We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the “Jeffery orbits.” We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyze how the linear stability of the “log-rolling” orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general, both unsteady and nonlinear terms in the Navier-Stokes equations are important.

We explain how centrosymmetry, together with a dominant doublet of energy eigenstates in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalization of the chaos-assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behavior of characteristic statistical properties with the size of the network. We show that these analytical predictions compare well to numerical simulations, using Hamiltonians sampled from the Gaussian orthogonal ensemble.

By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the “entropy-gradient” type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.

Ehrenfest's urn model is modified by introducing nonlinear terms in the associated transition probabilities. It is shown that these modifications lead, in the continuous limit, to a Fokker-Planck equation characterized by two competing diffusion terms, namely, the usual linear one and a nonlinear diffusion term typical of anomalous diffusion. By considering a generalized $H$ theorem, the associated entropy is calculated, resulting in a sum of Boltzmann-Gibbs and Tsallis entropic forms. It is shown that the stationary state of the associated Fokker-Planck equation satisfies precisely the same equation obtained by extremization of the entropy. Moreover, the effects of the nonlinear contributions on the entropy production phenomenon are also analyzed.

We study chemotaxis of a single E. coli bacterium in a medium where the nutrient chemical is also undergoing diffusion and its concentration has the form of a Gaussian whose width increases with time. We measure the average first passage time of the bacterium at a region of high nutrient concentration. In the limit of very slow nutrient diffusion, the bacterium effectively experiences a Gaussian concentration profile with a fixed width. In this case we find that there exists an optimum width of the Gaussian when the average first passage time is minimum, i.e., the search process is most efficient. We verify the existence of the optimum width for the deterministic initial position of the bacterium and also for the stochastic initial position, drawn from uniform and steady state distributions. Our numerical simulation in a model of a non-Markovian random walker agrees well with our analytical calculations in a related coarse-grained model. We also present our simulation results for the case when the nutrient diffusion and bacterial motion occur over comparable time scales and the bacterium senses a time-varying concentration field.

Entry of virions into the host cells is either endocytotic or fusogenic. In both cases, it occurs via reversible formation of numerous relatively weak bonds resulting in wrapping of a virion by the host membrane with subsequent membrane rupture or scission. The corresponding kinetic models are customarily focused on the formation of bonds and do not pay attention to the energetics of the whole process, which is crucially dependent, especially in the case of endocytosis, on deformation of actin filaments forming the cytoskeleton of the host cell. The kinetic model of endocytosis, proposed by the author, takes this factor into account and shows that the whole process can be divided into a rapid initial transient stage and a long steady-state stage. The entry occurs during the latter stage and can be described as a first-order reaction. Depending on the details of the dependence of the grand canonical potential on the number of bonds, the entry can be limited either by the interplay of bond formation and membrane rupture (or scission) or by reaching a maximum of this potential.

Structural relaxations in humid silk fibers exposed to tensile stress have been reported to take place on a very wide range of time scales from a few milliseconds to several hours. The time-dependence of the measured tensile force following a quasi-instantaneously applied external strain on the fibers can be understood in terms of a fractional viscoelastic relaxation function introducing memory effects by which the mechanical state of a fiber depends on its tensile history. An analog fractional relaxation also gives rise to the subdiffusion observed on picosecond time scales, which governs the mobility of the amorphous polymer chains and adsorbed water on the molecular level. The reduction of the subdiffusive memory effect in stretched fibers compared to native fibers is consistent with the higher order of the polymers in the stretched state.

While correlated activity is observed ubiquitously in the brain, its role in neural coding has remained controversial. Recent experimental results have demonstrated that correlated but not single-neuron activity can encode the detailed time course of the instantaneous amplitude (i.e., envelope) of a stimulus. These have furthermore demonstrated that such coding required and was optimal for a nonzero level of neural variability. However, a theoretical understanding of these results is still lacking. Here we provide a comprehensive theoretical framework explaining these experimental findings. Specifically, we use linear response theory to derive an expression relating the correlation coefficient to the instantaneous stimulus amplitude, which takes into account key single-neuron properties such as firing rate and variability as quantified by the coefficient of variation. The theoretical prediction was in excellent agreement with numerical simulations of various integrate-and-fire type neuron models for various parameter values. Further, we demonstrate a form of stochastic resonance as optimal coding of stimulus variance by correlated activity occurs for a nonzero value of noise intensity. Thus, our results provide a theoretical explanation of the phenomenon by which correlated but not single-neuron activity can code for stimulus amplitude and how key single-neuron properties such as firing rate and variability influence such coding. Correlation coding by correlated but not single-neuron activity is thus predicted to be a ubiquitous feature of sensory processing for neurons responding to weak input.

Epidemic outbreaks of new pathogens, or known pathogens in new populations, cause a great deal of fear because they are hard to predict. For theoretical models of disease spreading, on the other hand, quantities characterizing the outbreak converge to deterministic functions of time. Our goal in this paper is to shed some light on this apparent discrepancy. We measure the diversity of (and, thus, the predictability of) outbreak sizes and extinction times as functions of time given different scenarios of the amount of information available. Under the assumption of perfect information—i.e., knowing the state of each individual with respect to the disease—the predictability decreases exponentially, or faster, with time. The decay is slowest for intermediate values of the per-contact transmission probability. With a weaker assumption on the information available, assuming that we know only the fraction of currently infectious, recovered, or susceptible individuals, the predictability also decreases exponentially most of the time. There are, however, some peculiar regions in this scenario where the predictability decreases. In other words, to predict its final size with a given accuracy, we would need increasingly more information about the outbreak.

In turbulent scalar mixing, starting from random initial conditions, the root-mean-square advection term rapidly drops as the flow and the scalar field organize. We show first analytically, for the simplified case of a blob in shear flow with a finite correlation time, how the advection term is reduced compared to a randomly aligned scalar structure. This picture is then generalized to turbulent mixing. These examples show that the rapid depletion of advection depends on the lifetime of turbulent structures, compared to the local straining time scale. A turbulence closure is used to show that the Lagrangian correlation time indeed determines the deviation from Gaussian behavior. In particular it is shown that in the inertial range the depletion mechanism is self-similar, since a constant ratio is observed between the advection spectrum and its Gaussian equivalent. Finally, direct numerical simulation shows that in the limit of an infinite correlation time of the turbulent eddies, corresponding to a frozen velocity field, the mean-square advection tends to a zero fraction of its Gaussian estimate.

By means of a simple theoretical model and numerical simulations, we demonstrate the presence of persistent energy currents in a lattice of classical nonlinear oscillators with uniform temperature and chemical potential. In analogy with the well-known Josephson effect, the currents are proportional to the sine of the phase differences between the oscillators. Our results elucidate general aspects of nonequilibrium thermodynamics and point towards a way to practically control transport phenomena in a large class of systems. We apply the model to describe the phase-controlled spin-wave current in a bilayer nanopillar.

We study the leaf-to-leaf distances on one-dimensionally ordered, full and complete $m$-ary tree graphs using a recursive approach. In our formulation, unlike in traditional graph theory approaches, leaves are ordered along a line emulating a one-dimensional lattice. We find explicit analytical formulas for the sum of all paths for arbitrary leaf separation $r$ as well as the average distances and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large $r$.

The second virial coefficient, $B_2$ is computed of linear rigid rods composed of $m$ equally spaced sites interacting with sites on other rods via the hard-sphere or Weeks-Chandler-Andersen (WCA) pair potentials. The dependence of $B_2$ on a wide range of separation distance between the sites $L$ and $m$ for both types of potential is computed. Molecular dynamics simulations were carried out of the thermodynamic, static, and percolation properties of the WCA rigid rods in the isotropic phase as a function of rod number density $\rho$. Simple scaling relationships are discovered between thermodynamic and other static properties as a function of $\rho$ and $m$, which extend well into the semidilute density range. The percolation threshold distance (PTD) between the centers of mass of the rods complies well with a mean-field random orientation approximation from low density well into the semidilute regime. The corresponding site-site PTD proved more problematic to represent by simple functions, but at high rod density, scales better with the number of sites density rather than the rod number density.

We study the reversible crossover between stable and bistable phases of an overdamped Brownian bead inside an optical piston. The interaction potentials are solved developing a method based on Kramers's theory that exploits the statistical properties of the stochastic motion of the bead. We evaluate precisely the energy balance of the crossover. We show that the deformation of the optical potentials induced by the compression of the piston is related to a production of heat balanced between potential energy changes and the total amount of work performed by the piston. This reveals how specific thermodynamic processes can be designed and controlled with a high level of precision by tailoring the optical landscapes of the piston.

Random geometric graphs (RGGs) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables model and apply the resulting equations to RGGs. For any RGG, defined through a rigid or a soft geometric rule, the method reduces to a nontrivial satisfaction problem: Given $N$ nodes, a domain $\mathcal{D}$, and a desired average connectivity $\langle k\rangle$, find, if any, the distribution of nodes having support in $\mathcal{D}$ and average connectivity $\langle k\rangle$. We find out that, in the thermodynamic limit, nodes are either uniformly distributed or highly condensed in a small region, the two regimes being separated by a first-order phase transition characterized by a $O\left(N\right)$ jump of $\langle k\rangle$. Other intermediate values of $\langle k\rangle$ correspond to very rare graph realizations. The phase transition is observed as a function of a parameter $a\in [0,1]$ that tunes the underlying geometry. In particular, $a=1$ indicates a rigid geometry where only close nodes are connected, while $a=0$ indicates a rigid antigeometry where only distant nodes are connected. Consistently, when $a=1/2$ there is no geometry and no phase transition. After discussing the numerical analysis, we provide a combinatorial argument to fully explain the mechanism inducing this phase transition and recognize it as an easy-hard-easy transition. Our result shows that, in general, ad hoc optimized networks can hardly be designed, unless to rely to specific heterogeneous constructions, not necessarily scale free.

The disordered packings of tetrahedra often show no obvious macroscopic orientational or positional order for a wide range of packing densities, and it has been found that the local order in particle clusters is the main order form of tetrahedron packings. Therefore, a cluster analysis is carried out to investigate the local structures and properties of tetrahedron packings in this work. We obtain a cluster distribution of differently sized clusters, and peaks are observed at two special clusters, i.e., dimer and wagon wheel. We then calculate the amounts of dimers and wagon wheels, which are observed to have linear or approximate linear correlations with packing density. Following our previous work, the amount of particles participating in dimers is used as an order metric to evaluate the order degree of the hierarchical packing structure of tetrahedra, and an order map is consequently depicted. Furthermore, a constraint analysis is performed to determine the isostatic or hyperstatic region in the order map. We employ a Monte Carlo algorithm to test jamming and then suggest a new maximally random jammed packing of hard tetrahedra from the order map with a packing density of 0.6337.

The random Lorentz gas (RLG) is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions $d=2\text{–}6$. Comparison of the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with $d$. In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan-model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.

Recently, rheological hysteresis has been studied systematically in a wide range of complex fluids combining global rheology and time-resolved velocimetry. In this paper we present an analysis of the roles of the three most fundamental mechanisms in simple-yield-stress fluids: structure dynamics, viscoelastic response, and spatial flow heterogeneities, i.e., time-dependent shear bands. Dynamical hysteresis simulations are done analogously to rheological ramp-up and -down experiments on a coupled model which incorporates viscoelasticity and time-dependent structure evolution. Based on experimental data, a coupling between hysteresis measured from the local velocity profiles and that measured from the global flow curve has been suggested. According to the present model, even if transient shear banding appears during the shear ramps, in typical narrow-gap devices, only a small part of the hysteretic response can be attributed to heterogeneous flow. This results in decoupling of the hysteresis measured from the local velocity profiles and the global flow curve, demonstrating that for an arbitrary time-dependent rheological response this proposed coupling can be very weak.

The solvation of hard spherocylindrical solutes is analyzed within the context of scaled-particle theory, which takes the view that the free energy of solvating an empty cavitylike solute is equal to the pressure-volume work required to inflate a solute from nothing to the desired size and shape within the solvent. Based on our analysis, an end cap approximation is proposed to predict the solvation free energy as a function of the spherocylinder length from knowledge regarding only the solvent density in contact with a spherical solute. The framework developed is applied to extend Reiss's classic implementation of scaled-particle theory and a previously developed revised scaled-particle theory to spherocylindrical solutes. To test the theoretical descriptions developed, molecular simulations of the solvation of infinitely long cylindrical solutes are performed. In hard-sphere solvents classic scaled-particle theory is shown to provide a reasonably accurate description of the solvent contact correlation and resulting solvation free energy per unit length of cylinders, while the revised scaled-particle theory fitted to measured values of the contact correlation provides a quantitative free energy. Applied to the Lennard-Jones solvent at a state-point along the liquid-vapor coexistence curve, however, classic scaled-particle theory fails to correctly capture the dependence of the contact correlation. Revised scaled-particle theory, on the other hand, provides a quantitative description of cylinder solvation in the Lennard-Jones solvent with a fitted interfacial free energy in good agreement with that determined for purely spherical solutes. The breakdown of classical scaled-particle theory does not result from the failure of the end cap approximation, however, but is indicative of neglected higher-order curvature dependences on the solvation free energy.

Direct observations of the surface and shape of model nanocolloidal gels associated with measurements of the spatial distribution of water content during drying show that air starts to significantly penetrate the sample when the material stops shrinking. We show that whether the material fractures or not during desiccation, as air penetrates the porous body, the water saturation decreases but remains almost homogeneous throughout the sample. This air invasion is at the origin of another type of fracture due to capillary effects; these results provide insight into the liquid dynamics at the nanoscale.