If a fluid flow is driven by a weak Gaussian random force, the nonlinearity in the Navier-Stokes equations is negligibly small and the resulting velocity field obeys Gaussian statistics. Nonlinear effects become important as the driving becomes stronger and a transition occurs to turbulence with anomalous scaling of velocity increments and derivatives. This process has been described by Yakhot and Donzis [Phys. Rev. Lett. 119, 044501 (2017)] for homogeneous and isotropic turbulence. In more realistic flows driven by complex physical phenomena, such as instabilities and nonlocal forces, the initial state itself, and the transition to turbulence from that initial state, is much more complex. In this paper, we discuss the Reynolds-number dependence of moments of the kinetic energy dissipation rate of orders 2 and 3 obtained in the bulk of thermal convection in the Rayleigh-Bénard system. The data are obtained from three-dimensional spectral element direct numerical simulations in a cell with square cross section and aspect ratio 25 by Pandey et al. [Nat. Commun. 9, 2118 (2018)]. Different Reynolds numbers $1\lesssim {\mathrm{Re}}_{\ell }\lesssim 1000$ which are based on the thickness of the bulk region $\ell$ and the corresponding root-mean-square velocity are obtained by varying the Prandtl number $\mathrm{Pr}$ from 0.005 to 100 at a fixed Rayleigh number $\mathrm{Ra}={10}^5$. A few specific features of the data agree with the theory. The normalized moments of the kinetic energy dissipation rate ${\mathcal{E}}_n$ show a nonmonotonic dependence for small Reynolds numbers before obeying the algebraic scaling prediction for the turbulent state. Implications and reasons for this behavior are discussed.

We study the response of a rarefied gas in a slab to the motion of its boundaries in the tangential direction. Different from previous investigations, we consider boundaries displacements at nonsmall Mach ($\mathrm{Ma}$) numbers, coupling the dynamic and thermodynamic gas states, and deviating the system from its low-velocity isothermal condition. The problem is studied in the entire range of gas rarefaction rates, combining limited case ballistic- and continuum-flow analyses with direct simulation Monte Carlo computations. A nonlinear solution is derived in the ballistic regime for arbitrary velocity profiles and amplitudes. At near-continuum conditions, a slip-flow time-periodic solution is obtained for the case of oscillatory boundary motion, by expanding the flow field in an asymptotic Mach power series. The effect of replacing between isothermal and adiabatic surfaces is examined. The results indicate that, at all Knudsen ($\mathrm{Kn}$) numbers, the thermodynamic fields and normal velocity component are dominated by double-frequency (and descending higher-order even-frequency harmonic) time dependence, different from the fundamental-frequency time dependence dominating the tangential gas velocity. At continuum-limit conditions, this stems from the quadratic viscous dissipation term (negligible at low-Mach conditions), coupling the square of the tangential velocity gradient as a forcing term. System nonlinearity also results in an unsteady normal force acting on the boundaries, overcoming the tangential force with increasing $\mathrm{Ma}$. A marked difference from the latter is that the normal force either decreases with $\mathrm{Kn}$ or, at sufficiently small actuation frequencies, varies nonmonotonically with $\mathrm{Kn}$, reaching a maximum at some intermediate rarefaction conditions.

Radiative properties play a pivotal role in astrophysical plasma flows and are needed in radiation-hydrodynamic simulations in order to understand their behavior and also to interpret the plasma emission spectra, which are valuable diagnostic tools. Radiative properties of astrophysical plasma mixtures have been commonly calculated for low-density optically thin plasmas assuming coronal equilibrium and for high density assuming local thermodynamic equilibrium. However, there are wide ranges of conditions in which these thermodynamic regimes are not achieved and the plasma is in the nonlocal thermodynamic equilibrium regime. In the present work, a study of the plasma radiative properties of oxygen and iron and an astrophysical plasma mixture in nonlocal thermodynamic steady-state equilibrium is carried out. The ranges of electron temperatures and densities considered are 1–1000 eV and ${10}^{11}\text{–}{10}^{20}{\mathrm{cm}}^{-3}$, respectively. In the study, departures from coronal and local thermodynamic equilibria in terms of the density and temperature are also analyzed. Large differences in the radiative properties that can reach two orders of magnitude when the plasma is far from these thermodynamic regimes are obtained. These analyses are done assuming the plasma to be optically thin. A brief study of the influence of the plasma self-absorption in the radiative properties of oxygen and iron is made. For that purpose, the plasma is assumed with planar geometry and the study is performed in terms of the width of the plasma slab and electron temperature and density.

All possible nonisomorphic arrangements of 12 spheres kissing a central sphere (the Gregory-Newton problem) are obtained for the sticky-hard-sphere (SHS) model and subsequently projected by geometry optimization onto a set of structures derived from an attractive Lennard-Jones (LJ) type of potential. It is shown that all 737 derived SHS contact graphs corresponding to the 12 outer spheres are (edge-induced) subgraphs of the icosahedral graph. The most widely used LJ(6,12) potential has only one minimum structure corresponding to the ideal icosahedron where the 12 outer spheres do not touch each other. The point of symmetry breaking away from the icosahedral symmetry towards the SHS limit is obtained for general LJ($a,b$) potentials with exponents $a,b\in {\mathbb{R}}_{+}$. Only if the potential becomes very repulsive in the short range, determined by the LJ hard-sphere radius $\sigma$, are symmetry-broken solutions observed.

We show that the average optimal cost for the traveling salesman problem in two dimensions, which is the archetypal problem in combinatorial optimization, in the bipartite case, is simply related to the average optimal cost of the assignment problem with the same Euclidean, increasing, convex weights. In this way we extend a result already known in one dimension where exact solutions are available. The recently determined average optimal cost for the assignment when the cost function is the square of the distance between the points provides therefore an exact prediction $\overline{E_N}=\frac{1}{\pi }logN$ for large number of points $2N$. As a by-product of our analysis, also the loop covering problem has the same optimal average cost. We also explain why this result cannot be extended to higher dimensions. We numerically check the exact predictions.

We investigate the dynamics of overdamped $D$-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, $V\left(r\right)\sim r^{-\lambda }(\lambda /D>1)$. We show that such systems obey a nonlinear diffusion equation, and that their stationary state extremizes a $q$-generalized nonadditive entropy. Here we focus on the dynamical evolution of these systems. Our first-principle $D=1,2$ many-body numerical simulations (based on Newton's law) confirm the predictions obtained from the time-dependent solution of the nonlinear diffusion equation and show that the one-particle space distribution $P(x,t)$ appears to follow a compact-support $q$-Gaussian form, with $q=1-\lambda /D$. We also calculate the velocity distributions $P(v_x,t)$, and, interestingly enough, they follow the same $q$-Gaussian form (apparently precisely for $D=1$, and nearly so for $D=2$). The satisfactory match between the continuum description and the molecular dynamics simulations in a more general, time-dependent framework neatly confirms the idea that the present dissipative systems indeed represent suitable applications of the $q$-generalized thermostatistical theory.

The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behavior. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a nontrivial eigenfunction distribution is obtained in a closed form.

A model is proposed that describes the diffusion of molecules in a disordered medium with binding sites (traps) and obstacles (barriers). The equations of the model are obtained using the subordination method. As the parent process, random walks on a disordered lattice are taken, described by the random barrier model. As the leading process, the renewal process that corresponds to the multiple-trapping model is used. Theoretical expressions are derived for the curves obtained in the experiments using fluorescence microscopy (fluorescence recovery after photobleaching, fluorescence correlation spectroscopy, and single-particle tracking). Generalizations of the model are proposed to consider the correlations in the mutual arrangement of the traps and obstacles. This model can be used to determine parameters characterizing the diffusion and binding properties of molecules in crowded environments.

Information dynamics is an emerging description of information processing in complex systems that describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper we make a formal analogy between information dynamics and stochastic thermodynamics that describes the thermal behavior of small irreversible systems. As stochastic dynamics is increasingly being utilized to quantify the thermodynamics associated with the processing of information we suggest such an analogy is instructive, highlighting that existing thermodynamic quantities can be described solely in terms of extant information theoretic measures related to information processing. In this contribution we construct irreversibility measures in terms of these quantities and relate them to the physical entropy productions that characterize the behavior of single and composite systems in stochastic thermodynamics illustrating them with simple examples. Moreover, we can apply such a formalism to systems that do not have a bipartite structure. In particular we demonstrate that, given suitable nonbipartite processes, the heat flow in a subsystem can still be identified, and one requires the present formalism to recover generalizations of the second law. In these systems residual irreversibility is associated with neither subsystem and this must be included in the generalized second laws. This opens up the possibility of describing all physical systems in terms of computation allowing us to propose a framework for discussing the reversibility of systems traditionally out of scope of stochastic thermodynamics.

In the present paper we study the connection between local stability and energetic properties in low-dissipation heat engines operating in the maximum-power and maximum-compromise ($\mathrm{\Omega }$) regimes. We consider two different feedback regulatory pathways: (1) one in which restitutive forces linearly depend on the deviations from the stationary values of the heat exchanges with the hot and cold reservoirs and (2) another where restitutive forces depend on the deviations from the stationary values of the power output and the heat outflux into the cold reservoir. The first dynamics leads to an isolated stable point while in the second one the system is metastable. Further analysis of random perturbations from the steady state gives valuable information about the dynamic behavior of thermodynamic properties like entropy, power, and efficiency in both operation regimes.

In Escherichia coli bacterium, the molecular compounds involved in protein synthesis, messenger RNAs (mRNAs) and ribosomes, show marked intracellular localization patterns. Yet a quantitative understanding of the physical principles which would allow one to control protein synthesis by designing, bioengineering, and optimizing these localization patterns is still lacking. In this study, we consider a scenario where a synthetic modification of mRNA reaction-diffusion properties allows for controlling the localization and stoichiometry of mRNAs and polysomes—complexes of multiple ribosomes bound to mRNAs. Our analysis demonstrates that protein synthesis can be controlled, e.g., optimally enhanced or inhibited, by leveraging mRNA spatial localization and stoichiometry only, without resorting to alterations of mRNA expression levels. We identify the physical mechanisms that control the protein-synthesis rate, highlighting the importance of colocalization between mRNAs and freely diffusing ribosomes, and the interplay between polysome stoichiometry and excluded-volume effects due to the DNA nucleoid. The genome-wide, quantitative predictions of our work may allow for a direct verification and implementation in cell-biology experiments, where localization patterns and protein-synthesis rates may be monitored by fluorescence microscopy in single cells and populations.

We numerically examine solutal convection in porous media, driven by the dissolution of carbon dioxide (${\mathrm{CO}}_2$) into water—an effective mechanism for ${\mathrm{CO}}_2$ storage in saline aquifers. Dissolution is associated with slow diffusion of free-phase ${\mathrm{CO}}_2$ into the underlying aqueous phase followed by density-driven convective mixing of ${\mathrm{CO}}_2$ throughout the water-saturated layer. We study the fluid dynamics of ${\mathrm{CO}}_2$ convection in the single aqueous-phase region. A comparison is made between two different boundary conditions in the top of the formation: (i) a constant, maximum aqueous-phase concentration of ${\mathrm{CO}}_2$, and (ii) a constant, low injection-rate of ${\mathrm{CO}}_2$, such that all ${\mathrm{CO}}_2$ dissolves instantly and the system remains in single phase. The latter model is found to involve a nonlinear evolution of ${\mathrm{CO}}_2$ composition and associated aqueous-phase density, which depend on the formation permeability. We model the full nonlinear phase behavior of water-${\mathrm{CO}}_2$ mixtures in a confined domain, consider dissolution and fluid compressibility, and relax the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characteristics of spreading, mixing, and a dissolution flux in two- and three-dimensional media for both boundary conditions. We also revisit the scaling behavior of Sherwood number (Sh) with Rayleigh number (Ra), which has been under debate for porous-media convection. Our measurements from the solutal convection in the range $1500\lesssim \mathrm{Ra}\lesssim 135000$ show that the classical linear scaling Sh $\sim$ Ra is attained asymptotically for the constant-concentration case. Similarly, linear scaling is recovered for the constant-flux model problem. The results provide a new perspective into how boundary conditions may affect the predictive powers of numerical models, e.g., for both the short-term and long-term dynamics of convective mixing rate and dissolution flux in porous media at a wide range of Rayleigh numbers.

We develop a model for the microstructure and the stress, in dense suspensions of non-Brownian, perfectly smooth spheres at vanishing particle Reynolds number. These quantities are defined in terms of the second-order moment $\mathit{a}$ of the distribution function of the orientation unit vector between hydrodynamically interacting particles. We show, from first principles, that the evolution equation of $\mathit{a}$ contains a source term that accounts for the association and the dissociation of interacting particle pairs. This term provides a microscopic explanation for typical non-Newtonian behavior, observed in experiments in the literature, including normal stress differences in steady shear flow, as well as time-dependent stress after abruptly reversed shear flow and during oscillating shear flow.

Many-body dissipative particle dynamics (MDPD) is a mesoscale method capable of reproducing liquid-vapor coexistence in a single simulation. Despite having been introduced more than a decade ago, this method remains broadly unexplored, and as a result, relatively unused for modeling of industrially important soft matter systems. In this work, we systematically investigate the structure and properties of an MDPD fluid. We show that, besides the liquid phase, the MDPD potential can also yield a gas phase and a thermodynamically stable solid phase with a bcc lattice, but lacking a proper stress-strain relation. For the liquid phase, we determine the dependence of density and surface tension on the interaction parameters, and devise a top-down parametrization protocol for real liquids.

The study of Mayer's cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE nonphysical behavior at condensed states of fluids. In particular, a general equation of state is derived for finite closed systems of interacting particles, where the pressure is expressed directly in terms of the density (or system volume) and temperature-volume-dependent reducible cluster integrals. Although its accuracy is now greatly affected by the limited character of the existing data on the reducible cluster integrals and, especially, the absence of any information on their density dependence, a number of simple approximations indicate the qualitative adequacy of this equation in various regimes of a fluid: from gaseous to liquid states (including the transition region).

We propose a simple construction of shortcuts to adiabaticity tracking instantaneous stationary states in classical spin systems without knowing tracked stationary states. In our construction, control fields of counterdiabatic driving are composed of state-dependent magnetic fields, which can be easily determined with an aid of numerical calculations. Easiness of our construction is a remarkable feature since it is usually a hard task to determine explicit expression of required counterdiabatic terms in many-body systems. We also argue that our method can be applied to solve combinatorial optimization problems by considering classical spin dynamics under a time-dependent Hamiltonian, which mimics the procedure of quantum annealing.

The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here we consider the specific example of diffusion-limited coalescence and annihilation reactions in one-dimensional space. In the static case, such reactions are among the few systems amenable to exact solution, which can be obtained by means of a well-known method of intervals. In the case of a uniformly growing domain, we show that a double transformation in time and space allows one to extend this method to compute the main quantities characterizing the spatial and temporal behavior. We show that a sufficiently fast domain growth brings about drastic changes in the behavior. In this case, the reactions stop prematurely, as a result of which the survival probability of the reacting particles tends to a finite value at long times and their spatial distribution freezes before reaching the fully self-ordered state. We obtain exact results for the survival probability and for key properties characterizing the degree of self-ordering induced by the chemical reactions, i.e., the interparticle distribution function and the pair correlation function. These results are confirmed by numerical simulations.

Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto model of globally coupled identical oscillators with time-delayed positive and negative couplings to explore the effects of such couplings in collective phase synchronization. We analytically derive the exact boundaries for stable incoherent and coherent states in terms of the system parameters allowing us to examine the interplay of symmetric and asymmetric time delays and couplings in collective synchronization. Dependent on these parameters, regions of coherent, incoherent, and mixed (coherent, partially coherent, incoherent) states with hysteresis are possible. The region of stability for incoherent states decreases with increasing time delay in all cases and it overall gets reduced in the presence of a time delay in repulsive coupling. The time-delay effects for instability can become more significant at the delay values that are about half an oscillation period length, or its multiples in the case of positive time-delay couplings, and is about a full period or its multiples in case of negative delayed couplings. The mixed state region shows multistability among fully coherent, fully incoherent, and partially coherent (clustered) states. Partially coherent or clustered states occur near the instability-stability boundaries and can show quasiperiodic and nonstationary behaviors. We discuss the implications of the model and the results for natural systems, particularly neuronal network systems in the brain.

We consider the two-dimensional Gross-Pitaevskii equation describing a Bose-Einstein condensate in an isotropic harmonic trap. In the small coupling regime, this equation is accurately approximated over long times by the corresponding nonlinear resonant system whose structure is determined by the fully resonant spectrum of the linearized problem. We focus on two types of consistent truncations of this resonant system: first, to sets of modes of fixed angular momentum, and, second, to excited Landau levels. Each of these truncations admits a set of explicit analytic solutions with initial conditions parametrized by three complex numbers. Viewed in position space, the fixed angular-momentum solutions describe modulated oscillations of dark rings, while the excited Landau level solutions describe modulated precession of small arrays of vortices and antivortices. We place our findings in the context of similar results for other spatially confined nonlinear Hamiltonian systems in recent literature.

Stimulated by the growing interest in the applications of complex networks framework for time series analysis, we devise a network model in which each of $N$ nodes is associated with a random walk of length $L$. Connectivity between any two nodes is established when the Pearson correlation coefficient (PCC) between the corresponding time series is greater than or equal to a threshold $H$, resulting in similarity networks with interesting properties. In particular, these networks can have high average clustering coefficients and the “small world” property, and their degree distribution can vary from scale-free to quasiconstant depending on $H$. A giant component of size $N$ exists until a critical threshold $H_c$ is crossed, at which point relatively rare walks begin to detach from it and remain isolated. This model can be used as a first step for building a null hypothesis for networks constructed from time series.