An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time evolutions of the original reaction system, the dual process is dealt with. Usually, if one changes rate constants of the original reaction system, the direct time evolutions should be performed again, using the new rate constants. On the other hands, only one solution of an extended dual process can be reused to calculate the transition probabilities for various rate constant cases. The idea is demonstrated in a parameter estimation problem for the Lotka-Volterra system.

We have intensively examined the dynamic behavior of flame front instability in a lean swirling premixed flame generated by a change in gravitational orientation [H. Gotoda, T. Miyano, and I. G. Shepherd, Phys. Rev. E 81, 026211 (2010)] from the viewpoints of complex networks, symbolic dynamics, and statistical complexity. Here, we considered the permutation entropy in combination with the surrogate data method, the permutation spectrum test, and the multiscale complexity-entropy causality plane incorporating a scale-dependent approach, none of which have been considered in the study of flame front instabilities. Our results clearly show the possible presence of chaos in flame front dynamics induced by the coupling of swirl-buoyancy interaction in inverted gravity. The flame front dynamics also possesses a scale-free structure, which is reasonably shown by the probability distribution of the degree in $\epsilon$-recurrence networks.

We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models. Using continuum elasticity theory, we trace the absence of the Peierls-Nabarro barrier for the kink motion to the topological boundary term which ensures that only the kink configuration, and not the antikink, costs zero potential energy. Further, we study the eigenmodes around the kink and antikink configurations using a tangent stiffness matrix approach appropriate for prestressed structures to explicitly show how the usual energy degeneracy between the two no longer holds. We show how the kink-antikink asymmetry also manifests in the way these nonlinear excitations interact with impurities introduced in the chain as disorder in the spring stiffness. Finally, we discuss the effect of impurities in the (bond) spring length and build prototypes based on simple linkages that verify our predictions.

We performed extensive simulations of the random-bond Ising model confined between walls where competitive surface fields act. By properly taking the thermodynamic limit we unambiguously determined wetting transition points of the system, as extrapolation of localization-delocalization transitions of the interface between domains of different orientation driven by the respective fields. The finite-size scaling theory for wetting with short-range fields [E. V. Albano and K. Binder, Phys. Rev. Lett. 109, 036101 (2012)] establishes that the average magnetization of the sample, with critical exponent $\beta$, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by $\gamma +2\beta ={\nu }_{\parallel }+{\nu }_{\perp }$ requires $\beta =1/2$ ($\gamma =4, {\nu }_{\parallel }=3$, and ${\nu }_{\perp }=2$), the thermodynamic scaling establishes that ${\mathrm{\Delta }}_s=\gamma +\beta$, which in contrast requires $\beta =0$ (${\mathrm{\Delta }}_s=4$), where $\gamma , {\nu }_{\parallel }, {\nu }_{\perp }$, and ${\mathrm{\Delta }}_s$ are the critical exponents of the susceptibility, the correlation lengths parallel and perpendicular to the interface, and the gap exponent, respectively. So, we formulate a finite-size scaling theory for wetting without hyperscaling and perform numerical simulations that provide strong evidence of hyperscaling violation (i.e., $\beta =0$) and a direct measurement of the susceptibility critical exponent $\gamma /{\nu }_{\perp }=2.0\pm 0.2$, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise.

Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered solids: a random lattice, the bond-depleted fcc lattice, and the fcc lattice with vacancies. Within the harmonic approximation for central-force lattices, we applied sum rules for viscoelastic response derived on the basis of nonaffine atomic motions. The latter motions are a direct result of local structural disorder, and in particular, of the lack of inversion symmetry in disordered lattices. By defining a suitable quantitative and general atomic-level measure of nonaffinity and inversion symmetry, we show that the viscoelastic responses of all three systems collapse onto a master curve upon normalizing by the overall strength of inversion-symmetry breaking in each system. Close to the isostatic point for central-force lattices, power-law creep $G\left(t\right)\sim t^{-1/2}$ emerges as a consequence of the interplay between soft vibrational modes and nonaffine dynamics, and various analytical scalings, supported by numerical calculations, are predicted by the theory.

Modeling flow in porous media is usually focused on the governing equations for mass and momentum transport, which yield the velocity and pressure at the pore or Darcy scales. However, in many applications, it is important to determine the work (or power) needed to induce flow in porous media, and this can be achieved when the mechanical energy equation is taken into account. At the macroscopic scale, this equation may be postulated to be the result of the inner product of Darcy's law and the seepage velocity. However, near the porous medium boundaries, this postulate seems questionable due to the spatial variations of the effective properties (velocity, permeability, porosity, etc.). In this work we derive the macroscopic mechanical energy equation using the method of volume averaging for the simple case of incompressible single-phase flow in porous media. Our analysis shows that the result of averaging the pore-scale version of the mechanical energy equation at the Darcy scale is not, in general, the expected product of Darcy's law and the seepage velocity. As a matter of fact, this result is only applicable in the bulk region of the porous medium and, in the derivation of this result, the properties of the permeability tensor are determinant. Furthermore, near the porous medium boundaries, a more novel version of the mechanical energy equation is obtained, which incorporates additional terms that take into account the rapid variations of structural properties taking place in this particular portion of the system. This analysis can be applied to multiphase and compressible flows in porous media and in many other multiscale systems.

We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)], which explicitly takes the excitation of electrons into consideration. Nonequilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in ${\mathrm{D}}_2$ molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on large scales, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor that accounts for the “bump” structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion.

An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990); R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992); P. J. Dellar, Phys. Rev. E 65, 036309 (2002)] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, $c$, the variation of effective shear viscosity, ${\eta }_{\text{eff}}={\eta }_1[1+f({\eta }_1,{\eta }_2)c]$, with respect to $c$ for a sheared, two-dimensional, initially crystalline emulsion [here ${\eta }_1$ (${\eta }_2$) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent lattice Boltzmann method, using average shear stress and hydrodynamic dissipation, agree well once appropriate corrections to Landau's volume average shear stress [L. Landau and E. M. Lifshitz, Fluid Mechanics, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for $f({\eta }_i,{\eta }_2)$, and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932)] to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.

Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent “dry” sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf et al., J. Chem. Phys. 144, 134106 (2016)] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a “smearing out” of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.

Microstructured metallic devices have been extensively studied because of their interesting properties for controlling the transmission, reflection, and absorption of electromagnetic waves. A very simple implementation is an array of infinitely long parallel metal strips printed on a dielectric substrate. In the past few years, several analytical models have been reported based on the use of equivalent circuits with distributed and lumped components to account for the electrical performance of these structures. However, the proposed models are restricted to highly symmetrical configurations of the basic unit cell of the periodic structure. The purpose of this paper is to present the nontrivial extension of such circuit models to deal with nonsymmetrical structures. More specifically, a wideband equivalent-circuit model will be developed to describe the scattering properties of a pair of coupled different nonaligned slit gratings printed on a dielectric slab of arbitrary thickness. The relevant consequences of the lack of symmetry of the structures under study will be thoroughly discussed. The obtained equivalent network can be straightforwardly used to model stacked structures with an arbitrary number of nonsymmetrical striplike arrays.

The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle systems with zero-range interactions. Interestingly, it is known that the theorem is violated by systems with exclusion interactions. These two paradigmatic interactions differ by two qualitative aspects: the range of interactions and the dependence of branching fractions on the state of the system. In this work two different models are studied in order to identify the qualitative property of the interaction that leads to breakdown of no pumping. A model with finite-range interaction is shown analytically to satisfy no pumping. In contrast, a model in which the interaction affects the probabilities of reaching different sites, given that a particle is making a transition, is shown numerically to violate the no-pumping theorem. The results suggest that systems with interactions that lead to state-dependent branching fractions do not satisfy the no-pumping theorem.

We explore numerically the morphological patterns of thermodiffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the recent model of Brailovsky et al. to include distinct process kinetics and reactant heterogeneity. The generalized model is derived analytically and validated with other established models in the limit of infinite Lewis number for zero-order and first-order kinetics. Cellular and dendritic instabilities are found at low Lewis numbers. These are studied using a dynamic adaptive mesh refinement technique that allows very large computational domains, thus allowing us to reduce finite-size effects that can affect or even preclude the emergence of these patterns. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky et al. The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells to continued tip splitting and cell merging, are well described within the framework of thermodiffusive instabilities and are consistent with previous numerical studies. These types of dynamics are classified as “quasilinear” and characterized by low-amplitude cells that may be strongly affected by the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly nonlinear effects become prominent and large-amplitude, complex cellular and seaweed dendritic morphologies emerge.

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.

We present a systematic experimental study of the dynamic behavior of monodisperse and bidisperse two-dimensional colloidal hard-sphere fluids. We consider the diffusive behavior of the two types of particles for systems with a variety of compositions and total area fractions. In particular, we measure the short- and long-time diffusion coefficients for both species independently. We find that the short-time self-diffusion coefficients show an approximately linear dependence on the area fraction and that the long-time self-diffusion coefficients are well described by an expression dependent upon only the area fraction and contact value of the radial distribution function. Finally, we consider the effect of composition change and find some variation in the long-time self-diffusion coefficients, which we ascribe to the complex packing effects exhibited by binary systems.

We report imaging of the director field near edge dislocations in thermotropic antiferroelecric smectic-$C_A^{*}$ $\left(\mathrm{Sm}{C}_A^{*}\right)$ liquid crystal. Measurements were made in freestanding films with thickness from two to ten smectic layers. We find two different orientations of the molecular tilt plane with respect to the edge dislocation line. The orientation is determined by the value of the Burgers vector of the dislocation. Elementary edge dislocation and dislocations with a Burgers vector equal to an odd number of layers orient the tilt plane perpendicular on the two sides of the dislocation. Dislocations with a Burgers vector equal to an even number of layers orient the molecular tilt plane parallel to the dislocation line. Difference in the orientation for an odd Burgers vector can be attributed to breaking of antiferroelectric symmetry by the edge dislocation.

The results of numerical studies of the interaction forces between two finite-size charged spherical conductive particles embedded into weakly ionized strongly collisional isothermal plasma-like medium are presented. The studies are performed for the case of particles with fixed electric charge under the assumption that particles do not absorb electrons and ions from the surrounding plasma (colloidal particles) as well as for particles charged by plasma currents (grains). In the first case the Poisson-Boltzmann model was used and in the second the dynamics of grain charging is described in the drift-diffusion approximation. It is shown that at the large distances the interaction force between colloidal particles has the Debye screened asymptotic while for the grains the Coulomb-like behavior is observed. The dependence of the grain charge collected due to the plasma particle absorption on the distance between two grains is studied. The possibility of introducing effective Coulomb description of finite-size grain interaction in weakly ionized strongly collisional plasma is discussed.

The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.

How to best exploit patchy resources? We introduce a minimal exploitation-migration model that incorporates the coupling between a searcher's trajectory, modeled by a random walk, and ensuing depletion of the environment by the searcher's consumption of resources. The searcher also migrates to a new patch when it takes $\mathcal{S}$ consecutive steps without finding resources. We compute the distribution of consumed resources $F_t$ at time $t$ for this non-Markovian searcher and show that consumption is maximized by exploring multiple patches. In one dimension, we derive the optimal strategy to maximize $F_t$. This strategy is robust with respect to the distribution of resources within patches and the criterion for leaving the current patch. We also show that $F_t$ has an optimum in the ecologically relevant case of two-dimensional patchy environments.

We experimentally examine the equivalence between the entropy production evaluated from irreversibility of trajectories and the physical dissipation in dissipative processes via electric resistor-capacitor (RC) circuits. The examinations are performed for two nonequilibrium steady states that are driven by an injected current and temperature difference, respectively. Such an equivalence demonstrates a parameter-free method to evaluate the entropy production of a system. The effects of configurational and temporal resolutions are also studied.