The ${\mathrm{Na}}^{+}$ current in nerve and muscle membranes may be described in terms of the activation variable $m\left(t\right)$ and the inactivation variable $h\left(t\right)$, which are dependent on the transitions of S4 sensors of each of the ${\mathrm{Na}}^{+}$ channel domains DI to DIV. The time-dependence of the ${\mathrm{Na}}^{+}$ current and the rate equations satisfied by $m\left(t\right)$ and $h\left(t\right)$ may be derived from the solution to a master equation that describes the coupling between two or three activation sensors regulating the ${\mathrm{Na}}^{+}$ channel conductance and a two-stage inactivation process. If the inactivation rate from the closed or open states increases as the S4 sensors activate, a more general form of the Hodgkin-Huxley expression for the open-state probability may be derived where $m\left(t\right)$ is dependent on both activation and inactivation processes. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined expressions and exhibit saturation for both depolarized and hyperpolarized clamp potentials.

Using molecular dynamics simulations we investigate the finite-size dependence of the dynamical properties of a diatomic supercooled liquid. The simplicity of the molecule permits us to access the microsecond time scale. We find that the relaxation time decreases simultaneously with the strength of cooperative motions when the size of the system decreases. While the decrease of the cooperative motions is in agreement with previous studies, the decrease of the relaxation time opposes what has been reported to date in monatomic glass formers and in silica. This result suggests the presence of different competing physical mechanisms in the relaxation process. For very small box sizes the relaxation times behavior reverses itself and increases strongly when the box size decreases, thus leading to a nonmonotonic behavior. This result is in qualitative agreement with defect and facilitation theories.

Resonant x-ray scattering experiments revealed transitional subphases near the electric-field-induced phase transition of a Se-containing chiral liquid crystal in a planar aligned cell geometry. In the lower-temperature range ($\mathrm{Sm}-C_A^{*}$ and three-layer periodicity $\mathrm{Sm}-C_{\gamma }^{*}$ phases), the six-layer periodicity subphase appeared with increasing electric field during the field-induced transition from $\mathrm{Sm}-C_{\gamma }^{*}$ to Sm-$C^{*}$. In the higher-temperature range [four-layer periodicity antiferroelectric (AF) phase], the peak positions of the three-layer satellites shifted to those of the four-layer satellites and then the satellites corresponding to the five- through seven-layer periodicity appeared in sequence. Near the AF to $\mathrm{Sm}-C_{\alpha }^{*}$ phase transition temperature, the layer periodicity increased with applied field. The molecular configurations of the subphases near the field-induced transition are discussed based on the Ising, distorted clock, and perfect clock models.

Over a range of liquid-solid contact angles, an open-channel capillary with curved or angled sides can show a maximum in the Laplace pressure as a function of the filling state. Examples include double-angle wedges, grooves scored into flat surfaces, steps on surfaces, and the groove between touching parallel cylinders. The liquid in such a channel exhibits a beading instability if the channel is filled beyond the Laplace pressure maximum. The subsequent droplet coarsening takes place by hydraulic transport through the connecting liquid columns that remain in the groove. A mean-field scaling argument predicts the characteristic droplet radius $R\sim t^{1/7}$, as a function of time $t$. This is confirmed by one-dimensional simulations of the coarsening kinetics. Some remarks are also made on the spreading kinetics of an isolated drop deposited in such a channel.

Turbulent plasma flow, amplified by rapid three-dimensional compression, can be suddenly dissipated under continuing compression. This effect relies on the sensitivity of the plasma viscosity to the temperature, $\mu \sim T^{5/2}$. The plasma viscosity is also sensitive to the plasma ionization state. We show that the sudden dissipation phenomenon may be prevented when the plasma ionization state increases during compression, and we demonstrate the regime of net viscosity dependence on compression where sudden dissipation is guaranteed. Additionally, it is shown that, compared to cases with no ionization, ionization during compression is associated with larger increases in turbulent energy and can make the difference between growing and decreasing turbulent energy.

A right-hand circularly polarized electromagnetic wave can propagate in a sufficiently magnetized plasma of any density without encountering cutoff in the whistler mode. With the recent realization of tens-kilotesla magnetic fields, laser propagation in highly magnetized high-density plasmas has become of practical interest, especially for heating plasmas to high energy density and igniting fusion targets. In this paper, the whistler regime of laser-plasma interaction is discussed. It is shown by one- and two-dimensional particle-in-cell simulations that moderately intense right-hand circularly polarized laser light can enter and propagate in high-density plasma and heat it efficiently because of the significantly reduced wave length and speed.

Microscopic stress fields are widely used in molecular simulations to understand mechanical behavior. Recently, decomposition methods of multibody forces to central force pairs between the interacting particles have been proposed. Here, we introduce a force center of a three-body potential and propose different force decompositions that also satisfy the conservation of translational and angular momentum. We compare the force decompositions by stress-distribution magnitude and discuss their difference in the stress profile of a bilayer membrane by using coarse-grained and atomistic molecular dynamics simulations.

Particle-in-cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including, e.g., laser-wakefield acceleration, when viewed in a Lorentz-boosted frame) but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.

In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transition in a random-field Heisenberg chain. We demonstrate that the fidelity and fidelity susceptibility can be utilized to characterize the interaction-driven many-body localization transition in this closed spin system which is in agreement with previous analytical and numerical results [S. Garnerone, N. T. Jacobson, S. Haas, and P. Zanardi, Phys. Rev. Lett. 102, 057205 (2009); P. Zanardi and N. Paunkovic, Phys. Rev. E 74, 031123 (2006)]. In particular, instead of ground-state fidelity, we test the fidelity between two diagonal ensembles related by a small parameter perturbation $\delta h$, it is special that here the parameter perturbation $\delta h_i$ for each site are random variables like $h_i$. It shows that fidelity of the diagonal ensemble develop a pronounced drop at the transition. We utilize fidelity to estimate the critical disorder strength $h_c$ for different system size, we get $h_c\in$ [2.5,3.9] and get a power-law decay with an exponent of roughly $-1.49\left(2\right)$ for system size $N$, and can extrapolate $h_c^{\inf }$ of the infinite system is about 2.07 which all agree with a recent work by Huse and Pal, in which the MBL transition in the same model was predicted to be hc [2,4]. We also estimate the scaling of maximum of averaged fidelity susceptibility as a function of system size $N$, it shows a power law increase with an exponent of about 5.05(1).

Cold atomic clouds have been shown to have some similarities with plasmas. Previous studies showed that such clouds exhibit instabilities induced by long-range interactions. However, they did not describe the spatial properties of the dynamics. In this paper, we study experimentally the spatial nature of stochastic instabilities, and we find out that the dynamics is localized. Data are analyzed both in the spectral domain and in the spatial domain (principal component analysis). Both methods fail to describe the dynamics in terms of eigenmodes, showing that space and time are not separable.

Sound propagation through a rarefied gas inside a two-dimensional cavity is investigated on the basis of the linearized Boltzmann equation, where one of the cavity walls oscillates harmonically in the direction normal to its own surface and is considered as a sound source. An analytical solution at high oscillation frequencies is obtained and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillation frequency on the average gas pressure exerted on the oscillating plate is studied. It is found that, at large values of the aspect ratio, the average pressure oscillates when the sound frequency varies, due to the sound resonance and antiresonance along the oscillation direction of the plate. However, at small values of the aspect ratio, the average pressure is a monotonically decreasing function of the sound frequency, which cannot be observed in the corresponding one-dimensional counterpart. This is explained by the sound interference in the direction parallel to the oscillating plate. The influence of both the cavity aspect ratio and oscillation frequency on the sound speed is also investigated: Again it is found that a different aspect ratio leads to the different behavior of the sound speed as a function of the oscillation frequency.

Nonequilibrium systems lack an explicit characterization of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of the parameters of a model when its dynamics lacks detailed balance. Such nonequilibrium systems occur naturally in applications like neural networks and gene regulatory networks. Here, we focus on the paradigmatic asymmetric Ising model and show that we can learn its parameters from independent samples of the nonequilibrium steady state. We present both an exact inference algorithm and a computationally more efficient, approximate algorithm for weak interactions based on a systematic expansion around mean-field theory. Obtaining expressions for magnetizations and two- and three-point spin correlations, we establish that these observables are sufficient to infer the model parameters. Further, we discuss the symmetries characterizing the different orders of the expansion around the mean field and show how different types of dynamics can be distinguished on the basis of samples from the nonequilibrium steady state.

Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system's configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities.

We report time-dependent probability density functions (PDFs) for a nonlinear stochastic process with a cubic force using analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF $p(x,t)$ in general involves a time integral, and useful PDFs with explicit dependence on $x$ and $t$ are presented in certain limits (e.g., in the short and long time limits). Numerical simulations of the Fokker-Planck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that transient PDFs behave drastically differently from the stationary PDFs in regard to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric with the kurtosis smaller than 3, transient PDFs are skewed with the kurtosis larger than 3; transient PDFs are much broader than stationary PDFs. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in the relaxation process.

We realize an extensive numerical study of the naming game model with a noise term which accounts for perturbations. This model displays a nonequilibrium phase transition between an absorbing ordered consensus state, which occurs for small noise, and a disordered phase with fragmented clusters characterized by heterogeneous memories, which emerges at strong noise levels. The nature of the phase transition is studied by means of a finite-size scaling analysis of the moments. We observe a scaling behavior typical of a discontinuous transition and we are able to estimate the thermodynamic limit. The scaling behavior of the clusters size seems also compatible with this kind of transition.

Akin to electric circuits, we construct biocircuits that are manipulated by cutting and assembling channels through which stochastic information flows. This diagrammatic manipulation allows us to create a method which constructs networks by joining building blocks selected so that (a) they cover only basic processes; (b) it is scalable to large networks; (c) the mean and variance-covariance from the Pauli master equation form a closed system; and (d) given the initial probability distribution, no special boundary conditions are necessary to solve the master equation. The method aims to help with both designing new synthetic signaling pathways and quantifying naturally existing regulatory networks.

We present analytical and numerical results on localized fluidization within a granular layer subjected to a local injection of fluid. As the injection rate increases the three different regimes previously reported in the literature are recovered: homogeneous expansion of the bed, fluidized cavity in which fluidization starts developing above the injection area, and finally the chimney of fluidized grains when the fluidization zone reaches the free surface. The analytical approach is at the continuum scale, based on Darcy's law and Therzaghi's effective stress principle. It provides a good description of the phenomenon as long as the porosity of the granular assembly remains relatively homogeneous, i.e., for small injection rates. The numerical approach is at the particle scale based on the coupled discrete element method and a pore-scale finite volume method. It tackles the more heterogeneous situations which occur at larger injection rates. The results from both methods are in qualitative agreement with data published independently. A more quantitative agreement is achieved by the numerical model. A direct link is evidenced between the occurrence of the different regimes of fluidization and the injection aperture. While narrow apertures let the three different regimes be distinguished clearly, larger apertures tend to produce a single homogeneous fluidization regime. In the former case, it is found that the transition between the cavity regime and the chimney regime for an increasing injection rate coincides with a peak in the evolution of inlet pressure. Finally, the occurrence of the different regimes is defined in terms of the normalized flux and aperture.

We consider the dynamical properties of boundary lubrication in contact between two atomically smooth solid surfaces separated by an ultrathin layer of lubricant. In contrast to previous works on this topic, we explicitly consider the heterogeneity of tangential stresses, which arises in a contact of elastic bodies that are moved tangentially relative to each other. To describe phase transitions between structural states of the lubricant we use an approach based on the field theory of phase transitions. It is assumed that the lubricant layer, when stressed, can undergo a shear-melting transition of first or second order. While solutions for the homogeneous system can be easily obtained analytically, the kinetics of the phase transitions in the spatially heterogeneous system can only be studied numerically. In our numerical experiments melting of the lubricant layer starts from the outer boundary of contact and propagates to its center. The melting wave is followed by a wave of solidification. This process repeats itself periodically, following the stick-slip pattern that is characteristic of such systems. Depending on the thermodynamic and kinetic parameters of the model, different modes of sliding with almost complete or only partial intermediate solidification are possible.

Synthetic turbulence models are useful tools that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of one-dimensional (1D) and 3D synthetic turbulence previously developed still required large computational resources. A “wavelet-based” model of synthetic turbulence, able to produce a field with tunable spectral law, intermittency, and anisotropy, is presented here. The rapid algorithm introduced, based on the classic $p$-model of intermittent turbulence, allows us to reach a broad spectral range using a modest computational effort. The model has been tested against the standard diagnostics for intermittent turbulence, i.e., the spectral analysis, the scale-dependent statistics of the field increments, and the multifractal analysis, all showing an excellent response.