Algorithms to determine transition probabilities in Monte Carlo simulations are tested using a system of classical particles with effective interactions which reproduce Bose-Einstein statistics. The system is appropriate for testing different Monte Carlo simulation methods in out-of-equilibrium situations since nonequivalent results are produced. We compare mobility numerical results obtained with transition probabilities derived from Glauber and Metropolis algorithms. Then, we compare these with a recent method, the interpolation algorithm, appropriate for nonequilibrium systems in homogeneous substrata and without phase transitions. The results of mobility obtained from the interpolation algorithm are qualitatively verified with molecular dynamics simulations for low concentrations.

In a disordered system, a quantity is self-averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases. Here, we consider a chaotic disordered many-body quantum system and search for a relationship between self-averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales. An exponential distribution, as found for the survival probability at long times, explains its lack of self-averaging, since the mean and the dispersion are equal. Gaussian distributions, however, are obtained for both self-averaging and non-self-averaging quantities. Our studies show also that one can make conclusions about the self-averaging behavior of one quantity based on the distribution of another related quantity. This strategy allows for semianalytical results, and thus circumvents the limitations of numerical scaling analysis, which are restricted to few system sizes.

We calculate the maximal Lyapunov exponent for a bulk system of 256 Lennard-Jones particles in constant energy molecular dynamics simulations deep into the supercritical state. We find that the maximal Lyapunov exponent undergoes a crossover and that this crossover coincides with the dynamical crossover at the Frenkel line from liquid physics. We explain this crossover in terms of two different contributions to dynamical instability: diffusion in the liquidlike state below the Frenkel line and collisions in the gaslike state above. These results provide insight into the phase-space dynamics far from the melting line and densities where rare-gas approximation are inapplicable.

We describe the dynamic of excitons through single inhomogeneous $\alpha$-helical proteins with off-diagonal and diagonal couplings. Inhomogeneities considered are either localized or periodic. Intensive numerical simulations carried show stable structures and allow us to single out important features of excitons dynamic. In the absence of inhomogeneities, the interplay between off-diagonal and diagonal couplings leads to two distinct types of solitary waves. Bright solitary waves correspond to an off-diagonal coupling constant lower than a critical diagonal coupling constant, while dark solitary waves are obtained in the opposite case. Inclusion of inhomogeneities profoundly affects the profiles, amplitudes, and energies transported by the waves. For relatively small strength of inhomogeneities, only the profiles of the waves significantly change, the other properties remaining almost unchanged. Large strength inhomogeneities sensitively twist the profiles and increase amplitudes and energies of the waves. Our study suggests that small strength inhomogeneities allow a coherent transport of energy and the biological functions remain unchanged, but large strengths of inhomogeneities affect the biological functioning of the $\alpha$-helical protein chains. Hence, large strengths of inhomogeneities may amplify the energy of the molecule and could be used to treat some diseases.

Two scalar fields characterizing respectively pseudo-Hölder exponents and local energy transfers are used to capture the topology and the dynamics of the velocity fields in areas of lesser regularity. The present analysis is conducted using velocity fields from two direct numerical simulations of the Navier-Stokes equations in a triply periodic domain. A typical irregular structure is obtained by averaging over the 213 most irregular events. Such structure is similar to a Burgers vortex, with nonaxisymmetric corrections. A possible explanation for such asymmetry is provided by a detailed time-resolved analysis of birth and death of the irregular structures, which shows that they are connected to vortex interactions, possibly vortex reconnection.

Active Brownian engines rectify energy from reservoirs composed of self-propelling nonequilibrium molecules into work. We consider a class of such engines based on an underdamped Brownian particle trapped in a power-law potential. The energy they transform has thermodynamic properties of heat only if the nonequilibrium reservoir can be assigned a suitable effective temperature consistent with the second law and thus yielding an upper bound on the engine efficiency. The effective temperature exists if the total force exerted on the particle by the bath is not correlated with the particle position. In general, this occurs if the noise autocorrelation function and the friction kernel are proportional as in the fluctuation-dissipation theorem. But even if the proportionality is broken, the effective temperature can be defined in restricted, fine-tuned, parameter regimes, as we demonstrate on a specific example with harmonic potential.

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links. Herein, we first compute the statistical length and the thermodynamic cost function for transitions in the probability space, highlighting contributions from total, environmental, and resetting (unidirectional) entropy production. Then we derive the thermodynamic bound on the speed limit to connect two distributions separated by a finite time, showing the effect of the presence of unidirectional transitions. Uncertainty relationships can be found for the temporal first and second moments of the average resetting entropy production. We derive simple expressions in the limit of slow unidirectional transition rates. Finally, we present a refinement of the thermodynamic bound by means of an optimization procedure. We numerically investigate these results on systems that stochastically reset with constant and periodic resetting rate.

The diffusion of space-time correlated continuous-time random walk moving in the velocity field, which includes the fluid flowing freely and the fluid flowing through porous media, is investigated in this paper. Results reveal that it presents anomalous diffusion merely caused by space-time correlation in the freely flowing fluid, and the bias from the velocity field only supplies a standard advection, which is verified by the corresponding generalized diffusion equation which includes a standard advection term. However, the diffusion in the fluid flowing through porous media, i.e., the mean squared displacement, can display a bifractional form of which one originates from space-time correlation and the other one originates from dispersive bias caused by sticking of the porous media. The fractional advection term emerging in the corresponding generalized diffusion equation confirms the results. Moreover, the coexistence of correlation and dispersive bias result in crossover phenomenon in-between the diffusive process at an intermediate timescale, but just as the definition of diffusion, the one owning the largest diffusion exponent always prevails at large timescales. However, since the two fractional diffusions originate from a different mechanism, even if it owns the smaller diffusion exponent, that one can dominate the diffusion if it fluctuates much stronger than the other one, which no longer obeys the previous conclusion.

We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.

Biased lattice random walks (BLRW) are used to model random motion with drift in a variety of empirical situations in engineering and natural systems such as phototaxis, chemotaxis, or gravitaxis. When motion is also affected by the presence of external borders resulting from natural barriers or experimental apparatuses, modelling biased random movement in confinement becomes necessary. To study these scenarios, confined BLRW models have been employed but so far only through computational techniques due to the lack of an analytic framework. Here, we lay the groundwork for such an analytical approach by deriving the Green's functions, or propagators, for the confined BLRW in arbitrary dimensions and arbitrary boundary conditions. By using these propagators we construct explicitly the time-dependent first-passage probability in one dimension for reflecting and periodic domains, while in higher dimensions we are able to find its generating function. The latter is used to find the mean first-passage passage time for a $d$-dimensional box, $d$-dimensional torus or a combination of both. We show the appearance of surprising characteristics such as the presence of saddles in the spatiotemporal dynamics of the propagator with reflecting boundaries, bimodal features in the first-passage probability in periodic domains and the minimization of the mean first-return time for a bias of intermediate strength in rectangular domains. Furthermore, we quantify how in a multitarget environment with the presence of a bias shorter mean first-passage times can be achieved by placing fewer targets close to boundaries in contrast to many targets away from them.

We study the quantum manifestations of homogeneous and inhomogeneous oscillation suppression states in coupled identical quantum oscillators. We consider quantum van der Pol oscillators coupled via weighted mean-field diffusive coupling and, using the formalism of open quantum systems, we show that, depending on the coupling and the density of mean-field, two types of quantum amplitude death occurs, namely, squeezed and nonsqueezed quantum amplitude death. Surprisingly, we find that the inhomogeneous oscillation suppression state (or the oscillation death state) does not occur in the quantum oscillators in the classical limit. However, in the deep quantum regime we discover an oscillation death-like state which is manifested in the phase space through the symmetry-breaking bifurcation of the Wigner function. Our results also hint toward the possibility of the transition from quantum amplitude death to oscillation death state through the “quantum” Turing-type bifurcation. We believe that the observation of quantum oscillation death state will deepen our knowledge of symmetry-breaking dynamics in the quantum domain.

Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, especially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erdős-Rényi (ER) random networks by means of two adjacency matrix representations, namely, (1) weighted non-Hermitian random matrices and (2) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model 1 and from Poisson to Gaussian unitary ensemble statistics for model 2. Eigenvector delocalization effects of directed networks are also discussed.

For prebiotic chemistry to succeed in producing a starting metastable, autocatalytic and reproducing system subject to evolutionary selection it must satisfy at least two apparently contradictory requirements: Because such systems are rare, a search among vast numbers of molecular combinations must take place naturally, requiring rapid rearrangement and breaking of covalent bonds. But once a relevant system is found, such rapid disruption and rearrangement would be very likely to destroy the system before much evolution could take place. In this paper we explore the possibility, using a model developed previously, that the search process could occur under different environmental conditions than the subsequent fixation and growth of a lifelike chemical system. We use the example of a rapid change in temperature to illustrate the effect and refer to the rapid change as a “quench”borrowing terminology from study of the physics and chemistry of glass formation. The model study shows that interrupting a high-temperature nonequilibrium state with a rapid quench to lower temperatures can substantially increase the probability of producing a chemical state with lifelike characteristics of nonequilibrium metastability, internal dynamics and exponential population growth in time. Previously published data on the length distributions of proteomes of prokaryotes may be consistent with such an idea and suggest a prebiotic high-temperature “search” phase near the boiling point of water. A rapid change in $p\mathrm{H}$ could have a similar effect. We discuss possible scenarios on early Earth which might have allowed frequent quenches of the sort considered here to have occurred. The models show a strong dependence of the effect on the number of chemical monomers available for bond formation.

Changes in membrane deformation and compressibility, induced by an external electric field, are investigated using coarse-grained martini force field simulations in a salt-free environment. We observe changes in the area of the membrane above a critical electric field. Below this value, the membrane compressibility modulus is found to decrease monotonically. For higher electric fields, the membrane projected area remains constant while the net interfacial area increases, with the corresponding compressibility moduli, show the opposite behavior. We find that the mechanical parameters, surface tension and bending modulus, of a freely floating membrane in the absence of explicit ions, are unaffected by the presence of the electric field. We believe these results have a bearing on our understanding of the electroformation of uncharged lipids in a salt-free environment.

In the textbook formulation of dry friction laws, static and dynamic friction (stick and slip) are qualitatively different and sharply separated phenomena. However, accurate measurements of stick-slip motion generally show that static friction is not truly static but characterized by a slow creep that, upon increasing tangential load, smoothly accelerates into bulk sliding. Microscopic, contact-mechanical, and phenomenological models have been previously developed to account for this behavior. In the present work, we show that it may instead be a systemic property of the measurement apparatus. Using a mechanical model that exhibits the characteristics of typical setups of measuring friction forces—which usually have very high transverse stiffness—and assuming a small but nonzero misalignment angle in the contact plane, we observe some fairly counterintuitive behavior: Under increasing longitudinal loading, the system almost immediately starts sliding perpendicularly to the pulling direction. Then the friction force vector begins to rotate in the plane, gradually approaching the pulling direction. When the angle between the two becomes small, bulk sliding sets in quickly. Although the system is sliding the entire time, macroscopic stick-slip behavior is reproduced very well, as is the accelerated creep during the “stick” phase. The misalignment angle is identified as a key parameter governing the stick-to-slip transition. Numerical results and theoretical considerations also reveal the presence of high-frequency transverse oscillations during the “static” phase, which are also transmitted into the longitudinal direction by nonlinear processes. Stability analysis is carried out and suggests dynamic probing methods for the approaching moment of bulk slip and the possibility of suppressing stick-slip instabilities by changing the misalignment angle and other system parameters.

The surface height in a shallow water accretion flow experiment is measured by means of Fourier transform profilometry and the fluctuations are characterized. The shallow water analog of the standing accretion shock instability (SWASI) appears with an azimuthal mode number of one in the presence of supercritical flow in the radial direction. During the occurrence of the SWASI, surface gravity waves preferentially propagate radially outward. This is consistent with the advective-acoustic cycle driving the shallow water analog of the standing accretion shock instability.

Nanoporous membranes provide an attractive approach for rapid filtering of nanoparticles at high-throughput volume, a goal useful to many fields of science and technology. Creating a device to readily separate different particles would require an extensive knowledge of particle-nanopore interactions and particle translocation dynamics. To this end, we use a multiscale model for the separation of nanoparticles by combining microscopic Brownian dynamics simulations to simulate the motion of spherical nanoparticles of various sizes and charges in a system with nanopores in an electrically biased membrane with a macroscopic filtration model accounting for bulk diffusion of nanoparticles and membrane surface pore density. We find that, in general, the separation of differently sized particles is easier to accomplish than of differently charged particles. The separation by charge can be better performed in systems with low pore density and/or smaller filtration chambers when electric nanopore-particle interactions are significant. The results from these simple cases can be used to gain insight in the more complex dynamics of separating, for example, globular proteins.

The kinetic analyses are quite important when it comes to understanding the particle behavior in any device as they start to deviate from a continuum nature. In the present study, kinetic simulations are performed using the particle-in-cell method to analyze the behavior of ions inside a cylindrical inertial electrostatic confinement fusion (IECF) device which is being developed as a tabletop neutron source. Here, the lighter ions, like deuterium, are accelerated by applying an electrostatic field between the chamber wall (anode) and the cathode (cylindrical gridded wire), placed at the center of the device. The plasma potential profiles obtained from the simulated results indicate the formation of multiple potential well structures inside the cathode grid depending upon the applied cathode potential (from $-1$ to $-5$ kV). The ion density at the core region of the device is found to be of the order of ${10}^{16}{\text{m}}^{-3}$, which closely resembles the experimental observations. Spatial variation of ion energy distribution function has been measured in order to observe the characteristics of ions at different cathode voltages. Finally, the simulated results are compared and found to be in good agreement with the experimental profiles. The present analysis can serve as a reference guide to optimize the technological parameters of the discharge process in IECF devices.

We propose a numerical technique to compute the equilibrium free energy of glasses that cannot be prepared quasireversibly. For such systems, standard techniques for estimating the free energy by extrapolation cannot be used. Instead, we use a procedure that samples the equilibrium partition function of the basins of attraction of the different inherent structures (local potential energy minima) of the system. If all relevant inherent structures could be adequately sampled in the (supercooled) liquid phase, our approach would be rigorous. In any finite simulation, we will miss the lower-energy inherent structures that become dominant at very low temperatures. We find that our free energy estimates for a Kob-Andersen glass are lower than those obtained by very slow cooling, even at temperatures down to one-third of the glass transition temperature. The current approach could be applied to compute the chemical potential of ultrastable glassy materials and should enable the estimation of their solubility.