It is shown that a subluminal electromagnetic plasma wave, propagating in phase with a background subluminal gravitational wave in a dispersive medium, can undergo parametric amplification. For these phenomena to occur, the dispersive characteristics of the two waves must properly match. The response frequencies of the two waves (medium dependent) must lie within a definite and restrictive range. The combined dynamics is represented by a Whitaker-Hill equation, the quintessential model for parametric instabilities. The exponential growth of the electromagnetic wave is displayed at the resonance; the plasma wave grows at the expense of the background gravitational wave. Different physical scenarios, where the phenomenon can be possible, are discussed.

Using Monte Carlo simulations we study phase-ordering dynamics of a multispecies system modeled via the prototype $q$-state Potts model. In such a multispecies system, we identify a spin state or species as the winner if it has survived as the majority in the final state, otherwise, we mark them as loser. We disentangle the time $\left(t\right)$ dependence of the domain length of the winner from losers, rather than monitoring the average domain length obtained by treating all spin states or species alike. The kinetics of domain growth of the winner at a finite temperature in space dimension $d=2$ reveal that the expected Lifshitz-Cahn-Allen scaling law $\sim t^{1/2}$ can be realized with no early-time corrections, even for system sizes much smaller than what is traditionally used. Up to a certain period, all others species, i.e., the losers, also show a growth that, however, is dependent on the total number of species, and slower than the expected $\sim t^{1/2}$ growth. Afterwards, the domains of the losers start decaying with time, for which our numerical data appear to be consistent with a $\sim t^{-2}$ behavior. We also demonstrate that this approach of looking into the kinetics even provides new insights for the special case of phase ordering at zero temperature, both in $d=2$ and $d=3$.

The critical behavior of the Ising model on a fractal lattice, which has the Hausdorff dimension ${log}_{4}12\approx 1.792$, is investigated using a modified higher-order tensor renormalization group algorithm supplemented with automatic differentiation to compute relevant derivatives efficiently and accurately. The complete set of critical exponents characteristic of a second-order phase transition was obtained. Correlations near the critical temperature were analyzed through two impurity tensors inserted into the system, which allowed us to obtain the correlation lengths and calculate the critical exponent $\nu$. The critical exponent $\alpha$ was found to be negative, consistent with the observation that the specific heat does not diverge at the critical temperature. The extracted exponents satisfy the known relations given by various scaling assumptions within reasonable accuracy. Perhaps most interestingly, the hyperscaling relation, which contains the spatial dimension, is satisfied very well, assuming the Hausdorff dimension takes the place of the spatial dimension. Moreover, using automatic differentiation, we have extracted four critical exponents $(\alpha ,$ $\beta ,$ $\gamma , \mathrm{and} \delta )$ globally by differentiating the free energy. Surprisingly, the global exponents differ from those obtained locally by the technique of the impurity tensors; however, the scaling relations remain satisfied even in the case of the global exponents.

Useful dynamical processes often begin through barrier-crossing dynamical transitions; engineering system dynamics in order to make such transitions reliable is therefore an important task for biological or artificial microscopic machinery. Here, we first show by example that adding even a small amount of back-reaction to a control parameter, so that it responds to the system's evolution, can significantly increase the fraction of trajectories that cross a separatrix. We then explain how a post-adiabatic theorem due to Neishtadt can quantitatively describe this kind of enhancement without having to solve the equations of motion, allowing systematic understanding and design of a class of self-controlling dynamical systems.

We consider the spread of epidemic in a spatial metapopulation system consisting of weakly interacting patches. Each local patch is represented by a network with a certain node degree distribution and individuals can migrate between neighboring patches. Stochastic particle simulations of the SIR model show that after a short transient, the spatial spread of epidemic has a form of a propagating front. A theoretical analysis shows that the speed of front propagation depends on the effective diffusion coefficient and on the local proliferation rate similarly to fronts described by the Fisher-Kolmogorov equation. To determine the speed of front propagation, first, the early-time dynamics in a local patch is computed analytically by employing degree based approximation for the case of a constant disease duration. The resulting delay differential equation is solved for early times to obtain the local growth exponent. Next, the reaction diffusion equation is derived from the effective master equation and the effective diffusion coefficient and the overall proliferation rate are determined. Finally, the fourth order derivative in the reaction diffusion equation is taken into account to obtain the discrete correction to the front propagation speed. The analytical results are in a good agreement with the results of stochastic particle simulations.

We present an experimental study of the dynamics of a set of magnets within a fluid in which a remote torque applied by a vertical oscillating magnetic field transfers angular momentum to individual magnets. This system differs from previous experimental studies of granular gas where the energy is injected by vibrating the boundaries. Here, we do not observe any cluster formation, orientational correlation and equipartition of the energy. The magnets' linear velocity distributions are stretched exponentials, similar to three-dimensional boundary-forced dry granular gas systems, but the exponent does not depend on the number of magnets. The value of the exponent of the stretched exponential distributions is close to the value of 3/2 previously derived theoretically. Our results also show that the conversion rate of angular momentum into linear momentum during the collisions controls the dynamics of this homogenously forced granular gas. We report the differences among this homogeneously forced granular gas, ideal gas, and nonequilibrium boundary-forced dissipative granular gas.

The combined effects of compressive stress, applied pressure, and edge folding of a freestanding thin film have been theoretically investigated on the buckle morphologies of the structure. In the framework of the Föppl–von Kármán theory of thin plates, the different buckle profiles have been analytically determined, and two buckling regimes have been identified for the film: one regime where the transition from upward to downward buckling is continuous, and one that is discontinuous (snap-through). The critical pressures characterizing the different regimes have then been determined, and an hysteresis cycle has been identified through the study of buckling versus pressure. The case in which the thin film is deposited on a substrate has also been discussed.

The generation of spikes and bubbles, a typical characteristic of the nonlinear regime in the Rayleigh-Taylor instability, is found to occur as well during the linear regime in an elastic-plastic solid medium caused, however, by a very different mechanism. This singular feature originates in the differential loads at different locations of the interface, which makes that the transition from the elastic to the plastic regime takes place at different times, thus producing an asymmetric growth of peaks and valleys that rapidly evolves in exponentially growing spikes, while bubbles can also grow exponentially at a lower rate.

We report a systematic study of the dynamics of self-propelled particles (SPPs) over a one-dimensional periodic potential landscape $U_0\left(x\right)$, which is fabricated on a microgroove-patterned polydimethylsiloxane (PDMS) substrate. From the measured nonequilibrium probability density function $P(x;F_0)$ of the SPPs, we find that the escape dynamics of the slow rotating SPPs across the potential landscape can be described by an effective potential $U_{\text{eff}}(x;F_0)$, once the self-propulsion force $F_0$ is included into the potential under the fixed angle approximation. This work demonstrates that the parallel microgrooves provide a versatile platform for a quantitative understanding of the interplay among the self-propulsion force $F_0$, spatial confinement by $U_0\left(x\right)$, and thermal noise, as well as its effects on activity-assisted escape dynamics and transport of the SPPs.

In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to compressed sensing. By considering compressed sensing as a randomly correlated many-body problem, statistical mechanics methods can be used to analyze the problem. In this paper, the estimation accuracy of compressed sensing with the horseshoe prior is evaluated by the statistical mechanical methods of random systems. It is found that there exists a phase transition in signal recoverability in the plane of the number of observations and the number of nonzero signals, and that the recoverable phase is more extended than that using the well-known $l_1$ norm regularization.

The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree distribution in the high-connectivity limit. Depending on the distribution of the threshold noise that governs the microscopic dynamics, the model evolves to nonequilibrium stationary states. We obtain an exact dynamical equation for the distribution of local magnetizations, from which we find the critical line that separates the paramagnetic from the ferromagnetic phase. For random graphs with a negative binomial degree distribution, we demonstrate that the stationary critical behavior as well as the long-time critical dynamics of the first two moments of the local magnetizations depend on the distribution of the threshold noise. In particular, for an algebraic threshold noise, these critical properties are determined by the power-law tails of the distribution of thresholds. We further show that the relaxation time of the average magnetization inside each phase exhibits the standard mean-field critical scaling. The values of all critical exponents considered here are independent of the variance of the negative binomial degree distribution. Our work highlights the importance of certain details of the microscopic dynamics for the critical behavior of nonequilibrium spin systems.

The quantum reservoirs commonly considered in open-quantum systems theory are those modeled by quantum harmonic oscillators, which are called bosonic reservoirs. Recently, quantum reservoirs modeled by two-level systems, the so-called fermionic reservoirs, have received attention due to their features. Given that the components of these reservoirs have a finite number of energy levels, unlike bosonic reservoirs, some studies are being carried out to explore the advantages of using this type of reservoir, especially in the operation of heat machines. In this paper, we carry out a case study of a quantum refrigerator operating in the presence of bosonic or fermionic thermal reservoirs, and we show that fermionic baths have advantages over bosonic ones.

We revisit the scaling properties of growing spheres randomly seeded in $d=2,3$, and 4 dimensions using a mean-field approach. We model the insertion probability without assuming a priori a functional form for the radius distribution. The functional form of the insertion probability shows an unprecedented agreement with numerical simulations in $d=2,3$, and 4 dimensions. We infer from the insertion probability the scaling behavior of the random Apollonian packing and its fractal dimensions. The validity of our model is assessed with sets of 256 simulations each containing $20\times {10}^6$ spheres in two, three, and four dimensions.

We analyze a delay differential equation model for a swept semiconductor laser and demonstrate existence of various periodic solutions that are subharmonically locked to the sweep rate. These solutions provide optical frequency combs in spectral domain. We investigate the problem numerically and show that, due to the translational symmetry of the model, there exists a hysteresis loop formed by branches of steady states solutions, bridges of periodic solutions connecting stable and unstable steady state branches, and isolated branches of limit cycles. We discuss the role of bifurcation points and limit cycles embedded into the loop in the formation of the subharmonic dynamics.

Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted, and stored using far fewer measurements than done by conventional means employing the Nyquist sampling theorem. Since many naturally occurring signals are sparse (in some domain), compressed sensing has rapidly seen popularity in a number of applied physics and engineering applications, particularly in designing signal and image acquisition strategies, e.g., magnetic resonance imaging, quantum state tomography, scanning tunneling microscopy, and analog to digital conversion technologies. Contemporaneously, causal inference has become an important tool for the analysis and understanding of processes and their interactions in many disciplines of science, especially those dealing with complex systems. Direct causal analysis for compressively sensed data is required to avoid the task of reconstructing the compressed data. Also, for some sparse signals, such as for sparse temporal data, it may be difficult to discover causal relations directly using available data-driven or model-free causality estimation techniques. In this work, we provide a mathematical proof that structured compressed sensing matrices, specifically circulant and Toeplitz, preserve causal relationships in the compressed signal domain, as measured by Granger causality (GC). We then verify this theorem on a number of bivariate and multivariate coupled sparse signal simulations which are compressed using these matrices. We also demonstrate a real world application of network causal connectivity estimation from sparse neural spike train recordings from rat prefrontal cortex. In addition to demonstrating the effectiveness of structured matrices for GC estimation from sparse signals, we also show a computational time advantage of the proposed strategy for causal inference from compressed signals of both sparse and regular autoregressive processes as compared to standard GC estimation from original signals.

Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.

Molecular dynamics simulations are used to study the effects of different cations on the permeation of charged polymers through flat capillaries with heights below 2 nm. Interestingly, we found that, despite being monovalent, ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{K}}^{+}$ cations have different effects on polymer permeation, which consequently affects their transmission speed throughout those capillaries. We attribute this phenomenon to the interplay of the cations' hydration free energies and the hydrodynamic drag in front of the polymer when it enters the capillary. Different alkali cations exhibit different surface versus bulk preferences in small clusters of water under the influence of an external electric field. This paper presents a tool to control the speed of charged polymers in confined spaces using cations.

Density functional theory (DFT) calculations and x-ray diffraction techniques were employed to evaluate the value of the tilt angle in ferroelectric smectic $C^{*}$ and antiferroelectric smectic $C_A^{*}$ phases. Five homologues from the chiral series denoted as $3\mathrm{F}m\mathrm{HPhF}6(m=2,4,5,6,7)$, based on 4-(1-methylheptyloxycarbonyl) phenyl 4'-octyloxybiphenyl-4-carboxylate (MHPOBC), were studied. Two types of conformations for the nonchiral terminal chain (fully extended and $gauche$) and three types of deviation from the rodlike shape of the molecules (hockey stick, zigzag, and $\mathsf{C}$ shape) were computationally considered. The nonlinear shape of the molecules was accounted for by introducing a shape parameter $\delta \mathrm{\Theta }$. We observe that calculations of the tilt angle which consider the $\mathsf{C}$-shaped structures, in both the fully extended or $gauche$ conformations, lead to good agreement with the values of the tilt angle obtained from electro-optical measurements below the saturation temperature. The results allow us to conclude that such structures are adopted by molecules in the examined series of smectogens. Additionally, this study proves the presence of the standard orthogonal $\mathrm{Sm}{A}^{*}$ phase for the homologues with $m=6$, 7, and the de Vries $\mathrm{Sm}{A}^{*}$ phase for $m=5$.

Soft layered systems buckling to form surface patterns has been widely studied under quasistatic loading. Here, we study the dynamic formation of wrinkles in a stiff-film-on-viscoelastic-substrate system as a function of impact velocity. We observe a spatiotemporally varying range of wavelengths, which display impactor velocity dependence and exceed the range exhibited under quasistatic loading. Simulations suggest the importance of both inertial and viscoelastic effects. Film damage is also examined, and we find that it can tailor dynamic buckling behavior. We expect our work to have applications to soft elastoelectronic and optic systems and open routes for nanofabrication.

Introduced in the early days of random matrix theory, the autocovariances $\delta I_k^j=\mathrm{cov}(s_j,s_{j+k})$ of level spacings $\left\{s_j\right\}$ accommodate detailed information on the correlations between individual eigenlevels. It was first conjectured by Dyson that the autocovariances of distant eigenlevels in the unfolded spectra of infinite-dimensional random matrices should exhibit a power-law decay $\delta I_k^j\approx -1/\beta {\pi }^2{k}^2$, where $\beta$ is the symmetry index. In this Letter, we establish an exact link between the autocovariances of level spacings and their power spectrum, and show that, for $\beta =2$, the latter admits a representation in terms of a fifth Painlevé transcendent. This result is further exploited to determine an asymptotic expansion for autocovariances that reproduces the Dyson formula as well as provides the subleading corrections to it. High-precision numerical simulations lend independent support to our results.