The random sequential adsorption (RSA) of identical elongated particles (discorectangles) on a line (“Paris car parking problem”) was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The possible orientations of the discorectanles were restricted between $\theta \in [-{\theta }_{\text{m}};{\theta }_{\text{m}}]$ while the aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;100]$. Additionally, the limiting case $\varepsilon =\infty$ (i.e., widthless sticks) was considered. We observed that the RSA deposition for the problem under consideration was governed by the formation of rarefied holes (containing particles oriented along a line) surrounded by comparatively dense stacks (filled with almost parallel particles oriented in the vertical direction). The kinetics of the changes of the order parameter and the packing density are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, ${\phi }_{\text{j}}$, and shifted the cusps in the ${\phi }_{\text{j}}\left(\varepsilon \right)$ dependencies. This can be explained by the effects on the competition between the particles' orientational degrees of freedom and the excluded volume effects.

The fast-forward (FF) scheme proposed by Masuda and Nakamura [Proc. R. Soc. A 466, 1135 (2010)] in the context of conservative quantum dynamics can reproduce a quasistatic dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high- ($T_h$) and low- ($T_c$) temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally adiabatic processes and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency $\eta$ at the maximum power of this engine is found to be ${\eta }^{*}=\frac{1}{2}\left\{1+\frac{1}{2}{\left(\frac{T_c}{T_h}\right)}^{\frac{1}{2}}-\frac{5}{4}\frac{T_c}{T_h}+O\left[{\left(\frac{T_c}{T_h}\right)}^{\frac{3}{2}}\right]\right\}$ and ${\eta }^{*}=1-{\left(\frac{T_c}{T_h}\right)}^{\frac{1}{2}}$, respectively, in the cases of strong and weak dissipation. The result is justified for a wide family of time-scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.

Pair correlation functions provide a summary statistic which quantifies the amount of spatial correlation between objects in a spatial domain. While pair correlation functions are commonly used to quantify continuous-space point processes, the on-lattice discrete case is less studied. Recent work has brought attention to the discrete case, wherein on-lattice pair correlation functions are formed by normalizing empirical pair distances against the probability distribution of random pair distances in a lattice with Manhattan and Chebyshev metrics. These distance distributions are typically derived on an ad hoc basis as required for specific applications. Here we present a generalized approach to deriving the probability distributions of pair distances in a lattice with discrete Manhattan and Chebyshev metrics, extending the Manhattan and Chebyshev pair correlation functions to lattices in $k$ dimensions. We also quantify the variability of the Manhattan and Chebyshev pair correlation functions, which is important to understanding the reliability and confidence of the statistic.

We apply generalizations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional $\pm 1$ random-bond Ising model. The behavior of the model is determined by the temperature $T$ and the concentration $p$ of negative (antiferromagnetic) bonds. The ground state is ferromagnetic for $0\le p<p_c$, and a spin glass for $p_c<p\le 0.5$ where $p_c\simeq 0.222$. We investigate the percolation transition of the Fortuin-Kasteleyn clusters as a function of temperature for large system sizes up to $N={200}^3$ spins. Except for $p=0$ the Fortuin-Kasteleyn percolation transition occurs at a higher temperature than the magnetic ordering temperature. This was known before for $p=\frac{1}{2}$ but here we provide evidence for a difference in transition temperatures even for $p$ arbitrarily small. Furthermore, for all values of $p>0$, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for $p=0$ where the clusters are strictly tied to Ising correlations so the percolation transition is in the Ising universality class.

The paper considers the probability distributions of the nonlinear wave characteristics in nondispersive media that satisfy the Riemann- and the Kardar-Parisi-Zhang-type equations. By using the Lagrangian and Euler relations of statistical descriptions, expressions are obtained for the probability density of the Riemann wave (displacement) integral through the initial probability density of displacement, velocity, and acceleration. The case of Gaussian initial statistics is considered when multivalued sections in nonlinear waves arise at arbitrarily small distances from the entrance. The expressions obtained in this case should be interpreted as the relative residence time of the process in a certain displacement range. It is shown that, due to the Riemann equation locality, the appearance of ambiguity in the wave profile, which occurs mainly at negative values, does not affect the probability density form at positive bias values.

We study the stationary dynamics of energy exchange in an ensemble of phase oscillators, coupled through a mean-field mechanical interaction and added with friction and an external periodic excitation. The degree of entrainment between different parts of the ensemble and the external forcing determines three dynamical regimes, each of them characterized by specific rates of energy exchange. Using suitable approximations, we are able to obtain analytical expressions for those rates, which are in satisfactory agreement with results from numerical integration of the equations of motion. In some of the dynamical regimes, the rates of energy exchange show nontrivial dependence on the friction coefficients—in particular, nonmonotonic behavior and sign switching. This suggests that, even in this kind of stylized model, power transfer between different parts of the ensemble and to the environment can be manipulated by a convenient choice of the individual oscillator parameters.

In this paper, a prey-predator system described by a couple of advection-reaction-diffusion equations is studied theoretically and numerically, where the migrations of both prey and predator are considered and depicted by the unidirectional flow (advection term). To investigate the effect of population migration, especially the relative migration between prey and predator, on the population dynamics and spatial distribution of population, we systematically study the bifurcation and pattern dynamics of a prey-predator system. Theoretically, we derive the conditions for instability induced by flow, where neither Turing instability nor Hopf instability occurs. Most importantly, linear analysis indicates the instability induced by flow depends only on the relative flow velocity. Specifically, when the relative flow velocity is zero, the instability induced by flow does not occur. Moreover, the diffusion-driven patterns at the same flow velocity may not be stationary because of the contribution of flow. Numerical bifurcation analyses are consistent with the analytical results and show that the patterns induced by flow may be traveling waves with different wavelengths, amplitudes, and speeds, which are illustrated by numerical simulations.

We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We demonstrate how schemes based on the move of single nodes between groups systematically fail at correctly sampling from the posterior distribution even on small networks, and how our merge-split approach behaves significantly better, and improves the mixing time of the Markov chain by several orders of magnitude in typical cases. We also show how the scheme can be straightforwardly extended to nested versions of the SBM, yielding asymptotically exact samples of hierarchical network partitions.

The formation of chemical waves in a nonlinear spatially extended system is one of the most fascinating far-from-equilibrium phenomena. An externally imposed thermal gradient in a liquid mixture may induce a concentration gradient generating a thermodynamic cross-flow, which is known as thermal diffusion or the Ludwig-Soret effect. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fraction in space and time. Here, we show that under an externally imposed constant thermal gradient, a traveling wave can emerge in a solution of self-propelled neutral colloid. An exact analytic solution of the spatially extended system is presented in one dimension for a constant thermal gradient to show the time development of a traveling wave. We analyze the effect of a small finite relaxation time of flux, which takes care of the finite inertia of the dispersing colloidal species. While the wave speed remains unaffected, the wave shape is significantly modified by the presence of the finite relaxation time of flux. Our result demonstrates that the traveling wave may reduce to a shock wave provided the product of the square of the wave speed and the relaxation time exactly balances the mass diffusion coefficient. This condition can be achieved by suitably adjusting the velocity of the emergent traveling wave by tuning the value of the constant thermal gradient and maintaining the appropriate boundary condition.

The supersoft elasticity and slow dynamics of isotropic-genesis polydomain nematic elastomers are investigated by loading- and strain-rate-controlled tests. Loading-controlled tests reveal the stretching-driven polydomain-to-monodomain (PM) transition under true equilibrium condition without viscoelastic (time) effect. The equilibrium PM transition is observed as a discontinuous dimensional change at a threshold stress with extremely small magnitude (${\sigma }_{\mathrm{PM}}^{\infty }\approx 1\mathrm{kPa}$). The mechanical work required for 80% elongation of the elastomer accompanying the PM transition is only 2% of that required in the high-temperature isotropic state, reflecting the supersoft elasticity effect. The dimensional growth rate ($R$) under constant loading becomes low as the imposed stress (${\sigma }_0$) approaches ${\sigma }_{\mathrm{PM}}^{\infty }$. The dependency of the dimension on the reduced time ($\mathit{Rt}$) is, however, independent of ${\sigma }_0$. In the strain-rate ($\dot{\varepsilon }$) controlled tests, the stress-stretch curves show a plateau region characteristic of the PM transition in a finite range of stretch, which is equivalent to the discontinuous stretch in the loading-controlled tests. The plateau stress ${\sigma }_{\mathrm{pl}}$ significantly decreases with decreasing $\dot{\varepsilon },$ whereas the ${\sigma }_{\mathrm{pl}}$ at the practically accessible low strain rate (on the order of ${10}^{-4}{\mathrm{s}}^{-1}$ ) is still significantly higher than ${\sigma }_{\mathrm{PM}}^{\infty }$. The dependency of ${\sigma }_{\mathrm{pl}}$ on $\dot{\varepsilon }$ is almost similar to the dependency of ${\sigma }_0$ on $R$ in the loading-controlled tests. This similarity signifies that the two types of tests with different controlled stimuli are governed by the same dynamics of the local director.

Two-dimensional particle-in-cell simulations are presented of the linear and nonlinear developments of stimulated Raman scattering in two overlapping laser beams. The development of the most unstable mode in the linear stage is consistent with a previous paper [C. Z. Xiao et al., Phys. Plasmas 26, 062109 (2019)] where SL mode (two beams share a common scattered light) is dominant in the overlapping region. This mode is enhanced with plasma density and correlation of beam polarizations. When lasers are cross-polarized, it backs to the single-beam Raman backscattering with weak intensity. Trapping-induced nonlinear frequency shift leads to the saturation of SL mode by detuning the coupling and broadening the spectrum. An interesting result that SL mode becomes stronger as the incidence angle increases is contrary to the theoretical prediction and it is a consequence of less efficient saturation in the nonlinear stage.

A high-intensity laser beam propagating through a dense plasma drives a strong current that robustly sustains a strong quasistatic azimuthal magnetic field. The laser field efficiently accelerates electrons in such a field that confines the transverse motion and deflects the electrons in the forward direction. Its advantage is a threshold rather than resonant behavior, accelerating electrons to high energies for sufficiently strong laser-driven currents. We study the electron dynamics via a test-electron model, specifically deriving the corresponding critical current density. We confirm the model's predictions by numerical simulations, indicating energy gains two orders of magnitude higher than achievable without the magnetic field.

Here we show that, although quantum fidelity can truly identify two quantum phase transitions of a one-dimensional spin-1/2 quantum Ising model with competing nearest and next-nearest neighbor interactions in a transverse magnetic field, it may not be a suitable approach for analyzing its ground-state phase diagram.

We disagree with the objections raised by Nemati et al. regarding the phase transitions reported in our paper, where we used the fidelity method. Contrary to their claims, our fidelity calculations do not depend on energy level crossing between excited states. We obtain the same results just by analyzing the second derivative of the ground-state energy with respect to the interaction energy coupling $J_2$.

The Kuramoto model serves as a paradigm to study the phenomenon of spontaneous collective synchronization. We study here a nontrivial generalization of the Kuramoto model by including an interaction that breaks explicitly the rotational symmetry of the model. In an inertial frame (e.g., the laboratory frame), the Kuramoto model does not allow for a stationary state, that is, a state with time-independent value of the so-called Kuramoto (complex) synchronization order parameter $z\equiv r{e}^{i\psi }$. Note that a time-independent $z$ implies $r$ and $\psi$ are both time independent, with the latter fact corresponding to a state in which $\psi$ rotates at zero frequency (no rotation). In this backdrop, we ask: Does the introduction of the symmetry-breaking term suffice to allow for the existence of a stationary state in the laboratory frame? Compared to the original model, we reveal a rather rich phase diagram of the resulting model, with the existence of both stationary and standing wave phases. While in the former the synchronization order parameter $r$ has a long-time value that is time independent, one has in the latter an oscillatory behavior of the order parameter as a function of time that nevertheless yields a nonzero and time-independent time average. Our results are based on numerical integration of the dynamical equations as well as an exact analysis of the dynamics by invoking the so-called Ott-Antonsen ansatz that allows to derive a reduced set of time-evolution equations for the order parameter.

We present a molecular dynamics study of the flow of rigid spherical nanoparticles in a simple fluid. We evaluate the viscosity of the dispersion as a function of shear rate and nanoparticle volume fraction. We observe shear-thinning behavior at low volume fractions; as the shear rate increases, the shear forces overcome the Brownian forces, resulting in more frequent and more violent collisions between the nanoparticles. This in turn results in more dissipation. We show that in order to be in the shear-thinning regime the nanoparticles have to order themselves into layers longitudinal to the flow to minimize the collisions. As the nanoparticle volume fraction increases there is less room to form the ordered layers; consequently as the shear rate increases the nanoparticles collide more, which results in turn in shear thickening. Most interestingly, we show that at intermediate volume fractions the system exhibits metastability, with successions of ordered and disordered states along the same trajectory. Our results suggest that for nanoparticles in a simple fluid the hydroclustering phenomenon is not present; instead the order-disorder transition is the leading mechanism for the transition from shear thinning to shear thickening.

Polymers in shear flow are ubiquitous and we study their motion in a viscoelastic fluid under shear. Employing Hookean dumbbells as representative, we find that the center-of-mass motion follows: $\langle x_c^2\left(t\right)\rangle \sim {\dot{\gamma }}^2{t}^{\alpha +2}$, generalizing the earlier result: $\langle x_c^2\left(t\right)\rangle \sim {\dot{\gamma }}^2{t}^3(\alpha =1)$. Here $0<\alpha <1$ is the coefficient defining the power-law decay of noise correlations in the viscoelastic media. Motion of the relative coordinate, on the other hand, is quite intriguing in that $\langle x_r^2\left(t\right)\rangle \sim t^{\beta }$ with $\beta =2(1-\alpha )$, for small $\alpha$. This implies nonexistence of the steady state, making it inappropriate for addressing tumbling dynamics. We remedy this pathology by introducing a nonlinear spring with FENE-LJ interaction and study tumbling dynamics of the dumbbell. We find that the tumbling frequency exhibits a nonmonotonic behavior as a function of shear rate for various degrees of subdiffusion. We also find that this result is robust against variations in the extension of the spring. We briefly discuss the case of polymers.

We examine the underlying fracture mechanics of the human skin dermal-epidermal layer's microinterlocks using a physics-based cohesive zone finite-element model. Using microfabrication techniques, we fabricated highly dense arrays of spherical microstructures of radius $\approx 50\mu \mathrm{m}$ without and with undercuts, which occur in an open spherical cavity whose centroid lies below the microstructure surface to create microinterlocks in polydimethylsiloxane layers. From experimental peel tests, we find that the maximum density microinterlocks without and with undercuts enable the respective $\approx 4$-fold and $\approx 5$-fold increase in adhesion strength as compared to the plain layers. Critical visualization of the single microinterlock fracture from the cohesive zone model reveals a contact interaction-based phenomena where the primary propagating crack is arrested and the secondary crack is initiated in the microinterlocked area. Strain energy energetics confirmed significantly lower strain energy dissipation for the microinterlock with the undercut as compared to its nonundercut counterpart. These phenomena are completely absent in a plain interface fracture where the fracture propagates catastrophically without any arrests. These events confirm the difference in the experimental results corroborated by the Cook-Gordon mechanism. The findings from the cohesive zone simulation provide deeper insights into soft microinterlock fracture mechanics that could prominently help in the rational designing of sutureless skin grafts and electronic skin.

A theory explaining how deep learning works is yet to be developed. Previous work suggests that deep learning performs a coarse graining, similar in spirit to the renormalization group (RG). This idea has been explored in the setting of a local (nearest-neighbor interactions) Ising spin lattice. We extend the discussion to the setting of a long-range spin lattice. Markov-chain Monte Carlo (MCMC) simulations determine both the critical temperature and scaling dimensions of the system. The model is used to train both a single restricted Boltzmann machine (RBM) network, as well as a stacked RBM network. Following earlier Ising model studies, the trained weights of a single-layer RBM network define a flow of lattice models. In contrast to results for nearest-neighbor Ising, the RBM flow for the long-ranged model does not converge to the correct values for the spin and energy scaling dimension. Further, correlation functions between visible and hidden nodes exhibit key differences between the stacked RBM and RG flows. The stacked RBM flow appears to move toward low temperatures, whereas the RG flow moves toward high temperature. This again differs from results obtained for nearest-neighbor Ising.

Pandemic propagation of COVID-19 motivated us to discuss the impact of the human network clustering on epidemic spreading. Today, there are two clustering mechanisms which prevent of uncontrolled disease propagation in a connected network: an “internal” clustering, which mimics self-isolation (SI) in local naturally arranged communities, and an “external” clustering, which looks like a sharp frontiers closing (FC) between cities and countries, and which does not care about the natural connections of network agents. SI networks are “evolutionarily grown” under the condition of maximization of small cliques in the entire network, while FC networks are instantly created. Running the standard SIR model on clustered SI and FC networks, we demonstrate that the evolutionary grown clustered network prevents the spread of an epidemic better than the instantly clustered network with similar parameters. We find that SI networks have the scale-free property for the degree distribution $P\left(k\right)\sim k^{\eta }$, with a small critical exponent $-2<\eta <-1$. We argue that the scale-free behavior emerges as a result of the randomness in the initial degree distributions.