Two-dimensional particle-in-cell simulations for laser plasma interaction with laser intensity of ${10}^{16}\mathrm{W}/{\mathrm{cm}}^2$, plasma density range of $0.01–0.28n_c$, and scale length of $230–330\mu \mathrm{m}$ showed significant pump depletion of the laser energy due to stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) in the low-density region ($n_e=0.01–0.2n_c$). The simulations identified hot electrons generated by SRS in the low-density region with moderate energy and by two-plasmon-decay near $n_e=0.25n_c$ with higher energy. The overall hot electron temperature (46 keV) and conversion efficiency (3%) were consistent with the experiment's measurements. The simulations also showed artificially reducing SBS would lead to stronger SRS and a softer hot-electron spectrum.

Complex plasma mixtures with three or more components are often encountered in astrophysics or in inertial confinement fusion (ICF) experiments. For mixtures containing species with large differences in atomic number Z, the modeling needs to consider at the same time the kinetic theory for low-Z elements combined with the theory of strongly coupled plasma for high-Z elements, as well as all the intermediate situations that can appear in multicomponent systems. For such cases, we study the pair distribution functions, self-diffusions, mutual diffusion, and viscosity for ternary mixtures at extreme conditions. These quantities can be produced from first principles using orbital free molecular dynamics at the computational expense of very intensive simulations to reach good statistics. Utilizing the first-principles results as reference data, we assess the merit of a global analytic model for transport coefficients, “pseudo-ions in jellium” (PIJ), based on an isoelectronic assumption (iso-${\mathrm{n}}_e$). With a multicomponent hypernetted-chain integral equation, we verify the quality of the iso-${\mathrm{n}}_e$ prescription for describing the static structure of the mixtures. This semianalytical modeling compares well with the simulation results and allows one to consider plasma mixtures not accessible to simulations. Applications are given for the mix of materials in ICF experiments. A reduction of a multicomponent mixture to an effective binary mixture is also established in the hydrodynamic limit and compared with PIJ estimations for ICF relevant mixtures.

In this paper we present a technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. To extract certain quantities of two-point functions, such as spectral densities, mass poles or multiparticle thresholds, it is necessary to perform an analytic continuation of the correlator in question. At one-loop level in Euclidean space, this results in the necessity to deform the integration contour of the loop integral in the complex plane of the square of the loop momentum, to avoid nonanalyticities in the integration plane. Using a toy model for which an exact solution is known, we train a reinforcement learning agent to perform the required contour deformations. Our study shows great promise for an agent to be deployed in iterative numerical approaches used to compute nonperturbative two-point functions, such as the quark propagator Dyson-Schwinger equation, or more generally, Fredholm equations of the second kind, in the complex domain.

Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, by canceling and restarting any cooperative-chain realization reaching the boundary with a smaller number of steps than the bulk cooperativity, we account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasing temperature within a finite temperature window. Comprehensive numerical simulations of the corresponding Langevin equation performed with unprecedented resolution allow us to construct a phase diagram for the occurrence of the nonmonotonic temperature dependence of the diffusion coefficient. We discuss the relation of the later effect with the phenomenon of giant diffusion.

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function $g_2\left(r\right)$ or its corresponding structure factor $S\left(k\right)$ is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density $\rho$ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including $d$-dimensional Gaussian structure factors, $d$-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the $d$-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including “hyposurficial” and “antihyperuniform” examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. Our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for $g_2\left(\mathbf{r}\right)$ and $S\left(\mathbf{k}\right)$ associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

Different attempts to describe financial markets, and stock prices in particular, with the tools of statistical mechanics can be found in the literature, although a general framework has not been achieved yet. In this paper we use the physics of many-particle systems and the typical concepts of soft matter to study two sets of US and European stocks, comprising the biggest and most stable companies in terms of stock price and trading. Upon correcting for the center-of-mass motion, the structure and dynamics of the systems are studied (in the European set, the structure is studied for the UK subset only). The pair distribution of the stocks, corrected to account for the nonuniform distribution of prices, is close to 1, indicating that there is no direct interaction between stocks, similar to an ideal gas of particles. The dynamics is studied with the mean-squared price displacement (MSPD); the price correlation function, equivalent to the intermediate scattering function; the price fluctuation distribution; and two parameters for collective motions. The MSPD grows linearly and the velocity autocorrelation function is zero, as for isolated Brownian particles. However, the intermediate scattering function follows a stretched exponential decay, the fluctuation distributions deviate from the Gaussian shape, and strong collective motions are identified. These results indicate that the dynamics is much more complex than an ideal gas of Brownian particles, and similar, to some extent, to that of undercooled systems. Finally, two physical systems are discussed to aid in the understanding of these results: a low density colloidal gel, and a dense system of ideal, infinitely thin stars. The former reproduces the dynamical properties of stocks, linear mean-squared displacement (MSD), non-Gaussian fluctuation distribution, and collective motions, but also has strong structural correlations, whereas the latter undergoes a glass transition with the structure of an ideal gas, but the MSD has the typical two-step growth of undercooled systems.

A cell can be described as a complex viscoelastic material with structural relaxations that is modulated by thermal and chemically nonequilibrium processes. Tissue morphology and function rely upon cells' physical responses to mechanical force. We measured the frequency-dependent mechanical relaxation response of adherent human airway smooth muscle cells under adenosine triphosphate (ATP) depletion and normal ATP conditions. The frequency dependence of the complex compliance $J^{*}$ and modulus $G^{*}$ was measured over the frequencies ${10}^{-1}<f<{10}^3$ Hz at selected temperatures between $4<T<54{}^{\circ }\mathrm{C}$. Our results show characteristic relaxation features which can be interpreted by the mode-coupling theory (MCT) of viscoelastic liquids. We analyze the shape of the spectra in terms of a so-called $A_4$ scenario with logarithmic scaling laws. Characteristic timescales ${\tau }_{\beta }$ and ${\tau }_{\alpha }$ appear with corresponding energy barriers $E_{\beta }\approx \left(10\text{–}20\right)k_{\mathrm{B}}T$ and $E_{\alpha }\approx \left(20\text{–}30\right)k_{\mathrm{B}}T$. We demonstrate that cells are close to a glass transition. We find that the cell becomes softer around physiological temperatures, where its surface structure is more liquid-like with a plateau modulus around $0.1\text{–}0.8$ kPa compared with the more solid-like interior cytoskeletal structures with a plateau modulus $1\text{–}15$ kPa. Corresponding values for the viscosity are ${10}^2\text{–}{10}^3$ Pa s for the surface structures closer to the membrane and ${10}^4\text{–}{10}^6$ Pa s for the core cytoskeletal structures.

The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work we develop such a theory for a class of deterministic individual-based models describing individual births and deaths, which captures the essential features of standard stochastic individual-based models and becomes identical to the latter under maximal competition. The key motivation is to derive the canonical equation of adaptive dynamics from this microscopic ecological model, which can be regarded as a paradigm to study evolution in a simple way and give it an intuitive geometric interpretation. Another goal is to study evolution and sympatric speciation under maximal competition. We show that these models, in the deterministic limit of adaptive dynamics, lead to the same equations that describe the unraveling of the mean evolutionary trajectory as those obtained from the standard stochastic models. We further study conditions under which these models lead to evolutionary branching and find them to be similar to those obtained from the standard stochastic models. We find that, although deterministic models result in a strong competition that leads to a speedup in the temporal dynamics of a population cloud in the phenotypic space as well as an increase in the rate of generation of biodiversity, they do not seem to result in an absolute increase in biodiversity as far as the total number of species is concerned. Hence, they essentially capture all the features of the standard stochastic model. Interestingly, the notion of a fitness function does not explicitly enter in our derivation of the canonical equation, thereby advocating a mechanistic view of evolution based on fundamental birth-death events where fitness is a derived quantity rather than a fundamental ingredient. We illustrate our work with the help of several examples and qualitatively compare the rate of unraveling of evolutionary trajectory and generation of biodiversity for the deterministic and standard individual-based models by showing the motion of population clouds in the trait space.

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition theories. In these systems glassy behavior arises as the density of the particles is increased. Thus, soft colloidal particles with varying degree of softness capture diverse glass-forming properties, observed normally in molecular glasses. Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions show that tuning the softness of the interaction potential, achievable by changing the monovalent salt concentration results in a continuous transition from fragile to strong behavior. Remarkably, this is found in a system where the well characterized interaction potential between the colloidal particles is isotropic. We also show that the predictions of the random first-order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, $\xi \sim {\left(\frac{{\varphi }_K}{\varphi }-1\right)}^{-\nu }$ with $\nu =\frac{2}{3}$ where ${\varphi }_K$, the analog of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity as the system is compressed. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular and polymer glasses. The large variations in the fragility are normally found only when the temperature dependence of the viscosity is examined for a large class of diverse glass-forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses.

We report experimental studies on the phase behavior of binary mixtures of 1″,7″-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB) and 4,4-diheptyloxyazoxybenzene, which exhibit, apart from the nematic ($N$) and twist-bend nematic ($N_{\mathrm{TB}}$) phases, the induced smectic-$A$ ($\mathrm{Sm}-A$) phase for weight fraction of CB7CB between 0.05 and 0.70. In planar nematic layers, the $N_{\mathrm{TB}}$ phase separates as droplets of tactoidlike planform; the chirality of droplets manifests in the optical dissimilarity between their opposite angular ends. Our main result is that, in the appropriate two phase region, $\mathrm{Sm}-A$ nuclei with positive dielectric anisotropy change over to disks immersed in the nematic above some electric field, their edges decorated by periodic bright spots, a result which was earlier reported in another binary system exhibiting the induced $\mathrm{Sm}-A$ phase [R. Pratibha and N. V. Madhusudana, Physica A 224, 9 (1996)]. We develop a simple theory for the threshold of this distortion, which is a periodic undulation of the edge of the disk, demonstrating that it arises from saddle-splay elasticity of $\mathrm{Sm}-A$, the low $\mathrm{Sm}-A–N$ interfacial tension unable to suppress the distortion. The observed increases in the number of bright spots with field, and with the radius of the disk at a given field, in both the experimental systems are also accounted for by the model. The distortion, which results in the most direct visualization of saddle splay in $\mathrm{Sm}-A$, is also exhibited by disks nucleating on surfaces treated for homeotropic anchoring.

We present direct measurements of electron temperature variations within an inertially confined deuterium-tritium plasma caused by localized mix of higher-Z materials into the central hot spot. The data are derived from newly developed differentially filtered penumbral imaging of the bremsstrahlung continuum emission. Our analysis reveals distinct localized emitting features in the stagnated hot-spot plasma, and we infer spatial variations in the electron temperature: the mixed region is $660\pm 130\mathrm{eV}$ colder than the surrounding hot-spot plasma at $3.26\pm 0.11\mathrm{keV}$. Our analysis of the energy flow shows that we measure approximately steady-state conditions where the radiative losses in the mix region are balanced by heat conduction from the surrounding hot deuterium-tritium plasma.

A tensor variant of molecular-statistical theory is developed, within the framework of which it is possible to describe the appearance of spontaneous magnetization of anisotropic ferromagnetic nanoparticles dispersed in a nematic liquid crystal. Along with the tensor order parameters characterizing the orientational ordering of the liquid crystal and dispersed anisometric particles, the vector order parameter determining the magnetization of the ensemble of particles is additionally taken into account. A comparison between the previously known phenomenological theories of ferronematics and the proposed molecular-statistical theory is made. Phase diagrams of the suspension are constructed and the mean-field theory parameters are calculated on the basis of experimental data available in the literature.

Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Einstein condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the $1\leftrightarrow 2$ interactions between the condensate and the excited atoms. The other two describe the $2\leftrightarrow 2$ and $1\leftrightarrow 3$ interactions between the excited atoms themselves.

The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency $\omega$ in structural glasses, $\mathcal{D}\left(\omega \right)$, was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, $\mathcal{D}\left(\omega \right)$ increases from zero frequency as ${\omega }^4$, independent of spatial dimension and of microscopic details. However, it has been shown [Lerner and Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)] that the preparation protocol employed to create glassy samples may affect the form of their resulting $\mathcal{D}\left(\omega \right)$: glassy samples rapidly quenched from high-temperature liquid states were shown to feature $\mathcal{D}\left(\omega \right)\sim {\omega }^{\beta }$ with $\beta <4$, presumably limiting the degree of universality of the ${\omega }^4$ law. Here we show that exponents $\beta <4$ are seen only in small glassy samples quenched from high-temperature liquid states—whose sizes are comparable to or smaller than the size of the disordered core of soft quasilocalized vibrations—while larger glassy samples made with the same protocol feature the universal ${\omega }^4$ law. Our results demonstrate that observations of $\beta <4$ in the nonphononic density of states stem from finite-size effects, and we thus conclude that the ${\omega }^4$ law should be featured by any sufficiently large glass quenched from a melt.

We explore the role of inertia in the properties of active Brownian particles (ABPs) immersed in an underdamped background in two dimensions using Langevin dynamics computer simulation. Similar to an equilibrium two-dimensional passive interacting particle system, the system of ABPs transits from a liquid phase to a solid phase with the change in the coupling parameter, which is the ratio of interaction potential energy and thermal energy of the background solvent. Important qualitative and quantitative differences are found in the liquid-solid phase transition with increasing strength of activity as compared to those found in the conventional overdamped background limit. In the underdamped background, inherent activity is found to lead to a temperature, called the active temperature and defined by average velocity fluctuations of the ABPs, that is different from the fixed background solvent temperature. A new scaling law for active temperature as a function of activity strength is found near the liquid-solid boundary. Active temperature, which behaves similar to the thermodynamic equilibrium temperature, is also found to depend upon the interaction strength between the active particles and the strength of the background dissipation. With an increase in background dissipation, the difference between active temperature and the background solvent temperature decreases and the difference is found to eventually vanish in the overdamped limit, demonstrating the correctness of the calculation.

The symmetric harmonic three-mass system with finite rest lengths, despite its apparent simplicity, displays a wide array of interesting dynamics for different energy values. At low energy the system shows regular behavior that produces a deformation-induced rotation with a constant averaged angular velocity. As the energy is increased this behavior makes way to a chaotic regime with rotational behavior statistically resembling Lévy walks and random walks. At high enough energies, where the rest lengths become negligible, the chaotic signature vanishes and the system returns to regularity, with a single dominant frequency. The transition to and from chaos, as well as the anomalous power-law statistics measured for the angular displacement of the harmonic three-mass system are largely governed by the structure of regular solutions of this mixed Hamiltonian system. Thus, a deeper understating of the system's irregular behavior requires mapping out its regular solutions. In this work we provide a comprehensive analysis of the system's regular regimes of motion, using perturbative methods to derive analytical expressions of the system as almost-integrable in its low- and high-energy extremes. The compatibility of this description with the full system is shown numerically. In the low-energy regime, the Birkhoff normal form method is utilized to circumvent the low-order 1:1 resonance of the system, and the conditions for Kolmogorov-Arnold-Moser theory are shown to hold. The integrable approximations provide the back-bone structure around which the behavior of the full nonlinear system is organized and provide a pathway to understanding the origin of the power-law statistics measured in the system.

The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of the reduced density matrix, explicit expressions for the time-dependence of entanglement entropies, including the von Neumann entropy, are given. An appropriate rescaling of time and the entropies by their saturation values leads a universal curve, independent of the interaction. The extension to the nonperturbative regime is performed using a recursively embedded perturbation theory to produce the full transition and the saturation values. The analytical results are found to be in good agreement with numerical results for random matrix computations and a dynamical system given by a pair of coupled kicked rotors.

In this paper the time evolution of a finite bipartite graph initially comprising two sorts of isolated vertices is considered. The graph is assumed to evolve by adding edges, one at a time. Each new edge connects either two linked components and forms a new component of a larger order (coalescence of graphs) or increases (by one) the number of edges in a given linked component (cycling). Any state of the graph is thus characterized by the set of occupation numbers (the numbers of linked components comprising a given numbers of vertexes of the both sorts and a given number of edges. Once the rate of appearance of an extra edge in the graph being known, the master equation governing the time evolution of the probability to find the random graph in a given state is reformulated in terms of the functional generating the probability to find the evolving graph in a given state. The exact solution of the evolution equation for the generating functional applies for analyzing the average population numbers of linked components. In the limit of large order of the graph the distribution factorizes into two multipliers, one of which is just the spectrum of linked components in the infinite bipartite graph, The second multiplier includes the dependence on the total size of the graph. Both these multipliers contain information on the emergence of the giant component that forms at a critical time.

We investigate the Brownian dynamics of a nanoparticle bound to a thermally undulating elastic membrane. The ligand-functionalized nanoparticle is assumed to interact monovalently with the receptor expressed on the membrane. In order to resolve the nanoparticle transient motion subject to the instantaneous membrane configuration in a consistent manner, we employ a set of coupled Langevin equations that simultaneously incorporate the hydrodynamic effects, ligand-receptor binding interaction, intramembrane elastic forces, and thermal fluctuations. We show that the presence of a deformable, elastic fluid membrane not only affects the dynamics of a bound nanoparticle but also alters the effective binding potential felt by the nanoparticle. In contrast to a nanoparticle bound to a flat surface, the oscillatory characteristics of the nanoparticle velocity autocorrelation function are suppressed and transition to an anticorrelated long-time tail. Moreover, the nanoparticle position fluctuation becomes more coherent with that of the membrane binding site, and the width of the distribution of the nanoparticle distance from the membrane decreases with increasing membrane bending rigidity. By introducing a locally harmonic, bistable potential as an effective potential for the ligand-receptor pair, the rate of nanoparticle transitioning between two bound states is facilitated by membrane undulations as a result of stronger positional variations associated with the nanoparticle.