision probability, until a dissipative event accelerates the droplets towards each other. We study the relation between the local dissipation rate and the local collision kernel and vary the averaging scale to relate the results to the globally averaged collision and dissipation rates. It is noted that, unlike enstrophy, there is a positive correlation between the dissipation rate and collision efficiency that extends from the largest to the smallest scales of the flow.

A simple model for the dielectric function of a completely ionized plasma with an arbitrary ionic charge that is valid for long-wavelength high-frequency perturbations is derived using an approximate solution of a linearized Fokker-Planck kinetic equation for electrons with a Landau collision integral. The model accounts for both the electron-ion collisions and the collisions of the subthermal (cold) electrons with thermal ones. The relative contribution of the latter collisions to the dielectric function is treated phenomenologically, introducing some parameter $\varkappa$ that is chosen in such a way as to get a well-known expression for stationary electric conductivity in the low-frequency region and fulfill the requirement of a vanishing contribution of electron-electron collisions in the high-frequency region. This procedure ensures the applicability of our model in a wide range of plasma parameters as well as the frequency of the electromagnetic radiation. Unlike the interpolation formula proposed earlier by Brantov et al. [Brantov et al., JETP 106, 983 (2008)], our model fulfills the Kramers-Kronig relations and permits a generalization for the cases of degenerate and strongly coupled plasmas. With this in mind, a generalization of the well-known Lee-More model [Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984)] for stationary conductivity and its extension to dynamical conductivity [O. F. Kostenko and N. E. Andreev, GSI Annual Report No. GSI-2008-2, 2008 (unpublished), p. 44] is proposed for the case of plasmas with arbitrary ionic charge.

Structural analysis is very important to understanding the physics of atomic or particle systems of various types. However, properly characterizing the structures at different packing fraction ρ is still a challenge. Here we analyze the local structure, in terms of the so-called common-neighbor-subcluster (CNS), of sphere packings with ρ ∈ (0.2, 0.74). We show that although complicated in structure, there are totally 39 kinds of CNSs of which 12 are dominant. The evolution of these CNSs with the increase of ρ is quantified, and the rules governing the evolution are explored. The results are found to be useful in constructing a comprehensive picture about the critical states and their transition in sphere packing.

All observations of photodegradation and self-healing follow the predictions of the correlated chromophore domain model [Ramini et al., Polym. Chem. 4, 4948 (2013)]. In the present work, we generalize the domain model to describe the effects of an electric field by including induced dipole interactions between molecules in a domain by means of a self-consistent field approach. This electric field correction is added to the statistical mechanical model to calculate the distribution of domains that are central to healing. Also included in the model are the dynamics due to the formation of an irreversibly damaged species, which we propose involves damage to the polymer mediated through energy transfer from a dopant molecule after absorbing a photon. As in previous studies, the model with one-dimensional domains best explains all experimental data of the population as a function of time, temperature, intensity, concentration, and now applied electric field. Though the precise nature of a domain is yet to be determined, the fact that only one-dimensional domain models are consistent with observations suggests that they might be made of correlated dye molecules along polymer chains. Furthermore, the voltage-dependent measurements suggest that the largest polarizability axis of the molecules are oriented perpendicular to the chain.

We report the existence of diverse routes of transition from amplitude death to oscillation death in three different diffusively coupled systems, which are perturbed by a symmetry breaking repulsive coupling link. For limit-cycle systems the transition is through a pitchfork bifurcation, as has been noted before, but in chaotic systems it can be through a saddle-node or a transcritical bifurcation depending on the nature of the underlying dynamics of the individual systems. The diversity of the routes and their dependence on the complex dynamics of the coupled systems not only broadens our understanding of this important phenomenon but can lead to potentially new practical applications.

Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a $\pi$-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.

For pressure-driven turbulent channel flows undergoing spanwise system rotation, it has been observed that the absolute vorticity, i.e., the sum of the averaged spanwise flow vorticity and system rotation, tends to zero in the central region of the channel. This observation has so far eluded a convincing theoretical explanation, despite experimental and numerical evidence reported in the literature. Here we show experimentally that three-dimensional laminar structures in plane Couette flow, which appear under anticyclonic system rotation, give the same effect, namely, that the absolute vorticity tends to zero if the rotation rate is high enough. It is shown that this is equivalent to a local Richardson number of approximately zero, which would indicate a stable condition. We also offer an explanation based on Kelvin's circulation theorem to demonstrate that the absolute vorticity should remain constant and approximately equal to zero in the central region of the channel when going from the nonrotating fully turbulent state to any state with sufficiently high rotation.

One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial region has a finite (i.e., noninfinitesimal) thickness known as a diffuse interface. In simulations of, e.g., bubble or drop dynamics, for problems involving nonideal gases, one frequently observes that the diffuse interface method produces a spontaneous, nonphysical shrinkage of the bubble or drop radius. In this paper, we analyze in detail a single-fluid two-phase model and use a LBE model for nonideal gases in order to explain this fundamental problem. For simplicity, we only investigate the static bubble or droplet problem. We find that the method indeed produces a density shift, bubble or droplet shrinkage, as well as a critical radius below which the bubble or droplet eventually vanishes. Assuming that the ratio between the interface thickness $D$ and the initial bubble or droplet radius $r_0$ is small, we analytically show the existence of this density shift, bubble or droplet radius shrinkage, and critical bubble or droplet survival radius. Numerical results confirm our analysis. We also consider droplets on a solid surface with different curvatures, contact angles, and initial droplet volumes. Numerical results show that the curvature, contact angle, and the initial droplet volume have an effect on this spontaneous shrinkage process, consistent with the survival criterion.

We provide molecular-dynamics simulation of heat transport in one-dimensional molecular chains with different interparticle pair potentials. We show that the thermal conductivity is finite in the thermodynamic limit in chains with the potentials that allow for bond dissociation. The Lennard-Jones, Morse, and Coulomb potentials are such potentials. The convergence of the thermal conductivity is provided by phonon scattering on the locally strongly stretched loose interatomic bonds at low temperature and by the many-particle scattering at high temperature. On the other hand, chains with a confining pair potential, which does not allow for bond dissociation, possess anomalous thermal conductivity, diverging with the chain length. We emphasize that chains with a symmetric or asymmetric Fermi-Pasta-Ulam potential or with combined potentials, containing a parabolic and/or a quartic confining potential, all exhibit anomalous heat transport.

Biopolymer length regulation is a complex process that involves a large number of biological, chemical, and physical subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres—nucleoprotein structures at the ends of linear chromosomes consisting of tandemly repeated DNA sequences and a specialized set of proteins. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination. Various linear and circular DNA structures were identified to participate in ALT, however, dynamics of the whole process is still poorly understood. We propose a chemical kinetics model of ALT with kinetic rates systematically derived from the biophysics of DNA diffusion and looping. The reaction system is reduced to a coagulation-fragmentation system by quasi-steady-state approximation. The detailed treatment of kinetic rates yields explicit formulas for expected size distributions of telomeres that demonstrate the key role played by the J factor, a quantitative measure of bending of polymers. The results are in agreement with experimental data and point out interesting phenomena: an appearance of very long telomeric circles if the total telomere density exceeds a critical value (excess mass) and a nonlinear response of the telomere size distributions to the amount of telomeric DNA in the system. The results can be of general importance for understanding dynamics of telomeres in telomerase-independent systems as this mode of telomere maintenance is similar to the situation in tumor cells lacking telomerase activity. Furthermore, due to its universality, the model may also serve as a prototype of an interaction between linear and circular DNA structures in various settings.

Branching processes have served as a model for chemical reactions, biological growth processes, and contagion (of disease, information, or fads). Through this connection, these seemingly different physical processes share some common universalities that can be elucidated by analyzing the underlying branching process. In this work we focus on coupled branching processes as a model of infectious diseases spreading from one population to another. An exceedingly important example of such coupled outbreaks are zoonotic infections that spill over from animal populations to humans. We derive several statistical quantities characterizing the first spillover event from animals to humans, including the probability of spillover, the first passage time distribution for human infection, and disease prevalence in the animal population at spillover. Large stochastic fluctuations in those quantities can make inference of the state of the system at the time of spillover difficult. Focusing on outbreaks in the human population, we then characterize the critical threshold for a large outbreak, the distribution of outbreak sizes, and associated scaling laws. These all show a strong dependence on the basic reproduction number in the animal population and indicate the existence of a novel multicritical point with altered scaling behavior. The coupling of animal and human infection dynamics has crucial implications, most importantly allowing for the possibility of large human outbreaks even when human-to-human transmission is subcritical.