Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of straight semirigid rods adsorbed on two-dimensional square lattices. The depositing objects can be adsorbed on the surface forming two layers. The filling of the lattice is carried out following a generalized random sequential adsorption (RSA) mechanism. In each elementary step, (i) a set of $k$ consecutive nearest-neighbor sites (aligned along one of two lattice axes) is randomly chosen and (ii) if each selected site is either empty or occupied by a $k$-mer unit in the first layer, then a new $k$-mer is then deposited onto the lattice. Otherwise, the attempt is rejected. The process starts with an initially empty lattice and continues until the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. A wide range of values of $k$ ($2\le k\le 64$) is investigated. The study of the kinetic properties of the system shows that (1) the jamming coverage ${\theta }_{j,k}$ is a decreasing function with increasing $k$, with ${\theta }_{j,k\to \infty }=0.7299\left(21\right)$ the limit value for infinitely long $k$-mers and (2) the jamming exponent ${\nu }_j$ remains close to 1, regardless of the size $k$ considered. These findings are discussed in terms of the lattice dimensionality and number of sites available for adsorption. The dependence of the percolation threshold ${\theta }_{c,k}$ as a function of $k$ is also determined, with ${\theta }_{c,k}=A+Bexp(-k/C)$, where $A={\theta }_{c,k\to \infty }=0.0457\left(68\right)$ is the value of the percolation threshold by infinitely long $k$-mers, $B=0.276\left(25\right)$, and $C=14\left(2\right)$. This monotonic decreasing behavior is completely different from that observed for the standard problem of straight rods on square lattices, where the percolation threshold shows a nonmonotonic $k$-mer size dependence. The differences between the results obtained from bilayer and monolayer phases are explained on the basis of the transversal overlaps between rods occurring in the bilayer problem. This effect (which we call a “cross-linking effect”), its consequences on the filling kinetics, and its implications in the field of conductivity of composites filled with elongated particles (or fibers) are discussed in detail. Finally, the precise determination of the critical exponents $\nu , \beta$, and $\gamma$ indicates that, although the increasing in the width of the deposited layer drastically affects the behavior of the percolation threshold with $k$ and other critical properties (such as the crossing points of the percolation probability functions), it does not alter the nature of the percolation transition occurring in the system. Accordingly, the bilayer model belongs to the same universality class as two-dimensional standard percolation model.

We analyze large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time $t$ depends itself on the value $q_t$ of the time-averaged quantity. First we consider the elephant random walk and a Gaussian variant of this model, identifying two mechanisms for unusual fluctuation behavior, which differ from the Markovian case. In particular, the memory can lead to large-deviation principles with reduced speeds and to nonanalytic rate functions. We then explain how the mechanisms operating in these two models are generic for memory-dependent dynamics and show other examples including a non-Markovian simple exclusion process.

Multiple species in the ecosystem are believed to compete cyclically for maintaining balance in nature. The evolutionary dynamics of cyclic interaction crucially depends on different interactions representing different natural habits. Based on a rock-paper-scissors model of cyclic competition, we explore the role of mortality of individual organisms in the collective survival of a species. For this purpose a parameter called “natural death” is introduced. It is meant for bringing about the decease of an individual irrespective of any intra- and interspecific interaction. We perform a Monte Carlo simulation followed by a stability analysis of different fixed points of defined rate equations and observe that the natural death rate is surprisingly one of the most significant factors in deciding whether an ecosystem would come up with a coexistence or a single-species survival.

Periodic pulse train stimulation is generically used to study the function of the nervous system and to counteract disease-related neuronal activity, e.g., collective periodic neuronal oscillations. The efficient control of neuronal dynamics without compromising brain tissue is key to research and clinical purposes. We here adapt the minimum charge control theory, recently developed for a single neuron, to a network of interacting neurons exhibiting collective periodic oscillations. We present a general expression for the optimal waveform, which provides an entrainment of a neural network to the stimulation frequency with a minimum absolute value of the stimulating current. As in the case of a single neuron, the optimal waveform is of bang-off-bang type, but its parameters are now determined by the parameters of the effective phase response curve of the entire network, rather than of a single neuron. The theoretical results are confirmed by three specific examples: two small-scale networks of FitzHugh-Nagumo neurons with synaptic and electric couplings, as well as a large-scale network of synaptically coupled quadratic integrate-and-fire neurons.

We explore the intriguing effects of the underlying star topological structure in the framework of Schelling's segregation model with blocks. The significant consequences exerted by the star topology are both theoretically analyzed and numerically simulated with and without introducing a fraction of altruistic agents, respectively. The collective utility of the model with egoists alone can be optimized and the optimum stationary state is achieved with the underlying star topology of blocks. More surprisingly, once a proportion of altruists is introduced, the average utility gradually decreases as the fraction of altruists increases. This presents a sharp contrast to the results in Schelling's model with a lattice topology of blocks. Furthermore, an adding-link mechanism is introduced to bridge the gap between the lattice and the star topologies and extend our analysis to more general scenarios. A scaling law of the average utility function is found for the star topology of blocks.

Density-dependent potentials are frequently used in materials simulations because of their approximate description of many-body effects at minimal computational cost. However, in order to apply such models to multicomponent systems, an appropriate definition of total local particle density is required. Here, we discuss two definitions of local density in the context of many-body dissipative particle dynamics. We show that only a potential which combines local densities from all particle types in its argument gives physically meaningful results for all composition ratios. Drawing on the ideas from metal potentials, we redefine local density such that it can accommodate different intertype interactions despite the constraint to keep the main interaction parameter constant, known as Warren's no-go theorem, and generalize the many-body potential to heterogeneous systems. We then show via simulation how liquid-liquid and liquid-solid coexistence can arise just by tuning the interaction parameters.

We focus on the asymmetry of the interaction in the optimal velocity (OV) model, which is a model of self-driven particles, and analytically investigate the effects of the asymmetry on the fluctuation-response relation, which is one of the remarkable relationships in statistical physics. By linearizing a modified OV model, i.e., the backward-looking optimal velocity model, which can easily control the magnitude of asymmetry in the interaction, we derive $n$ coupled linear oscillators with asymmetric interactions. We analytically solve the equations of the $n$ coupled linear oscillators and calculate the response and correlation functions. We find that the fluctuation response relation does not hold in the $n$ coupled linear oscillators with asymmetric interactions. Moreover, as the magnitude of the asymmetry increases, the difference between the response and correlation functions increases .

We investigate the validity of using the low-dissipation model (LD model) to describe the maximum power regime of the endoreversible model under Newton's law of cooling. We find it valid only when the temperature difference of heat reservoirs ($T_h-T_c, T_h>T_c$) is small. Thus the efficiency at maximum power derived from the LD model is valid to the first order of Carnot efficiency when describing endoreversible heat engines. We conclude that the LD model produces the Curzon-Ahlborn efficiency (${\eta }_{\text{CA}}=1-\sqrt{T_h/T_c}$) in the maximum power regime with no dependence on dissipation ratios.

Formation of consensus, in binary yes-no type of voting, is a well-defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly opinionated individuals could create a condition of “support-bubbles” or spontaneous polarization that renders consensus virtually unattainable (e.g., the question of the UK exiting the EU). There have been earlier attempts in capturing the dynamics of consensus formation in societies through simple $Z_2$-symmetric models hoping to capture the essential dynamics of average behavior of a large number of individuals in a statistical sense. However, in absence of external noise, they tend to reach a frozen state with fragmented and polarized states, i.e., two or more groups of similarly opinionated groups with frozen dynamics. Here we show in a kinetic exchange opinion model considered on $L\times L$ square lattices, that while such frozen states could be avoided, an exponentially slow approach to consensus is manifested. Specifically, the system could either reach consensus in a time that scales as $L^2$ or a long-lived metastable state (termed a “domain-wall state”) for which formation of consensus takes a time scaling as $L^{3.6}$. The latter behavior is comparable to some voterlike models with intermediate states studied previously. The late-time anomaly in the timescale is reflected in the persistence probability of the model. Finally, the interval of zero crossing of the average opinion, i.e., the time interval over which the average opinion does not change sign, is shown to follow a scale-free distribution, which is compared with that seen in the opinion surveys regarding Brexit and associated issues since the late 1970s. The issue of minority spreading is also addressed by calculating the exit probability.

Numerical solutions of the mode-coupling theory (MCT) equations for a hard-sphere fluid confined between two parallel hard walls are elaborated. The governing equations feature multiple parallel relaxation channels which significantly complicate their numerical integration. We investigate the intermediate scattering functions and the susceptibility spectra close to structural arrest and compare to an asymptotic analysis of the MCT equations. We corroborate that the data converge in the $\beta$-scaling regime to two asymptotic power laws, viz. the critical decay and the von Schweidler law. The numerical results reveal a nonmonotonic dependence of the power-law exponents on the slab width and a nontrivial kink in the low-frequency susceptibility spectra. We also find qualitative agreement of these theoretical results to event-driven molecular dynamics simulations of polydisperse hard-sphere systems. In particular, the nontrivial dependence of the dynamical properties on the slab width is well reproduced.

Heterogeneity and macroscopic anisotropy of porous media play an important role for dilution and reaction enhancement of conservative and reactive plumes. In this study, we perform numerical simulations to investigate steady-state flow and transport in three-dimensional heterogeneous porous media. We consider two macroscopic anisotropic inclusions resulting in helical flows with twisting streamlines in a three-dimensional flow-through domain. The inclusions are obtained by alternating two layers of angled slices of coarse and fine porous media with different hydraulic conductivity. We investigate flow and transport scenarios considering different geometry and relative position of the two anisotropic inclusions yielding helical flow fields with different extent of interaction. We use metrics of stretching and folding to characterize the flow field and entropy-based metrics for the analysis of the conservative and reactive transport problems. The outcomes show that the two helices result in different patterns of twisting streamlines, which cause distinct deformation of the plumes. However, mixing and reaction enhancement could not be directly related to the extent of the flow field deformation: Configurations with strong deformation can result in only moderate mixing enhancement, whereas configurations with limited deformation of the flow field can lead to significant mixing of the solute plume. Finally, we explore the impact of different degradation rates on reactive transport and the role of reaction kinetics on the entropy balance for a reactant undergoing transport and mixing-controlled degradation in the twisting flow fields. The results show that strong mixing enhancement due to helical flow increases the importance of the reaction kinetics that becomes the rate-limiting process for solute reactive transport.

Stratification due to ion-ion friction in a magnetized multiple-ion species plasma is shown to be accompanied by a heat pump effect, transferring heat from one ion species to another as well as from one region of space to another. The heat pump is produced via identified heating mechanisms associated with charge incompressibility and the Ettingshausen effect. Besides their academic interest, these effects may have useful applications to plasma technologies that involve rotation or compression.

In this work, in the first instance, the multipseudopotential interaction (MPI) model's capabilities are extended for hydrodynamic simulations. This is achieved by combining MPI with the multiple-relaxation-time collision operator and with surface tension modification methods. A method of approaching thermodynamic consistency is also proposed, which consists of splitting the ${\varepsilon }_j$ term into separate terms. One of these terms is used in the calculation of the interparticle force, and the second one is used in the forcing scheme. Secondly, MPI is combined with thermal models in order to simulate droplet evaporation and bubble nucleation in pool boiling. Thermal coupling is implemented using a double distribution function thermal model and a hybrid thermal model. It is found that MPI thermal models obey the ${\mathrm{D}}^2$-law closely for droplet evaporation. MPI is also found to correctly simulate bubble nucleation and departure from the heating element during nucleate pool boiling. It can be suggested that MPI thermal models are comparatively better suited to thermal simulations at low reduced temperatures than single pseudopotential interaction models, although such cases remain very challenging. Droplet evaporation simulations are carried out at a reduced temperature $\left(T_r\right)$ of 0.6 by setting the parameters in the Peng-Robinson equation of state to $a=1/6272$ and $b=1/168$.

The nonexponential shape of the $\alpha$ process observed in supercooled liquids is considered as one of the hallmarks of glassy dynamics and has thus been under study for decades, but is still poorly understood. For a polar van der Waals liquid, we show here—in line with a recent theory—that dipole-dipole correlations give rise to an additional process in the dielectric spectrum slightly slower than the $\alpha$ relaxation, which renders the resulting combined peak narrower than observed by other experimental techniques. This is reminiscent of the Debye-process found in monohydroxy alcohols. The additional peak can be suppressed by weakening the dipole-dipole interaction via dilution with a nonpolar solvent.

We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates with the particle distance and allows for the existence of stable bound states, despite the purely repulsive character of the Coulomb interaction. We design an order parameter to classify these bound states and use it to identify a structural crossover of the particle order, occurring when the electric field strength is varied. Amorphous particle configurations for a vanishing electric field and crystalline order in the regime of a strong electric field are observed. We study the impact of parameter variations on the particle order and conclude that the crossover occurs for a wide range of parameter values and even holds for different helical systems.

We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such boundaries by imposing zero-current conditions, leading to Neumann or Robin boundary conditions, and how these conditions affect the driven process, which describes how large deviations arise in the long-time limit. The results are illustrated with the drifted Brownian motion and the Ornstein-Uhlenbeck process reflected at the origin. Other types of boundaries and applications are discussed.

We demonstrate the existence of vibrational resonance associated with the presence of an uneven boundary. When the motion of a Brownian particle is confined in a region with an uneven boundary, constrained to a double cavity, a high-frequency signal may produce a peak in the spectral power amplification of the other low-frequency signal and therefore to the appearance of the vibrational resonance phenomenon. The mechanism of vibrational resonance in constrained boundaries is different from that in energetic potentials and is termed entropic vibrational resonance (EVR). The EVR can be observed even if the bias force is absent in any direction. Through careful analysis, we clarify two types of mechanisms of the EVR. The one mechanism is ascribed to the transition from a bistable system to a monostable system, and the other corresponds to the match between the escape rate and the natural frequency of the low-frequency signal. Our work merges the vibrational resonance with an uneven boundary, thus extending the scope of the vibrational resonance and shedding new light on the concept of resonance.

We systematically study dynamics of a generalized Kuramoto model of globally coupled phase oscillators. The coupling of modified model depends on the fraction of phase-locked oscillators via a power-law function of the Kuramoto order parameter $r$ through an exponent $\alpha$, such that $\alpha =1$ corresponds to the standard Kuramoto model, $\alpha <1$ strengthens the global coupling, and the global coupling is weakened if $\alpha >1$. With a self-consistency approach, we demonstrate that bifurcation diagrams of synchronization for different values of $\alpha$ are thoroughly constructed from two parametric equations. In contrast to the case of $\alpha =1$ with a typical second-order phase transition to synchronization, no phase transition to synchronization is predicted for $\alpha <1$, as the onset of partial locking takes place once the coupling strength $K>0$. For $\alpha >1$, we establish an abrupt desynchronization transition from the partially (fully) locked state to the incoherent state, whereas there is no counterpart of abrupt synchronization transition from incoherence to coherence due to that the incoherent state remains linearly neutrally stable for all $K>0$. For each case of $\alpha$, by performing a standard linear stability analysis for the reduced system with Ott-Antonsen ansatz, we analytically derive the continuous and discrete spectra of both the incoherent state and the partially (fully) locked states. All our theoretical results are obtained in the thermodynamic limit, which have been well validated by extensive numerical simulations of the phase-model with a sufficiently large number of oscillators.

It has recently been reported that statistical signatures of brain criticality, obtained from distributions of neuronal avalanches, can depend on the cortical state. We revisit these claims with a completely different and independent approach, employing a maximum entropy model to test whether signatures of criticality appear in urethane-anesthetized rats. To account for the spontaneous variation of cortical states, we parse the time series and perform the maximum entropy analysis as a function of the variability of the population spiking activity. To compare data sets with different numbers of neurons, we define a normalized distance to criticality that takes into account the peak and width of the specific heat curve. We found a universal collapse of the normalized distance to criticality dependence on the cortical state, on an animal by animal basis. This indicates a universal dynamics and a critical point at an intermediate value of spiking variability.