We present a simple method to prepare a granular material with a controlled cohesion between particles. The granular material is made of spherical glass beads coated with a polyborosiloxane polymer. This material is proved to be stable in time and nonsensitive to temperature and humidity. The interparticle force is measured and related to the size of the grain and the polymer coating thickness. Classical measurements (packing fraction, repose angle, macroscopic cohesion) are performed with this cohesion-controlled granular material. This model material opens many perspectives to study in a controlled manner the flow of cohesive grains.

We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus $G^{\prime }$ and the loss modulus $G^{\prime \prime }$ in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying $G^{\prime }>0$) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed $G^{\prime }$ after the reduction of the strain amplitude depends on the phase of the external shear strain. The loss modulus $G^{\prime \prime }$ exhibits a discontinuous jump corresponding to discontinuous shear thickening in the fragile state.

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

Stress concentration at a crack tip engenders a process zone, a small domain containing a phase, different from that in the bulk of the solid. We demonstrate that this zone at the tip of a propagating crack exhibits a morphological transformation with an increase of the crack velocity. The concave zone shape with an invagination in its back that is characteristic of a slow crack transforms into a droplet-shaped convex zone upon exceeding a critical velocity value, $v_{\text{G}}$. In this latter case, a metastable wake follows the propagating zone. We obtained this result by computer simulation of a crack propagating in a solid exhibiting a first-order phase transformation.

The morphological transformation of the process zone at the tip of a propagating crack occurs with the increase of the crack velocity. The zone configuration changes its shape from concave to convex, dropletlike form. The latter exhibits a metastable wake. We prove that the transformation takes place as soon as the crack velocity exceeds Gordon's speed $V_{\text{G}}$. The latter is the velocity of motion of the interface between the stable and overheated metastable phases. We further analyze the dependence of geometrical parameters of the zone and wake on the crack tip velocity. We show that at a constant velocity, the size of the process zone grows with the approach to the binodal. However, it decreases by over three orders of magnitude as the crack's velocity increases. In contrast, the interval length where the zone or the wake comes in direct contact with the crack surface increases at $0\le V<V_{\text{G}}$, achieves its maximum at $V=V_{\text{G}}$, and then decreases with the further velocity increase. The zone vanishes as soon as the crack's velocity exceeds a critical speed $V_{\text{cr}}$.

We demonstrate that considerable variation of mean Prandtl number ($\mathrm{P}{\mathrm{r}}_0$) from unity brings in an additional length scale (called the viscous penetration depth, ${\delta }_{\mathrm{v}}$) into the dynamics of instantaneous as well as time-averaged (mean) flow induced by thermoviscous expansion along a periodically heated solid wall. We investigate the limiting cases of high and low Prandtl numbers ($\mathrm{P}{\mathrm{r}}_0\gg 1$ and $\mathrm{P}{\mathrm{r}}_0 \ll$ 1) through detailed order-of-magnitude analysis. Our study reveals that the viscous penetration depth scales universally with $\mathrm{P}{\mathrm{r}}_0$ so long as such depth remains small compared to the wavelength of the applied thermal wave. While a high $\mathrm{P}{\mathrm{r}}_0$ is found to obstruct the mean flow, the converse is not necessarily true. Subsequent analysis clearly shows that a low-$\mathrm{P}{\mathrm{r}}_0$ flow can induce negative thermoviscous force within the thermal boundary layer and thus retard the mean motion, leading to a nontrivial reduction of net mass flow along the plate. Numerical prediction of friction factor variation with $\mathrm{P}{\mathrm{r}}_0$ agrees well with the scaling estimates for both high-$\mathrm{P}{\mathrm{r}}_0$ and low-$\mathrm{P}{\mathrm{r}}_0$ fluids. The findings may very well act as fundamental design basis for engineering devices that may potentially be developed for thermal molecular trapping and particle sorting and accumulation based on unsteady heating.

Work statistics characterizes important features of a nonequilibrium thermodynamic process, but the calculation of the work statistics in an arbitrary nonequilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynman's path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schrödinger's formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach for the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.

We ask to what extent an isolated quantum system can eventually “contract” to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be measured in a fixed subspace, and maximizing this probability over all time. This is relevant, for example, in a cosmological context, which may have access to indefinite timescales. We find that when the subspace is much smaller than the entire space, this maximal probability goes to $\frac{1}{2}$ for real initial wave functions, and to ${\pi }^2/16$ when the initial wave function has been drawn from a complex ensemble. For example, when starting in a real generic state, the chances of collapsing all particles into a small box will be less than but come arbitrarily close to $50\%$. This contraction corresponds to an entropy reduction by a factor of approximately 2, thus bounding large downward fluctuations in entropy from generic initial states.

Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the statistical mechanical entropy is defined by Gibbs. The relation between these two definitions of entropy is still not fully explored. In this work, we study this problem by employing the phase-space formulation of quantum mechanics. For those quantum states having well-defined classical counterparts, we study the quantum-classical correspondence and quantum corrections of the entropy. We expand the von Neumann entropy in powers of $\hslash$ by using the phase-space formulation, and the zeroth-order term reproduces the Gibbs entropy. We also obtain the explicit expression of the quantum corrections of the entropy. Moreover, we find that for the thermodynamic equilibrium state, all terms odd in $\hslash$ are exactly zero. As an application, we derive quantum corrections for the net work extraction during a quantum Carnot cycle. Our results bring important insights into the understanding of quantum entropy and may have potential applications in the study of quantum heat engines.

The scaling limit of the Heisenberg $XXZ$ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having $N_x$ sites, the universal Casimir scaling function, which characterizes the leading finite-size correction term in the large-$N_x$ expansion of the ground-state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown that the same scaling function describes the temperature dependence of the free energy of the infinite $XXZ$ chain at low enough temperatures in the gapped scaling regime.

We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean-field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain a simple field theory which describes the first deviations from this uncorrelated behavior in a $\epsilon =d_c-d$ expansion below the upper critical dimension $d_c$ of the model. We apply it to calculate the correlations between (i) avalanche sizes (ii) avalanche dynamics in two successive avalanches, or more generally, in two avalanches separated by a uniform displacement $W$ of the interface. For (i) we obtain the correlations of the total sizes, of the local sizes, and of the total sizes with given seeds (starting points). For (ii) we obtain the correlations of the velocities, of the durations, and of the avalanche shapes. In general we find that the avalanches are anticorrelated, the occurrence of a larger avalanche making more likely the occurrence of a smaller one, and vice versa. Examining the universality of our results leads us to conjecture several exact scaling relations for the critical exponents that characterize the different distributions of correlations. The avalanche size predictions are confronted to numerical simulations for a $d=1$ interface with short range elasticity. They are also compared to our recent related work on static avalanches (shocks). Finally we show that the naive extrapolation of our result into the thermally activated creep regime at finite temperature predicts strong positive correlations between the forward motion events, as recently observed in numerical simulations.

The topic of microscopic heat engine has undergone intensive research in recent years. Microscopic heat engines can exploit thermal as well as active fluctuations to extract thermodynamic work. We investigate the properties of a microscopic Stirling's engine that uses an active (self-propelling) particle as a working substance, in contact with two thermal baths. It is shown that the presence of activity leads to an enhanced performance of the engine. The efficiency can be improved by increasing the activity strength for all cycle time, including the nonquasistatic regime. We verify that the analytical results agree very well with our simulations. The variation of efficiency with the temperature difference between the two thermal baths has also been explored. The optimum region of operation of the engine has been deduced, by using its efficient power (product of efficiency and power) as a quantifier. Finally, a simple model is provided that emulates the behavior of a flywheel driven by this engine.

Molecular machines are stochastic systems that catalyze the energetic processes keeping living cells alive and structured. Inspired by the examples of ${\mathrm{F}}_1$-ATP synthase and the bacterial flagellum, we present a minimal model of an externally driven stochastic rotary machine. We explore the trade-offs of work, driving speed, and driving accuracy when changing driving strength, speed, and the underlying system dynamics. We find an upper bound on accuracy and work for a particular speed. Our results favor slow driving when tasked with minimizing the work-accuracy ratio and maximizing the rate of successful cycles. Finally, in the parameter regime mapping to the dynamics of ${\mathrm{F}}_1$-ATP synthase, we find a significant decay of driving accuracy at physiological rotation rates, raising questions about how ATP synthase achieves reasonable or even remarkable efficiency in vivo.

Many methods have been employed to investigate the drift behavior of spiral waves in an effort to understand and control their dynamics. Here, we propose a joint method to control the dynamics of spiral waves by applying both a rotating external field and periodic forcing. First, spirals in different regimes (including rigidly rotating, meandering, and drifting spirals) are synchronized by suitable rotating external fields. Then, under weak periodic forcing at frequencies equal to those of the external fields, the synchronized spirals undergo a directional and simple drift. Dependence of the drift velocity of the synchronized spiral on the initial rotational phase of the rotating external field and on the initial phase of the periodic forcing is studied in detail. We hope that our theoretical results can be observed in experiments, such as in the Belousov-Zhabotinsky reaction.

We reveal the generic characteristics of wave-packet delocalization in two-dimensional nonlinear disordered lattices by performing extensive numerical simulations in two basic disordered models: the Klein-Gordon system and the discrete nonlinear Schrödinger equation. We find that in both models (a) the wave packet's second moment asymptotically evolves as $t^{a_m}$ with $a_m\approx 1/5$ ($1/3$) for the weak (strong) chaos dynamical regime, in agreement with previous theoretical predictions [S. Flach, Chem. Phys. 375, 548 (2010)]; (b) chaos persists, but its strength decreases in time $t$ since the finite-time maximum Lyapunov exponent $\mathrm{\Lambda }$ decays as $\mathrm{\Lambda }\propto t^{{\alpha }_{\mathrm{\Lambda }}}$, with ${\alpha }_{\mathrm{\Lambda }}\approx -0.37$ ($-0.46$) for the weak (strong) chaos case; and (c) the deviation vector distributions show the wandering of localized chaotic seeds in the lattice's excited part, which induces the wave packet's thermalization. We also propose a dimension-independent scaling between the wave packet's spreading and chaoticity, which allows the prediction of the obtained ${\alpha }_{\mathrm{\Lambda }}$ values.

The $\varepsilon$–susceptible-infected-susceptible (SIS) epidemic model on a graph adds an independent, Poisson self-infection process with rate $\varepsilon$ to the “classical” Markovian SIS process. The steady state in the classical SIS process (with $\varepsilon =0)$ on any finite graph is the absorbing or overall-healthy state, in which the virus is eradicated from the network. We report that there always exists a phase transition around ${\tau }_c^{\varepsilon }=O\left({\varepsilon }^{-\frac{1}{N-1}}\right)$ in the $\varepsilon$-SIS process on the complete graph $K_N$ with $N$ nodes, above which the effective infection rate $\tau >{\tau }_c^{\varepsilon }$ causes the average steady-state fraction of infected nodes to approach that of the mean-field approximation, no matter how small, but not zero, the self-infection rate $\varepsilon$ is. For $\tau <{\tau }_c^{\varepsilon }$ and small $\varepsilon$, the network is almost overall healthy. The observation was found by mathematical analysis on the complete graph $K_N$, but we claim that the phase transition of explosive type may also occur in any other finite graph. We thus conclude that the overall-healthy state of the classical Markovian SIS model is unstable in the $\varepsilon$-SIS process and, hence, unlikely to exist in reality, where “background” infection $\varepsilon >0$ is imminent.

In this paper we study the connection between the zeros of the expected Euler characteristic curve and the phenomenon which we refer to as homological percolation—the formation of “giant” cycles in persistent homology, which is intimately related to classical notions of percolation. We perform an experimental study that covers four different models: site percolation on the cubical and permutahedral lattices, the Poisson-Boolean model, and Gaussian random fields. All the models are generated on the flat torus ${\mathbb{T}}^d$ for $d=2,3,4$. The simulation results strongly indicate that the zeros of the expected Euler characteristic curve approximate the critical values for homological percolation. Our results also provide some insight about the approximation error. Further study of this connection could have powerful implications both in the study of percolation theory and in the field of topological data analysis.

A simple model of temperature-increase-driven homo- or heteroduplex dissociation is analyzed. It features a temperature-independent association constant, and a dissociation constant that increases with temperature according to an Arrhenius law. The model is analytically tractable for quasiequilibrium conditions, for two special cases in the intermediate regime, and in the strongly irreversible regime. In the latter, the fraction of isolated components depends on temperature according to a Gumbel minimal value distribution. The model suggests a logarithmic dependence of the dissociation temperature on the rate of temperature increase. It further predicts that the dissociation occurs in a twice broader temperature interval for slow than fast temperature increase. Finally, the model points to a previously overlooked source of discrepancy between apparent van't Hoff and calorimetric enthalpies. Applied to short double stranded DNA, the model explains the dependence of the melting temperature on the rate of temperature increase, and the twice lower width of the melting transition in low salt compared to high salt conditions.

The bending of nanostructures (NSs), such as nanopillars and nanowires, caused by cell adhesion is an interesting phenomenon and is important for the measurements of cellular forces, understanding the biological behavior of cells, and disease diagnosis. However, which factors are related to the bending of NSs and how the factors affect bending displacement are still not well understood. Here, we establish an analytic thermodynamic theory to study the bending mechanism of NSs caused by cellular force during the cell adhesion process, and analyze the factors affecting bending displacement. It is found that the bending of NSs is determined by the competition between the stretching energy of the membrane and the strain energy of the NSs. The bending displacement can be evaluated based on our model.

Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic coexistence. We discuss a computational study of inhomogeneous configurations that is based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic coexistence region, and that goes to infinity if the eigenvalues of the order parameter become nonphysical. Computations of the spatial profile of the order parameter are presented for an isotropic-nematic interface in one dimension, a tactoid in two dimensions, and a nematic disclination in two dimensions. We compare our results to those given by the Landau–de Gennes free energy for the same configurations and discuss the advantages of such a model over the latter.