Zipf's law establishes a scaling behavior for word frequencies in large text corpora. The appearance of Zipfian properties in vocabularies (viewed as an intermediate phase between referentially useless one-word systems and one-to-one word-meaning vocabularies) has been previously explained as an optimization problem for the interests of speakers and hearers. Remarkably, humanlike vocabularies can be viewed also as bipartite graphs. Thus, the aim here is double: within a bipartite-graph approach to human vocabularies, to propose a decentralized language game model for the formation of Zipfian properties. To do this, we define a language game in which a population of artificial agents is involved in idealized linguistic interactions. Numerical simulations show the appearance of a drastic transition from an initially disordered state towards three kinds of vocabularies. Our results open ways to study Zipfian properties in language, reconciling models seeing communication as a global minima of information entropic energies and models focused on self-organization.

Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The modulations of patterns, occurring on long spatial and temporal scales, cannot be captured by linear approximation analysis. Here, we show that, starting from a general model with long range couplings displaying patterns, the spatiotemporal evolution of large-scale modulations at the onset of instability is ruled by the well-known Ginzburg-Landau equation, independently of the details of the dynamics. Hence, we demonstrate the validity of such equation in the description of the behavior of a wide class of systems. We introduce a mathematical framework that is also able to retrieve the analytical expressions of the coefficients appearing in the Ginzburg-Landau equation as functions of the model parameters. Such framework can include higher order nonlocal interactions and has much larger applicability than the model considered here, possibly including pattern formation in models with very different physical features.

Isostable coordinates provide a convenient framework for understanding the transient behavior of dynamical systems with stable attractors. These isostable coordinates are often used to characterize the slowest decaying eigenfunctions of the Koopman operator; by neglecting the rapidly decaying Koopman eigenfunctions a reduced order model can be obtained. Existing work has focused primarily on nondegenerate isostable coordinates, that is, isostable coordinates that are associated with eigenvalues that have identical algebraic and geometric multiplicities. Current isostable reduction methods cannot be applied to characterize the decay associated with a defective eigenvalue. In this work, a degenerate isostable framework is proposed for use when eigenvalues are defective. These degenerate isostable coordinates are investigated in the context of various reduced order modeling frameworks that retain many of the important properties of standard (nondegenerate) isostable reduced modeling strategies. Reduced order modeling examples that require the use of degenerate isostable coordinates are presented with relevance to both circadian physiology and nonlinear fluid flows.

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

This paper reports the scaling laws to describe the time-evolution behavior of solvent-mediated strength at the interface between two identical thermoplastic polymers below the glass-transition temperature. Our results suggest that the evolution scales as $\sqrt{t}$, where $t$ is the curing time. It depends on the time evolution of interfacial stiffness and toughness, each of which scales as $\sqrt{t}$. Employing a combination of experiments and continuum scale simulations, we show that the evolution of strength, stiffness, and toughness is controlled by pure diffusion. It can therefore be treated as a Gaussian process. While the “saturation of strength,” which describes the transition of strength evolution into a steady state, does not strictly follow any power-law type behavior, a simple exponential law accurately characterizes both evolution and saturation of strength. This suggests that the longer timescale nonlinear processes (that are overdetermined by the power-law type scaling laws) diminish rapidly in approaching a steady state. Furthermore, the kinetics of the evolution processes is well captured by the dissolution of polymer particles. While dissolution involves a different timescale, it strongly correlates with the solvent-welding process upon normalization. The correlation highlights the equivalence of the dissolution and solvent-joining processes and offers an easier route to determining strength at arbitrary curing times. Additionally, the dissolution rate of polymer particles is shape dependent and governed by the surface-to-volume ratio.

We have studied the effect of osmotic pressure on complexes formed by DNA with the cationic surfactant cetyltrimethylammonium tosylate using small-angle x-ray scattering. Earlier studies have shown that these complexes exhibit three different phases depending on the DNA and surfactant concentrations in the solution. The hexagonal superlattice phase ($H_{I,s}^c$) is found to be corralled into the hexagonal phase ($H_I^c$) above a threshold osmotic pressure. We have also estimated the DNA to surfactant micelle stoichiometry of the complexes in the three phases using elemental analysis. Our results provide further support for the structures of these complexes proposed earlier based on small-angle x-ray scattering data.

We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.

The dynamics of an argon plasma in the gap of a thermionic diode is investigated using particle-in-cell (PIC) simulations. The time-averaged diode current, as a function of the relative electrical potential between the electrodes, is studied while the plasma density depletes due to recombination on the electrode surfaces. Simulations were performed in both one and two dimensions, and significant differences were observed in the plasma decay between the two cases. Specifically, in two dimensions it was found that the electrostatic potential gradually changes as the plasma decays, while in one dimension fluctuations in the plasma led to large potential fluctuations which changed the plasma decay characteristics relative to the two-dimensional case. This creates significant differences in the time-averaged diode current. Furthermore, it was found that the maximum time-averaged current is collected when the diode voltage is set to the flat-band condition, where the cathode and anode vacuum biases are equal. This suggests a novel technique of measuring the difference in work functions between the cathode and anode in a thermionic converter.

Dynamics of the transition from a linear plasma wave to a nonlinear state characterized by the Bernstein-Greene-Kruskal mode is studied within the framework of the Vlasov-Poisson system. In the linear stage, the plasma distribution function ($f$) develops finer and finer structures in velocity space through a series of “mixing” processes leading to the Landau damping of the plasma wave. These mixing processes inevitably result in strong phase irregularities in velocity space. Using numerical simulations, it was observed that starting from the wave-particle resonance region, this irregular phase pattern gets “smoothed out” through a process of spreading of phase synchronization, which tends to reduce Landau damping, facilitating the formation of the nonlinear plasma wave as a fully synchronized final state. It is also found that there exists a residual damping for the quasisteady nonlinear wave when the phases of the particles are not fully synchronized.

A high energy density plasma embedded in a neutral gas is able to launch an outward-propagating nonlinear electrostatic ionization wave that traps energetic electrons. The trapping maintains a strong sheath electric field, enabling rapid and long-lasting wave propagation aided by field ionization. Using 1D3V kinetic simulations, we examine the propagation of the ionization wave in the presence of a transverse MG-level magnetic field with the objective to identify qualitative changes in a regime where the initial thermal pressure of the plasma exceeds the pressure of the magnetic field ($\beta >1$). Our key finding is that the magnetic field stops the propagation by causing the energetic electrons sustaining the wave to lose their energy by emitting an electromagnetic wave. The emission is accompanied by the magnetic field expulsion from the plasma and an increased electron loss from the trapping wave structure. The described effect provides a mechanism mitigating rapid plasma expansion for those applications that involve an embedded plasma, such as high-flux neutron production from laser-irradiated deuterium gas jets.

A statistical learning approach is presented to predict the dependency of steady hydrodynamic interactions of thin oblate spheroidal particles on particle orientation and Reynolds number. The conventional empirical correlations that approximate such dependencies are replaced by a neural-network-based correlation which can provide accurate predictions for high-dimensional input spaces occurring in flows with nonspherical particles. By performing resolved simulations of steady uniform flow at $1\le \mathrm{Re}\le 120$ around a 1:10 spheroidal body, a database consisting of Reynolds number- and orientation-dependent drag, lift, and pitching torque acting on the particle is collected. A multilayer perceptron is trained and validated with the generated database. The performance of the neural network is tested in a point-particle simulation of the buoyancy-driven motion of a 1:10 disk. Our statistical approach outperforms existing empirical correlations in terms of accuracy. The agreement between the numerical results and the experimental observations prove the potential of the method.

We propose to use ultrahigh intensity laser pulses with wave-front rotation (WFR) to produce short, ultraintense surface plasma waves (SPW) on grating targets for electron acceleration. Combining a smart grating design with optimal WFR conditions identified through simple analytical modeling and particle-in-cell simulation allows us to decrease the SPW duration (down to a few optical cycles) and increase its peak amplitude. In the relativistic regime, for $I{\lambda }_0^2=3.4\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2\mu {\mathrm{m}}^2$, such SPW are found to accelerate high charge (few 10 s of pC), high energy (up to 70 MeV), and ultrashort (few fs) electron bunches.

We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates $K(k,l)=1/k+1/l$. In this case, it is possible to determine the behavior of large-size aggregates in the limit of large times in a way that allows a highly detailed analysis of the behavior of the system. This is the so-called scaling limit, in which the cluster size distribution collapses to a function of the ratio of the cluster size to a time-dependent typical size. The results confirm the far more general results of earlier work concerning a general scaling theory for so-called reaction rates of Type III, which are characterized by the property that aggregates of very different sizes react faster than comparable aggregates of similar sizes. For these, the cluster size distribution decays rapidly to zero both for sizes much larger and much smaller than the typical size, and is thus often described as being “bell-shaped”. For clusters much larger than the typical size, however, an unexpected subleading correction is discovered. Finally, several results going beyond the scope of the scaling limit are obtained: in particular the behavior of concentrations for fixed cluster size in the large-time limit and the large-size behavior for clusters at a fixed time. The latter again shows subleading deviations from the expected behavior.

In this work we consider search problems that evaluate the probability distribution of finding the source at each step in the search. We start with a sample strategy where the movement at each time step is in the immediate neighborhood. The jump probability is taken to be proportional to the normalized difference between the probability of finding the source at the jump location with the probability of finding the source at the present location. We evaluate a lower bound on the average search time for a searcher using this strategy. We next consider the problem of evaluating the lower bound on the search time for a generic strategy which would utilize the source probability distribution to figure out the position of the source. We derive an expression for the lower bound on the search time. We present an analytic expression for this lower bound in a case in which the particles emitted by the source diffuse in a homogeneous manner. For a general probability distribution with entropy $E$, we find that the lower bound goes as $e^{E/2}$.

We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the time-averaged velocity of the piston in the long-time limit, we perturbatively calculate the large deviation function of the time-averaged velocity. Then, we derive an infinite number of effective Langevin equations yielding the same large deviation function as in the original model. Finally, we provide two possibilities for uniquely determining the form of the effective model.

By means of extensive Monte Carlo simulation, we study extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearest neighbors for the simple cubic lattice. We find precise thresholds for 23 systems using a single-cluster growth algorithm. Site percolation on lattices with compact neighborhoods of connected sites can be mapped to problems of lattice percolation of extended objects of a given shape, such as disks and spheres, and the thresholds can be related to the continuum thresholds ${\eta }_c$ for objects of those shapes. This mapping implies $z{p}_c\sim 4{\eta }_c=4.51235$ in two dimensions and $z{p}_c\sim 8{\eta }_c=2.7351$ in three dimensions for large $z$ for circular and spherical neighborhoods, respectively, where $z$ is the coordination number. Fitting our data for compact neighborhoods to the form $p_c=c/(z+b)$ we find good agreement with this prediction, $c=2^d{\eta }_c$, with the constant $b$ representing a finite-$z$ correction term. We also examined results from other studies using this fitting formula. A good fit of the large but finite-$z$ behavior can also be made using the formula $p_c=1-exp(-2^d{\eta }_c/z)$, a generalization of a formula of Koza, Kondrat, and Suszcayński [J. Stat. Mech.: Theor. Exp. (2014) P11005]. We also study power-law fits which are applicable for the range of values of $z$ considered here.

Exact or precise thresholds have been intensively studied since the introduction of the percolation model. Recently, the critical polynomial $P_B(p,L)$ was introduced for planar-lattice percolation models, where $p$ is the occupation probability and $L$ is the linear system size. The solution of $P_B=0$ can reproduce all known exact thresholds and leads to unprecedented estimates for thresholds of unsolved planar-lattice models. In two dimensions, assuming the universality of $P_B$, we use it to study a nonplanar lattice model, i.e., the equivalent-neighbor lattice bond percolation, and the continuum percolation of identical penetrable disks, by Monte Carlo simulations and finite-size scaling analysis. It is found that, in comparison with other quantities, $P_B$ suffers much less from finite-size corrections. As a result, we obtain a series of high-precision thresholds $p_c\left(z\right)$ as a function of coordination number $z$ for equivalent-neighbor percolation with $z$ up to $\mathrm{O}\left({10}^5\right)$ and clearly confirm the asymptotic behavior $z{p}_c-1\sim 1/\sqrt{z}$ for $z\to \infty$. For the continuum percolation model, we surprisingly observe that the finite-size correction in $P_B$ is unobservable within uncertainty $\mathrm{O}\left({10}^{-5}\right)$ as long as $L\ge 3$. The estimated threshold number density of disks is ${\rho }_c=1.43632505\left(10\right)$, slightly below the most recent result ${\rho }_c=1.43632545\left(8\right)$ of Mertens and Moore obtained by other means. Our work suggests that the critical polynomial method can be a powerful tool for studying nonplanar and continuum systems in statistical mechanics.

Recent reports indicate that nanoparticle (NP) clusters near cell membranes could enhance local electric fields, leading to heightened electroporation. This aspect is quantitatively analyzed through numerical simulations whereby time dependent transmembrane potentials are first obtained on the basis of a distributed circuit mode, and the results then used to calculate pore distributions from continuum Smoluchowski theory. For completeness, both monopolar and bipolar nanosecond-range pulse responses are presented and discussed. Our results show strong increases in TMP with the presence of multiple NP clusters and demonstrate that enhanced poration could be possible even over sites far away from the poles at the short pulsing regime. Furthermore, our results demonstrate that nonuniform distributions would work to enable poration at regions far away from the poles. The NP clusters could thus act as distributed electrodes. Our results were roughly in line with recent experimental observations.

Cellular appendages conferring motility, such as flagella and cilia, are known to synchronise their periodic beats. The origin of synchronization is a combination of long-range hydrodynamic interactions with physical mechanisms allowing the phases of these biological oscillators to evolve. Two of such mechanisms have been identified by previous work, the elastic compliance of the periodic orbit or oscillations driven by phase-dependent biological forcing, both of which can lead generically to stable phase locking. In order to help uncover the physical mechanism for hydrodynamic synchronization most essential overall in biology, we theoretically investigate in this paper the effect of strong confinement on the effectiveness of hydrodynamic synchronization. Following past work, we use minimal models of cilia where appendages are modeled as rigid spheres forced to move along circular trajectories near a rigid surface. Strong confinement is modeled by adding a second nearby surface, parallel to the first one, where the distance between the surfaces is much smaller than the typical distance between the cilia, which results in a qualitative change in the nature of hydrodynamic interactions. We calculate separately the impact of hydrodynamic confinement on the synchronization dynamics of the elastic compliance and the force modulation mechanisms and compare our results to the usual case with a single surface. Applying our results to the biologically relevant situation of nodal cilia, we show that force modulation is a mechanism that leads to phase-locked states under strong confinement that are very similar to those without confinement as a difference with the elastic compliance mechanism. Our results point therefore to the robustness of force modulation for synchronization, an important feature for biological dynamics that therefore suggests it could be the most essential physical mechanism overall in arrays of nodal cilia. We further examine the distinct biologically relevant situation of primary cilia and show in that case that the difference in robustness of the mechanisms is not as pronounced but still favors the force modulation.