Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs.

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two subpopulations, one for each plate, and integrates out one subpopulation to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard-sphere overlap are unavoidable, and thus rule out configurations.

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.

The goal of this paper is to develop a high-order numerical method based on the kinetic inviscid flux (KIF) method and flux reconstruction (FR) framework. The KIF aims to find a balance between the excellent merits of the gas-kinetic scheme (GKS) and the lower computational costs. The idea of KIF can be viewed as an inviscid-viscous splitting version of the gas-kinetic scheme, and Shu and Ohwada have made the fundamental contribution. The combination of totally thermalized transport (TTT) scheme and kinetic flux vector splitting (KFVS) method are achieved in KIF. Using a coefficient which is related to time step and averaged collision time, KIF can adjust the weights of TTT and KFVS flux in the simulation adaptively. By doing the inviscid-viscous splitting, KIF is very suitable and easy to integrate into the existing framework. The well-understood FR framework is used widely for the advantages of robustness, economical costs, and compactness. The combination of KIF and FR is originated by three motivations. The first purpose is to develop a high-order method based on the gas-kinetic theory. The second reason is to keep the advantages of GKS. The last aim is that the designed method should be more efficient. In present work, we use the KIF method to replace the Riemann flux solver applied in the interfaces of elements. The common solution at the interface is computed according to the gas-kinetic theory, which makes the combination of KIF and FR scheme more reasonable and available. The accuracy and performance of present method are validated by several numerical cases. The Taylor-Green vortex problem has been used to verify its potential to simulate turbulent flows.

Treating the fermionic ground state-problem as a constrained stochastic optimization problem, a formalism for fermionic quantum Monte Carlo is developed that makes no reference to a trial wave function. Exchange symmetry is enforced by nonlocal terms appearing in the Green's function corresponding to an additional walker propagation channel. Complemented by a treatment of diffusion that encourages the formation of a stochastic nodal surface, we find that an approximate long-range extension of walker cancellations can be employed without introducing significant bias, reducing the number of walkers required for a stable calculation. A proof-of-concept implementation is shown to give a stable fermionic ground state for simple harmonic and atomic systems.

The Sitnikov problem is a classical problem broadly studied in physics which can represent an illustrative example of chaotic scattering. The relativistic version of this problem can be attacked by using the post-Newtonian formalism. Previous work focused on the role of the gravitational radius $\lambda$ on the phase space portrait. Here we add two relevant issues on the influence of the gravitational radius in the context of chaotic scattering phenomena. First, we uncover a metamorphosis of the KAM islands for which the escape regions change insofar as $\lambda$ increases. Second, there are two inflection points in the unpredictability of the final state of the system when $\lambda \simeq 0.02$ and $\lambda \simeq 0.028$. We analyze these inflection points in a quantitative manner by using the basin entropy. This work can be useful for a better understanding of the Sitnikov problem in the context of relativistic chaotic scattering. In addition, the described techniques can be applied to similar real systems, such as binary stellar systems, among others.

We study the Bohmian trajectories of a generic entangled two-qubit system, composed of coherent states of two harmonic oscillators with noncommensurable frequencies and focus on the relation between ergodicity and the dynamical approach to Born's rule for arbitrary distributions of initial conditions. We find that most Bohmian trajectories are ergodic and establish the same invariant ergodic limiting distributions of their points for any nonzero amount of entanglement. In the case of strong entanglement the distribution satisfying Born's rule is dominated by chaotic-ergodic trajectories. Therefore, $P\to {\left|\mathrm{\Psi }\right|}^2$ for an arbitrary $P_0$. However, when the entanglement is weak the distribution satisfying Born's rule is dominated by ordered trajectories, which are not ergodic. In this case the ergodic trajectories do not, in general, lead to the distribution of Born's rule, therefore $P={\left|\mathrm{\Psi }\right|}^2$ is guaranteed only if $P_0={\left|{\mathrm{\Psi }}_0\right|}^2$. Consequently, the existence of chaotic and ergodic Bohmian trajectories does not always lead to the dynamical establishment of Born's rule.

Adhesion between two bodies is a key parameter in wear processes. At the macroscale, strong adhesive bonds are known to lead to high wear rates, as observed in clean metal-on-metal contact. Reducing the strength of the interfacial adhesion is then desirable, and techniques such as lubrication and surface passivation are employed to this end. Still, little is known about the influence of adhesion on the microscopic processes of wear. In particular, the effects of interfacial adhesion on the wear particle size and on the surface roughness evolution are not clear and are therefore addressed here by means of molecular dynamics simulations. We show that, at short timescales, the surface morphology and not the interfacial adhesion strength dictates the minimum size of wear particles. However, at longer timescales, adhesion alters the particle motion and thus the wear rate and the surface morphology.

This paper is the conclusion of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019); Phys. Rev. E 100, 033105 (2019)]. The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of a gas bubble. In our previous papers, general equations were derived to describe the velocity field of acoustic microstreaming produced by modes $m$ and $n$ of bubble oscillations. Particular cases of mode interaction were derived, such as the $0\text{−}n, 1\text{−}1, 1\text{−}m$, and $n\text{−}n$ interactions. Here the general case of interaction between modes $n$ and $m, n>m$, is solved analytically. Solutions are expressed in terms of complex mode amplitudes, meaning that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The $n\text{−}m$ interaction results in specific streaming patterns: At large distance from the bubble interface the pattern exhibits $2|n-m|$ lobes, while $2\min (m,n)$ lobes exist in the bubble vicinity. The spatial organization of the recirculation zones is unique for the interaction of two distinct nonspherical modes and therefore appears as a signature of the $n\text{−}m$ interaction.

Laboratory realizations of two-dimensional (2D) plasma crystals typically involve monodisperse microparticles confined into horizontal monolayers in radio-frequency (rf) plasma sheaths. This gives rise to the so-called plasma wakes beneath the microparticles. The presence of wakes renders the interactions in such systems nonreciprocal, a fact that can lead to a quite different behavior from the one expected for their reciprocal counterparts. Here we examine the buckling of a hexagonal 2D plasma crystal, occurring as the confinement strength is decreased, taking explicitly into account the nonreciprocity of the system via a well-established point-wake model. We observe that for a finite wake charge, the monolayer hexagonal crystal undergoes a transition first to a bilayer hexagonal structure, unrealizable in harmonically confined reciprocal Yukawa systems, and subsequently to a bilayer square structure. Our theoretical results are confirmed by molecular dynamics simulations for experimentally relevant parameters, indicating the potential of their observation in state-of-the-art experiments with 2D complex plasmas.

In this article we report acceleration observed for the ions produced in a 50-nm-thick nickel film coated on a quartz substrate, under nanosecond laser ablation, in the rear ablation geometry. A detailed study with varying background pressure and laser energy is done. Spectroscopic study including spectroscopic time of flight (STOF) measurements of ionic and other neutral transitions from the plasma has been undertaken. The STOF spectra recorded for ionic transition clearly show an enhancement in the velocity of the slow component as the background pressure increases. In addition, a large asymmetric spectral broadening in the 712.22-nm neutral line is observed, which increases with background pressure. While these observations have similarity to some of the reported studies on the acceleration of ionic species through double-layer formation, the electric fields calculated from the measured acceleration appear to be anomalously higher, and a double-layer concept seems to be inadequate. Moreover, the large asymmetry observed in the neutral line profile is indicative of microelectric fields present inside the laser produced plasma plume, which may play a role in the continuous acceleration of the ions. Interestingly, this asymmetry in spectral broadening exhibits temporal and spatial dependence, which indicates that significant electric field is present in the plasma plume even for longer duration and larger distance from the target. These spectroscopic observations of acceleration have also been complemented by triple Langmuir probe measurements. To the best of our information, such observations regarding large ion acceleration for the rather low laser intensities as used in this experiment have not been reported in literature so far.

In this work, the recent lattice Boltzmann model with self-tuning equation of state (EOS) [R. Huang et al., J. Comput. Phys. 392, 227 (2019)] is improved in three aspects to simulate the thermal flows beyond the Boussinesq and ideal-gas approximations. First, an improved scheme is proposed to eliminate the additional cubic terms of velocity, which can significantly improve the numerical accuracy. Second, a local scheme is proposed to calculate the density gradient instead of the conventional finite-difference scheme. Third, a scaling factor is introduced into the lattice sound speed, which can be adjusted to effectively enhance numerical stability. The thermal Couette flow of a nonattracting rigid-sphere fluid, which is described by the Carnahan-Starling EOS, is first simulated, and the better performance of the present improvements on the numerical accuracy and stability is demonstrated. As a further application, the turbulent Rayleigh-Bénard convection in a supercritical fluid slightly above its critical point, which is described by the van der Waals EOS, is successfully simulated by the present lattice Boltzmann model. The piston effect of the supercritical fluid is successfully captured, which induces a fast and homogeneous increase of the temperature in the bulk region, and the time evolution from the initiation of heating to the final turbulent state is analyzed in detail and divided into five stages.

The spectral statistics of Hermitian random Toeplitz matrices with independent and identically distributed elements are investigated numerically. It is found that eigenvalue statistics of complex Toeplitz matrices are surprisingly well approximated by the semi-Poisson distribution belonging to intermediate-type statistics observed in certain pseudointegrable billiards. The origin of intermediate behavior could be attributed to the fact that Fourier transformed random Toeplitz matrices have the same slow decay outside the main diagonal as critical random matrix ensembles. The statistical properties of the full spectrum of real random Toeplitz matrices are close to the Poisson distribution, but each of their constituent subspectra is again well described by the semi-Poisson distribution. The findings indicate that intermediate statistics in general and the semi-Poisson distribution in particular are more universal than considered before.

When an experimentalist measures a time series of qubits, the outcomes constitute a classical stochastic process. We show that projective measurement induces high complexity in these processes in two specific senses: They are inherently random (finite Shannon entropy rate) and they require infinite memory for optimal prediction (divergent statistical complexity). We identify nonorthogonality of the quantum states as the mechanism underlying the resulting complexities and examine the influence that measurement choice has on the randomness and structure of measured qubit processes. We introduce quantitative measures of this complexity and provide efficient algorithms for their estimation.

We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show that the statistical properties of the wave field rely critically on the structure of the discrete resonant manifold (DRM). To demonstrate this, we simulate the two-dimensional Majda-McLaughlin-Tabak equation on rational and irrational tori, resulting in remarkably different power-law spectra and energy cascades at low nonlinearity levels. The difference is explained in terms of different structures of the DRM, which makes use of recent number theory results.

A charged particle moving through a plasma experiences a friction force that commonly acts antiparallel to its velocity. It was recently predicted that in strongly magnetized plasmas, in which the plasma particle gyrofrequency exceeds the plasma frequency, the friction also includes a transverse component that is perpendicular to both the velocity and Lorentz force. Here, this prediction is confirmed using molecular-dynamics simulations, and it is shown that the relative magnitude of the transverse component increases with plasma coupling strength. This result influences single-particle motion and macroscopic transport in strongly magnetized plasmas found in a broad range of applications.

A two-leg quenched random bond disordered antiferromagnetic $\mathrm{spin}-1/2$ Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.

Modeling efforts in opinion dynamics have to a large extent ignored that opinion exchange between individuals can also have an effect on how willing they are to express their opinion publicly. Here, we introduce a model of public opinion expression. Two groups of agents with different opinion on an issue interact with each other, changing the willingness to express their opinion according to whether they perceive themselves as part of the majority or minority opinion. We formulate the model as a multigroup majority game and investigate the Nash equilibria. We also provide a dynamical systems perspective: Using the reinforcement learning algorithm of $Q$-learning, we reduce the $N$-agent system in a mean-field approach to two dimensions which represent the two opinion groups. This two-dimensional system is analyzed in a comprehensive bifurcation analysis of its parameters. The model identifies social-structural conditions for public opinion predominance of different groups. Among other findings, we show under which circumstances a minority can dominate public discourse.

When some ‘entities’ are related by the ‘features’ they share they are amenable to a bipartite network representation. Plant-pollinator ecological communities, co-authorship of scientific papers, customers and purchases, or answers in a poll, are but a few examples. Analyzing clustering of such entities in the network is a useful tool with applications in many fields, like internet technology, recommender systems, or detection of diseases. The algorithms most widely applied to find clusters in bipartite networks are variants of modularity optimization. Here, we provide a hierarchical clustering algorithm based on a dissimilarity between entities that quantifies the probability that the features shared by two entities are due to mere chance. The algorithm performance is $O\left(n^2\right)$ when applied to a set of $n$ entities, and its outcome is a dendrogram exhibiting the connections of those entities. Through the introduction of a ‘susceptibility’ measure we can provide an ‘optimal’ choice for the clustering as well as quantify its quality. The dendrogram reveals further useful structural information though—like the existence of subclusters within clusters or of nodes that do not fit in any cluster. We illustrate the algorithm by applying it first to a set of synthetic networks, and then to a selection of examples. We also illustrate how to transform our algorithm into a valid alternative for one-mode networks as well, and show that it performs at least as well as the standard, modularity-based algorithms—with a higher numerical performance. We provide an implementation of the algorithm in python freely accessible from GitHub.

Population structure has been widely reported to foster cooperation in spatially structured populations, where individuals interact with all of their network neighbors defined by the spatial structure in each generation. However, most results rely on the assumption that individuals strictly interact with all of their neighbors during evolution. In reality, human beings, with sophisticated psychology, are willing to interact with some of their neighbors from time to time. Thus, individuals may not play games with all neighbors due to their psychological factors. Here we investigate how the autonomy, one of the basic psychological needs, affects the fate of cooperators in various social networks. By constructing a dynamical effective network, we find that the introduction of autonomy favors cooperative behavior. Further systematical studies by eliminating heterogeneity and the dynamic characteristics of the network reveal that autonomy plays a pivotal role in the evolution of cooperation. Moreover, we find that a moderate effective network degree, defined by the product of the original network degree and the level of autonomy, maximizes the cooperation on networks connecting individuals with fixed neighbors. Our results offer a possible way for organizations to improve individuals' cooperation and shed light on the importance of individuals' psychology on the evolution of cooperation.