Colloidal suspensions have a rich rheology and can exhibit shear thinning as well as shear thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions between them. Here, we consider the ideal limit of a dense bath of soft colloids following an underdamped Langevin dynamics. We use a mean-field equation for the colloidal density to get an analytical expression of the drag force felt by a probe pulled at constant velocity through the suspension. Our results show that inertia can indeed induce shear thickening by allowing density waves to propagate through the suspension.

We represent explicitly the excluded volume $V_{\mathrm{e}}\{{\mathcal{B}}_1,{\mathcal{B}}_2\}$ of two generic cylindrically symmetric, convex rigid bodies, ${\mathcal{B}}_1$ and ${\mathcal{B}}_2$, in terms of a family of shape functionals evaluated separately on ${\mathcal{B}}_1$ and ${\mathcal{B}}_2$. We show that $V_{\mathrm{e}}\{{\mathcal{B}}_1,{\mathcal{B}}_2\}$ fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended.

Simplified neuronal models capture the essence of the electrical activity of a generic neuron, besides being more interesting from the computational point of view when compared to higher-dimensional models such as the Hodgkin-Huxley one. In this work, we propose a generalized resonate-and-fire model described by a generalized Langevin equation that takes into account memory effects and colored noise. We perform a comprehensive numerical analysis to study the dynamics and the point process statistics of the proposed model, highlighting interesting new features such as (i) nonmonotonic behavior (emergence of peak structures, enhanced by the choice of colored noise characteristic time scale) of the coefficient of variation (CV) as a function of memory characteristic time scale, (ii) colored noise-induced shift in the CV, and (iii) emergence and suppression of multimodality in the interspike interval (ISI) distribution due to memory-induced subthreshold oscillations. Moreover, in the noise-induced spike regime, we study how memory and colored noise affect the coherence resonance (CR) phenomenon. We found that for sufficiently long memory, not only is CR suppressed but also the minimum of the CV-versus-noise intensity curve that characterizes the presence of CR may be replaced by a maximum. The aforementioned features allow to interpret the interplay between memory and colored noise as an effective control mechanism to neuronal variability. Since both variability and nontrivial temporal patterns in the ISI distribution are ubiquitous in biological cells, we hope the present model can be useful in modeling real aspects of neurons.

High-throughput experimental techniques and bioinformatics tools make it possible to obtain reconstructions of the metabolism of microbial species. Combined with mathematical frameworks such as flux balance analysis, which assumes that nutrients are used so as to maximize growth, these reconstructions enable us to predict microbial growth. Although such predictions are generally accurate, these approaches do not give insights on how different nutrients are used to produce growth, and thus are difficult to generalize to new media or to different organisms. Here, we propose a systems-level phenomenological model of metabolism inspired by the virial expansion. Our model predicts biomass production given the nutrient uptakes and a reduced set of parameters, which can be easily determined experimentally. To validate our model, we test it against in silico simulations and experimental measurements of growth, and find good agreement. From a biological point of view, our model uncovers the impact that individual nutrients and the synergistic interaction between nutrient pairs have on growth, and suggests that we can understand the growth maximization principle as the optimization of nutrient synergies.

Current fluctuation analysis has been successfully used over the years to investigate the physical properties of different systems. Here, we perform single-channel time-resolved current experiments in a protein channel to evaluate the different transport mechanisms governing the channel function. Using different salts of monovalent and divalent cations in a wide range of concentrations and applied potentials, we analyze current fluctuations focusing on the voltage dependence of the additional white noise that appears in the low-frequency range of the spectra. We demonstrate that the channel displays two characteristic transport regimes: at low salt concentrations (10 mM to 1 M) ion permeation is controlled by the protein fixed charges that induce accumulation or exclusion of ions to preserve local electroneutrality. At high salt concentrations $(>1\mathrm{M})$ adsorption processes associated to the binding of cations to the channel charges regulate the transport properties.

Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

The subject of the experimental research supported with numerical simulations presented in this paper is an analog electrical circuit representing the ring of unidirectionally coupled single-well Duffing oscillators. The research is concentrated on the existence of the stable three-frequency quasiperiodic attractor in this system. It is shown that such solution can be robustly stable in a wide range of parameters of the system under consideration in spite of a parameter mismatch which is unavoidable during experiment.

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite-time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semiordered (or semichaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase space associated to them. Applying our methodology to a chain of coupled standard maps we obtain (i) that it allows for an improved numerical characterization of stickiness in high-dimensional Hamiltonian systems, when compared to the previous analyses based on the distribution of recurrence times; (ii) that the transition probabilities between different regimes are determined by the phase-space volume associated to the corresponding regions; and (iii) the dependence of the Lyapunov exponents with the coupling strength.

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to ${10}^3$ sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on ${10}^4$ lattice sites and with some effort on ${10}^5$ lattice sites, representing the record lattice sizes studied for this family of models.

Acceleration of relaxation toward a fixed stationary distribution via violation of detailed balance was reported in the context of a Markov chain Monte Carlo method recently. Inspired by this result, systematic methods to violate detailed balance in Langevin dynamics were formulated by using exponential and rotational nonconservative forces. In the present paper, we accentuate that such specific nonconservative forces relate to the large deviation of total heat in an equilibrium state. The response to these nonconservative forces can be described by the intrinsic fluctuation of the total heat in the equilibrium state. Consequently, the fluctuation-dissipation relation for nonequilibrium steady states is derived without recourse to a linear response approximation.

We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum $H$ theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929)]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example.

If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly oscillating periodic field with enough strength to compete with the spin-spin interaction. By analyzing correlation functions and the distribution of domain lengths both analytically and numerically, we observe nontrivial correlation with more than one length scale at the threshold field strength.

Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ${\varphi }_{\mathrm{Bernal}}\approx 0.64$. We study packings of monosized hard spheres whose density spans over a wide range $(0.59<\varphi <0.72)$. These experiments harness x-ray computed tomography, three-dimensional image analysis, and numerical simulations to access precisely the geometry and the 3D structure of internal forces within the sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ${\varphi }_{\mathrm{Bernal}}\approx 0.64$ and ${\varphi }_c\approx 0.68$. These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable.

We present experimental results on the endurance of arches that block the outlet of a two-dimensional silo when subjected to vertical vibration. In a recent paper [C. Lozano et al., Phys. Rev. Lett. 109, 068001 (2012)], it was shown that the arch resistance against vibrations is determined by the maximum angle among those formed between each particle in the bridge and its two neighbors: the larger the maximum angle is, the weaker the bridge. It has also been reported that the breaking time distribution shows a power-law tail with an exponent that depends on the outlet size, the vibration intensity, and the load [I. Zuriguel et al., Sci. Rep. 4, 7324 (2014)]. Here we connect these previous works, demonstrating the importance of the maximum angle in the arch on the exponent of the breaking time distribution. Besides, we find that the acceleration needed to break an arch does not depend on the ramp rate of the applied acceleration, but it does depend on the outlet size above which the arch is formed. We also show that high frequencies of vibration reveal a change in the behavior of the arches that endure very long times. These arches have been identified as a subset with special geometrical features. Therefore, arches that cannot be broken by means of a given external excitation might exist.

Single-molecule force spectroscopy is widely used to determine kinetic parameters of dissociation by analyzing bond rupture data obtained via applying mechanical force to cells, capsules, and beads that are attached to an intermolecular bond. The bond rupture data are obtained in experiments either at a constant force or at a constant loading rate. We explore the effect of cellular viscoelasticity in constant-force experiments. Specifically, we perform Monte Carlo simulations of bond rupture at a given constant force to obtain the bond lifetime as a function of force in the absence and in the presence of bond force modulation due to cellular viscoelasticity, to explore its effect on the bond lifetime.

The emergence and maintenance of cooperative behavior is a fascinating topic in evolutionary biology and social science. The public goods game (PGG) is a paradigm for exploring cooperative behavior. In PGG, the total resulting payoff is divided equally among all participants. This feature still leads to the dominance of defection without substantially magnifying the public good by a multiplying factor. Much effort has been made to explain the evolution of cooperative strategies, including a recent model in which only a portion of the total benefit is shared by all the players through introducing a new strategy named persistent cooperation. A persistent cooperator is a contributor who is willing to pay a second cost to retrieve the remaining portion of the payoff contributed by themselves. In a previous study, this model was analyzed in the framework of well-mixed populations. This paper focuses on discussing the persistent cooperation in lattice-structured populations. The evolutionary dynamics of the structured populations consisting of three types of competing players (pure cooperators, defectors, and persistent cooperators) are revealed by theoretical analysis and numerical simulations. In particular, the approximate expressions of fixation probabilities for strategies are derived on one-dimensional lattices. The phase diagrams of stationary states, and the evolution of frequencies and spatial patterns for strategies are illustrated on both one-dimensional and square lattices by simulations. Our results are consistent with the general observation that, at least in most situations, a structured population facilitates the evolution of cooperation. Specifically, here we find that the existence of persistent cooperators greatly suppresses the spreading of defectors under more relaxed conditions in structured populations compared to that obtained in well-mixed populations.

We study the dynamics of two conservatively coupled Hénon maps at different levels of dissipation. It is shown that the decrease of dissipation leads to changes in the structure of the parameter plane and the scenarios of transition to chaos compared to the case of infinitely strong dissipation. Particularly, the Feigenbaum line becomes divided into several fragments. Some of these fragments have critical points of different types, namely, of C and H type, as their terminal points. Also the mechanisms of formation of these Feigenbaum line ruptures are described.

A series of experiments were carried out to evaluate the energy-coupling efficiency from heating laser to a fuel core in the fast-ignition scheme of laser-driven inertial confinement fusion. Although the efficiency is determined by a wide variety of complex physics, from intense laser plasma interactions to the properties of high-energy density plasmas and the transport of relativistic electron beams (REB), here we simplify the physics by breaking down the efficiency into three measurable parameters: (i) energy conversion ratio from laser to REB, (ii) probability of collision between the REB and the fusion fuel core, and (iii) fraction of energy deposited in the fuel core from the REB. These three parameters were measured with the newly developed experimental platform designed for mimicking the plasma conditions of a realistic integrated fast-ignition experiment. The experimental results indicate that the high-energy tail of REB must be suppressed to heat the fuel core efficiently.

Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical physics. We analyze a new percolation problem in which the first-order nature of an equilibrium percolation transition can be established analytically and verified numerically. The rules for this site percolation model are physical and very simple, requiring only the introduction of a weight $W\left(n\right)=n+1$ for a cluster of size $n$. This establishes that a discontinuous percolation transition can occur with qualitatively more local interactions than in all currently considered examples of explosive percolation; and that, unlike these, it can be reversible. This greatly extends both the applicability of such percolation models in principle and their reach in practice.

We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and find that within selected parameter regimes it evolves in three distinct stages: initially as superdiffusion, next as subdiffusion, and finally as normal diffusion in the asymptotic long-time limit. We show how crossover times that separates these stages can be controlled by temperature and an external magnetic flux. The first two stages can last many orders longer than characteristic time scales of the system, thus being comfortably detectable experimentally. The origin of abnormal behavior is noticeable related to the ratchet form of the potential revealing an entirely new mechanism of emergence of anomalous diffusion. Moreover, a normal diffusion coefficient exhibits nonmonotonic dependence on temperature leading to an intriguing phenomenon of thermal noise suppressed diffusion. The proposed setup for experimental verification of our findings provides a new and promising testing ground for investigating anomalies in diffusion phenomena.