We examine the contact line friction coefficient of viscous droplets spreading and retracting on solid surfaces immersed in ambient oil. By using the electrowetting effect, we generate a surface tension imbalance to drive the spreading and the retracting motion of the three-phase contact line (TCL). We show that neither the driving force intensity nor TCL direction significantly influences the friction coefficient. Instead, the friction coefficient depends equivalently on the viscosity of liquid droplets and the surrounding oil. We derive and experimentally verify a transient timescale that can be used to characterize both the spreading and retracting dynamics.

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

We consider a cellular monolayer, described using a vertex-based model, for which cells form a spatially disordered array of convex polygons that tile the plane. Equilibrium cell configurations are assumed to minimize a global energy defined in terms of cell areas and perimeters; energy is dissipated via dynamic area and length changes, as well as cell neighbor exchanges. The model captures our observations of an epithelium from a Xenopus embryo showing that uniaxial stretching induces spatial ordering, with cells under net tension (compression) tending to align with (against) the direction of stretch, but with the stress remaining heterogeneous at the single-cell level. We use the vertex model to derive the linearized relation between tissue-level stress, strain, and strain rate about a deformed base state, which can be used to characterize the tissue's anisotropic mechanical properties; expressions for viscoelastic tissue moduli are given as direct sums over cells. When the base state is isotropic, the model predicts that tissue properties can be tuned to a regime with high elastic shear resistance but low resistance to area changes, or vice versa.

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

We study the short-time distribution $\mathcal{P}\left(H,L,t\right)$ of the two-point two-time height difference $H=h(L,t)-h(0,0)$ of a stationary Kardar-Parisi-Zhang interface in 1+1 dimension. Employing the optimal-fluctuation method, we develop an effective Landau theory for the second-order dynamical phase transition found previously for $L=0$ at a critical value $H=H_c$. We show that $\left|H\right|$ and $L$ play the roles of inverse temperature and external magnetic field, respectively. In particular, we find a first-order dynamical phase transition when $L$ changes sign, at supercritical $H$. We also determine analytically $\mathcal{P}\left(H,L,t\right)$ in several limits away from the second-order transition. Typical fluctuations of $H$ are Gaussian, but the distribution tails are highly asymmetric. The tails $-ln\mathcal{P}\sim {\left|H\right|}^{3/2}/\sqrt{t}$ and $-ln\mathcal{P}\sim {\left|H\right|}^{5/2}/\sqrt{t}$, previously found for $L=0$, are enhanced for $L\ne 0$. At very large $\left|L\right|$ the whole height-difference distribution $\mathcal{P}\left(H,L,t\right)$ is time-independent and Gaussian in $H, -ln\mathcal{P}\sim {\left|H\right|}^2/\left|L\right|$, describing the probability of creating a ramplike height profile at $t=0$.

A relation ${\mathcal{M}}_{\mathrm{SHS}\to \mathrm{LJ}}$ between the set of nonisomorphic sticky-hard-sphere clusters ${\mathcal{M}}_{\mathrm{SHS}}$ and the sets of local energy minima ${\mathcal{M}}_{LJ}$ of the $(m,n)$-Lennard-Jones potential $V_{mn}^{\mathrm{LJ}}\left(r\right)=\frac{\varepsilon }{n-m}[m{r}^{-n}-n{r}^{-m}]$ is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both $m$ and $n$ and increases exponentially with increasing cluster size $N$ for $N\gtrsim 10$. While the map from ${\mathcal{M}}_{\mathrm{SHS}}\to {\mathcal{M}}_{\mathrm{SHS}\to \mathrm{LJ}}$ is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to $N=13$, and most of the missing structures correspond to energetically unfavorable minima even for fairly low $(m,n)$. Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.

Escape of colloidal-size particles from various kinds of solids, such as aggregates and surfaces, occurs in a wide variety of settings of both fundamental and applied scientific interest. In this paper an exact solution for the detachment of adhesive spheres from each other by means of diffusion is presented. The solution takes into account repeated detachment and reattachment events in the course of time on the way toward the permanently separated state. For strongly adhesive spheres this state is approached in an exponential manner essentially regardless of how the bound state is specified. The analytical solution is shown to capture semiquantitatively the escape from more realistic potential wells using a mapping procedure whereby equality of second virial coefficients is imposed.

In a dynamical system, the transition between reactants and products is typically mediated by an energy barrier whose properties determine the corresponding pathways and rates. The latter is the flux through a dividing surface (DS) between the two corresponding regions, and it is exact only if it is free of recrossings. For time-independent barriers, the DS can be attached to the top of the corresponding saddle point of the potential energy surface, and in time-dependent systems, the DS is a moving object. The precise determination of these direct reaction rates, e.g., using transition state theory, requires the actual construction of a DS for a given saddle geometry, which is in general a demanding methodical and computational task, especially in high-dimensional systems. In this paper, we demonstrate how such time-dependent, global, and recrossing-free DSs can be constructed using neural networks. In our approach, the neural network uses the bath coordinates and time as input, and it is trained in a way that its output provides the position of the DS along the reaction coordinate. An advantage of this procedure is that, once the neural network is trained, the complete information about the dynamical phase space separation is stored in the network's parameters, and a precise distinction between reactants and products can be made for all possible system configurations, all times, and with little computational effort. We demonstrate this general method for two- and three-dimensional systems and explain its straightforward extension to even more degrees of freedom.

We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, respectively. In the supercooled regime, the structural relaxation time ${\tau }_{\alpha }$ of both systems grows steeply with volume fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of ${\tau }_{\alpha }$ on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equilibrium. In this nonequilibrium regime, ${\tau }_{\alpha }$ depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing density typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequilibrium aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.

The statistics and scaling of compressible isotropic turbulence in the presence of large-scale shock waves are investigated by using numerical simulations at turbulent Mach number $M_t$ ranging from 0.30 to 0.65. The spectra of the compressible velocity component, density, pressure, and temperature exhibit a $k^{-2}$ scaling at different turbulent Mach numbers. The scaling exponents for structure functions of the compressible velocity component and thermodynamic variables are close to 1 at high orders $n\ge 3$. The probability density functions of increments of the compressible velocity component and thermodynamic variables exhibit a power-law region with the exponent $-2$. Models for the conditional average of increments of the compressible velocity component and thermodynamic variables are developed based on the ideal shock relations and are verified by numerical simulations. The overall statistics of the compressible velocity component and thermodynamic variables are similar to one another at different turbulent Mach numbers. It is shown that the effect of shock waves on the compressible velocity spectrum and kinetic energy transfer is different from that of acoustic waves.

Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but it also allows fluctuation measurements that may reveal the structure and dynamics of the underlying biochemical network. Here, we study nonequilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general microscopically reversible cycles. We define a stochastic period for reversible cycles and present analytical solutions for its moments. Furthermore, we associate the two forms of the randomness parameter with the thermodynamic uncertainty relation, which sets limits on the timing precision of the cycle in terms of thermodynamic quantities. Our results should prove useful also for the study of temporal fluctuations in more general networks.

Applying a force to certain supramolecular bonds may initially stabilize them, manifested by a lower dissociation rate. We show that this behavior, known as catch bonding and by now broadly reported in numerous biophysics bonds, is generically expected when either or both the trapping potential and the force applied to the bond possess some degree of nonlinearity. We enumerate possible scenarios and for each identify the possibility and, if applicable, the criterion for catch bonding to occur. The effect is robustly predicted by Kramers theory and Mean First Passage Time theory and confirmed in direct molecular dynamics simulation. Among the catch scenarios, one plays out essentially any time the force on the bond originates in a polymeric object, implying that some degree of catch bond behavior is to be expected in many settings relevant to polymer network mechanics or optical tweezer experiments.

Biopolymer gels such as fibrin and collagen networks are known to develop tensile axial stress when subject to torsion. This negative normal stress is opposite to the classical Poynting effect observed for most elastic solids including synthetic polymer gels, where torsion provokes a positive normal stress. As shown recently, this anomalous behavior in fibrin gels depends on the open, porous network structure of biopolymer gels, which facilitates interstitial fluid flow during shear and can be described by a phenomenological two-fluid model with viscous coupling between network and solvent. Here we extend this model and develop a microscopic model for the individual diagonal components of the stress tensor that determine the axial response of semiflexible polymer hydrogels. This microscopic model predicts that the magnitude of these stress components depends inversely on the characteristic strain for the onset of nonlinear shear stress, which we confirm experimentally by shear rheometry on fibrin gels. Moreover, our model predicts a transient behavior of the normal stress, which is in excellent agreement with the full time-dependent normal stress we measure.

We present experiments on one-way barriers that block reaction fronts in a fully three-dimensional (3D) fluid flow. Fluorescent Belousov-Zhabotinsky reaction fronts are imaged with laser-scanning in a laminar, overlapping vortex flow. The barriers are analyzed with a 3D extension to burning invariant manifold (BIM) theory that was previously applied to two-dimensional advection-reaction-diffusion processes. We discover tube and sheet barriers that guide the front evolution. The experimentally determined barriers are explained by BIMs calculated from a model of the flow.

T cell receptors (TCRs) bind foreign or self-peptides attached to major histocompatibility complex (MHC) molecules, and the strength of this interaction determines T cell activation. Optimizing the ability of T cells to recognize a diversity of foreign peptides yet be tolerant of self-peptides is crucial for the adaptive immune system to properly function. This is achieved by selection of T cells in the thymus, where immature T cells expressing unique, stochastically generated TCRs interact with a large number of self-peptide-MHC; if a TCR does not bind strongly enough to any self-peptide-MHC, or too strongly with at least one self-peptide-MHC, the T cell dies. Past theoretical work cast thymic selection as an extreme value problem and characterized the statistical enrichment or depletion of amino acids in the postselection TCR repertoire, showing how T cells are selected to be able to specifically recognize peptides derived from diverse pathogens yet have limited self-reactivity. Here, we investigate how the diversity of the postselection TCR repertoire is modified when TCRs make nonuniform contacts with peptide-MHC. Specifically, we were motivated by recent experiments showing that amino acids at certain positions of a TCR sequence have large effects on thymic selection outcomes, and crystal structure data that reveal a nonuniform contact profile between a TCR and its peptide-MHC ligand. Using a representative TCR contact profile as an illustration, we show via simulations that the statistical enrichment or depletion of amino acids now varies by position according to the contact profile, and, importantly, it depends on the implementation of nonuniform contacts during thymic selection. We explain these nontrivial results analytically. Our study has implications for understanding the selection forces that shape the functionality of the postselection TCR repertoire.

We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power $\alpha$ of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For $0\le \alpha <1$, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size $N$, the stationary current is independent on $N$. For $\alpha >1$, heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an $\alpha$-dependent characteristic exponent.

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive topologies: a 64-residue $\alpha /\beta$ chymotrypsin inhibitor 2 (CI2) protein, and a 57-residue $\beta$-barrel $\alpha$-spectrin Src-homology 3 domain (SH3) protein. When comparing the protein folding kinetics simulated with Brownian dynamics in the presence of HI to that in the absence of HI, we find that the effect of HI on protein folding appears to have a “crossover” behavior about the folding temperature. This means that at a temperature greater than the folding temperature, the enhanced friction from the hydrodynamic solvents between the beads in an unfolded configuration results in lowered folding rate; conversely, at a temperature lower than the folding temperature, HI accelerates folding by the backflow of solvent toward the folded configuration of a protein. Additionally, the extent of acceleration depends on the topology of a protein: for a protein like CI2, where its folding nucleus is rather diffuse in a transition state, HI channels the formation of contacts by favoring a major folding pathway in a complex free energy landscape, thus accelerating folding. For a protein like SH3, where its folding nucleus is already specific and less diffuse, HI matters less at a temperature lower than the folding temperature. Our findings provide further theoretical insight to protein folding kinetic experiments and simulations.

This article focuses on liquefaction of saturated granular soils, triggered by earthquakes. Liquefaction is defined here as the transition from a rigid state, in which the granular soil layer supports structures placed on its surface, to a fluidlike state, in which structures placed initially on the surface sink to their isostatic depth within the granular layer. We suggest a simple theoretical model for soil liquefaction and show that buoyancy caused by the presence of water inside a granular medium has a dramatic influence on the stability of an intruder resting at the surface of the medium. We confirm this hypothesis by comparison with laboratory experiments and discrete-element numerical simulations. The external excitation representing ground motion during earthquakes is simulated via horizontal sinusoidal oscillations of controlled frequency and amplitude. In the experiments, we use particles only slightly denser than water, which as predicted theoretically increases the effect of liquefaction and allows clear depth-of-sinking measurements. In the simulations, a micromechanical model simulates grains using molecular dynamics with friction between neighbors. The effect of the fluid is captured by taking into account buoyancy effects on the grains when they are immersed. We show that the motion of an intruder inside a granular medium is mainly dependent on the peak acceleration of the ground motion and establish a phase diagram for the conditions under which liquefaction happens, depending on the soil bulk density, friction properties, presence of water, and peak acceleration of the imposed large-scale soil vibrations. We establish that in liquefaction conditions, most cases relax toward an equilibrium position following an exponential in time. We also show that the equilibrium position itself, for most liquefaction regimes, corresponds to the isostatic equilibrium of the intruder inside a medium of effective density. The characteristic time to relaxation is shown to be essentially a function of the peak ground velocity.