The frequency spectra of the entropy and kinetic energy along with the power spectrum of the thermal flux are computed from direct numerical simulations for turbulent Rayleigh-Bénard convection with uniform rotation about a vertical axis in low-Prandtl-number fluids $\left(\mathrm{Pr}<0.6\right)$. Simulations are done for convective Rossby numbers $\mathrm{Ro}\ge 0.2$. The temporal fluctuations of these global quantities show two scaling regimes: (i) ${\omega }^{-2}$ at higher frequencies for all values of $\text{Ro}$ and (ii) ${\omega }^{-{\gamma }_1}$ at intermediate frequencies with ${\gamma }_1\approx 4$ for $\mathrm{Ro}>1$, while $4<{\gamma }_1<6.6$ for $0.2\le \mathrm{Ro}<1$.

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or “classical” observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.

Network infrastructures are essential for the distribution of resources such as electricity and water. Typical strategies to assess their resilience focus on the impact of a sequence of random or targeted failures of network nodes or links. Here we consider a more realistic scenario, where elements fail based on their usage. We propose a dynamic model of transport based on the Bak–Tang–Wiesenfeld sandpile model where links fail after they have transported more than an amount $\mu$ (threshold) of the resource and we investigate it on the square lattice. As we deal with a new model, we provide insight on its fundamental behavior and dependence on parameters. We observe that, for low values of the threshold due to a positive feedback of link failure, an avalanche develops that leads to an abrupt collapse of the lattice. By contrast, for high thresholds the lattice breaks down in an uncorrelated fashion. We determine the critical threshold ${\mu }^{*}$ separating these two regimes and show how it depends on the toppling threshold of the nodes and the mass increment added stepwise to the system. We find that the time of major disconnection is well described with a linear dependence on $\mu$. Furthermore, we propose a lower bound for ${\mu }^{*}$ by measuring the strength of the dynamics leading to abrupt collapses.

We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically “typical” initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.

We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single heat bath becomes possible if the system also interacts with an information reservoir. We obtain an inequality, and the corresponding fluctuation theorem, generalizing the standard entropy production of stochastic thermodynamics. From this inequality we can derive an information processing entropy production, which gives the second law in the presence of information reservoirs. We also develop a systematic linear response theory for information processing machines. For a unicyclic machine powered by an information reservoir, the efficiency at maximum power can deviate from the standard value of $1/2$. For the case where energy is consumed to erase the tape, the efficiency at maximum erasure rate is found to be $1/2$.

Subdiffusion in a system in which mobile particles $A$ can chemically react with static particles $B$ according to the rule $A+B\to B$ is considered within a persistent random-walk model. This model, which assumes a correlation between successive steps of particles, provides hyperbolic Cattaneo normal diffusion or fractional subdiffusion equations. Starting with the difference equation, which describes a persistent random walk in a system with chemical reactions, using the generating function method and the continuous-time random-walk formalism, we will derive the Cattaneo-type subdiffusion differential equation with fractional time derivatives in which the chemical reactions mentioned above are taken into account. We will also find its solution over a long time limit. Based on the obtained results, we will find the Cattaneo-type subdiffusion-reaction equation in the case in which mobile particles of species $A$ and $B$ can chemically react according to a more complicated rule.

Small-angle neutron scattering (SANS) studies have been carried out to examine the evolution of interaction and structure in a nanoparticle (silica)–polymer (polyethylene glycol) system. The nanoparticle-polymer solution interestingly shows a reentrant phase behavior where the one-phase charged stabilized nanoparticles go through a two-phase system (nanoparticle aggregation) and back to one-phase as a function of polymer concentration. Such phase behavior arises because of the nonadsorption of polymer on nanoparticles and is governed by the interplay of polymer-induced attractive depletion with repulsive nanoparticle-nanoparticle electrostatic and polymer-polymer interactions in different polymer concentration regimes. At low polymer concentrations, the electrostatic repulsion dominates over the depletion attraction. However, the increase in polymer concentration enhances the depletion attraction to give rise to the nanoparticle aggregation in the two-phase system. Further, the polymer-polymer repulsion at high polymer concentrations is believed to be responsible for the reentrance to one-phase behavior. The SANS data in polymer contrast-matched conditions have been modeled by a two-Yukawa potential accounting for both repulsive and attractive parts of total interaction potential between nanoparticles. Both of these interactions (repulsive and attractive) are found to be long range. The magnitude and the range of the depletion interaction increase with the polymer concentration leading to nanoparticle clustering. At higher polymer concentrations, the increased polymer-polymer repulsion reduces the depletion interaction leading to reentrant phase behavior. The nanoparticle clusters in the two-phase system are characterized by the surface fractal with simple cubic packing of nanoparticles within the clusters. The effect of varying ionic strength and polymer size in tuning the interaction has also been examined.

Elastic constants in liquid crystals are known to be in the range of pico- and several-tens piconewton (pN). We report herein that a bend elastic constant, $K_{33}$, remarkably varies depending on a slight modification of the chemical structure in an analogous series of calamitic liquid crystals. In contrast to the record-high bend elastic constants (hundreds pN or sub-nN) reported previously in a compound with an azo linkage, analogous compounds with tolan and ester linkages show several-tens pN and pN, respectively. X-ray diffraction studies of these compounds reveal that smectic-like layer structures $\left(cybotacticclusters\right)$ are formed in the nematic phase of only the homologous compounds with an azo linkage, certifying the idea that the existence of cybotactic clusters strongly enhances $K_{33}$. Two theoretical considerations were made: (1) Based on molecular conformation calculation, flat molecules that have high torsional potential energy, such as the one with an azo linkage, easily pack to form cybotactic clusters. (2) Theoretical estimation was made of how much cluster volume ratio is necessary to give about 100-times-larger $K_{33}\mathrm{s}$.

Swimming microorganisms in biological complex fluids may be greatly influenced by heterogeneous media and microstructure with length scales comparable to the organisms. A fundamental effect of swimming in a heterogeneous rather than homogeneous medium is that variations in local environments lead to swimming velocity fluctuations. Here we examine long-range hydrodynamic contributions to these fluctuations using a Najafi-Golestanian swimmer near spherical and filamentous obstacles. We find that forces on microstructures determine changes in swimming speed. For macroscopically isotropic networks, we also show how the variance of the fluctuations in swimming speeds are related to density and orientational correlations in the medium.

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion system with cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both $u$ and $v$ is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface.

We compute the full order statistics of a one-dimensional gas of spinless fermions (or, equivalently, hard bosons) in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the $k\mathrm{th}$ smallest eigenvalue ${\lambda }_{\left(k\right)}$ of a large dimensional Gaussian random matrix. We find that this probability behaves for large $N$ as $\mathcal{P}[{\lambda }_{\left(k\right)}=x]\approx exp[-\beta N^2\psi (k/N,x)]$, where $\beta$ is the Dyson index of the ensemble. The rate function $\psi (c,x)$, computed explicitly as a function of $x$ in terms of the intensive label $c=k/N$, has a quadratic behavior modulated by a weak logarithmic singularity at its minimum. This is shown to be related to phase transitions in the associated Coulomb gas problem. The connection with statistics of extreme eigenvalues and order stastistics of random matrices is also discussed. We find that, as a function of $c$ and keeping the value of $x$ fixed, the rate function $\psi (c,x)$ describes the statistics of the shifted index number, generalizing known results on its typical fluctuations; as a function of $x$ and keeping the fraction $c=k/N$ fixed, the rate function $\psi (c,x)$ also describes the statistics of the $k\mathrm{th}$ eigenvalue in the bulk, generalizing as well the results on its typical fluctuations. Moreover, for $k=1$ (respectively, for $k=N$), the rate function captures both the fluctuations to the left and to the right of the typical value of ${\lambda }_{\left(1\right)}$ (respectively, of ${\lambda }_{\left(N\right)}$).

Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equilibrium by the contact at its boundaries with two different reservoirs, leading to a constant flow of magnetization from one bath to the other. The nonunitary dynamics of this system, which is modeled by a Lindblad master equation, is treated exactly for small sizes and numerically for larger ones. The functional dependence of the rectification coefficient on the model parameters (anisotropy, field amplitude, and out of equilibrium driving strength) is investigated in full detail. Close to the XX point and at small inhomogeneity and low driving, we have found an explicit expression for the rectification coefficient that is valid at all system sizes. In particular, it shows that the phenomenon of rectification persists even in the thermodynamic limit. Finally, we prove that in the case of the XX chain, there is no rectification.

We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the $1/\sqrt{t}$ correction to the average position of the rightmost particle of a branching random walk for large times $t\gg 1$, computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

Wishart ensembles of random matrix theory have been useful in modeling positive definite matrices encountered in classical and quantum chaotic systems. We consider nonzero means for the entries of the constituting matrix $\mathbb{A}$ which defines the correlated Wishart matrix as $\mathbb{W}={\mathbb{AA}}^{†}$, and refer to the ensemble of such Wishart matrices as the noncentral correlated Wishart ensemble (nc-CWE). We derive the Pastur self-consistent equation which describes the spectral density of nc-CWE at large matrix dimension.

We define geometric critical exponents for systems that undergo continuous second-order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two-dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.

We have performed an extensive analysis of a single-particle stochastic heat engine constructed by manipulating a Brownian particle in a time-dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems, we observe that the operational characteristics are model dependent. Our results clearly rule out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.

In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via plastic instabilities, and the geometric responses of the oligomers themselves to a mechanical load. We present a microscopic theory that explains the numerically observed phenomena, including an exact theory of the shear modulus and of the plastic instabilities, both local and system spanning. In addition we present a model to explain the geometric changes in the oligomeric chains under increasing strains.

We present a pressure-dependence study of the dynamics of lysozyme protein powder immersed in deuterated $\alpha ,\alpha$-trehalose environment via quasielastic neutron scattering (QENS). The goal is to assess the baroprotective benefits of trehalose on biomolecules by comparing the findings with those of a trehalose-free reference study. While the mean-square displacement of the trehalose-free protein (hydrated to $d_{{\mathrm{D}}_2\mathrm{O}}\simeq 40$ w%) as a whole, is reduced by increasing pressure, the actual observable relaxation dynamics in the picoseconds to nanoseconds time range remains largely unaffected by pressure—up to the maximum investigated pressure of 2.78(2) Kbar. Our observation is independent of whether or not the protein is mixed with the deuterated sugar. This suggests that the hydrated protein's conformational states at atmospheric pressure remain unaltered by hydrostatic pressures, below 2.78 Kbar. We also found the QENS response to be totally recoverable after ambient pressure conditions are restored. Small-angle neutron diffraction measurements confirm that the protein-protein correlation remains undisturbed. We observe, however, a clear narrowing of the QENS response as the temperature is decreased from 290 to 230 K in both cases, which we parametrize using the Kohlrausch-Williams-Watts stretched exponential model. Only the fraction of protons that are immobile on the accessible time window of the instrument, referred to as the elastic incoherent structure factor, is observably sensitive to pressure, increasing only marginally but systematically with increasing pressure.

Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model.

An energy-conserving lattice Boltzmann (LB) model based on the entropic theory of admissible higher-order lattice is presented in detail. The entropy supporting ‘zero-one-three” lattice is used to construct a model capable of reproducing the full Fourier-Navier-Stokes equations at low Mach numbers. The proposed direct approach of constructing thermal models overcomes the shortcomings of existing models and retains one of the most important advantages of the LB methods, the exact space discretization of the advection step, thus paving the way for direct numerical simulation of thermal flows. New thermal wall boundary condition capable of handling curved geometries immersed in a multispeed lattice is proposed by extending the Tamm-Mott-Smith boundary condition. Entropic realization of the current model ensures stability of the model also for subgrid simulations. Numerical validation and thermodynamic consistency is demonstrated with classical setups such as thermal Couette flow, Rayleigh-Bénard natural convection, acoustic waves, speed of sound measurements, and shock tube simulations.