Saddle points are responsible for threshold phenomena of many biological systems. In the heart, saddle points determine the normal excitability and conduction, but are also responsible for certain abnormal action potential behaviors associated with lethal arrhythmias. We investigate the dynamical mechanisms for the genesis of lethal extra heartbeats in heterogeneous cardiac tissue under two diseased conditions. For both conditions, the lethal events occur when the system is close to the saddle point, implying the pivotal role of the saddle point in cardiac arrhythmogenesis.

The segregation of large intruders in an agitated granular system is of high practical relevance, yet the accurate modeling of the segregation (lift) force is challenging as a general formulation of a granular equivalent of a buoyancy force remains elusive. Here, we critically assess the validity of a granular buoyancy model using a generalization of the Archimedean formulation that has been proposed very recently for chute flows. The first model system studied is a convection-free vibrated system, allowing us to calculate the buoyancy force through three different approaches, i.e., a generalization of the Archimedean formulation, the spring force of a virtual spring, and through the granular pressure field. The buoyancy forces obtained through these three approaches agree very well, providing strong evidence for the validity of the generalization of the Archimedean formulation of the buoyancy force which only requires an expression for the solid fraction of the intruder, hence allowing for a computationally less demanding calculation of the buoyancy force as coarse graining is avoided. In a second step, convection is introduced as a further complication to the granular system. In such a system, the lift force is composed of granular buoyancy and a drag force. Using a drag model for the slow-velocity regime, the lift force, directly measured through a virtual spring, can be predicted accurately by adding a granular drag force to the generalization of the Archimedean formulation of the granular buoyancy. The developed lift force model allows us to rationalize the dependence of the lift force on the density of the bed particles and the intruder diameter, the independence of the lift force on the intruder diameter, and the independence of the lift force on the intruder density and the vibration strength (once a critical value is exceeded).

We apply a holistic two-dimensional (2D) Tetris-like model, where particles move based on prescribed rules, to investigate the flow rate enhancement from a hopper. This phenomenon was originally reported in the literature as a feature of placing an obstacle at an optimal location near the exit of a hopper discharging athermal granular particles under gravity. We find that this phenomenon is limited to a system of sufficiently many particles. In addition to the waiting room effect, another mechanism able to explain and create the flow rate enhancement is the concentration mechanism of particles on their way to reaching the hopper exit after passing the obstacle. We elucidate the concentration mechanism by decomposing the flow rate into its constituent variables: the local area packing fraction ${\varphi }_l^E$ and the averaged particle velocity $v_y^E$ at the hopper exit. In comparison to the case without an obstacle, our results show that an optimally placed obstacle can create a net flow rate enhancement of relatively weakly driven particles, caused by the exit-bottleneck coupling if ${\varphi }_l^E>{\varphi }_o^c$, where ${\varphi }_o^c$ is a characteristic area packing fraction marking a transition from fast to slow flow regimes of Tetris particles. Utilizing the concentration mechanism by artificially guiding particles into the central sparse space under the obstacle or narrowing the hopper exit angle under the obstacle, we can create a manmade flow rate peak of relatively strongly driven particles that initially exhibit no flow rate peak. Additionally, the enhanced flow rate can be maximized by an optimal obstacle shape, particle acceleration rate toward the hopper exit, or exit geometry of the hopper.

Soft solids such as silicone gels, with bulk shear modulus ranging from $\sim 10$ to $1000\mathrm{kPa}$, exhibit strongly strain-dependent surface stresses. Moreover, unlike conventional stiffer materials, the effects of surface stress in these materials manifest at length scales of tens of micrometers rather than nanometers. However, the calibration of constitutive parameters for surface hyperelasticity has proved to be challenging. Using a reasonably general surface constitutive model, we explore the possibility of obtaining its parameters from force-twist, torque-twist, and force-extension (force-compression) responses of a soft cylinder held between two inert, rigid plates. The motivation behind using these responses is derived from the fact that the roles of the surface constitutive parameters, under suitably ideal conditions, are neatly separated from each other and the three responses easily yield values of the three parameters. Moreover, through large deformation finite-element simulations with coupled bulk and surface hyperelasticity, we delineate the extent to which deviation from the ideal conditions may be tolerated. Using an example with previously reported material parameters, we estimate that, for cylindrical specimens with a radius of the order of $100\mu \mathrm{m}$, the capability to measure forces and torques of the order of $1–100\mu \mathrm{N}$ and ${10}^3–{10}^5\mu \mathrm{N}\text{−}\mu \mathrm{m}$, respectively, will be required to determine the parameters accurately.

We present a model for electron-ion transport in warm dense matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although the model presented here can be derived rigorously in the classical limit [S. D. Baalrud and J. Daligault, Phys. Plasmas 26, 082106 (2019)], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. We use the Uehling-Uhlenbeck equation to predict the momentum and temperature relaxation times and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.

We present the algorithm for generating strictly saturated random sequential adsorption packings built of rounded polygons. It can be used in studying various properties of such packings built of a wide variety of different shapes, and in modeling monolayers obtained during irreversible adsorption processes of complex molecules. Here, we apply the algorithm to study the densities of packings built of rounded regular polygons. Contrary to packings built of regular polygons, where the packing fraction grows with an increasing number of polygon sides, here the packing fraction reaches its maximum for packings built of rounded regular triangles. With a growing number of polygon sides and increasing rounding radius, the packing fractions tend to the limit given by a packing built of disks. However, they are still slightly higher, even for the rounded 25-gon, which is the highest-sided regular polygon studied here.

Network dismantling aims at breaking a network into disconnected components and attacking vertices that intersect with many loops has proven to be a most efficient strategy. Yet existing loop-focusing methods do not distinguish the short loops within densely connected local clusters (e.g., cliques) from the long loops connecting different clusters, leading to lowered performance of these algorithms. Here we propose a new solution framework for network dismantling based on a two-scale bipartite factor-graph representation, in which long loops are maintained while local dense clusters are simplistically represented as individual factor nodes. A mean-field spin-glass theory is developed for the corresponding long-loop feedback vertex set problem. The framework allows for the advancement of various existing dismantling algorithms; we developed the new version of two benchmark algorithms BPD (which uses the message-passing equations of the spin-glass theory as the solver) and CoreHD (which is fastest among well-performing algorithms). New solvers outperform current state-of-the-art algorithms by a considerable margin on networks of various sorts. Further improvement in dismantling performance is achievable by opting flexibly the choice of local clusters.

In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent ${\gamma }_{S/T}$ (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.

The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now also facilitates the study of $D_n$ root lattices in $n$ dimensions as well as $E_8$-related lattices. Here, we consider the percolation problem on $D_n$ for $n=3$ to 13 and on $E_8$ relatives for $n=6$ to 9. Precise estimates for both site and bond percolation thresholds obtained from invasion percolation simulations are compared with dimensional series expansion based on lattice animal enumeration for $D_n$ lattices. As expected, the bond percolation threshold rapidly approaches the Bethe lattice limit as $n$ increases for these high-connectivity lattices. Corrections, however, exhibit clear yet unexplained trends. Interestingly, the finite-size scaling exponent for invasion percolation is found to be lattice and percolation-type specific.

A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at low shear rate or stress followed by a Newtonian plateau (constant viscosity) at intermediate shear rate or stress values which transitions to shear thickening (increasing viscosity) beyond a critical shear rate or stress value and finally undergoes a second shear thinning transition at extremely high shear rate or stress values. In this study, we unify and quantitatively reproduce all the disparate rate-dependent regimes and the corresponding transitions for a dense non-Brownian suspension with increasing shear rate or stress. We employ discrete particle dynamics simulations based on the proposed mechanism to elucidate its accuracy. We find that a competition between interparticle interactions of hydrodynamic and nonhydrodynamic origins and the switching in the dominant stress scale with increasing the shear rate or stress lead to each of the above transitions. Inclusion of traditional hydrodynamic interactions, attractive or repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions the interparticle contact interactions, and a constant friction (or other constraint mechanism) reproduces the initial thinning as well as the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional nonhydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential, thus providing an explanation for the presence of the intermediate Newtonian plateau along with reproducing the second shear thinning in a single framework. Expressions utilized for various interactions and friction are determined from experimental measurements and hence result in excellent quantitative agreement between the simulations and previous experiments.

We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons with packings of soft circular particles. We characterize the evolution of the packing fraction, the elastic modulus, and the microstructure (particle rearrangement, connectivity, contact force, and particle stress distributions) as a function of the applied stresses. Both systems behave similarly: the packing fraction increases and tends asymptotically to a maximum value ${\varphi }_{\max }$, where the bulk modulus diverges. At the microscopic scale we show that particle rearrangements occur even beyond the jammed state, the mean coordination increases as a square root of the packing fraction, and the force and stress distributions become more homogeneous as the packing fraction increases. Soft pentagons experience larger particle rearrangements than circular particles, and such behavior decreases proportionally to the friction. Interestingly, the friction between particles also contributes to a better homogenization of the contact force network in both systems. From the expression of the granular stress tensor we develop a model that describes the compaction behavior as a function of the applied pressure, the Young modulus, and the initial shape of the particles. This model, settled on the joint evolution of the particle connectivity and the contact stress, provides outstanding predictions from the jamming point up to very high densities.

Localized acoustic surface waves supported by a “soft” elastic plate in water are explored. Unlike many materials, such as aluminum, for soft interfaces the Scholte wave, a localized interface wave, has a speed well below that of sound in water, and the energy of the Scholte wave is no longer mainly localized to the water. We note that the Scholte velocity is largely independent of Poisson's ratio in the solid, and rather than the bulk speeds of sound, the ratio between the Young's modulus and the density of the solid may better indicate whether an interface is soft. The behavior of the coupled Scholte modes along a thin plate with soft interfaces are investigated. It is demonstrated, and experimentally verified using acrylic plates underwater, that for soft interfaces, the symmetric coupled Scholte mode exhibits dispersive behavior, and deviates from the Scholte and the fluid velocities at low frequencies.

We investigate the influence of gravity and heat loss on the long-time nonlinear dynamics of premixed flames. We show that even when their influence remains weak in the linear regime they can significantly modify the long-time behavior. We suggest that the presence of such a large-scale stabilizing effect could be responsible for the creation of new cells on the front and the appearance of the strong persistent patterns observed in several recent experimental and numerical studies. It could also explain some statistical anomalies observed in the topology of flame fronts.

In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically affects the pressure drop at the fluid-fluid interface by introducing a nonlinear dependence on the interfacial velocity. In this framework, two cases of interest are analyzed: The injection-driven flow (expanding evolution), and the lifting plate flow (shrinking evolution). In particular, we investigate the possibility of controlling the development of fingering instabilities in these two different Hele-Shaw setups when wetting effects are taken into account. By employing linear stability theory, we find the proper time-dependent injection rate $Q\left(t\right)$ and the time-dependent lifting speed $\dot{b}\left(t\right)$ required to control the number of emerging fingers during the expanding and shrinking evolution, respectively. Our results indicate that the consideration of wetting leads to an increase in the magnitude of $Q\left(t\right)$ [and $\dot{b}\left(t\right)$] in comparison to the nonwetting strategy. Moreover, a spectrally accurate boundary integral approach is utilized to examine the validity and effectiveness of the controlling protocols at the fully nonlinear regime of the dynamics and confirms that the proposed injection and lifting schemes are feasible strategies to prescribe the morphologies of the resulting patterns in the presence of the wetting film.

A method for the calculation of elastic constants in the $NVT$ ensamble using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential is studied in detail. It is shown that, in such $NVT$ MD simulations, the evaluation of elastic constants is robust and accurate because it gives the elastic tensor in a single simulation which converges using a small number of time steps and particles. These results highlight the applicability of this method in (i) the calculation of local elastic constants of nonhomogeneous crystalline materials and (ii) the calibration of interatomic potentials, as a fast and accurate alternative to the common method of explicit deformation, which requires a set of consistent simulations at different conditions. The method is demonstrated for the calculation of the elastic constants of copper in the temperature range of 0–1000 K, and results agree with the target values used for the potential calibration. The various contributions to the values of the elastic constants, namely, the Born, stress fluctuation, and ideal gas terms, are studied as a function of temperature.

We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly into the regime of complete confusion when memory load exceeds a sharp threshold. This latter circumstance, together with an increase of the storage capacity, renders such a modified Hopfield model a promising candidate for further research, with possible diverse applications.

Resonances in particle transmission through a 1D finite lattice are studied in the presence of a finite number of impurities. Although this is a one-dimensional system that is classically integrable and has no chaos, studying the statistical properties of the spectrum such as the level spacing distribution and the spectral rigidity shows the same statistics as the one obtained for chaotic systems. Using a dimensionless parameter that reflects the degree of state localization, we demonstrate how the transition from Poisson-level statistics to the Wigner-Dyson is affected by state localization. The resonance positions are calculated using both the Wigner-Smith time delay and a Siegert state method, which are in good agreement. Our results show the dependence of the level statistics on the localization length as it evolves from a Poisson distribution to Wigner-Dyson.

Evacuation dynamics of pedestrians in a square room with one exit is studied. The movement of the pedestrians is guided by the static floor field model. Whenever multiple pedestrians are trying to move to the same target position, a game theoretical framework is introduced to address the conflict. Depending on the payoff matrix, the game that the pedestrians are involved in may be either hawk-dove or prisoner's dilemma, from which the reaped payoffs determine the capacities, or probabilities, of the pedestrians occupying the preferred vacant sites. The pedestrians are allowed to adjust their strategies when competing with others, and a parameter $\kappa$ is utilized to characterize the extent of their self-interest. It is found that self-interest may induce either positive or negative impacts on the evacuation dynamics depending on whether it can facilitate the formation of collective cooperation in the population or not. Particularly, a resonance-like performance of evacuation is realized in the regime of prisoner's dilemma. The effects of placing an obstacle in front of the exit and the diversity of responses of the pedestrians to the space competition on the evacuation dynamics are also discussed.

We report Brownian dynamics simulation results for the relative permittivity of electrorheological (ER) fluids in an applied electric field. The relative permittivity of an ER fluid can be calculated from the Clausius-Mosotti (CM) equation in the small applied field limit. When a strong field is applied, however, the ER spheres are organized into chains and assemblies of chains in which case the ER spheres are polarized not only by the external field but by each other. This manifests itself in an enhanced dielectric response, e.g., in an increase in the relative permittivity. The correction to the relative permittivity and the time dependence of this correction is simulated on the basis of a model in which the ER particles are represented as polarizable spheres. In this model, the spheres are also polarized by each other in addition to the applied field. Our results are qualitatively similar to those obtained by Horváth and Szalai experimentally [Phys. Rev. E 86, 061403 (2012)]. We report characteristic time constants obtained from biexponential fits that can be associated with the formation of pairs and short chains as well as with the aggregation of chains. The electric field dependence of the induced dielectric increment reveals the same qualitative behavior that experiments did: three regions with different slopes corresponding to different aggregation processes are identified.

We investigate the local and long-range structure of several space-filling cellular patterns: bubbles in a quasi-two-dimensional foam, and Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton patterns), and displaced from a lattice by Gaussian noise (Einstein patterns). We study local structure with distributions of quantities including cell areas and side numbers. The former is the widest for the bubbles making foams the most locally disordered, while the latter show no major differences between the cellular patterns. To study long-range structure, we begin by representing the cellular systems as patterns of points, both unweighted and weighted by cell area. For this, foams are represented by their bubble centroids and the Voronoi constructions are represented by the centroids as well as the points from which they are created. Long-range structure is then quantified in two ways: by the spectral density, and by a real-space analog where the variance of density fluctuations for a set of measuring windows of diameter $D$ is made more intuitive by conversion to the distance $h\left(D\right)$ from the window boundary where these fluctuations effectively occur. The unweighted bubble centroids have $h\left(D\right)$ that collapses for the different ages of the foam with random Poissonian fluctuations at long distances. The area-weighted bubble centroids and area-weighted Voronoi points all have constant $h\left(D\right)=h_e$ for large $D$; the bubble centroids have the smallest value $h_e=0.084\sqrt{〈a〉}$, meaning they are the most uniform. Area-weighted Voronoi centroids exhibit collapse of $h\left(D\right)$ to the same constant $h_e=0.084\sqrt{〈a〉}$ as for the bubble centroids. A similar analysis is performed on the edges of the cells and the spectra of $h\left(D\right)$ for the foam edges show $h\left(D\right)\sim D^{1-\epsilon }$ where $\epsilon =0.30\pm 0.15$.