Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.

We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical $(u,v)$ flower network with $u\le v$. Highest degree nodes are linked directly without intermediate nodes for $u=1$, while this is not the case for $u\ne 1$. Using the renormalization-group-like procedure, we derive the recursion relations for the percolating probability and the percolation order parameter, from which the percolation threshold and the critical exponents are obtained. When $u\ne 1$, the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When $u=1$, the DOP and the bond percolation have the same vanishing percolation threshold but the critical behaviors are different. Implication to an epidemic spreading phenomenon is discussed.

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

We study dynamical systems on a hypernetwork, namely by coupling them through several variables. For the case when the coupling(s) are all linear, a comprehensive analysis of the master stability function (MSF) for synchronized dynamics is presented and, through application to a number of paradigmatic examples, the typical forms of the MSF are discussed. The MSF formalism for hypernetworks also provides a framework to study synchronization in systems that are diffusively coupled through dissimilar variables—the so-called conjugate coupling that can lead to amplitude or oscillation death.

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

We investigate the bounds between normal or anomalous effective diffusion for inertial particles transported by parallel flows. The infrared behavior of the fluid kinetic-energy spectrum, i.e., the possible presence of long-range spatiotemporal correlations, is modeled as a power law by means of two parameters, and the problem is studied as a function of these latter. Our results, obtained in the limit of weak relative inertia, extend well-known results for tracers and apply to particles of any mass density, subject to gravity and Brownian diffusion. We consider both steady and time-dependent flows, and cases of both vanishing and finite particle sedimentation.

We propose an efficient numerical method to study the transport properties of armchair graphene ribbons in the presence of a generic external potential. The method is based on a continuum envelope-function description with physical boundary conditions. The envelope functions are computed in the reciprocal space, and the transmission is then obtained with a recursive scattering matrix approach. This allows a significant reduction of the computational time with respect to finite difference simulations.

We report a different kind of particle clustering caused purely by gravity, discovered in our simulation of particle-laden turbulence. Clustering in a vertical strip pattern forms when strong gravity acts on heavy particles. This phenomenon is explained by the skewness of the flow velocity gradient in the gravitational direction experienced by particles, which causes horizontal convergence of particles.

Dense-plasma-focus (DPF) $Z$-pinch devices are sources of copious high-energy electrons and ions, x rays, and neutrons. The mechanisms through which these physically simple devices generate such high-energy beams in a relatively short distance are not fully understood and past optimization efforts of these devices have been largely empirical. Previously we reported on fully kinetic simulations of a DPF and compared them with hybrid and fluid simulations of the same device. Here we present detailed comparisons between fully kinetic simulations and experimental data on a 1.2 kJ DPF with two electrode geometries, including neutron yield and ion beam energy distributions. A more intensive third calculation is presented which examines the effects of a fully detailed pulsed power driver model. We also compare simulated electromagnetic fluctuations with direct measurement of radiofrequency electromagnetic fluctuations in a DPF plasma. These comparisons indicate that the fully kinetic model captures the essential physics of these plasmas with high fidelity, and provide further evidence that anomalous resistivity in the plasma arises due to a kinetic instability near the lower hybrid frequency.

We consider a method for the accurate estimation of quenched random fields in the inverse Ising problem. Approximations such as the mean-field or Bethe methods are applied to estimate quenched random coupling parameters and external fields. A diagonal matching method is introduced to ensure consistency of the diagonal part of the susceptibility, and the method yields an accurate estimation of the external fields. We introduce the diagonal matching method into the mean-field, Thouless-Anderson-Palmer, and Bethe approximations, and we investigate the effect of the diagonal matching method on the accuracy of estimation of the external fields.

We investigate the low-energy properties as well as quantum and thermal phase transitions of the Baxter-Wu model in a transverse magnetic field. Our study relies on stochastic series expansion quantum Monte Carlo and on series expansions about the low- and high-field limits at zero temperature using the quantum finite-lattice method on the triangular lattice. The phase boundary consists of a second-order critical line in the four-state Potts model universality class starting from the pure Baxter-Wu limit meeting a first-order line connected to the zero-temperature transition point ($h\approx 2.4$, $T=0$). Both lines merge at a tricritical point approximately located at ($h\approx 2.3J$, $T\approx J$).

Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We employ the cavity method of statistical physics to find the optimal density matrix representation by slowly decreasing the temperature in an annealing algorithm, or by minimizing an approximate Bethe free energy depending on the reduced density matrices and some cavity messages originated from the Bethe approximation of the entropy. We obtain the classical Bethe expression for the entropy within a naive (mean-field) approximation of the cavity messages, which is expected to work well at high temperatures. In the next order of the approximation, we obtain another expression for the Bethe entropy depending only on the diagonal elements of the reduced density matrices. In principle, we can improve the entropy approximation by considering more accurate cavity messages in the Bethe approximation of the entropy. We compare the annealing algorithm and the naive approximation of the Bethe entropy with exact and approximate numerical simulations for small and large samples of the random transverse Ising model on random regular graphs.

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic $I_3/I_1$ shows a power-law behavior with strain amplitude. In addition, $I_3/I_1$ and the elastic component of stress amplitude ${\sigma }_0^E$ show a very prominent maximum at the strain value where the number density $\left(n_v\right)$ of the Taylor vortices is maximum. A subsequent increase in applied strain $\left(\gamma \right)$ results in the distortions of the vortices and a concomitant decrease in $n_v$, accompanied by a sharp drop in $I_3$ and ${\sigma }_0^E$. The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of $\gamma$ corresponding to the peak of $I_3$, similar to that observed for hard-sphere glasses.

When a liquid is rapidly quenched to a temperature below the glass-transition point, it is driven out of equilibrium; it then slowly relaxes to a (quasi)equilibrium state. This slow relaxation process is called aging. By definition, any glasses are inevitably in the process of aging and actually slowly evolving with time. Thus the study of aging phenomena is of fundamental importance for understanding not only the nonequilibrium nature of the glass transition, but also the stability of glassy materials. Here we consider aging after a rather shallow quench, for which a system is still able to reach (metastable) equilibrium. By using polydisperse colloidal liquids as a model, we show the validity of dynamical scaling that there is only one relevant length scale not only for a quasiequilibrium supercooled state but also for a nonequilibrium process of aging, which is reminiscent of dynamical critical phenomena. Our finding indicates that the aging toward (metastable) equilibrium may be regarded as the growth process of critical-like fluctuations of static order associated with low-free-energy configurations, further suggesting that this ordering is the origin of cooperative slow dynamics in the systems studied. The generality of this statement for other glass-forming systems remains for a future study.

The creation of synthetic systems that emulate the defining properties of living matter, such as motility, gradient-sensing, signaling, and replication, is a grand challenge of biomimetics. Such imitations of life crucially contain active components that transform chemical energy into directed motion. These artificial realizations of motility point in the direction of a new paradigm in engineering, through the design of emergent behavior by manipulating properties at the scale of the individual components. Catalytic colloidal swimmers are a particularly promising example of such systems. Here we present a comprehensive theoretical description of gradient-sensing of an individual swimmer, leading controllably to chemotactic or anti-chemotactic behavior, and use it to construct a framework for studying their collective behavior. We find that both the positional and the orientational degrees of freedom of the active colloids can exhibit condensation, signaling formation of clusters and asters. The kinetics of catalysis introduces a natural control parameter for the range of the interaction mediated by the diffusing chemical species. For various regimes in parameter space in the long-ranged limit our system displays precise analogs to gravitational collapse, plasma oscillations, and electrostatic screening. We present prescriptions for how to tune the surface properties of the colloids during fabrication to achieve each type of behavior.

The dynamics of charged colloids in an electrolyte solution is studied using direct numerical simulations via the smoothed profile method. We calculated the complex electrophoretic mobility ${\mu }^{*}\left(\omega \right)$ of the charged colloids under an oscillating electric field of frequency $\omega$. We show the existence of three dynamically distinct regimes, determined by the momentum diffusion and ionic diffusion time scales. The present results agree well with approximate theories based on the cell model in dilute suspensions; however, systematic deviations between the simulation results and theoretical predictions are observed as the volume fraction of colloids is increased, similar to the case of constant electric fields.

We investigate the structural properties of a small binary system of dusty plasma subjected to an anisotropic external confinement. We have found that the ground state can form various symmetrical configurations, which generally correspond to variations of a multiple-ring structure. The presence of such structures is given through a detailed phase diagram constructed for the systems with $N=18$ and 24 particles. Furthermore, we show that the configurations of multiple rings can present a persistent behavior for the case in which the number of less-charged particles is equal to a multiple of the number of particles per ring. Finally, we discuss the main characteristics of the transitions of first and second orders since these are related to the main configurational changes of the ground states.

This paper explores asymmetric elasticity of a double-stranded helical chain, which serves as a minimal model of biopolymers. The model consists of two elastic chains that mutually intertwine in a right-handed manner, forming a double-stranded helix. A simple numerical experiment for structural relaxation, which reduces the total elastic energy of the model monotonically without thermal fluctuations, reveals possible asymmetric elasticity inherent in the helical chain. It is first shown that a short segment of the double-stranded helical chain has a tendency to unwind when it is bent. It is also shown that a short segment of the helical chain has a tendency to writhe in the left direction upon bending. This tendency gives rise to a propensity for a longer segment of the chain to form a left-handed superhelix spontaneously upon bending. Finally, this propensity of the helical chain to form a left-handed superhelix is proposed to be a possible origin of the uniform left-handed wrapping of DNA around nucleosome core particles in nature. The results presented here could provide deeper insights into the roles and significance of helical chirality of biopolymers.

We investigate the dynamics of a conductance-based neuron model coupled to a model of intracellular calcium uptake and release by the endoplasmic reticulum. The intracellular calcium dynamics occur on a time scale that is orders of magnitude slower than voltage spiking behavior. Coupling these mechanisms sets the stage for the appearance of chaotic dynamics, which we observe within certain ranges of model parameter values. We then explore the question of whether one can, using observed voltage data alone, estimate the states and parameters of the voltage plus calcium (V+Ca) dynamics model. We find the answer is negative. Indeed, we show that voltage plus another observed quantity must be known to allow the estimation to be accurate. We show that observing both the voltage time course $V\left(t\right)$ and the intracellular Ca time course will permit accurate estimation, and from the estimated model state, accurate prediction after observations are completed. This sets the stage for how one will be able to use a more detailed model of V+Ca dynamics in neuron activity in the analysis of experimental data on individual neurons as well as functional networks in which the nodes (neurons) have these biophysical properties.

Symmetry restrictions due to fluidity require the strain energy in the Helfrich theory of lipid membranes to be locally isotropic in nature. Although this framework is suitable for modeling the interaction of membranes with proteins that generate spherical curvature such as clathrin, there are other important membrane-bending proteins such as BIN-amphiphysin-Rvs proteins that form a cylindrical coat with different curvatures in the longitudinal and the circumferential directions. In this work, we present a detailed mathematical treatment of the theory of lipid membranes incorporating anisotropic spontaneous curvatures. We derive the associated Euler-Lagrange equations and the edge conditions in a generalized setting that allows spatial heterogeneities in the properties of the membrane-protein system. We employ this theory to model the constriction of a membrane tubule by a cylindrical scaffold. In particular, we highlight the role of the equilibrium equation in the tangential plane in regulating the spatial variation of the surface tension field.