Granular flows in rotating drums transition between two regimes characterized by straight and curved free surfaces. Here we predict this behavior using a depth-integrated theory applicable to general eroding flows. Closure is achieved by a local $\mu \left(I\right)$ rheology and an equation for kinetic energy. Spanning the transition, the theory yields relations for all flow properties in terms of a single dimensionless rotation rate. In accord with experiments, distinct scaling laws are obtained for slow and fast rates, dominated respectively by local energy dissipation and longitudinal energy transfer.

Non-Gaussian normal diffusion, i.e., the probability density function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical simulations that this phenomenon may manifest itself in energy diffusion along a lattice at a nonzero, finite temperature. The studied model is a one-dimensional disordered lattice with on-site potential. We find that the energy density fluctuations are spatially localized if the nonlinear interaction is suppressed, but may spread with a non-Gaussian PDF and a linear time-dependent MSD when the nonlinear interaction is turned on. Our analysis suggests that the mechanism lies in the delocalization properties of the localized modes.

The $H$ theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the $H$ theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time $\tau$ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any $\tau$. We find that the extracted work per engine cycle is maximum when $\tau$ approaches infinity, while the power is maximum when $\tau$ approaches zero.

We propose a setup based on two coupled quantum dots where thermodynamics of a measurement can be quantitatively characterized. The information obtained in the measurement can be utilized by performing feedback in a manner apparently breaking the second law of thermodynamics. In this way the setup can be operated as a Maxwell's demon, where both the measurement and feedback are performed separately by controlling an external parameter. This is analogous to the case of the original Szilard engine. Since the setup contains both the microscopic demon and the engine itself, the operation of the whole measurement-feedback cycle can be explained in detail at the level of single realizations. In addition, we derive integral fluctuation relations for both the bare and coarse-grained entropy productions in the setup.

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space ${\lambda }_1<\lambda <{\lambda }_2$, suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at ${\lambda }_2$. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at ${\lambda }_c=0$. Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.

We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series.

Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions $\varphi \approx 0.75$, a value that is similar to close packing of equal-sized spheres. A limitation of these analyses was the use of extended atom models, rather than the more physically accurate explicit hydrogen model. The validity of the explicit hydrogen model was proved in our previous studies by its ability to predict the side chain dihedral angle distributions observed in proteins. In contrast, the extended atom model is not able to recapitulate the side chain dihedral angle distributions, and gives rise to large atomic clashes at side chain dihedral angle combinations that are highly probable in protein crystal structures. Here, we employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high-resolution protein structures. We find that these protein cores have $\varphi \approx 0.56$, which is similar to results obtained from simulations of random packings of individual amino acids. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations to protein cores and interfaces of known structure.

We investigate a newly framed two-time property for the nonequilibrium evolution dynamics during the collapse of a homopolymer via Monte Carlo simulations of a model polymer. Our results show evidence of aging effects, as observed in the slow dynamics of structural and spin glasses, along with the presence of a dynamic scaling of the autocorrelation function $\sim x^{-{\lambda }_c}$ ($x$ being the ratio of the cluster sizes at two different times). We estimate the value of ${\lambda }_c$ unambiguously by applying a finite-size scaling analysis to the numerical data. The value thus obtained obeys a bound which we predict via general theoretical arguments. The results presented should be of general validity and may trigger direct experimental verification in single-polymer dynamics.

We analyze a near-second-order transition occurring in solutions of living polymers confined by two parallel surfaces in equilibrium with a reservoir solution. The molecular self-consistent field theory in the regime of weak adsorption or depletion is mapped to phenomenological Landau theory, where the order parameter is the average degree of polymerization or, equivalently, the normalized chain-end concentration. The distance between two surfaces at which the transition occurs scales as ${\ell }_c^2\left|c\right|$ where ${\ell }_c$ is the correlation length of the polymer solution in the reservoir and $c^{-1}$ is de Gennes adsorption length. In the second half of the paper we focus on experimentally observable features. The predicted transition can be detected experimentally by probing the living-polymer mediated disjoining potential between surfaces by means of, e.g., colloidal probe atomic force microscopy. To facilitate experimental investigations we derive simple explicit expressions for the disjoining potential for several regimes. By comparison with full numerical calculations it was verified that these are quite accurate.

The inverse Schulze-Hardy rule was recently proposed based on experimental observations. This rule describes an interesting situation of the aggregation of charged colloidal particles in the presence of the multivalent coions. Specifically, it can be shown that the critical coagulation concentration is inversely proportional to the coion valence. Here the derivation of the inverse Schulze-Hardy rule based on purely theoretical grounds is presented. This derivation complements the classical Schulze-Hardy rule, which describes the multivalent counterion systems.

The effect of kinetic helicity (velocity–vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters the Reynolds stress (mirror-symmetric tensor) expression in the form of a helicity gradient as the coupling coefficient for the mean vorticity and/or the angular velocity (axial vector), which suggests the possibility of mean-flow generation in the presence of inhomogeneous helicity. This inhomogeneous helicity effect, which was previously confirmed at the level of a turbulence- or closure-model simulation, is examined with the aid of direct numerical simulations of rotating turbulence with nonuniform helicity sustained by an external forcing. The numerical simulations show that the spatial distribution of the Reynolds stress is in agreement with the helicity-related term coupled with the angular velocity, and that a large-scale flow is generated in the direction of angular velocity. Such a large-scale flow is not induced in the case of homogeneous turbulent helicity. This result confirms the validity of the inhomogeneous helicity effect in large-scale flow generation and suggests that a vortex dynamo is possible even in incompressible turbulence where there is no baroclinicity effect.

Elastic fingering supplements the already interesting features of the traditional viscous fingering phenomena in Hele-Shaw cells with the consideration that the two-fluid separating boundary behaves like an elastic membrane. Sophisticated numerical simulations have shown that under maximum viscosity contrast the resulting patterned shapes can exhibit either finger tip-splitting or side-branching events. In this work, we employ a perturbative mode-coupling scheme to get important insights into the onset of these pattern formation processes. This is done at lowest nonlinear order and by considering the interplay of just three specific Fourier modes: a fundamental mode $n$ and its harmonics $2n$ and $3n$. Our approach further allows the construction of a morphology diagram for the system in a wide range of the parameter space without requiring expensive numerical simulations. The emerging interfacial patterns are conveniently described in terms of only two dimensionless controlling quantities: the rigidity fraction $C$ and a parameter $\mathrm{\Gamma }$ that measures the relative strength between elastic and viscous effects. Visualization of the rigidity field for the various pattern-forming structures supports the idea of an elastic weakening mechanism that facilitates finger growth in regions of reduced interfacial bending rigidity.

We study coupling of vibrational relaxation and chemical reactions in nonequilibrium viscous multitemperature flows. A general theoretical model is proposed on the basis of the Chapman-Enskog method modified for strongly nonequilibrium reacting flows; the model differs from models commonly used in computational fluid dynamics since it is able to capture additional cross-coupling terms arising in viscous flow due to compressibility and mutual influence of all nonequilibrium processes occurring in a mixture. The set of fluid dynamic equations is derived starting from the Boltzmann equation; the relaxation terms in these equations are described using the kinetic transport theory formalism. Reaction and relaxation rates depend on the distribution function and thus differ in the zero-order and first-order approximations of the Chapman-Enskog method. An algorithm for the calculation of multitemperature reaction and relaxation rates in both inviscid and viscous flows is proposed for the harmonic oscillator model. This algorithm is applied to estimate the mutual effect of vibrational relaxation and dissociation in binary mixtures of ${\mathrm{N}}_2$ and N, and ${\mathrm{O}}_2$ and O, under various nonequilibrium conditions. It is shown that modification of the Landau-Teller expression for the VT relaxation term works rather well in nitrogen, whereas it fails to predict correctly the relaxation rate in oxygen at high temperatures. In oxygen (in contrast to nitrogen), the first-order cross effects of dissociation and VT relaxation are found to be significant. A method for calculation of vibrational relaxation time based on the kinetic theory definition is suggested. Two-temperature dissociation rate coefficients are calculated in the zero- and first-order approximations and compared to other models.

We consider the separate spin evolution of electrons and positrons in electron-positron and electron-positron-ion plasmas. We consider the oblique propagating longitudinal waves in these systems. Working in a regime of high-density $n_0\sim {10}^{27}{\mathrm{cm}}^{-3}$ and high-magnetic-field $B_0={10}^{10}$ G, we report the presence of the spin-electron acoustic waves and their dispersion dependencies. In electron-positron plasmas, similarly to the electron-ion plasmas, we find one spin-electron acoustic wave (SEAW) at the propagation parallel or perpendicular to the external field and two spin-electron acoustic waves at the oblique propagation. At the parallel or perpendicular propagation of the longitudinal waves in electron-positron-ion plasmas, we find four branches: the Langmuir wave, the positron-acoustic wave, and a pair of waves having spin nature, they are the SEAW and the wave discovered in this paper, called the spin-electron-positron acoustic wave (SEPAW). At the oblique propagation we find eight longitudinal waves: the Langmuir wave, the Trivelpiece–-Gould wave, a pair of positron-acoustic waves, a pair of SEAWs, and a pair of SEPAWs. Thus, for the first time, we report the existence of the second positron-acoustic wave existing at the oblique propagation and the existence of SEPAWs.

We analyze hydrodynamic fluctuations of a hybrid simulation under shear flow. The hybrid simulation is based on the Navier-Stokes (NS) equations on one domain and dissipative particle dynamics (DPD) on the other. The two domains overlap, and there is an artificial boundary for each one within the overlapping region. To impose the artificial boundary of the NS solver, a simple spatial-temporal averaging is performed on the DPD simulation. In the artificial boundary of the particle simulation, four popular strategies of constraint dynamics are implemented, namely the Maxwell buffer [Hadjiconstantinou and Patera, Int. J. Mod. Phys. C 08, 967 (1997)], the relaxation dynamics [O'Connell and Thompson, Phys. Rev. E 52, R5792 (1995)], the least constraint dynamics [Nie et al., J. Fluid Mech. 500, 55 (2004); Werder et al., J. Comput. Phys. 205, 373 (2005)], and the flux imposition [Flekkøy et al., Europhys. Lett. 52, 271 (2000)], to achieve a target mean value given by the NS solver. Going beyond the mean flow field of the hybrid simulations, we investigate the hydrodynamic fluctuations in the DPD domain. Toward that end, we calculate the transversal autocorrelation functions of the fluctuating variables in $k$ space to evaluate the generation, transport, and dissipation of fluctuations in the presence of a hybrid interface. We quantify the unavoidable errors in the fluctuations, due to both the truncation of the domain and the constraint dynamics performed in the artificial boundary. Furthermore, we compare the four methods of constraint dynamics and demonstrate how to reduce the errors in fluctuations. The analysis and findings of this work are directly applicable to other hybrid simulations of fluid flow with thermal fluctuations.

This paper expands a recent proposal by the authors to rederive the Langevin equation for a test particle in a finite-size thermal bath using a perturbation approach that yields a cascade of Langevin-type equations. Such an approach produces a different viewpoint for the fluctuation-dissipation duality by expressing them on similar scales. General properties of energy sharing between the test particle and the bath are outlined, investigating the resonant and nonresonant conditions.