Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in nonequilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equations for internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equations and boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation.

We analyze numerically the Marangoni flow around an immiscible droplet submerged in a stably stratified mixture of ethanol and water. The linear stability analysis shows that the base flow undergoes a supercritical Hopf bifurcation that leads to oscillations. The theoretical prediction for the critical droplet radius is consistent with previous experimental results. Ethanol diffusion in water is critical in the flow stability for both low and high droplet viscosity. Direct numerical simulations of the nonlinear oscillatory flow show that the frequency of those oscillations approximately equals that of the critical eigenmode. The nonlinear convective term of the ethanol diffusive-convective transport equation fixes the amplitude of the droplet oscillations. The viscous dissipation associated with the Marangoni flow inside the droplet considerably reduces the oscillation.

We use a semi-Markov process method to calculate large deviations of counting statistics for three open quantum systems, including a resonant two-level system and resonant three-level systems in the $\mathrm{\Lambda }$ and $V$ configurations. In the first two systems, radical solutions to the scaled cumulant generating functions are obtained. Although this is impossible in the third system, since a general sixth-degree polynomial equation is present, we still obtain asymptotically large deviations of the complex system. Our results show that, in these open quantum systems, the large deviation rate functions at zero current are equal to two times the largest nonzero real parts of the eigenvalues of operator $-\mathrm{i}\widehat{H}$, where $\widehat{H}$ is a non-Hermitian Hamiltonian, while at a large current these functions possess a unified formula.

Self-renewing tissues require that a constant number of proliferating cells is maintained over time. This maintenance can be ensured at the single-cell level or the population level. Maintenance at the population level leads to fluctuations in the number of proliferating cells over time. Often, it is assumed that those fluctuations can be reduced by increasing the number of asymmetric divisions, i.e., divisions where only one of the daughter cells remains proliferative. Here, we study a model of cell proliferation that incorporates a stem-cell niche of fixed size, and explicitly model the cells inside and outside the niche. We find that in this model, fluctuations are minimized when the difference in growth rate between the niche and the rest of the tissue is maximized and all divisions are symmetric divisions, producing either two proliferating or two nonproliferating daughters. We show that this optimal state leaves visible signatures in clone size distributions and could thus be detected experimentally.

In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise nonoverlapping unstructured population of individuals mating at random. Our main finding is that the dynamics is gradient-like when the point mutations at the two loci are independent. This is in stark contrast to the case of one-locus–multi-allele where the existence gradient behavior is contingent on a specific relationship between the mutation rates. When the mutations are not independent in the two-locus–two-allele system, there is the possibility of nonconvergent outcomes, like asymptotically stable oscillations, through either the Hopf bifurcation or the Neimark-Sacker bifurcation depending on the strength of the weak selection. The results can be straightforwardly extended for multilocus–two-allele systems.

The article presents the results of the study of electrons, emitted by the plasma of a low-inductance vacuum spark. It was found that a 50-kA discharge with a 3.4-µs period of current oscillations produces electrons with the energy higher than 100 keV, which leave the discharge plasma in the direction perpendicular to the discharge axis. The electrons have an energy spectrum close to monoenergetic. They appear after the first quarter period of discharge current oscillations and are emitted during about 1 µs. So, the origin of the electrons has no relation to the process of plasma pinching. The time behavior of the electron energy was studied. It gradually diminishes from a value of about 100 keV just after the maximum of the discharge current down to about 10 kV after reversal of the current direction. This phenomenon points out the redistribution of the discharge current, resulting in the disappearance of the magnetic field on the line of sight perpendicular to the discharge axis.

The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes. This ordinal tool also serves to identify optimal operating conditions in the machine learning approach of reservoir computing. These results allow us to envision potential applications for the handling and characterization of large amounts of data, paving the way for addressing some of the most pressing issues facing the current big data paradigm.

We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover relationships between the thermodynamic potentials, and fill some lacunae in previous results on the singularities of these potentials at the critical point and behavior in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulas step by step throughout. Additionally, we comment on a quasiprobabilistic normalization of configuration weights, which was considered in some recent studies.

We calculate analytically the Rényi entropy for the zeta-urn model with a Gibbs measure definition of the microstate probabilities. This allows us to obtain the singularities in the Rényi entropy from those of the thermodynamic potential, which is directly related to the free-energy density of the model. We enumerate the various possible behaviors of the Rényi entropy and its singularities, which depend on both the value of the power law in the zeta urn and the order of the Rényi entropy under consideration.

The pseudofractal scale-free web (PSFW) is a well-known model for a scale-free network with small-world characteristics. Understanding the dynamic properties of this network can provide valuable insights into dynamic processes occurring in general scale-free and small-world networks. In this study we investigate search processes using discrete-time random walks on the PSFW to reveal the impact of the resetting position on optimizing search efficiency, as measured by the mean first-passage time (MFPT). At each step the walker has two options: with a probability of $1-\gamma$, it moves to one of the neighboring sites, and with a probability of $\gamma$, it resets to the predefined resetting position. We explore various choices for the resetting position, present rigorous results for the MFPT to a given node of the network, determine the optimal resetting probability ${\gamma }^{*}$ where the MFPT reaches its minimum, and evaluate the ratio of the minimum for MFPT to the MFPT without resetting for each case. Results show that, in large PSFWs, both the degree of the resetting position and the distance between the target and the resetting position significantly affect the search efficiency. A higher degree of the resetting position leads to a slower convergence of the walker to the target, while a greater distance between the target and the resetting position also results in a slower convergence. Additionally, we observe that resetting to a vertex randomly selected from the stationary distribution can significantly expedite the process of the walker reaching the target. The findings presented in this study shed light on optimizing stochastic search processes on large networks, offering valuable insights into improving search efficiency in real-world applications, where the target node's location is unknown.

The coagulation (or aggregation) equation was introduced by Smoluchowski in 1916 to describe the clumping together of colloidal particles through diffusion, but has been used in many different contexts as diverse as physical chemistry, chemical engineering, atmospheric physics, planetary science, and economics. The effectiveness of clumping is described by a kernel $K(x,y)$, which depends on the sizes of the colliding particles $x,y$. We consider kernels $K={\left(xy\right)}^{\gamma }$, but any homogeneous function can be treated using our methods. For sufficiently effective clumping $1\ge \gamma >1/2$, the coagulation equation produces an infinitely large cluster in finite time (a process known as the gel transition). Using a combination of analytical methods and numerics, we calculate the anomalous scaling dimensions of the main cluster growth. Apart from the solution branch which originates from the exactly solvable case $\gamma =1$, we find a branch of solutions near $\gamma =1/2$, which violates matching conditions for the limit of small cluster sizes, widely believed to hold on a universal basis.

We perform kinetic Monte Carlo simulations of film growth in simple cubic lattices with solid-on-solid conditions, Ehrlich-Schwoebel (ES) barriers at step edges, and a kinetic barrier related to the hidden off-plane diffusion at multilayer steps. Broad ranges of the diffusion-to-deposition ratio $R$, detachment probability per lateral neighbor, $\epsilon$, and monolayer step crossing probability $P=exp[-E_{ES}/\left(k_{B}T\right)]$ are studied. Without the ES barrier, four possible scaling regimes are shown as the coverage $\theta$ increases: nearly layer-by-layer growth with damped roughness oscillations; kinetic roughening in the Villain-Lai–Das Sarma (VLDS) universality class when the roughness is $W\sim 1$ (in lattice units); unstable roughening with mound nucleation and growth, where slopes of $logW\times log\theta$ plots reach values larger than 0.5; and asymptotic statistical growth with $W={\theta }^{1/2}$ solely due to the kinetic barrier at multilayer steps. If the ES barrier is present, the layer-by-layer growth crosses over directly to the unstable regime, with no transient VLDS scaling. However, in simulations up to $\theta ={10}^4$ (typical of films with a few micrometers), low temperatures (small $R, \epsilon$, or $P$) may suppress the two or three initial regimes, while high temperatures and $P\sim 1$ produce smooth surfaces at all thicknesses. These crossovers help to explain proposals of nonuniversal exponents in previous works. We define a smooth film thickness ${\theta }_c$ where $W=1$ and show that VLDS scaling at that point indicates negligible ES barriers, while rapidly increasing roughness indicates a small ES barrier ($E_{ES}\sim k_{B}T$). ${\theta }_c$ scales as $\sim exp(\text{const}\times P^{2/3})$ if the other parameters are kept fixed, which represents a high sensitivity on the ES barrier. The analysis of recent experimental data in the light of our results distinguishes cases where $E_{ES}/\left(k_{B}T\right)$ is negligible, $\sim 1$, or $\ll 1$.

Acoustic traps use forces exerted by sound waves to confine and transport small objects. The dynamics of an object moving in the force landscape of an acoustic trap can be significantly influenced by the inertia of the surrounding fluid medium. These inertial effects can be observed by setting a trapped object in oscillation and tracking it as it relaxes back to mechanical equilibrium in its trap. Large deviations from Stokesian dynamics during this process can be explained quantitatively by accounting for boundary-layer effects in the fluid. The measured oscillations of a perturbed particle then can be used not only to calibrate the trap but also to characterize the particle.

The contribution of the electron drift instability to anomalous electron transport is experimentally assessed in a Hall effect discharge. The transport is represented by an anomalous collision frequency, which is related through quasilinear theory to the energy and growth rate of the instability. The wave energy is measured directly with ion saturation probes, while estimates of the growth rate are employed based on both linearized theory and direct measurement. The latter measurement is performed with a bispectral analysis method. The wave-driven collision frequency is compared to measurements of the actual collision frequency inferred from a method based on laser-induced fluorescence. It is found that estimates for transport using linearized theory for the growth differ by over an order of magnitude from the actual anomalous collision frequency in the plasma. The wave-driven anomalous collision frequency with measured growth, however, is shown to agree with the electron collision frequency in magnitude and capture aspects of the trends in spatial variation. This result demonstrates experimentally that wave-driven effects ultimately can explain the observed cross-field transport in these devices. The implications of this finding are discussed in the context of the key lengthscales that drive the transport as well as the implications identifying reduced fidelity models that could be used to predict anomalous collision frequency.

Dawkins introduced a groundbreaking concept suggesting that humans, similar to other animals, operate as gene-propagating machines. Following in his footsteps, Blackmore posits that humans might distinguish themselves from other animals by also serving as specialized meme-replicating machines. Here we introduce a mathematical model that examines the impact of social conformity on the propagation of bad memes (memes with low intrinsic appeal). We state the meme equations, which give us the number of different kinds of memes living in the population and its total amount. We show that, unlike a virus, bad memes have a very low probability of initially spreading. However, as memes are produced in large numbers, some will eventually experience a stochastic rise and persist for extended periods, aided by social conformism within groups. We develop analytical approximations to calculate the mean time taken for memes to become extinct and the mean time spent in each population state. These approximations enable us to apply the meme equations to conduct a qualitative analysis.

We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs $2A\to \varnothing$, triplets $3A\to \varnothing$, and quadruplets $4A\to \varnothing$ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to $2A\to \varnothing$, while the mean-field power-law prediction just acquires a logarithmic correction for $3A\to \varnothing$ and is exact for $4A\to \varnothing$. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in $3A\to \varnothing$ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.

We investigate the effect of localization on the local charging of quantum batteries (QBs) modeled by disordered spin systems. Two distinct schemes based on the transverse-field random Ising model are considered, with Ising couplings defined on a Chimera graph and on a linear chain with up to next-to-nearest-neighbor interactions. By adopting a low-energy demanding charging process driven by local fields only, we obtain that the maximum extractable energy by unitary processes (ergotropy) is highly enhanced in the ergodic phase in comparison with the many-body localization (MBL) scenario. As we turn off the next-to-nearest-neighbor interactions in the Ising chain, we have the onset of the Anderson localization phase. We then show that the Anderson phase exhibits a hybrid behavior, interpolating between large and small ergotropy as the disorder strength is increased. We also consider the splitting of total ergotropy into its coherent and incoherent contributions. This incoherent part implies in a residual ergotropy that is fully robust against dephasing, which is a typical process leading to the self-discharging of the battery in a real setup. Our results are experimentally feasible in scalable systems, such as in superconducting integrated circuits.

A colony of the queenless ant species, Pristomyrmex punctatus, can broadly be seen as consisting of small-body sized worker ants and relatively larger body-sized cheater ants. Hence, in the presence of intercolony migration, a set of constituent colonies act as a metapopulation exclusively composed of cooperators and defectors. Such a setup facilitates an evolutionary game-theoretic replication-selection model of population dynamics of the ants in a metapopulation. Using the model, we analytically probe the effects of territoriality induced hostility. Such hostility in the ant metapopulation proves to be crucial in preventing the tragedy of the commons, specifically, the workforce, a social good formed by cooperation. This mechanism applies to any metapopulation—not necessarily the ants—composed of cooperators and defectors where interpopulation migration occurs asymmetrically, i.e., cooperators and defectors migrate at different rates. Furthermore, our model validates that there is evolutionary benefit behind the queenless ants' behavior of showing more hostility towards the immigrants from nearby colonies than those from the far-off ones. In order to calibrate our model's parameters, we have extensively used the data available on the queenless ant species, P. punctatus.

The study of the active forces acting on semiflexible filaments networks such as the cytoskeleton requires noninvasive tools able to explore the deformation of single filaments in their natural environment. We propose here a practical method based on the solution of the hydrodynamic beam equation in the presence of transverse forces. We found that the derivative of the local curvature presents discontinuities that match the location of the applied forces, in contrast to the smooth curvature function obtained for the case of compressing longitudinal forces. These patterns can be easily appreciated in a kymograph of the curvature, which also reflects the temporal behavior of the forces. We assessed the method performance with numerical simulations describing the deformation of single microtubules provoked by the action of intracellular active forces.