This paper presents an efficient high-order radial basis-function-based differential quadrature–finite volume method for incompressible flows on unstructured grids. In this method, a high-order polynomial based on the Taylor series expansion is applied within each control cell to approximate the solution. The derivatives in the Taylor series expansion are approximated by the mesh-free radial basis-function-based differential quadrature method. The recently proposed lattice Boltzmann flux solver is applied to simultaneously evaluate the inviscid and viscous fluxes at the cell interface by the local solution of the lattice Boltzmann equation. In the present high-order method, a premultiplied coefficient matrix appears in the time-dependent term, reflecting the implicit nature. The implicit time-marching techniques, i.e., the lower-upper symmetric Gauss-Seidel and the explicit first stage, singly diagonally implicit Runge-Kutta schemes, are incorporated to efficiently solve the resultant ordinary differential equations. Several numerical examples are tested to validate the accuracy, efficiency, and robustness of the present method on unstructured grids. Compared with the $k$-exact method, the present method enjoys higher accuracy and better computational efficiency.

Electric vehicles may dominate motorized transport in the next decade, yet the impact of the collective dynamics of electric mobility on long-range traffic flow is still largely unknown. We demonstrate a type of congestion that arises if charging infrastructure is limited or electric vehicle density is high. This congestion emerges solely through indirect interactions at charging infrastructure by queue-avoidance behavior that—counterintuitively—induces clustering of occupied charging stations and phase separation of the flow into free and congested stations. The resulting congestion waves always propagate forward in the direction of travel, in contrast to typically backward-propagating congestion waves known from traditional traffic jams. These results may guide the planning and design of charging infrastructure and decision support applications in the near future.

Motivated by the observations of intracellular phase separations and the wetting of cell membranes by protein droplets, we study the nonequilibrium surface wetting by Monte Carlo simulations of a lattice gas model involving particle creation. We find that, even when complete wetting should occur in equilibrium, the fast creation of particles can hinder the surface wetting for a long time due to the bulk droplet formation. Performing molecular dynamics simulations, we show that this situation also holds in colloidal particle systems when the disorder density is sufficiently high. The results suggest an intracellular control mechanism of surface wetting by changing the speed of component synthesis.

The isolation of infectious individuals is a key measure of public health for the control of communicable diseases. However, involving a strong perturbation of daily life, it often causes psychosocial distress, and severe financial and social costs. These may act as mechanisms limiting the adoption of the measure in the first place or the adherence throughout its full duration. In addition, difficulty of recognizing mild symptoms or lack of symptoms may impact awareness of the infection and further limit adoption. Here we study an epidemic model on a network of contacts accounting for limited adherence and delayed awareness to self-isolation, along with fatigue causing overhasty termination. The model allows us to estimate the role of each ingredient and analyze the tradeoff between adherence and duration of self-isolation. We find that the epidemic threshold is very sensitive to an effective compliance that combines the effects of imperfect adherence, delayed awareness and fatigue. If adherence improves for shorter quarantine periods, there exists an optimal duration of isolation, shorter than the infectious period. However, heterogeneities in the connectivity pattern, coupled to a reduced compliance for highly active individuals, may almost completely offset the effectiveness of self-isolation measures on the control of the epidemic.

Microbial communities are ubiquitous in nature and come in a multitude of forms, ranging from communities dominated by a handful of species to communities containing a wide variety of metabolically distinct organisms. This huge range in diversity is not a curiosity—microbial diversity has been linked to outcomes of substantial ecological and medical importance. However, the mechanisms underlying microbial diversity are still under debate, as simple mathematical models only permit as many species to coexist as there are resources. A plethora of mechanisms have been proposed to explain the origins of microbial diversity, but many of these analyses omit a key property of real microbial ecosystems: the propensity of the microbes themselves to change their growth properties within and across generations. In order to explore the impact of this key property on microbial diversity, we expand upon a recently developed model of microbial diversity in fluctuating environments. We implement changes in growth strategy in two distinct ways. First, we consider the regulation of a cell's enzyme levels within short, ecological times, and second we consider evolutionary changes driven by mutations across generations. Interestingly, we find that these two types of microbial responses to the environment can have drastically different outcomes. Enzyme regulation may collapse diversity over long enough times while, conversely, strategy-randomizing mutations can produce a “rich-get-poorer” effect that promotes diversity. This paper makes explicit, using a simple serial-dilutions framework, the conflicting ways that microbial adaptation and evolution can affect community diversity.

Mutations not only alter allele frequencies in a genetic pool but may also determine the fate of an evolutionary process. Here we study which allele fixes in a one-step, one-way model including the wild type and two adaptive mutations. We study the effect of the four basic evolutionary mechanisms—genetic drift, natural selection, mutation, and gene flow—on mutant fixation and its kinetics. Determining which allele is more likely to fix is not simply a question of comparing fitnesses and mutation rates. For instance, if the allele of interest is less fit than the other, then not only must it have a greater mutation rate, but also its mutation rate must exceed a specific threshold for it to prevail. We find exact expressions for such conditions. Our conclusions are based on the mathematical description of two extreme but important regimes, as well as on simulations.

We report segregation between the athermal active and passive particles mediated by the local alignment interaction in a confined space. The competition between the alignment interaction and self-propulsion force results in a transition between disordered and ordered phases. We show that as the coordination between the particles increases, they form an ordered mill, which helps the particles to aggregate into isotropic clusters. As a result, particles segregate into active core and passive shells. This segregation phenomenon is adversely affected by the packing fraction and the size dispersion between active and passive particles. We show that this adverse effect can be overcome by incorporating higher coordination in the system. We report that the monodispersed system is more desirable for segregation in a binary mixture than a bidispersed system, as the latter favors the mixed state.

We establish an explicit data-driven criterion for identifying the solid-liquid transition of two-dimensional self-propelled colloidal particles in the far from equilibrium parameter regime, where the transition points predicted by different conventional empirical criteria for melting and freezing diverge. This is achieved by applying a hybrid machine learning approach that combines unsupervised learning with supervised learning to analyze a huge amount of the system's configurations in the nonequilibrium parameter regime on an equal footing. Furthermore, we establish a generic data-driven evaluation function, according to which the performance of different empirical criteria can be systematically evaluated and improved. In particular, by applying this evaluation function, we identify a new nonequilibrium threshold value for the long-time diffusion coefficient, based on which the predictions of the corresponding empirical criterion are greatly improved in the far from equilibrium parameter regime. These data-driven approaches provide a generic tool for investigating phase transitions in complex systems where conventional empirical ones face difficulties.

Numerous experiments on laser-driven proton acceleration in the MeV range have been performed with a large variety of laser parameters since its discovery around the year 2000. Both experiments and simulations have revealed that protons are accelerated up to a maximum cut-off energy during this process. Several attempts have been made to find a universal model for laser proton acceleration in the target normal sheath acceleration regime. While these models can qualitatively explain most experimental findings, they can hardly be used as predictive models, for example, for the energy cut-off of accelerated protons, as many of the underlying parameters are often unknown. Here we analyze experiments on laser proton acceleration in which scans of laser and target parameters were performed. We derive empirical scaling laws from these parameter scans and combine them in a scaling law for the proton energy cut-off that incorporates the laser pulse energy, the laser pulse duration, the focal spot radius, and the target thickness. Using these scaling laws, we give examples for predicting the proton energy cut-off and conversion efficiency for state-of-the-art laser systems.

Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and charge conservation. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The first ones are realized in experiments, since the standard junctions connecting the bonds obey Neumann boundary conditions due to current conservation. On average, the corresponding Neumann and Dirichlet eigenvalues alternate as a function of the wave number, with the consequence that the Neumann spectrum is described by random matrix theory only locally, but adopts features of the interlacing Dirichlet spectrum for long-range correlations. Another spectral interlacing is found for the Green's function, which in contrast to the secular determinant is experimentally accessible. This is illustrated by microwave studies and numerics.

We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hard-core lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first $k$ next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for $k=1,2,3$ both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.

We introduce the theoretical background needed to perform thermodynamic calculations using reverse Monte Carlo (RMC). The theory is developed for binary $A_x{B}_{1-x}$ lattice systems. The main assumption is that the arrangement of $A$ and $B$ atoms can be described using short-ranged order (SRO) parameters. The detailed balance equation, which is expressed in terms of SRO parameters, is solved to obtain the equilibrium SRO parameter value for the given material interactions, temperature, and composition. Thermodynamic properties, such as the chemical potential, are evaluated using the equilibrium SRO parameter value. RMC enables the calculation of the probability distribution of the local atomic environments, which is needed in the detailed balance equation. We illustrate the application of our method to bulk lattice materials with different first nearest neighbor pair interactions. The main advantage of our approach is that the probability distribution from RMC can be stored in form of look-up tables, and used with a variety of interaction strengths and temperature for rapid estimation of thermodynamic properties. In all examples, the chemical potential is accurately evaluated in the matter of a few seconds on a desktop computer.

We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing.

All higher-spin $(s\ge 1/2)$ Ising spin glasses are studied by renormalization-group theory in spatial dimension $d=3$, exactly on a $d=3$ hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The $s$-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in $d=3$, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of $s\to \infty$. The phase diagrams, with increasing spin $s$, saturate to a limit value. The spin-glass phase, for all $s$, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of $\lambda =1.93$ and runaway exponent of $y_R=0.24$, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at $p_t=0.37$ and 0.63 are unaffected by $s$, confirming the percolative nature of this phase transition.

The loop model is an important model of statistical mechanics and has been extensively studied in two-dimensional lattices. However, it is still difficult to simulate the loop model directly in three-dimensional lattices, especially in lattices with coordination numbers larger than 3. In this paper, a cluster weight Ising model is proposed by introducing an additional cluster weight $n$ in the partition function of the traditional Ising model. This model is equivalent to the loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. By using a Monte Carlo method with cluster updates and color assignment, we obtain the global phase diagram containing the paramagnetic and ferromagnetic phases. The phase transition between the two phases is second order at $1\le n<n_{cri}$ and first order at $n\ge n_{cri}$, where $n_{cri}\approx 2$. The thermal exponent $y_t$ is equal to the system dimension $d$ when the first-order transition occurs. For the second-order transitions, the numerical estimation of $y_t$ and the magnetic exponent $y_m$, shows that the universalities of the two models on the three-dimensional lattice are different. Our results are helpful in the understanding of some traditional statistical mechanics models.

A framework is developed to derive nonlinear dynamical systems that chaotically generate arbitrary multivariate probability distributions with smooth, deterministic trajectories. The ideas are used to extend the Nosé-Hoover thermostat methodology to three-dimensional cases where the momentum distribution is nonisotropic and/or non-Gaussian. Toy models that generate several well-known distributions in physics are given as pedagogical examples.

Do individuals enjoying a higher baseline payoff behave similarly in competitive scenarios compared to their counterparts? The classical replicator equation does not answer such a question since it is invariant to the background or baseline payoff of individuals. In reality, however, if one's baseline payoff is higher than the possible payoffs of an interaction (or game), the individual may respond generously or indifferently if s(he) is satisfied with the prevailing benchmark payoff. This work intends to explore such a phenomenon within the realm of pairwise interactions—taking the prisoner's dilemma as a metaphor—in well-mixed finite and infinite populations. In this framework, a player uses the payoff (comprising baseline and game payoffs) -expectation difference to estimate a degree of eagerness and, with that degree of eagerness, revises his or her strategy with a certain probability. We adopt two approaches to explore such a context, naming them as the Fermi and imitation processes, in which the former uses a pairwise Femi function and the latter considers the relative fitness to estimate probabilities for strategy revision. In a finite population, we examine the effect of intensities to payoff-expectation and strategic payoff differences (denoted by $k_1$ and $k_2$, respectively) as well as the level of contentment ($\omega$) on the fixation probability and fixation time (for a single defector). We observe that the fixation probability surges with the increase of intensity parameters. Nevertheless, the maximum fixation probability may require a substantially larger time to fixate, especially when the expectation is lower than the baseline payoff. This means that cooperators can persist for a longer period of time. A higher expectation or greed, however, considerably reduces the fixation time. Interestingly, our numerical simulation reveals that both approaches are equivalent under weak $k_2\left(\ll 1\right)$ in the Fermi process. We further derive mean-field equations for both approaches in the context of an infinite population, where we observe two possible evolutionary consequences: either full-scale defection or the persistence of the initial frequency of cooperators. The latter scenario indicates players’ uninterested or neutral behavior in relation to the interaction due to their satisfaction on the baseline payoff.

Network embedding techniques aim to represent structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph embedding methods available on the market is large, and practitioners face the nontrivial choice of selecting the proper approach for a given application. The present work attempts to close this gap of knowledge through a systematic comparison of 11 different methods for graph embedding. We consider methods for embedding networks in the hyperbolic and Euclidean metric spaces, as well as nonmetric community-based embedding methods. We apply these methods to embed more than 100 real-world and synthetic networks. Three common downstream tasks — mapping accuracy, greedy routing, and link prediction — are considered to evaluate the quality of the various embedding methods. Our results show that some Euclidean embedding methods excel in greedy routing. As for link prediction, community-based and hyperbolic embedding methods yield an overall performance that is superior to that of Euclidean-space-based approaches. We compare the running time for different methods and further analyze the impact of different network characteristics such as degree distribution, modularity, and clustering coefficients on the quality of the embedding results. We release our evaluation framework to provide a standardized benchmark for arbitrary embedding methods.

Lipids and proteins of plasma membranes of eukaryotic cells are supposed to form protein-lipid domains, characterized by a different molecular order, bilayer thickness, and elastic parameters. Several mechanisms of preferable distribution of transmembrane proteins to the ordered or disordered membrane domains have been revealed. The mismatch between the length of the protein transmembrane domain and hydrophobic thickness of the lipid bilayer is considered to be an important driving force of protein lateral sorting. Utilizing the continuum theory of elasticity, we analyzed optimal configurations and preferable membrane domains for single-pass transmembrane peptides of various hydrophobic lengths and effective molecular shapes. We obtained that short transmembrane peptides stand perpendicularly to the membrane plane. The exceedance of a certain characteristic length leads to the tilt of the peptide. This length depends on the bilayer thickness. Thus, in the membrane with coexisting ordered (thicker) and disordered (thinner) phases tilting of the peptide in each phase is governed by its individual characteristic length. The lateral distribution of the peptides between ordered and disordered membrane domains is shown to be described by two additional characteristic lengths. The exceedance of the smaller one drives the peptide towards a more ordered and thicker membrane, while the exceedance of the larger characteristic length switches the preferable membrane domain from ordered and thicker to disordered and thinner. Thus, membrane proteins with long enough transmembrane domains are predicted to accumulate in the thinner disordered membrane as compared to the thicker ordered bilayer. For hourglass-like and barrel-like shaped transmembrane peptides the specific regime of sorting was obtained: the peptides distributed almost equally between the phases in a wide range of peptide lengths. This finding allowed explaining the experimental data on lateral distribution of transmembrane peptide tLAT.