Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixed point and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This paper focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential—a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.

In this paper we analyze diffusive transport of noninteracting electrically uncharged solute molecules through a cylindrical membrane channel with a constriction located in the middle of the channel. The constriction is modeled by an infinitely thin partition with a circular hole in its center. The focus is on how the presence of the partition slows down the transport governed by the difference in the solute concentrations in the two reservoirs separated by the membrane. It is assumed that the solutions in both reservoirs are well stirred. To quantify the effect of the constriction we use the notion of diffusion resistance defined as the ratio of the concentration difference to the steady-state flux. We show that when the channel length exceeds its radius, the diffusion resistance is the sum of the diffusion resistance of the cylindrical channel without a partition and an additional diffusion resistance due to the presence of the partition. We derive an expression for the additional diffusion resistance as a function of the tube radius and that of the hole in the partition. The derivation involves the replacement of the nonpermeable partition with the hole by an effective uniform semipermeable partition with a properly chosen permeability. Such a replacement makes it possible to reduce the initial three-dimensional diffusion problem to a one-dimensional one that can be easily solved. To determine the permeability of the effective partition, we take advantage of the results found earlier for trapping of diffusing particles by inhomogeneous surfaces, which were obtained with the method of boundary homogenization. Brownian dynamics simulations are used to corroborate our approximate analytical results and to establish the range of their applicability.

Icing is a severe problem for many technical systems such as aircraft or systems for high-voltage power transmission and distribution. Ice nucleation in water droplets is affected by several influencing factors like impurities or the liquid temperature, which have been widely investigated. However, although an electric field affects nucleation, this influence has been far less investigated and is still not completely understood. The present work is focused on the influence of high alternating electric fields on ice nucleation in sessile water droplets, which is examined for a systematic variation of the electric field frequency and strength. All experiments used to determine the influence of a single parameter like the electric field strength or frequency are performed with the same set of droplets to ensure well-defined conditions and a high repeatability of the procedure. For each parameter variation a large number of nucleation events is observed and analyzed. Droplet survival curves and the nucleation site density are used to analyze the experiments and to determine the influence of the electric field on ice nucleation. Especially for high electric field strengths, a significant influence on nucleation is observed. Some droplets freeze earlier, which leads to a higher median nucleation temperature. On the other hand, the lowest temperature required to freeze all droplets is almost constant compared to the reference case without an electric field. It is shown that not all droplets are affected by the electric field in the same way, but the influence of the electric field on ice nucleation is rather of singular nature. In addition, the frequency of the applied electric field has an impact on the nucleation behavior. The present experimental data quantitatively demonstrate the effect of an electric field on ice nucleation and improves our understanding of heterogeneous nucleation of supercooled water subjected to high alternating electric fields.

The two-dimensional lattice Boltzmann method (LBM) was used to study the motion of two interacting particles with different densities (${\rho }_1$ and ${\rho }_2$) and diameters ($d_1$ and $d_2$), which were placed in a vertical channel under gravity. Both the density ratio $(\lambda ={\rho }_2/{\rho }_1)$ and diameter ratio ($r=d_2/d_1$) between the particles were considered. The transition boundaries between the regime where the particles settle separately and the regime where the particles interact are identified by ${\lambda }_{max}\left(r\right)$ and ${\lambda }_{min}\left(r\right)$; they exhibit excellent power-law relationships with $r$. A pattern of horizontal oscillatory motion (HOM), characterized by a structure with a large (but light) particle right above a small (but heavy) one and strong oscillations of both particles in the horizontal direction, was revealed for $r\sim 0.3$ at intermediate Reynolds numbers. The results indicate that the magnitude of oscillations decreases with $\lambda$, whereas the frequency displays the opposite trend. A sudden increase in the terminal velocity of particles is seen, illustrating a transition from the classical pattern of drafting, kissing, and tumbling to the HOM at a certain $\lambda$. Upon increasing $\lambda$, the pattern of HOM may bifurcate into a vertical steady state at low Re or small $r$. Furthermore, the effects of the confinement ratio and particle-to-fluid density ratio were also examined. The existence of a critical confinement ratio is observed, beyond which the particles interact in a different manner.

Two-temperature rotational energy distributions from rarefied diatomic molecules are very often observed in laboratory plasmas. There has been much debate over the years about the physical meaning of this kind of rotational energy distributions and the associated statistical physics. We show here that under certain reasonable assumptions and constraints the condition of Shannon-Jaynes entropy maximization may produce a two-temperature distribution. This may happen, for instance, when a system is simultaneously coupled to different thermal baths. In plasmas this is possible because rarefied molecular species may be immersed in a medium where electrons and the dominant atomic species are quasidecoupled, each of them acting as distinct thermal baths. Considering that molecular species may interact both with electrons and heavy neutral species, we may ask what should be the resulting molecular energy distribution. We answer this question in this paper and give some examples on how this can be used to interpret experimental molecular distribution from partially ionized plasmas.

We study theoretically the size distributions of nanoparticles (islands, droplets, nanowires) whose time evolution obeys the kinetic rate equations with size-dependent condensation and evaporation rates. Different effects are studied which contribute to the size distribution broadening, including kinetic fluctuations, evaporation, nucleation delay, and size-dependent growth rates. Under rather general assumptions, an analytic form of the size distribution is obtained in terms of the natural variable $s$ which equals the number of monomers in the nanoparticle. Green's function of the continuum rate equation is shown to be Gaussian, with the size-dependent variance. We consider particular examples of the size distributions in either linear growth systems (at a constant supersaturation) or classical nucleation theory with pumping (at a time-dependent supersaturation) and compare the spectrum broadening in terms of $s$ versus the invariant variable $\rho$ for which the regular growth rate is size independent. For the growth rate scaling with $s$ as $s^{\alpha }$ (with the growth index $\alpha$ between 0 and 1), the size distribution broadens for larger $\alpha$ in terms of $s$, while it narrows with $\alpha$ if presented in terms of $\rho$. We establish the conditions for obtaining a time-invariant size distribution over a given variable for different growth laws. This result applies for a wide range of systems and shows how the growth method can be optimized to narrow the size distribution over a required variable, for example, the volume, surface area, radius or length of a nanoparticle. An analysis of some concrete growth systems is presented from the viewpoint of the obtained results.

Excitable systems with delayed feedback are important in areas from biology to neuroscience and optics. They sustain multistable pulsing regimes with different numbers of equidistant pulses in the feedback loop. Experimentally and theoretically, we report on the pulse-timing symmetry breaking of these regimes in an optical system. A bifurcation analysis unveils that this originates in a resonance phenomenon and that symmetry-broken states are stable in large regions of the parameter space. These results have impact in photonics for, e.g., optical computing and versatile sources of optical pulses.

We investigate the escape of particles from the phase space produced by a two-dimensional, nonlinear and discontinuous, area-contracting map. The mapping, given in action-angle variables, is parametrized by $K$ and $\gamma$ which control the strength of nonlinearity and dissipation, respectively. We focus on two dynamical regimes, $K<1$ and $K\ge 1$, known as slow and quasilinear diffusion regimes, respectively, for the area-preserving version of the map (i.e., when $\gamma =0$). When a hole of hight $h$ is introduced in the action axis we find both the histogram of escape times $P_{\text{E}}\left(n\right)$ and the survival probability $P_{\text{S}}\left(n\right)$ of particles to be scale invariant, with the typical escape time $n_{\text{typ}}=exp\langle lnn\rangle$; that is, both $P_{\text{E}}(n/n_{\text{typ}})$ and $P_{\text{S}}(n/n_{\text{typ}})$ define universal functions. Moreover, for $\gamma \ll 1$, we show that $n_{\text{typ}}$ is proportional to $h^2/D$, where $D$ is the diffusion coefficient of the corresponding area-preserving map that in turn is proportional to $K^{5/2}$ and $K^2$ in the slow and the quasilinear diffusion regimes, respectively.

Among the many social influences expressed in $q$-voter models, independent agents are responsible for disordered behavior in an otherwise consensus-prone scheme. Despite some parametrizations allowing the model to converge to any given stationary concentration, small perturbations in its parameters cause the model to suffer great variations in its outcome. This paper proposes that an external field may explain less unstable outcomes in the $q$-voter model. We soften independence to become skepticism, a phenomenon induced by an unreliable external field interference in social processes. The external field, analogous to mass media in real settings, leads to both quicker convergence to a fairly ordered state when independence is low, and to higher disorder whenever it is under moderate perceived unreliability of the external field.

The prisoner's dilemma (PD) game offers a simple paradigm of competition between two players who can either cooperate or defect. Since defection is a strict Nash equilibrium, it is an asymptotically stable state of the replicator dynamical system that uses the PD payoff matrix to define the fitness landscape of two interacting evolving populations. The dilemma arises from the fact that the average payoff of this asymptotically stable state is suboptimal. Coaxing the players to cooperate would result in a higher payoff for both. Here we develop an optimal control theory for the prisoner's dilemma evolutionary game in order to maximize cooperation (minimize the defector population) over a given cycle time $T$, subject to constraints. Our two time-dependent controllers are applied to the off-diagonal elements of the payoff matrix in a bang-bang sequence that dynamically changes the game being played by dynamically adjusting the payoffs, with optimal timing that depends on the initial population distributions. Over multiple cycles $nT$ $(n>1)$, the method is adaptive as it uses the defector population at the end of the $n\mathrm{th}$ cycle to calculate the optimal schedule over the $n+1\mathrm{st}$ cycle. The control method, based on Pontryagin's maximum principle, can be viewed as determining the optimal way to dynamically alter incentives and penalties in order to maximize the probability of cooperation in settings that track dynamic changes in the frequency of strategists, with potential applications in evolutionary biology, economics, theoretical ecology, social sciences, reinforcement learning, and other fields where the replicator system is used.

We study the pair correlation of active Brownian particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: While particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity, where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Janus particles and indeed observe the depletion wings.

An electrically driven fluid pumping principle and a mechanism of kinklike distortion of the director field $\widehat{\mathbf{\text{n}}}$ in the microsized nematic volume has been described. It is shown that the interactions, on the one hand, between the electric field $\mathbf{\text{E}}$ and the gradient of the director's field $\mathbf{\nabla }\widehat{\mathbf{\text{n}}}$, and, on the other hand, between the $\mathbf{\nabla }\widehat{\mathbf{\text{n}}}$ and the temperature gradient $\mathbf{\nabla }T$ arising in a homogeneously aligned liquid crystal microfluidic channel, confined between two infinitely long horizontal coaxial cylinders, may excite the kinklike distortion wave spreading along normal to both cylindrical boundaries. Calculations show that the resemblance to the kinklike distortion wave depends on the value of radially applied electric field $\mathbf{\text{E}}$ and the curvature of these boundaries. Calculations also show that there exists a range of parameter values (voltage and curvature of the inner cylinder) producing a nonstandard pumping regime with maximum flow near the hot cylinder in the horizontal direction.

The azobenzene-containing crosslinked liquid crystalline polymer is a potential candidate for a stimuli-responsive soft robot, as it provides contactless actuation without the implementation of any separate component. For facilitating practical applications of this novel material, complicated and predefined motions have been realized by tailoring the chemical structure of the polymer network. However, conventional multiscale mechanical analysis, which utilizes the all-atom molecular dynamics to represent a microscopic model, is unsuitable for handling diverse material design parameters due to excessive computational costs. Hence, a multiscale optomechanical simulation framework, which combines the coarse-grained molecular dynamics (CG MD) and the finite-element (FE) method, is developed in this study. The CG MD simulation satisfactorily reproduces the light-induced phase transition and photosoftening effect on the mechanical properties. In particular, using the mesoscale analysis, the presented methodology can treat diverse morphology parameters (liquid crystal phase, spacer length, and crosslinking density) to observe the associated photodeformations. The photostrain and elastic modulus profiles in terms of photoisomerization ratio are implemented into the continuum-scale governing equation, which is based on the neoclassical elasticity theory. To efficiently reflect the light-induced large rotations of liquid crystal mesogens and the corresponding geometric nonlinearity, a corotational formulation is employed in the FE shell model. We examine the mesostructural-morphology-dependent photobending deformations of the nematic and smectic photoresponsive polymers (PRPs). In addition, the mesoscopic-texture-mediated unique 3D deformations are investigated by modeling the topological defects. This study offers insight into the engineering of PRP materials for designing the mechanical motions of smart actuators.

We present a simulation method to assess the quasistatic fracture resistance of materials. Set within a semi-grand-canonical Monte Carlo (SGCMC) simulation environment, an auxiliary field—the bond rupture potential—is introduced to generate a sufficiently large number of possible microstates in the semi-grand-canonical ensemble, and associated energy and bond fluctuations. The SGCMC approach permits identifying the full phase diagram of brittle fracture for harmonic and nonharmonic bond potentials, analogous to the gas-liquid phase diagram, with the equivalent of a liquidus line ending in a critical point. The phase diagram delineates a solid phase, a fractured phase, and a gas phase, and provides clear evidence of a first-order phase transition intrinsic to fracture. Moreover, energy and bond fluctuations generated with the SGCMC approach permit determination of the maximum energy dissipation associated with bond rupture, and hence of the fracture resistance of a widespread range of materials that can be described by bond potentials.

The influence of odd viscosity of Newtonian fluid on the instability of thin film flowing along an inclined plane under a normal electric field is studied. By odd viscosity, we mean apart from the well-known coefficient of shear viscosity, a classical liquid with broken time-reversal symmetry is endowed with a second viscosity coefficient in biological, colloidal, and granular systems. Under the long wave approximation, a nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion. The effects of the odd viscosity and external electric field are considered in this evolution equation and an analytical expression of critical Reynolds number is obtained. It is interesting to find that, by linear stability analysis, the critical Reynolds number increases with odd viscosity and decreases with external strength of electric field. In other words, odd viscosity has a stable effect and electric field has a destabilized effect on flowing of thin film. In addition, through nonlinear analysis, we obtain a Ginsburg-Landau equation and find that the film has not only the supercritical stability zone and the subcritical instability zone but also the unconditional stability zone and the explosive zone. The variations of each zone with related parameters, such as the strength of electric field, odd viscosity, and Reynolds number, etc., are investigated. The results are conducive to the further development of related experiments.

The worm algorithm is a versatile technique in the Markov chain Monte Carlo method for both classical and quantum systems. The algorithm substantially alleviates critical slowing down and reduces the dynamic critical exponents of various classical systems. It is crucial to improve the algorithm and push the boundary of the Monte Carlo method for physical systems. We here propose a directed worm algorithm that significantly improves computational efficiency. We use the geometric allocation approach to optimize the worm scattering process: worm backscattering is averted, and forward scattering is favored. Our approach successfully enhances the diffusivity of the worm head (kink), which is evident in the probability distribution of the relative position of the two kinks. Performance improvement is demonstrated for the Ising model at the critical temperature by measurement of exponential autocorrelation times and asymptotic variances. The present worm update is approximately 25 times as efficient as the conventional worm update for the simple cubic lattice model. Surprisingly, our algorithm is even more efficient than the Wolff cluster algorithm, which is one of the best update algorithms. We estimate the dynamic critical exponent of the simple cubic lattice Ising model to be $z\approx 0.27$ in the worm update. The worm and the Wolff algorithms produce different exponents of the integrated autocorrelation time of the magnetic susceptibility estimator but the same exponent of the asymptotic variance. We also discuss how to quantify the computational efficiency of the Markov chain Monte Carlo method. Our approach can be applied to a wide range of physical systems, such as the ${\left|\varphi \right|}^4$ model, the Potts model, the $\mathrm{O}\left(n\right)$ loop model, and lattice QCD.

Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, J. Chem. Phys. 152, 011102 (2020)] with isomorph theory, from a single simulation the structure of a single-component Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the temperature-density phase diagram. The LJ system exhibits two temperature ranges where the van't Hoff assumption that energetic and entropic forces are temperature independent is valid to a good approximation. A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden scale-invariant system obeying the van't Hoff assumption in the whole range of temperatures can be determined in the whole liquid region of the phase diagram from a single simulation.

We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperatures after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations, and efficiency, along with thermodynamic uncertainty relations between the signal-to-noise ratio of observed work and heat and the entropy production. We outline how the presented approach can be suitably applied to derive thermodynamic uncertainty relations for quantum Otto engines with alternative unitary strokes.

The phenomenon of crumpling is common in nature and our daily life. However, most of its properties, such as the power-law relation for pressure versus density and the ratio of bending and stretching energies, as well as the interesting statistical properties, were obtained by using flat sheets. This is in contrast to the fact that the majority of crumpled objects in the real world are three-dimensional. Notable examples are car wreckage, crushed aluminum cans, and blood cells that move through tissues constantly. In this work, we did a thorough examination of the properties of a crumpled spherical shell, hemisphere, cube, and cylinder via experiments and molecular-dynamics simulations. Physical arguments are provided to understand the discrepancies with those for flat sheets. The root of this disparity is found to lie less in the nonzero curvature, sharp edges and corner, and open boundary than in the dimensionality of the sample.