We consider a biological network of the hippocampal dentate gyrus (DG). Computational models suggest that the DG would be a preprocessor for pattern separation (i.e., a process transforming a set of similar input patterns into distinct nonoverlapping output patterns) which could facilitate pattern storage and retrieval in the CA3 area of the hippocampus. The main encoding cells in the DG are the granule cells (GCs) which receive the input from the entorhinal cortex (EC) and send their output to the CA3. We note that the activation degree of GCs is very low ($\sim 5\%$). This sparsity has been thought to enhance the pattern separation. We investigate the dynamical origin for winner-take-all (WTA) competition which leads to sparse activation of the GCs. The whole GCs are grouped into lamellar clusters. In each cluster, there is one inhibitory (I) basket cell (BC) along with excitatory (E) GCs. There are three kinds of external inputs into the GCs: the direct excitatory EC input; the indirect feedforward inhibitory EC input, mediated by the HIPP (hilar perforant path-associated) cells; and the excitatory input from the hilar mossy cells (MCs). The firing activities of the GCs are determined via competition between the external E and I inputs. The E-I conductance ratio ${{\mathcal{R}}_{\mathrm{E}-\mathrm{I}}^{\left(\mathrm{con}\right)}}^{*}$ (given by the time average of the ratio of the external E to I conductances) may represent well the degree of such external E-I input competition. It is thus found that GCs become active when their ${{\mathcal{R}}_{\mathrm{E}-\mathrm{I}}^{\left(\mathrm{con}\right)}}^{*}$ is larger than a threshold ${\mathcal{R}}_{\text{th}}^{*}$, and then the mean firing rates of the active GCs are strongly correlated with ${{\mathcal{R}}_{\mathrm{E}-\mathrm{I}}^{\left(\mathrm{con}\right)}}^{*}$. In each cluster, the feedback inhibition from the BC may select the winner GCs. GCs with larger ${{\mathcal{R}}_{\mathrm{E}-\mathrm{I}}^{\left(\mathrm{con}\right)}}^{*}$ than the threshold ${\mathcal{R}}_{\text{th}}^{*}$ survive, and they become winners; all the other GCs with smaller ${{\mathcal{R}}_{\mathrm{E}-\mathrm{I}}^{\left(\mathrm{con}\right)}}^{*}$ become silent. In this way, WTA competition occurs via competition between the firing activity of the GCs and the feedback inhibition from the BC in each cluster. Finally, we also study the effects of MC death and adult-born immature GCs on the WTA competition.

Equidiffusive premixed combustion in obstructed channels with both open, nonreflecting ends exhibits various forms of flame propagation: oscillations, acceleration or a combination of both regimes. Given the limited practicality of equidiffusive premixed combustion, it is important to understand how these modes of combustion are altered at nonequidiffusive conditions, characterized by a nonunity Lewis number (thermal to mass diffusivity ratio) $\mathrm{Le}\ne 1$. To achieve this, the impacts of $\mathrm{Le}$ on the flame dynamics and morphology are analyzed by means of the computational simulations of the reacting flow equations, with Arrhenius chemical kinetics, fully compressible hydrodynamics, and transport properties. In addition to varying $\mathrm{Le}$, the parametric study includes various blockage ratios, channel widths, obstacle spacing and thermal expansion ratios. It is identified how these parameters influence the burning velocities as well as the scaled oscillation amplitude and frequency. Specifically, in the narrow channels with small blockage ratios, the amplitude and frequency of the oscillations vary with $\mathrm{Le}$, with the frequency decreasing and the amplitude increasing as $\mathrm{Le}$ grows from 0.3 to 2. In other conditions, a transition from the flame oscillations to sudden flame acceleration or its propagation at a constant velocity is singularly influenced by $\mathrm{Le}$, or by the interplay of $\mathrm{Le}$ with the geometric parameters of a channel. The delay time before the onset of flame acceleration, especially at $\mathrm{Le}<1$, also varies as the channel width and the blockage ratio change. In all cases, $\mathrm{Le}$ has both quantitative and qualitative effects on flame propagation in obstructed channels with both open, nonreflecting ends.

Strongly coupled plasmas in a liquid phase can be characterized by a complex viscosity $\eta \left(\omega \right)$, which is a function of frequency. Data from a single experiment with dusty plasma were analyzed to compare $\eta \left(\omega \right)$ obtained by two fundamentally distinct methods. In a nonequilibrium method, a pair of counterpropagating laser beams, separated by a gap, applied a sinusoidal shear to a two-dimensional liquid, and $\eta \left(\omega \right)$ was determined using the constitutive relation. In an equilibrium method, there was no externally applied shear, so $\eta \left(\omega \right)$ could be calculated with a generalized Green-Kubo relation. The results for these two methods are compared for the real and imaginary parts of $\eta \left(\omega \right)$. For both parts, it is confirmed that the two methods yield results that agree qualitatively in their trends with frequency, with the real part diminishing with $\omega$ and the imaginary part increasing with $\omega$, as expected for viscoelastic liquids. Quantitatively, the values of $\eta \left(\omega \right)$ obtained by the two methods differ slightly. For the experiment that we analyze, values for the real and imaginary parts of $\eta \left(\omega \right)$ are substantially greater than those reported in an earlier experiment, which we attribute to shear thinning effects in the earlier experiment. The experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure $p_{\mathrm{cryst}}$, the monolayer always crystallizes; (ii) below a specific pressure $p_{\mathrm{MCI}}$, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between $p_{\mathrm{MCI}}$ and $p_{\mathrm{cryst}}$, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below $p_{\mathrm{MCI}}$, the monolayer remains in the fluid phase until it reaches $p_{\mathrm{cryst}}$ at which it recrystallizes; when decreasing the pressure from above $p_{\mathrm{cryst}}$, the monolayer remains in the crystalline phase until it reaches $p_{\mathrm{MCI}}$ at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of $p_{\mathrm{MCI}}$ as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with nontrivial symmetries such as labyrinthine patterns are observed in different physical contexts. Here we report stable localized disordered patterns in spatially extended dissipative systems. These two- and three-dimensional localized structures consist of an isolated labyrinth embedded in a homogeneous steady state. Their partial bifurcation diagram allows us to explain this phenomenon as a manifestation of a pinning-depinning transition. We illustrate our findings on the Swift-Hohenberg-type of equations and other well-established models for plant ecology, nonlinear optics, and reaction-diffusion systems.

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random-walk position, from which we obtain the second moment in the long-time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least $2/3$ of the mean resting time for superdiffusion to be possible. Monte Carlo simulations validate this theoretical result. This work demonstrates the possibility of extending the telegrapher's (or Cattaneo) equation by adding self-reinforcing directionality so that superdiffusion occurs even when rests are introduced.

In the evolutionary dynamics of a rock-paper-scissor model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model, becomes very sensitive toward this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a two-dimensional lattice having three cyclically competing species. The spatiotemporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of spiral patterns in the presence of mobility. It reveals that the joint effect of death rate and mobility (diffusion) leads to new coexistence and extinction scenarios.

We report experiments on an active camphor rotor. A camphor rotor is prepared by infusing camphor on a regular rectangular paper strip. It performs self-propelled motion at the air-water interface due to Marangoni driven forces. After some transient (periodic) dynamics, the rotor enters into the aperiodic bursting regime, which is characterized as an irregularly repeated rest (halt) and run (motion) of the rotor. Subsequently, this aperiodic (irregular) rotor is entrained to a periodic (regular) regime with the help of a suitable external periodic forcing. Furthermore, we conducted experiments on two such coupled aperiodic camphor rotors. In this set of experiments, synchronized bursting was observed. During this bursting motion, one rotor follows the movement of the other rotor. A numerical point particle model, incorporating excitable underlying equations, successfully replicated experimentally observed aperiodic bursting.

Circadian rhythms of physiological and behavioral activities are regulated by a central clock. This clock is located in the bilaterally symmetrical suprachiasmatic nucleus (SCN) of mammals. Each nucleus contains a light-sensitive group of neurons, named the ventrolateral (VL) part, with the rest of the neurons being insensitive to light, named the dorsomedial (DM) group. While the coupling between the VL and DM subgroups have been investigated quite well, the communication among the four subgroups across the nuclei did not get a lot of attention. In this article, we theoretically analyzed seven motiflike connection patterns to investigate the network of the two nuclei of the SCN as a whole in relation to the function of the SCN. We investigated the entrainment ability of the SCN and found that the entrainment range is larger in the motifs containing a link between the two VL parts across the nuclei, but it is smaller in the motifs that contain a link between the two DM parts across the nuclei. The SCN may strengthen or weaken connections between the left and right nucleus to accomodate changes in external conditions, such as resynchronization after a jet lag, adjustment to photoperiod or for the aging SCN.

First proposed as an empirical rule over half a century ago, the Richards growth equation has been frequently invoked in population modeling and pandemic forecasting. Central to this model is the advent of a fractional exponent $\gamma$, typically fitted to the data. While various motivations for this nonanalytical form have been proposed, it is still considered foremost an empirical fitting procedure. Here, we find that Richards-like growth laws emerge naturally from generic analytical growth rules in a distributed population, upon inclusion of (i) migration (spatial diffusion) among different locales, and (ii) stochasticity in the growth rate, also known as “seascape noise.” The latter leads to a wide (power law) distribution in local population number that, while smoothened through the former, can still result in a fractional growth law for the overall population. This justification of the Richards growth law thus provides a testable connection to the distribution of constituents of the population.

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.

We put forward a general field theory for nearly flat fluid membranes with embedded activators and analyze their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents $z=1$ and 2, respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, leads to an early-time behavior, which is representative of the spatiotemporal patterns observed at the leading edge of motile cells, such as oscillations superposed on the growth of the membrane width. In the case of mean-field diffusive scaling, one-loop corrections to the mean-field exponents reveal universal behavior distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behavior.

The Johari-Goldstein-β (JG-β) process is widely observed in a variety of glass-forming systems and recognized as an intrinsic process in deeply supercooled and glassy states. However, in some systems, e.g., glycerol, a clear sign of the JG-β process is often not apparent; for example, an isolated JG-β peak may not be observed in the dielectric relaxation spectrum. In this study, we directly investigated the angstrom-scale dynamics of glycerol through quasielastic scattering experiments using time-domain interferometry. The relaxation times of the local motions start to decouple from the timescale of the diffusion process and follow the established behavior of the JG-β process. This finding microscopically indicates the existence of the hidden JG-β process in glycerol. In addition, we succeeded in determining the decoupling temperature of the JG-β process by using the spatial-scale selectivity of the quasielastic scattering technique.

We derive the three-loop order renormalization group equations that describe the flat phase of polymerized membranes within the modified minimal subtraction scheme, following the pioneering one-loop order computation of Aronovitz and Lubensky [Phys. Rev. Lett. 60, 2634 (1988)] and the recent two-loop order one of Coquand, Mouhanna, and Teber [Phys. Rev. E 101, 062104 (2020)]. We analyze the fixed points of these equations and compute the associated field anomalous dimension $\eta$ at three-loop order. Our results display a marked proximity with those obtained using nonperturbative techniques and reexpanded in powers of $\epsilon =4-D$. Moreover, the three-loop order value that we get for $\eta$ at the stable fixed point, $\eta =0.8872$, in $D=2$, is compatible with known theoretical results and within the range of accepted numerical values.

We provide highly accurate equation-of-state data determined by means of cluster Monte Carlo simulations for the isotropic phase of oblate hard ellipsoids of revolution. Both equation-of-state data and phase boundaries of the isotropic phase are obtained from relatively large ensembles with typically 1000 particles. The comparison of simulation data with a virial approach gives evidence for the importance of high-order so-far-unknown virial coefficients and therewith many-particle interactions in dense, isotropic systems of anisotropic particles. While a virial approach with a rescaled Carnahan-Starling correction for the unknown, higher-order virial coefficients reproduces the simulation data of moderately anisotropic particles with high accuracy, we suggest for highly anisotropic shapes a simple, heuristic equation of state as a suitable approach.

Spiral waves lead to dangerous arrhythmias in the cardiac system. In 2015 Burton et al. demonstrated the reversal of the spiral wave chirality through the rotating spiral-shaped illumination on the optogenetically modified cardiac monolayers. We show that this process entails the recreation of a spiral wave. We show how this methodology can be used to control and create the desired spatial excitation pattern. We found that the control is sensitive to the area of illuminated region but independent of the phase difference of the existing spiral wave and the applied spiral-shaped light. We also discovered that our methodology can temporarily resynchronize a turbulent system. The results offer numerical evidence for the control of spatial pattern in biological excitable systems with optogenetics.

We present a path-integral formulation of the motion of a particle subjected to fluctuating active and thermal forces. This general framework predicts the statistical behavior associated with the stochastic trajectories of the particle, accounting for all possible realizations of Brownian and active forces, over an arbitrary potential landscape. Temporal correlations in the active forces result in non-Markovian statistics, necessitating the inclusion of a fixed active-force value at specified times within the statistical treatment. We specialize our theory to that of exponentially correlated active forces for a particle in a harmonic potential. We find the exact results for the statistical distributions for the initial position of the particle, accounting for the impact of the correlated active forces at all times prior to the initial time. Our theory is then used to find the two-point distribution for the active Brownian particle, which governs the joint probability that a particle begins and ends at specified locations. Analyses of the active Brownian statistics demonstrate that the impact of active forces can be interpreted through a time-dependent temperature whose influence depends on the competition of timescales of the active-force correlation and the relaxation time of the particle in the harmonic potential. The general results presented in this work are transferable to a broad range of nonequilibrium systems with active and Brownian motion, and the time-dependent temperature serves as a governing principle to describe the competition of timescales associated with active forces and internal relaxation processes.

Bistability in the firing rate is a prominent feature in different types of neurons as well as in neural networks. We show that for a constant input below a critical value, such bistability can lead to a giant spike-count diffusion. We study the transmission of a periodic signal and demonstrate that close to the critical bias current, the signal-to-noise ratio suffers a sharp increase, an effect that can be traced back to the giant diffusion and large Fano factor.

We analyze the conformational dynamics and statistical properties of an active polymer model. The polymer is described as a freely jointed bead-rod chain subject to stochastic active force dipoles that act on the suspending solvent where they drive long-ranged fluid flows. Using Langevin simulations of isolated chains in unconfined domains, we show how the coupling of active flows with polymer conformations leads to emergent dynamics. Systems with contractile dipoles behave similarly to passive Brownian chains with enhanced fluctuations due to dipolar flows. In systems with extensile dipoles, however, our simulations uncover an active coil-stretch transition whereby the polymer spontaneously unfolds and stretches out in its own self-induced hydrodynamic flow, and we characterize this transition in terms of a dimensionless activity parameter comparing active dipolar forces to thermal fluctuations. We discuss our findings in the context of the classic coil-stretch transition of passive polymers in extensional flows and complement our simulations with a simple kinetic model for an active trimer.

Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified in the past. Prime example systems are given by functionalized elastic composite materials or fluid colloidal suspensions. Here, we address the significantly less frequently studied situation of rigid inclusions in two-dimensional elastic or low-Reynolds-number fluid films. We concentrate on the situation in which disklike inclusions remain well separated from each other and do not get into contact. Specifically, we demonstrate and explain that the logarithmic divergence of the associated Green's function is removed in the absence of net external forces on the inclusions, in line with physical intuition. For instance, this situation applies when only pairwise mutual interactions between the inclusions prevail. Our results will support, for example, investigations on membranes functionalized by appropriate inclusions, both of technical or biological origin, or the dynamics of active microswimmers in appropriately prepared thin films.