The results of modeling shear flows in classical two-dimensional (2D) dipole systems are presented. We used the method of nonequilibrium molecular dynamics to calculate the viscosity at various shear rates. The coefficients of shear viscosity are given in the limit of low shear rates for various regimes of interparticle correlation from a weakly correlated gaseous state to a strongly nonideal liquid state near the crystallization point. The calculations were carried out for bare (unscreened) dipole systems, as well as for dipole systems in a polarizable medium that provide screening of the dipole-dipole interaction. The effect of shear thinning in 2D dipole systems is reported for low values of the coupling parameter. In addition, it is shown that dipole systems can become both less and more viscous due to the presence of a screening medium, depending on the degree of interparticle correlation. The optimal simulation parameters are discussed within the framework of the method of nonequilibrium molecular dynamics for determining the shear viscosity of two-dimensional dipole systems. Moreover, we present a simple fitting curve which provides a universal scaling law for both bare dipole-dipole interaction and screened dipole-dipole interaction.

Linear and nonlinear propagation characteristics of multidimensional drift ion-acoustic (IA) solitons are studied in an inhomogeneous partially degenerate electron-ion magnetoplasma. A modified Zakharov-Kuznetsov (mZK) equation is deduced, accounting for the longitudinal as well as the transverse dispersions. It is shown that the mZK equation admits a distinct solution, revealing excitation of a pulse-shaped soliton when the phase speed exceeds by the wave dispersion. For the instability condition of the waves, a novel growth rate $\left(\gamma \right)$ is derived by modifying the standard small-$\mathrm{k}$ expansion scheme. The instability criterion, given for long-wavelength IA waves, has not been described elsewhere. Numerical analysis show that solitary pulses gain energy from the ion drift, involving into instability: it saturates with amplification of the unstable potentials. Similarly trapped electrons lead to unstable growth of the solitary waves by enhancing $\gamma .$ This study is relevant to compact stars and to high-density facilities where density inhomogeneity ensues the unstable drift modes. The instability analysis is important in understanding anomalous diffusion, which reduces the lifespan $(\tau ={\gamma }^{-1})$ of magnetically confined plasma.

The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences for other growth equations, I find here that the KPZ growth exponents (related to the temporal scaling of the fluctuations) are given by ${\beta }_d=\frac{7}{8d+13}$. These exponents present an excellent agreement with the most accurate estimates for them in the literature. Moreover, they are confirmed here through extensive Monte Carlo simulations of discrete growth models and real-space renormalization group (RG) calculations for directed polymers in random media (DPRM), up to $d=15$. The left-tail exponents of the probability density functions for the DPRM energy provide another striking verification of the analytical result above.

Considering the paradigmatic driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We focus on the overdamped regime where exact optimal processes are known analytically and most experiments operate. This allows us to compare the optimal processes obtained in linear response and address their relevance to experiments using realistic parameter values from experiments with optical tweezers. Our results help assess the accuracy of perturbative methods in calculating the irreversible work for cases where the exact solution might be difficult to access. For that, we present a performance metric comparing the approximate optimal solution to the exact one. Our main result is that optimal linear-response processes can perform surprisingly well, even far from where they were expected.

A system can be driven between metastable configurations by a time-dependent driving protocol, which uses external control parameters to change the potential energy of the system. Here we investigate the correspondence between driving protocols that are designed to minimize work and the spontaneous transition paths of the system in the absence of driving. We study the spin-inversion reaction in a 2D Ising model, quantifying the timing of each spin flip and heat flow to the system during both a minimum-work protocol and a spontaneous transition. The general order of spin flips during the transition mechanism is preserved between the processes, despite the coarseness of control parameters that are unable to reproduce more detailed features of the spontaneous mechanism. Additionally, external control parameters provide energy to each system component to compensate changes in internal energy, showing how control parameters are tuned during a minimum-work protocol to counteract underlying energetic features. This paper supports a correspondence between minimum-work protocols and spontaneous transition mechanisms.

Brownian particles interacting sequentially with distinct temperatures and driving forces at each stroke have been tackled as a reliable alternative for the construction of engine setups. However, they can behave very inefficiently depending on the driving used for the work source and/or when temperatures of each stage are very different from each other. Inspired by some models for molecular motors and recent experimental studies, a coupling between driving and velocities is introduced and detail investigated from stochastic thermodynamics. Exact expressions for thermodynamic quantities and distinct maximization routes have been obtained. The search of an optimal coupling provides a substantial increase of engine performance (mainly efficiency), even for large $\mathrm{\Delta }T$. A simple and general argument for the optimal coupling can be estimated, irrespective of the driving and other model details.

Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems, however, require us to define intermediate quantities (e.g., the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined with the analysis of the resulting field equation involving a fractional Laplacian, will show that the critical diffusion equation cannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical superdiffusion equation. The analysis of this equation will reveal that nonnegligible departure from mean-field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.

We investigated properties of a singular billiard, that is, a quantum billiard which contains a pointlike (zero-range) perturbation. A singular billiard was simulated experimentally by a rectangular microwave flat resonator coupled to microwave power via wire antennas which act as singular scatterers. The departure from regularity was quantitatively estimated by the short-range plasma model in which the parameter $\eta$ takes the values 1 and 2 for the Poisson and semi-Poisson statistics, respectively. We show that in the regime of semi-Poisson statistics the experimental power spectrum and the second nearest-neighbor-spacing distribution $P(2,s)$ are in good agreement with their theoretical predictions. Furthermore, the measurement of the two-port scattering matrix allowed us to evaluate experimentally the enhancement factor $F\left({\gamma }^{\mathrm{tot}}\right)$ in the regime of the semi-Poisson statistics as a function of the total absorption factor ${\gamma }^{\mathrm{tot}}$. The experimental results were compared with the analytical formula for $F\left({\gamma }^{\mathrm{tot}}\right)$ evaluated in this article. The agreement between the experiment and theory is good.

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a robust assessment of complex networks that does not depend on the entire degree distribution, but only on its mean, range, and dispersion: summary statistics that are easy to obtain for most real-world networks. By solving several semi-infinite linear programs, we obtain tight (the sharpest possible) bounds for correlation and clustering measures, for all networks with degree distributions that share the same summary statistics. We identify various extremal random graphs that attain these tight bounds as the graphs with specific three-point degree distributions. We leverage the tight bounds to obtain robust laws that explain how degree-degree correlations and local clustering evolve as a function of node degrees and network size. These robust laws indicate that power-law networks with diverging variance are among the most extreme networks in terms of correlation and clustering, building a further theoretical foundation for the widely reported scale-free network phenomena such as correlation and clustering decay.

We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability $\omega \in [0,1)$. Otherwise, with probability $1-\omega$, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability $\omega$ affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on $\omega$. We also consider examples of real temporal networks, and we show that the considered model can adequately reproduce several of their dynamical properties. Our results advance our understanding of the realistic modeling of temporal networks and of the effects of link persistence on temporal network properties.

We study the quantum dynamics of a photoexcitation uniformly distributed at the periphery of an extended star network (with $N_B$ branches of length $L_B$). More specifically, we address here the question of the energy absorption at the core of the network and how this process can be improved (or not) by the inclusion of peripheral defects with a tunable energy amplitude $\mathrm{\Delta }$. Our numerical simulations reveal the existence of optimal value of energy defect ${\mathrm{\Delta }}^{*}$ which depends on the network architecture. Around this value, the absorption process presents a strong speedup (i.e., reduction of the absorption time) provided that $L_B\le L_B^{*}$ with $L_B^{*}\approx 12.5/ln\left(N_B\right)$. Analytical and numerical developments are then conducted to interpret this feature. We show that the origin of this speedup takes place in the hybridization of two upper-band excitonic eigenstates. This hybridization is important when $L_B\le L_B^{*}$ and vanishes almost totally when $L_B>L_B^{*}$. These structural rules we draw here could represent a potential guide for the practical design of molecular nanonetwork dedicated to the realization of efficient photoexcitation absorption.

Recently developed free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter has been applied for studying $L$-shell opacity of iron and chromium at $T=182$ eV. We use Mermin–Kohn–Sham density functional theory with a ground-state and a fully-temperature-dependent generalized gradient approximation exchange-correlation (XC) functionals. It is demonstrated that the role of XC at such a high-$T$ is negligible due to the total free energy of interacting systems being dominated by the noninteracting free-energy term, in agreement with estimations for the homogeneous electron gas. Our DFT predictions are compared with the radiative emissivity and opacity of the dense plasma model, with the real-space Green's function method, and with experimental measurements. Good agreement is found between all three theoretical methods, and in the bound-continuum region for Cr when compared with the experiment, while the discrepancy between direct DFT calculations and the experiment for Fe remains essentially the same as for plasma-physics models.

Recent remarkable developments in metamaterials and metadevices manipulating diffusive processes, such as thermal and electrical conduction, have enabled the control of multiple phenomena and the development of multifunctional devices. However, only either multiphysics operations or multiple functionalities are usually implemented on single metadevices. In this paper, we describe a method for the optimal design of metadevices that achieves both cloaking and focusing in the control of both heat flux and direct current by a single device, i.e., biphysical-bifunctional metadevices having four capabilities. Our design scheme performs well in terms of providing cloaking and focusing bifunctionality. Additionally, it assumes bulk natural materials without the use of metamaterials, which improves the manufacturability of the designed metadevices. Moreover, multidirectional metad evices are optimally designed for thermal-electrical conductions transmitted from multiple directions or from heat and voltage sources at various locations.

Biopolymer networks are common in biological systems from the cytoskeleton of individual cells to collagen in the extracellular matrix. The mechanics of these systems under applied strain can be explained in some cases by a phase transition from soft to rigid states. For collagen networks, it has been shown that this transition is critical in nature and it is predicted to exhibit diverging fluctuations near a critical strain that depends on the network's connectivity and structure. Whereas prior work focused mostly on shear deformation that is more accessible experimentally, here we study the mechanics of such networks under an applied bulk or isotropic extension. We confirm that the bulk modulus of subisostatic fiber networks exhibits similar critical behavior as a function of bulk strain. We find different nonmean-field exponents for bulk as opposed to shear. We also confirm a similar hyperscaling relation to what was previously found for shear.

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager–Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the $\ell$ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

Several recent inequalities bound the precision of a current, i.e., a counter of the net number of transitions in a system, by a thermodynamic measure of dissipation. However, while currents may be defined locally, dissipation is a global property. Inspired by the fact that, ever since Carnot, cycles are the unit elements of thermodynamic processes, we prove similar bounds tailored to cycle currents, counting net cycle completions, in terms of their conjugate affinities. We show that these inequalities are stricter than previous ones, even far from equilibrium, and that they allow us to tighten those on transition currents. We illustrate our results with a simple model and discuss some technical and conceptual issues related to shifting attention from transition to cycle observables.

The dielectric response of noninteracting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double-well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double-well potential model does not follow the Langevin function and only in the linear regime are the standard results recovered. If a finite asymmetry is assumed, then the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and fifth-order responses. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, then we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similarly to the two-state model for high barriers. For small barriers no clear-cut timescale separation between the barrier crossing process and the intrawell relaxation exists and the model exhibits a number of timescales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intrawell transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intrawell transitions play only a role at the lowest temperatures.

It is shown that by an appropriate canonical transformation, Kepler dynamics can be put in the form which allows one to exhibit the structure of the symmetry transformations related to the superintegrability. They appear to fit nicely into a general scheme of nonlinear realizations. In new coordinates, the Kepler dynamics results from dimensional reduction of that describing low-energy mesons with spontaneously broken chiral symmetry.

Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge. When this probability is a constant, we obtain a random hypergraph in the same spirit as the Erdos-Renyi graph. This framework also allows us to introduce different ingredients such as the preferential attachment for hypergraphs, or spatial random hypergraphs. In particular, we show that for the Erdos-Renyi case there is a transition threshold scaling as $1/\sqrt{EN}$ where $N$ is the number of nodes and $E$ the number of hyperedges. We also discuss a random geometric hypergraph which displays a percolation transition for a threshold distance scaling as $r_c^{*}\sim 1/\sqrt{E}$. For these various models, we provide results for the most interesting measures, and also introduce new ones in the spatial case for characterizing the geometrical properties of hyperedges. These different models might serve as benchmarks useful for analyzing empirical data.