The heart is an excitable medium which is excited by membrane potential depolarization and propagation. Membrane potential depolarization brings in calcium (Ca) through the Ca channels to trigger intracellular Ca release for contraction of the heart. Ca also affects voltage via Ca-dependent ionic currents, and thus, voltage and Ca are bidirectionally coupled. It has been shown that the voltage subsystem or the Ca subsystem can generate its own dynamical instabilities which are affected by their bidirectional couplings, leading to complex dynamics of action potential and Ca cycling. Moreover, the dynamics become spatiotemporal in tissue in which cells are diffusively coupled through voltage. A widely investigated spatiotemporal dynamics is spatially discordant alternans (SDA) in which action potential duration (APD) or Ca amplitude exhibits temporally period-2 and spatially out-of-phase patterns, i.e., APD-SDA and Ca-SDA patterns, respectively. However, the mechanisms of formation, stability, and synchronization of APD-SDA and Ca-SDA patterns remain incompletely understood. In this paper, we use cardiac tissue models described by an amplitude equation, coupled iterated maps, and reaction-diffusion equations with detailed physiology (the ionic model) to perform analytical and computational investigations. We show that, when the Ca subsystem is stable, the Ca-SDA pattern always follows the APD-SDA pattern, and thus, they are always synchronized. When the Ca subsystem is unstable, synchronization of APD-SDA and Ca-SDA patterns depends on the stabilities of both subsystems, their coupling strengths, and the spatial scales of the initial Ca-SDA patterns. Spontaneous (initial condition-independent) synchronization is promoted by enhancing APD instability and reducing Ca instability as well as stronger Ca-to-APD and APD-to-Ca coupling, a pattern formation caused by dynamical instabilities. When Ca is more unstable and APD is less unstable or APD-to-Ca coupling is weak, synchronization of APD-SDA and Ca-SDA patterns is promoted by larger initially synchronized Ca-SDA clusters, i.e., initial condition-dependent synchronization. The synchronized APD-SDA and Ca-SDA patterns can be locked in-phase, antiphase, or quasiperiodic depending on the coupling relationship between APD and Ca. These theoretical and simulation results provide mechanistic insights into the APD-SDA and Ca-SDA dynamics observed in experimental studies.

We address the effects of dry friction, which has emerged only recently to play an important role in some biological systems. In particular, we investigate the nonequilibrium dynamics of a mesoscopic particle, bound to a spring being pulled at a definite speed, moving on a surface with dry friction in a noisy environment. We model the dry friction phenomenologically with a term that is proportional to the sign of the velocity, and by means of numerical simulations of a Langevin equation we show that (a) the frictional force scales with the logarithm of the pulling velocity, (b) the probability distribution function of the spatial displacement away from the potential minimum is non-Gaussian, (c) the fluctuation-dissipation theorem is violated as expected, but (d) the work function obeys the stationary fluctuation theorem, with an effective temperature related to the noise of the system.

Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched Rosenbluth method Monte Carlo simulations are used to calculate the variation of the conformational free energy $F$ of a hard-sphere polymer with respect to the cone-tip-to-surface distance $h$ from which the variation of the entropic force $f\equiv |dF/dh|$ with $h$ is determined. We consider the following cases: a single freely jointed tethered chain, a single semiflexible tethered chain, and several freely jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi et al. [Maghrebi et al., Europhys. Lett. 96, 66002 (2011); Phys. Rev. E 86, 061801 (2012)] that $f\propto ({\gamma }_{\infty }-{\gamma }_0)h^{-1}$, where ${\gamma }_0$ and ${\gamma }_{\infty }$ are universal scaling exponents for the partition function of the tethered polymer for $h=0$ and $h=\infty$, respectively. The measured functions $f\left(h\right)$ are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.

Flow of size-bidisperse particle mixtures in a spherical tumbler rotating alternately about two perpendicular axes produces segregation patterns that track the location of nonmixing islands predicted by a dynamical systems approach. To better understand the paradoxical accumulation of large particles in regions defined by barriers to transport, we perform discrete element method (DEM) simulations to visualize the three-dimensional structure of the segregation patterns and track individual particles. Our DEM simulations and modeling results indicate that segregation pattern formation in the biaxial spherical tumbler is due to the interaction of size-driven radial segregation with the weak spanwise component of the advective surface flow. Specifically, we find that after large particles segregate to the surface, slow axial drift in the flowing layer, which is inherent to spherical tumblers, is sufficient to drive large particles across nominal transport barriers and into nonmixing islands predicted by an advective flow model in the absence of axial drift. Axial drift alters the periodic dynamics of nonmixing islands, turning them into “sinks” where large particles accumulate even in the presence of collisional diffusion. Overall, our results indicate that weak perturbation of chaotic flow has the potential to alter key dynamical system features (e.g., transport barriers), which ultimately can result in unexpected physical phenomena.

This study presents deep neural network solutions to a time-integrated Smoluchowski equation modeling the mean first passage time of nanoparticles traversing the slit-well microfluidic device. This physical scenario is representative of a broader class of parametrized first passage problems in which key output metrics are dictated by a complicated interplay of problem parameters and system geometry. Specifically, whereas these types of problems are commonly studied using particle simulations of stochastic differential equation models, here the corresponding partial differential equation model is solved using a method based on deep neural networks. The results illustrate that the neural network method is synergistic with the time-integrated Smoluchowski model: together, these are used to construct continuous mappings from key physical inputs (applied voltage and particle diameter) to key output metrics (mean first passage time and effective mobility). In particular, this capability is a unique advantage of the time-integrated Smoluchowski model over the corresponding stochastic differential equation models. Furthermore, the neural network method is demonstrated to easily and reliably handle geometry-modifying parameters, which is generally difficult to accomplish using other methods.

It is well known that an inverse turbulent cascade in a finite ($2\pi \times 2\pi$) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length $l_f=2\pi /k_f$ with $k_f$ ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior $\mathrm{\Omega }\left(r\right)={(3\epsilon /\alpha )}^{1/2}{r}^{-1}$, where $r$ is the distance to the vortex center, $\alpha$ is the bottom friction coefficient, and $\epsilon$ is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite $k_f$ the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with $r$, and show that in this case the vorticity profile can be flatter than the asymptotic limit.

Modeling the three-dimensional (3D) structure from a given 2D image is of great importance for analyzing and studying the physical properties of porous media. As an intractable inverse problem, many methods have been developed to address this fundamental problems over the past decades. Among many methods, the deep learning–(DL) based methods show great advantages in terms of accuracy, diversity, and efficiency. Usually, the 3D reconstruction from the 2D slice with a larger field-of-view is more conducive to simulate and analyze the physical properties of porous media accurately. However, due to the limitation of reconstruction ability, the reconstruction size of most widely used generative adversarial network–based model is constrained to ${64}^3$ or ${128}^3$. Recently, a 3D porous media recurrent neural network based method (namely, 3D-PMRNN) (namely 3D-PMRNN) has been proposed to improve the reconstruction ability, and thus the reconstruction size is expanded to ${256}^3$. Nevertheless, in order to train these models, the existed DL-based methods need to down-sample the original computed tomography (CT) image first so that the convolutional kernel can capture the morphological features of training images. Thus, the detailed information of the original CT image will be lost. Besides, the 3D reconstruction from a optical thin section is not available because of the large size of the cutting slice. In this paper, we proposed an improved recurrent generative model to further enhance the reconstruction ability (${512}^3$). Benefiting from the RNN-based architecture, the proposed model requires only one 3D training sample at least and generates the 3D structures layer by layer. There are three more improvements: First, a hybrid receptive field for the kernel of convolutional neural network is adopted. Second, an attention-based module is merged into the proposed model. Finally, a useful section loss is proposed to enhance the continuity along the $Z$ direction. Three experiments are carried out to verify the effectiveness of the proposed model. Experimental results indicate the good reconstruction ability of proposed model in terms of accuracy, diversity, and generalization. And the effectiveness of section loss is also proved from the perspective of visual inspection and statistical comparison.

In this paper, we focus on the link density in random geometric graphs (RGGs) with a distance-based connection function. After deriving the link density in $D$ dimensions, we focus on the two-dimensional (2D) and three-dimensional (3D) space and show that the link density is accurately approximated by the Fréchet distribution, for any rectangular space. We derive expressions, in terms of the link density, for the minimum number of nodes needed in the 2D and 3D spaces to ensure network connectivity. These results provide first-order estimates for, e.g., a swarm of drones to provide coverage in a disaster or crowded area.

For a broad class of distributions of temperature, concentration, or another quantity propagating rectilinearly, we show that temporally quasiperiodic behavior in the laboratory frame can be rendered periodic by Galilean transformation. The approach is illustrated analytically and numerically using as an example a closed-form model distribution generated from a one-dimensional partial differential equation, and a detailed process is developed to determine frame speed from more general quasiperiodic, one-dimensional, temporally- and spatially-discretized data. The approach is extended to two- and three-dimensional rectilinear propagation, and its application to nonrectilinear propagation, along with implications for interpreting noise-corrupted data, are also discussed.

The structural and magneto- and electro-optical properties of a self-organized ensemble of nematic domains formed on a polycarbonate film in the presence of a residual solvent are studied. The film covered one of the plane-parallel glass plates of a liquid crystal cell. The magnetic field stabilizing the planar alignment of the liquid crystal was applied parallel to the cell surfaces and the reorienting electric field, perpendicular to them. The voltage dependences of the intensity of light transmitted through the domain ensemble were obtained at different constant values of the magnetic field. The comparison of the experimental dependences with the dependences calculated using the liquid crystal free-energy minimization procedure has shown good agreement between them. The mutual effect of structural elements of the ensemble and the effects of phase modulation of light are analyzed by comparing the structural, magnetic, and electric coherence lengths.

In this article we develop a general method to numerically calculate physical properties for a system of anyons with path integral molecular dynamics. We provide a unified method to calculate the thermodynamics of identical bosons, fermions, and anyons. Our method is tested and applied to systems of anyons, bosons, and fermions in a two-dimensional harmonic trap. We also consider a method to calculate the energy for fermions as an application of the path integral molecular dynamics to simulate the anyon model.

We show that generic kinetic growth processes with surface relaxations can exhibit a hitherto unexplored crumpled phase with short-range orientational order at dimensions $d<4$. A sufficiently strong spatially nonlocal part of the chemical potential associated with the particle current above a threshold in the system can trigger this crumpling. The system can also be in a perturbatively accessible rough phase with long-range orientational order but short-range positional order at $d<4$ with known scaling exponents. Intriguingly, in $d>4$ we argue that there is no crumpling transition; instead, there is a roughening transition from a smooth to a rough phase for large enough nonlocal particle chemical potential. Experimental and theoretical implications of these results are discussed.

Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.

Synthetic and natural nanomaterials with self-propelling mechanisms continue to be explored to boost chain mobility beyond normal reptation in the crowded environments of entangled chains. Here we employ scaling theory and numerical simulations to demonstrate that activating one chain end of a singular or isolated chain boosts entanglement-constrained chain reptation from the one-dimensional diffusive mobility as described by the de Gennes–Edwards–Doi model to ballistic motion along the entanglement tube contour. The active chain is effectively screened from the constraint of entanglements on length scales exceeding the tube size.

We study the behavior of stationary nonequilibrium two-body correlation functions for diffusive systems with equilibrium reference states (DSe). We describe a DSe at the mesoscopic level by $M$ locally conserved continuum fields that evolve through coupled Langevin equations with white noises. The dynamic is designed such that the system may reach equilibrium states for a set of boundary conditions. In this form, we make the system driven to a nonequilibrium stationary state by changing the equilibrium boundary conditions. We decompose the correlations in a known local equilibrium part and another one that contains the nonequilibrium behavior and that we call correlation's excess $\overline{C}(x,z)$. We formally derive the differential equations for $\overline{C}$. To solve them order by order, we define a perturbative expansion around the equilibrium state. We show that the $\overline{C}$'s first-order expansion, ${\overline{C}}^{\left(1\right)}$, is always zero for the unique field case, $M=1$. Moreover, ${\overline{C}}^{\left(1\right)}$ is always long range or zero when $M>1$. We obtain the surprising result that their associated fluctuations, the space integrals of ${\overline{C}}^{\left(1\right)}$, are always zero. Therefore, fluctuations are dominated by local equilibrium up to second order in the perturbative expansion around the equilibrium. We derive the behaviors of ${\overline{C}}^{\left(1\right)}$ in real space for dimensions $d=1$ and 2 explicitly. Finally, we derive the two first perturbative orders of the correlation's excess for a generic $M=2$ case and a hydrodynamic model.

We consider scattering exponents arising in small-angle scattering from power-law polydisperse surface and mass fractals. It is shown that a set of fractals, whose sizes are distributed according to a power law, can change its fractal dimension when the power-law exponent is sufficiently big. As a result, the scattering exponent corresponding to this dimension appears due to the spatial correlations between positions of different fractals. For large values of the momentum transfer, the correlations do not play any role, and the resulting scattering intensity is given by a sum of intensities of all composing fractals. The restrictions imposed on the power-law exponents are found. The obtained results generalize Martin's formulas for the scattering exponents of the polydisperse fractals.

Engineering long-range interactions in experimental platforms has been achieved with great success in a large variety of quantum systems in recent years. Inspired by this progress, we propose a generalization of the classical Hamiltonian mean-field model to fermionic particles. We study the phase diagram and thermodynamic properties of the model in the canonical ensemble for ferromagnetic interactions as a function of temperature and hopping. At zero temperature, small charge fluctuations drive the many-body system through a first-order quantum phase transition from an ordered to a disordered phase. At higher temperatures, the fluctuation-induced phase transition remains first order initially and switches to second-order only at a tricritical point. Our results offer an intriguing example of tricriticality in a quantum system with long-range couplings, which bears direct experimental relevance. The analysis is performed by exact diagonalization and mean-field theory.