This paper resolves the long standing debate as to the proper time scale $\langle \tau \rangle$ of the onset of the immunological synapse bond, the noncovalent chemical bond defining the immune pathways involving T cells and antigen presenting cells. Results from our model calculations show $\langle \tau \rangle$ to be of the order of seconds instead of minutes. Close to the linearly stable regime, we show that in between the two critical spatial thresholds defined by the integrin:ligand pair (${\Delta }_2\sim$ 40–45 nm) and the T-cell receptor TCR:peptide-major-histocompatibility-complex pMHC bond (${\Delta }_1\sim$ 14–15 nm), $\langle \tau \rangle$ grows monotonically with increasing coreceptor bond length separation $\delta$ (= ${\Delta }_2-{\Delta }_1\sim$ 26–30 nm) while $\langle \tau \rangle$ decays with ${\Delta }_1$ for fixed ${\Delta }_2$. The nonuniversal $\delta$-dependent power-law structure of the probability density function further explains why only the TCR:pMHC bond is a likely candidate to form a stable synapse.

We examine numerically the influence of intrapulse Raman scattering (IRS) on the stable stationary pulses in the presence of constant linear and nonlinear gain as well as spectral filtering. Numerical results show that the small change of the value of the parameter describing IRS leads to qualitatively different behavior of the evolution of pulse amplitudes. We prove that the strong dependence of the pulse dynamics on the parameter describing IRS is related to the existence of the Poincaré-Andronov-Hopf bifurcation and the appearance of the unstable limit cycle.

We present a study of the molecular diffusion in freely suspended smectic-$A$ liquid crystal films with thicknesses ranging from 20 down to only two molecular layers. The molecular mobility is directly probed by determining the trajectories of single, fluorescent tracer molecules. We demonstrate, using several different smectic compounds, that a monotonic increase of the diffusion coefficient with decreasing film thickness is a general phenomenon. In two-layer films, the diffusion is enhanced by a factor of 3 to 5 compared to the corresponding bulk smectic phase. Molecular dynamics simulations of freely suspended smectic films are presented which support the experimental results.

We discuss the equivalence relation between the Euclidean bipartite matching problem on the line and on the circumference and the Brownian bridge process on the same domains. The equivalence allows us to compute the correlation function and the optimal cost of the original combinatorial problem in the thermodynamic limit; moreover, we solve also the minimax problem on the line and on the circumference. The properties of the average cost and correlation functions are discussed.

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of nonequilibrium dynamics into a unified formulation valid in all these contexts, which extends to such frameworks the concept of steepest entropy ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. Actually, the present formulation constitutes a generalization also for the quantum thermodynamics framework. The analysis emphasizes that in the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near-thermodynamic-equilibrium limit, the metric tensor is directly related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far-nonequilibrium domain, most of the existing theories of nonequilibrium thermodynamics can be cast in such a way that the state exhibits the spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. The non-negativity of the entropy production is a general and readily proved feature of SEA dynamics. In several of the different approaches to nonequilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called maximum entropy production principle. Therefore, it is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far nonequilibrium states. The mathematical frameworks we consider are the following: (A) statistical or information-theoretic models of relaxation; (B) small-scale and rarefied gas dynamics (i.e., kinetic models for the Boltzmann equation); (C) rational extended thermodynamics, macroscopic nonequilibrium thermodynamics, and chemical kinetics; (D) mesoscopic nonequilibrium thermodynamics, continuum mechanics with fluctuations; and (E) quantum statistical mechanics, quantum thermodynamics, mesoscopic nonequilibrium quantum thermodynamics, and intrinsic quantum thermodynamics.

We investigate the behavior of five hyperbolic reaction-diffusion equations most commonly employed to describe systems of interacting organisms or reacting particles where dispersal displays inertia. We first discuss the macroscopic or mesoscopic foundation, or lack thereof, of these reaction-transport equations. This is followed by an analysis of the temporal evolution of spatially uniform states. In particular, we determine the uniform steady states of the reaction-transport systems and their stability properties. We then address the spatiotemporal behavior of pure death processes. We end with a unified treatment of the front speed for hyperbolic reaction-diffusion equations with Kolmogorov–Petrosvskii–Piskunov kinetics. In particular, we obtain an exact expression for the front speed of a general class of reaction correlated random walk systems. Our results establish that three out of the five hyperbolic reaction-transport equations provide physically acceptable models of biological and chemical systems.

Atomic rearrangements induced by shear stress are fundamental for understanding deformation mechanisms in metallic glasses (MGs). Using molecular dynamic simulation, the atomic rearrangements characterized by nonaffine displacements (NADs) and their spatial distribution and evolution with tensile stress in ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ MG were investigated. It was found that in the elastic regime the atomic rearrangements with the largest NADs are relatively homogeneous in space, but exhibit strong spatial correlation, become localized and inhomogeneous, and form large clusters as strain increases, which may facilitate the so-called shear transformation zones. Furthermore, initially they prefer to take place around Cu atoms which have more nonicosahedral configurations. As strain increases, the preference decays and disappears in the plastic regime. The atomic rearrangements with the smallest NADs are preferentially located around Cu atoms, too, but with more icosahedral or icosahedral-like atomic configurations. The preference is maintained in the whole deformation process. In contrast, the atomic rearrangements with moderate NADs distribute homogeneously, and do not show explicit preference or spatial correlation, acting as matrix during deformation. Among the atomic rearrangements with different NADs, those with largest and smallest NADs are nearest neighbors initially, but separating with increasing strain, while those with largest and moderate NADs always avoid to each other. The correlations in the fluctuations of the NADs confirm the long-range strain correlation and the scale-free characteristic of NADs in both elastic and plastic deformation, which suggests a universality of the scaling in the plastic flow in MGs.

Locomotion of microorganisms plays a vital role in most of their biological processes. In many of these processes, microorganisms are exposed to complex fluids while swimming in confined domains, such as spermatozoa in mucus of mammalian reproduction tracts or bacteria in extracellular polymeric matrices during biofilm formation. Thus, it is important to understand the kinematics of propulsion in a viscoelastic fluid near a no-slip boundary. We use a squirmer model with a time-reversible body motion to analytically investigate the swimming kinematics in an Oldroyd-B fluid near a wall. Analysis of the time-averaged motion of the swimmer shows that both pullers and pushers in a viscoelastic fluid swim towards the no-slip boundary if they are initially located within a small domain of “attraction” in the vicinity of the wall. In contrast, neutral swimmers always move towards the wall regardless of their initial distance from the wall. Outside the domain of attraction, pullers and pushers are both repelled from the no-slip boundary. Time-averaged locomotion is most pronounced at a Deborah number of unity. We examine the swimming trajectories of different types of swimmers as a function of their initial orientation and distance from the no-slip boundary.

Rotating stratified flows in thermal wind balance are at the center of geophysical fluid dynamics. Recently, endeavors were put on studying the linear response of such flows to potential vorticity perturbations. It has been shown that the initial potential vorticity (PV) distribution is fundamental and is responsible for important transient growth of the perturbation and gravity-wave generation. Using Pfeiffer's theorem [J. Differ. Equat. 11, 145 (1972)], we give the mathematical demonstration of the stability of asymmetric perturbations $k_1\ne 0$ of a uniform, unbounded flow in thermal wind balance. Incidentally, we prove that both the wave mode (that corresponds to a vanishing PV) and the vortex mode (corresponding to a nonzero PV) are stable. The emphasis is put on the nontrivial behavior of inertia-gravity waves (IGWs) when deformed by a background shear. In particular, we show that in the linear limit, sheared inertia-gravity waves asymptotically oscillate at the inertial waves frequency, but their amplitude is sensitive to shear, stratification, and rotation. Last, we study the development of the IGWs dynamics considering isotropic initial conditions. Computations indicate that both the vortex mode and the wave mode generate IGWs, but the energy of the IGWs generated by the vortex mode is more important than the energy of the IGWs generated by the wave mode. It is also found that, at large times, the energy of the IGWs generated by the vortex mode increases as the ratio $k_v/k_h$ (initial vertical wavenumber over horizontal wavenumber) increases (like $k_v^2/k_h^2),$ while the energy of the IGWs generated by the wave mode oscillates in function of $k_v/k_h.$

The instability of the flow of a viscous fluid past a soft, two-layered gel is probed using experiments, and the observations are compared with results from a linear stability analysis. The experimental system consists of the rotating top plate of a rheometer and its stationary bottom plate on which the two-layer gel is placed. When the flow between the top plate and the two-layer gel is viscometric (i.e., laminar), the viscosity obtained from the rheometer is a measure of the material property of the fluid. However, after a critical shear stress, there is a sudden increase in apparent viscosity, indicating that the flow has undergone an instability due to the deformable nature of the two-layer gel. Experiments are carried out to quantify how the critical value of fluid shear stress required to destabilize the flow varies as a function of ratio of solid to fluid layer thickness, and the ratio of the shear moduli of the two gels. A linear stability analysis is carried out for plane Couette flow of a Newtonian fluid past the two-layered gel, by assuming the two solid layers to be elastic neo-Hookean materials. In order to compare the experimental and theoretical results, the effective shear modulus ($G_{\mathrm{eff}}$, defined by $H/G_{\mathrm{eff}}=H_1/G_1+H_2/G_2$) of the two-layer gel is found to be useful, where $H=H_1+H_2$. Here, $H_i$ and $G_i$ ($i=1,2$), respectively, denote the thickness and shear modulus of each layer. Results for the nondimensional parameter ${\Gamma }_{\mathrm{eff}}=\eta V/\left(d{G}_{\mathrm{eff}}\right)$ ($V$ is the velocity of the top plate; $\eta$ is fluid viscosity, $d$ is the fluid thickness) as a function of solid to fluid thickness $H/d$ obtained from the stability analysis agree well with experimental observations, without any fitting parameters. In general, we find that the flow is more unstable if the softer gel is adjacent to the fluid flow compared to the case when it is not. This suggests that the instability is more interfacial in nature and is crucially dependent on the relative placement of the two layers, and not just on the effective modulus of the two-layer gel. We further show that the theoretical and experimental data for two-layer gels can be suitably collapsed onto the results obtained for a single-gel layer.

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity $\left(\alpha \right)$ in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case $\alpha \to \infty$ [U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008)], is now shown to be true for any large, but finite, value of $\alpha$ greater than a crossover value ${\alpha }_{\mathrm{crossover}}$. We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows.

We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical and efficient algorithm like the Gillespie algorithm for Markovian processes, with the difference being that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of nonexponential interevent time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general because it can be implemented very easily in cases (such as for delays coupled to the evolution of the system) in which other algorithms do not work or need adapted versions that are less efficient in computational terms.

We study complex eigenvalues of the Wishart model for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as $\mathsf{C}={\mathsf{AB}}^t/T$, where ${\mathsf{B}}^t$ is the transpose of $\mathsf{B}$ and both matrices $\mathsf{A}$ and $\mathsf{B}$ are of dimensions $N\times T$. If $\mathsf{A}$ and $\mathsf{B}$ are uncorrelated, or equivalently if $\mathsf{C}$ vanishes on average, it is known that at large matrix dimension the domain of the eigenvalues of $\mathsf{C}$ is a circle centered-at-origin and the eigenvalue density depends only on the radial distances. We consider actual correlation in $\mathsf{A}$ and $\mathsf{B}$ and derive a result for the contour describing the domain of the bulk of the eigenvalues of $\mathsf{C}$ in the limit of large $N$ and $T$ where the ratio $N/T$ is finite. In particular, we show that the eigenvalue domain is sensitive to the correlations. For example, when $\mathsf{C}$ is diagonal on average with the same element $c\ne 0$, the contour is no longer a circle centered at origin but a shifted ellipse. In this case we explicitly derive a result for the spectral density which again depends only on the radial distances. For more general cases, we show that the contour depends on the symmetric and antisymmetric parts of the correlation matrix resulting from the ensemble-averaged $\mathsf{C}$. If the correlation matrix is normal, then the contour depends only on its spectrum. We also provide numerics to justify our analytics.

We generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward-path probability vanishes and the entropy production diverges, rendering conventional integral fluctuation theorems inapplicable. We identify the mathematical origins of absolute irreversibility as the singularity of probability measure. We demonstrate the validity of the obtained equalities for several models.

Although the fully connected Ising model does not have a length scale, we show that the critical exponents for thermodynamic quantities such as the mean magnetization and the susceptibility can be obtained using finite size scaling with the scaling variable equal to $N$, the number of spins. Surprisingly, the mean value and the most probable value of the magnetization are found to scale differently with $N$ at the critical temperature of the infinite system, and the magnetization probability distribution is not a Gaussian, even for large $N$. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show that hyperscaling can be restored by increasing $N$ while holding the Ginzburg parameter rather than the temperature fixed, or by doing finite size scaling at the pseudocritical temperature where the susceptibility is a maximum for a given value of $N$. We conclude that finite size scaling for the fully connected Ising model yields different results depending on how the mean-field limit is approached.

While the characteristics of the driven translocation for asymptotically long polymers are well understood, this is not the case for finite-sized polymers, which are relevant for real-world experiments and simulation studies. Most notably, the behavior of the exponent $\alpha$, which describes the scaling of the translocation time with polymer length, when the driving force $f_p$ in the pore is changed, is under debate. By Langevin dynamics simulations of regular and modified translocation models using the freely jointed-chain polymer model we find that a previously reported incomplete model, where the trans side and fluctuations were excluded, gives rise to characteristics that are in stark contradiction with those of the complete model, for which $\alpha$ increases with $f_p$. Our results suggest that contribution due to fluctuations is important. We construct a minimal model where dynamics is completely excluded to show that close alignment with a full translocation model can be achieved. Our findings set very stringent requirements for a minimal model that is supposed to describe the driven polymer translocation correctly.

Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted (“outliers”). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.

The spread of disease on complex networks has attracted wide attention in the physics community. Recent works have demonstrated that heterogeneous degree and weight distributions have a significant influence on the epidemic dynamics. In this study, a novel edge-weight-based compartmental approach is developed to estimate the epidemic threshold and epidemic size (final infected density) on networks with general degree and weight distributions, and a remarkable agreement with numerics is obtained. Even in complex networks with the strong heterogeneous degree and weight distributions, this approach is used. We then propose an edge-weight-based removal strategy with different biases and find that such a strategy can effectively control the spread of epidemic when the highly weighted edges are preferentially removed, especially when the weight distribution of a network is extremely heterogenous. The theoretical results from the suggested method can accurately predict the above removal effectiveness.

We investigate the influence of time-delayed coupling on the nature of the aging transition in a system of coupled oscillators that have a mix of active and inactive oscillators, where the aging transition is defined as the gradual loss of collective synchrony as the proportion of inactive oscillators is increased. We start from a simple model of two time-delay coupled Stuart-Landau oscillators that have identical frequencies but are located at different distances from the Hopf bifurcation point. A systematic numerical and analytic study delineates the dependence of the critical coupling strength (at which the system experiences total loss of synchrony) on time delay and the average distance of the system from the Hopf bifurcation point. We find that time delay can act to facilitate the aging transition by lowering the threshold coupling strength for amplitude death in the system. We then extend our study to larger systems of globally coupled active and inactive oscillators including an infinite system in the thermodynamic limit. Our model system and results can provide a useful paradigm for understanding the functional robustness of diverse physical and biological systems that are prone to aging transitions.