The prepulse current is an effective way to optimize the load structure and improve the implosion quality of the $Z$-pinch plasma. Investigating the strong coupling between the preconditioned plasma and pulsed magnetic field is essential for the design and improvement of prepulse current. In this study, the mechanism of the prepulse current on the $Z$-pinch plasma was revealed by determining the two-dimensional magnetic field distribution of preconditioned and nonpreconditioned single-wire $Z$-pinch plasma with a high-sensitivity Faraday rotation diagnosis. When the wire was nonpreconditioned, the current path was consistent with the plasma boundary. When the wire was preconditioned, the distributions of current and mass density presented good imploding axial uniformity, and the imploding speed of the current shell was higher than that of the mass shell. In addition, the mechanism of the prepulse current suppressing the magneto-Rayleigh-Taylor instability was revealed, which formed a sharp density profile of the imploding plasma and slowed the shock wave driven by the magnetic pressure. This discovery is essential and instructive for the design of preconditioned wire-array $Z$-pinch experiments.

We introduce the group-equivariant autoencoder (GE autoencoder), a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use group theory to deduce which symmetries of the system remain intact in all phases, and then use this information to constrain the parameters of the GE autoencoder such that the encoder learns an order parameter invariant to these “never-broken” symmetries. This procedure produces a dramatic reduction in the number of free parameters such that the GE-autoencoder size is independent of the system size. We include symmetry regularization terms in the loss function of the GE autoencoder so that the learned order parameter is also equivariant to the remaining symmetries of the system. By examining the group representation by which the learned order parameter transforms, we are then able to extract information about the associated spontaneous symmetry breaking. We test the GE autoencoder on the 2D classical ferromagnetic and antiferromagnetic Ising models, finding that the GE autoencoder (1) accurately determines which symmetries have spontaneously broken at each temperature; (2) estimates the critical temperature in the thermodynamic limit with greater accuracy, robustness, and time efficiency than a symmetry-agnostic baseline autoencoder; and (3) detects the presence of an external symmetry-breaking magnetic field with greater sensitivity than the baseline method. Finally, we describe various key implementation details, including a quadratic-programming-based method for extracting the critical temperature estimate from trained autoencoders and calculations of the DNN initialization and learning rate settings required for fair model comparisons.

We introduce a formalism to study nonequilibrium steady-state probability currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identification of the subspaces in which the system undergoes local rotations. In turn, this allows prediction of the counterparts in the real, physical space of these abstract probability currents. The results are presented for the case of the Active Model B undergoing motility-induced phase separation, which is known to be out of equilibrium but whose steady-state currents have not yet been observed, as well as for the Kardar-Parisi-Zhang equation. We locate and measure these currents and show that they manifest in real space as propagating modes localized in regions with nonvanishing gradients of the fields.

In a three-state kinetic exchange opinion formation model, the effect of extreme switches was considered in a recent paper. In the present work, we study the same model with disorder. Here disorder implies that negative interactions may occur with a probability $p$. In the absence of extreme switches, the known critical point is at $p_c=1/4$ in the mean-field model. With a nonzero value of $q$ that denotes the probability of such switches, the critical point is found to occur at $p=\frac{1-q}{4}$ where the order parameter vanishes with a universal value of the exponent $\beta =1/2$. Stability analysis of initially ordered states near the phase boundary reveals the exponential growth (decay) of the order parameter in the ordered (disordered) phase with a timescale diverging with exponent 1. The fully ordered state also relaxes exponentially to its equilibrium value with a similar behavior of the associated timescale. Exactly at the critical points, the order parameter shows a power-law decay with time with exponent $1/2$. Although the critical behavior remains mean-field-like, the system behaves more like a two-state model as $q\to 1$. At $q=1$ the model behaves like a binary voter model with random flipping occurring with probability $p$.

Fast scrambling, quantified by the exponential initial growth of out-of-time-ordered correlators (OTOCs), is the ability to efficiently spread quantum correlations among the degrees of freedom of interacting systems and constitutes a characteristic signature of local unstable dynamics. As such, it may equally manifest both in systems displaying chaos or in integrable systems around criticality. Here we go beyond these extreme regimes with an exhaustive study of the interplay between local criticality and chaos right at the intricate phase-space region where the integrability-chaos transition first appears. We address systems with a well-defined classical (mean-field) limit, as coupled large spins and Bose-Hubbard chains, thus allowing for semiclassical analysis. Our aim is to investigate the dependence of the exponential growth of the OTOCs, defining the quantum Lyapunov exponent ${\lambda }_q$ on quantities derived from the classical system with mixed phase space, specifically the local stability exponent of a fixed point ${\lambda }_{\text{loc}}$ as well as the maximal Lyapunov exponent ${\lambda }_L$ of the chaotic region around it. By extensive numerical simulations covering a wide range of parameters we give support to a conjectured linear dependence $2{\lambda }_q=a{\lambda }_L+b{\lambda }_{\text{loc}}$, providing a simple route to characterize scrambling at the border between chaos and integrability.

In a Vlasov equation, the destabilization of a homogeneous stationary state is typically described by a continuous bifurcation characterized by strong resonances between the unstable mode and the continuous spectrum. However, when the reference stationary state has a flat top, it is known that resonances drastically weaken and the bifurcation becomes discontinuous. In this article we analyze one-dimensional spatially periodic Vlasov systems, using a combination of analytical tools and precise numerical simulations to demonstrate that this behavior is related to a codimension-two bifurcation, which we study in detail.

Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as “stochastic resonance” (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name “inverse stochastic resonance” (ISR). Recent research has demonstrated that the ISR effect, like its close relative “nonstandard SR” [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum. To understand the underlying mechanism of the ISR and NIAA phenomena, we study the probability distribution function of a one-dimensional system subjected to a bistable potential that has the property of symmetry, i.e., if we change the sign of one of its parameters, we can obtain both phenomena with the same properties in the depth of the wells and the width of their basins of attraction subjected to Gaussian white noise with variable intensity. Previous work has shown that one can theoretically determine the probability distribution function using the convex sum between the behavior at small and high noise intensities. To determine the probability distribution function more precisely, we resort to the “weighted ensemble Brownian dynamics simulation” model, which provides an accurate estimate of the probability distribution function for both low and high noise intensities and, most importantly, for the transition of both behaviors. In this way, on the one hand, we show that both phenomena emerge from a metastable system where, in the case of ISR, the global minimum of the system is in a state of lower activity, while in the case of NIAA, the global minimum is in a state of increased activity, the importance of which does not depend on the width of the basins of attraction. On the other hand, we see that quantifiers such as Fisher information, statistical complexity, and especially Shannon entropy fail to distinguish them, but they show the existence of the mentioned phenomena. Thus, noise management may well be a mechanism by which Purkinje cells find an efficient way to transmit information in the cerebral cortex.

A simple model for the friction experienced by the one-dimensional water chains that flow through subnanometer diameter carbon nanotubes is studied. The model is based on a lowest order perturbation theory treatment of the friction experienced by the water chains due to the excitation of phonon and electron excitations in both the nanotube and the water chain, as a result of the motion of the chain. On the basis of this model, we are able to demonstrate how the observed flow velocities of water chains through carbon nanotubes of the order of several centimeters per second can be accounted for. If the hydrogen bonds between the water molecules are broken (as would occur if there were an electric field oscillating with a frequency equal to the resonant frequency of the hydrogen bonds present), it is shown that the friction experienced by the water flowing in the tube can be much smaller.

We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated using the full system of matrix-valued integro-differential equations. We investigate several dynamical properties of supercooled liquids including scattering functions, frequency-dependent susceptibilities, and mean-square displacements. Close to the glass transition, we find quantitative agreement between the coherent scattering function predicted from theory and that evaluated from simulations, which enables us to make quantitative statements on caging and relaxation dynamics of the confined hard-sphere fluid.

For stochastic lattice models in spatially uniform nonequilibrium steady states, an effective thermodynamic temperature $T$ and chemical potential $\mu$ can be defined via coexistence with heat and particle reservoirs. We verify that the probability distribution $P_N$ for the number of particles in the driven lattice gas with nearest-neighbor exclusion in contact with a particle reservoir with dimensionless chemical potential ${\mu }^{*}$ possesses a large-deviation form in the thermodynamic limit. This implies that the thermodynamic properties determined in isolation (fixed particle number representation) and in contact with a particle reservoir (fixed dimensionless chemical potential representation) are equal. We refer to this as description equivalence. This finding motivates investigation of whether the effective intensive parameters so obtained depend on the nature of the exchange between system and reservoir. For example, a stochastic particle reservoir is usually taken to insert or remove a single particle in each exchange, but one may also consider a reservoir that inserts or removes a pair of particles in each event. In equilibrium, equivalence of pair and single-particle reservoirs is guaranteed by the canonical form of the probability distribution on configuration space. Remarkably, this equivalence is violated in nonequilibrium steady states, limiting the generality of steady-state thermodynamics based on intensive variables.

We study conditions leading to collapse on a nonequilibrium toy model introduced here for the interaction dynamics between a social and an ecological system based on the concept of essentiality of services and goods. One key difference from previous models is the separation between purely environmental collapse and that caused by an imbalance in the population consumption of essential goods. By studying different regimes defined by phenomenological parameters, we identify sustainable and unsustainable phases as well as the likelihood of collapse. The behavior of the stochastic version of the model is analyzed with a combination of analytical and computational techniques introduced here and shown to be consistent with key features of such processes in real life.

The cellular uptake of self-propelled nonspherical nanoparticles (NPs) or viruses by cell membrane is crucial in many biological processes, but its universal dynamics have yet to be elucidated. In this study, using the Onsager variational principle, we obtain a general wrapping equation for nonspherical self-propelled nanoparticles. Two analytical critical conditions are theoretically found, indicating a continuous full uptake for prolate particles and a snapthrough full uptake for oblate particles. They precisely capture the full uptake critical boundaries in the phase diagrams numerically constructed in terms of active force, aspect ratio, adhesion energy density, and membrane tension. It is found that enhancing activity (active force), reducing effective dynamic viscosity, increasing adhesion energy density, and decreasing membrane tension can significantly improve the wrapping efficiency of the self-propelled nonspherical nanoparticles. These results give a panoramic view of the uptake dynamics of active nonspherical nanoparticles, and may offer instructions for designing an effective active NP-based vehicle for controlled drug delivery.

Pressurized membranes are usually used for low cost structures (e.g., inflatable beds), impact protections (e.g., airbags), or sport balls. The last two examples deal with impacts on the human body. Underinflated protective membranes are not effective whereas overinflated objects can cause injury at impact. The coefficient of restitution represents the ability of a membrane to dissipate energy during an impact. Its dependence on membrane properties and inflation pressure is investigated on a model experiment using a spherical membrane. The coefficient of restitution increases with inflation pressure but decreases with impact speed. For a spherical membrane, it is shown that kinetic energy is lost by transfer to vibration modes. A physical modeling of a spherical membrane impact is built considering a quasistatic impact with small indentation. Finally, the dependency of the coefficient of restitution with mechanical parameters, pressurization, and impact characteristics is given.

We derive a thermodynamic uncertainty relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to previous results and also holds at finite time. We apply our findings to experimental and numerical data for a vibrofluidized granular medium, characterized by regimes of anomalous diffusion. In some cases our relation can distinguish between equilibrium and nonequilibrium behavior, a nontrivial inference task, particularly for Gaussian processes.

The proposed study is motivated by the scenario of two-way vehicular traffic. We consider a totally asymmetric simple exclusion process in the presence of a finite reservoir along with the particle attachment, detachment, and lane-switching phenomena. The various system properties in terms of phase diagrams, density profiles, phase transitions, finite size effect, and shock position are analyzed, considering the available number of particles in the system and different values of coupling rate, by employing the generalized mean-field theory and the obtained results are detected to be a good match with the Monte Carlo simulation outcomes. It is discovered that the finite resources significantly affect the phase diagram for different coupling rate values, which leads to nonmonotonic changes in the number of phases in the phase plane for comparatively minor lane-changing rates and produces various exciting features. We calculate the critical value of the total number of particles in the system at which the multiple phases in the phase diagram appear or disappear. The competition between the limited particles, bidirectional motion, Langmuir kinetics, and particle lane-shifting behavior yields unanticipated and unique mixed phases, including the double shock phase, multiple reentrance and bulk-induced phase transitions, and phase segregation of the single shock phase.

We consider a model system of persistent random walkers that can jam, pass through each other, or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we find that the stationary interparticle distribution functions are governed by an inhomogeneous fourth-order differential equation. Our main focus is on determining the boundary conditions that these distribution functions should satisfy. We find that these do not arise naturally from physical considerations, but they need to be carefully matched to functional forms that arise from the analysis of an underlying discrete process. The interparticle distribution functions, or their first derivatives, are generically found to be discontinuous at the boundaries.

DNA naturally exists in a solvent environment, comprising water and salt molecules such as sodium, potassium, magnesium, etc. Along with the sequence, the solvent conditions become a vital factor determining DNA structure and thus its conductance. Over the last two decades, researchers have measured DNA conductivity both in hydrated and almost dry (dehydrated) conditions. However, due to experimental limitations (the precise control of the environment), it is very difficult to analyze the conductance results in terms of individual contributions of the environment. Therefore, modeling studies can help us to gain a valuable understanding of various factors playing a role in charge transport phenomena. DNA naturally has negative charges located at the phosphate groups in the backbone, which provides both the connections between the base pairs and the structural support for the double helix. Positively charged ions such as the sodium ion (${\mathrm{Na}}^{+}$), one of the most commonly used counterions, balance the negative charges at the backbone. This modeling study investigates the role of counterions both with and without the solvent (water) environment in charge transport through double-stranded DNA. Our computational experiments show that in dry DNA, the presence of counterions affects electron transmission at the lowest unoccupied molecular orbital energies. However, in solution, the counterions have a negligible role in transmission. Using the polarizable continuum model calculations, we demonstrate that the transmission is significantly higher at both the highest occupied and lowest unoccupied molecular orbital energies in a water environment as opposed to in a dry one. Moreover, calculations also show that the energy levels of neighboring bases are more closely aligned to ease electron flow in the solution.

The mesogen 1,′′7′′-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB), doped with a small quantity of an amphiphilic compound, is examined in its biphasic state in which twist-bend nematic ($N_{\mathrm{TB}}$) drops are dispersed in the isotropic fluid. Various flexoelectric and electrokinetic responses of small drops in their escaped-radial-like (ER) geometry, and also of larger ones with parabolic focal conic defects, are discussed. A pair of confocal parabolas with their axes along the applied low-frequency electric field undergo periodic dimensional changes so as to contribute flexoelectrically to free-energy reduction. In an ER droplet, the same result is achieved by periodic relocations of the hedgehog core. Sine-wave fields of low frequency and high voltage excite patterned states near zero-voltage crossings and homeotropic alignment at peak voltages. ER drops also exhibit electrohydrodynamic effects; in relatively weak fields, they undergo translatory motion with a velocity that is a quadratic in the field strength; the drift, which occurs over a very wide frequency range, extending from dc to MHz region, is enabled by radial symmetry breaking that their off-centered geometry entails; and the drift direction reverses across a critical frequency. In high fields, vortical flows occurring within an ER $N_{\mathrm{TB}}$ drop become discernible. The hydrodynamic effects are discussed based on the Taylor-Melcher leaky dielectric model.

For recent applications, liquid crystal-carbon nanotube based nanocomposite systems have been proven to be highly attractive. In this paper, we give a thorough analysis of a nanocomposite system made of both functionalized and nonfunctionalized multiwalled carbon nanotubes that are disseminated in a 4′-octyl-4-cyano-biphenyl liquid crystal medium. Thermodynamic study reveals a decrease in the nanocomposites’ transition temperatures. In contrast to nonfunctionalized multiwalled carbon nanotube dispersed systems, the enthalpy of functionalized multiwalled carbon nanotube dispersed systems has increased. In comparison to the pure sample, the dispersed nanocomposites have a smaller optical band gap. A rise in the longitudinal component of permittivity and, consequently, the dielectric anisotropy of the dispersed nanocomposites has been observed by dielectric studies. When compared to the pure sample, the conductivity of both dispersed nanocomposite materials has increased by two orders of magnitude. For the system with dispersed functionalized multiwalled carbon nanotubes, the threshold voltage, splay elastic constant, and rotational viscosity all decreased. For the dispersed nanocomposite of nonfunctionalized multiwalled carbon nanotubes, the value of the threshold voltage is somewhat decreased but the rotational viscosity and splay elastic constant both are enhanced. These findings show the applicability of the liquid crystal nanocomposites for display and electro-optical systems with appropriate tuning of the parameters.