We study how an evanescence process affects the number of distinct sites visited by a continuous-time random walker in one dimension. We distinguish two very different cases, namely, when evanescence can only occur concurrently with a jump, and when evanescence can occur at any time. The first is characteristic of trapping processes on a lattice, whereas the second is associated with spontaneous death processes such as radioactive decay. In both of these situations we consider three different forms of the waiting time distribution between jumps, namely, exponential, long tailed, and ultraslow.

Agitated wet granular matter can be considered as a nonequilibrium model system for phase transitions, where the macroscopic particles replace the molecules and the capillary bridges replace molecular bonds. It is demonstrated experimentally that a two-dimensional wet granular crystal driven far from thermal equilibrium melts from its free surface, preceded by an amorphous state. The transition into the surface melting state, as revealed by the bond orientational order parameters, behaves like a first order phase transition, with a threshold being traceable to the rupture energy of a single capillary bridge. The observation of such a transition in the macroscopic nonequilibrium system triggers the question of the universality of surface melting.

We utilize total-internal reflection to isolate the two-dimensional surface foam formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state where statistical distributions appear independent of time, except for an overall scale factor. There we find that statistical measures of side number distributions, size-topology correlations, and bubble shapes are all very similar to those for two-dimensional foams. However, the size number distribution is slightly broader, and the shapes are slightly more elongated. A more obvious difference is that T2 processes now include the creation of surface bubbles, due to rearrangement in the bulk, and von Neumann's law is dramatically violated for individual bubbles. But nevertheless, our most striking finding is that von Neumann's law appears to holds on average, namely, the average rate of area change for surface bubbles appears to be proportional to the number of sides minus six, but with individual bubbles showing a wide distribution of deviations from this average behavior.

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

The differential-flow-induced chemical instability is investigated in the context of two coupled reactors with cubic autocatalytic kinetics (the Gray-Scott model). Previous results for master-slave arrangement [Izús, Deza, and Sánchez, J. Chem. Phys. 132, 234112 (2010)] are extended in this study to include bidirectional coupling between reactions. Numerical simulations in the convectively unstable regime show that synchronized noise-sustained structures are developed in both reactors due to the selective amplification of noise. A theoretical analysis shows that the nature of the synchronization and the stability of the synchronized manifold are related with the properties of the critical modes.

A microscopic model is developed to analyze terahertz (THz) emission after ultrashort one- and two-color laser-pulse excitations of an atomic gas. Optical Bloch equations are derived to describe the pulse-induced ionization in the many-atom system including the Coulombic scattering of the ionized electrons. The model captures the continuous transition between the tunneling and the multiphoton ionization regimes. Numerical evaluations for a wide range of pulse configurations identify optimized excitation conditions for strong THz emission.

By a formal analytic argument based on Minkowski's expression for the isotropic average of the excluded volume of convex bodies, we reproduce the exact formula for the excluded volume of two spherorods—also known by the more traditional name of spherocylinders, which is classically derived through a geometric construction. By applying the same argument to spherodisks, which represent discotic platelets, we obtain a simple explicit formula for their excluded volume, whose validity is corroborated by a shape-reconstruction algorithm.

Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter $\sigma$) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the two-particle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to three-dimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.

We study the stability conditions of a class of branching processes prominent in the analysis and modeling of seismicity. This class includes the epidemic-type aftershock sequence (ETAS) model as a special case, but more generally comprises models in which the magnitude distribution of direct offspring depends on the magnitude of the progenitor, such as the branching aftershock sequence (BASS) model and another recently proposed branching model based on a dynamic scaling hypothesis. These stability conditions are closely related to the concepts of the criticality parameter and the branching ratio. The criticality parameter summarizes the asymptotic behavior of the population after sufficiently many generations, determined by the maximum eigenvalue of the transition equations. The branching ratio is defined by the proportion of triggered events in all the events. Based on the results for the generalized case, we show that the branching ratio of the ETAS model is identical to its criticality parameter because its magnitude density is separable from the full intensity. More generally, however, these two values differ and thus place separate conditions on model stability. As an illustration of the difference and of the importance of the stability conditions, we employ a version of the BASS model, reformulated to ensure the possibility of stationarity. In addition, we analyze the magnitude distributions of successive generations of the BASS model via analytical and numerical methods, and find that the compound density differs substantially from a Gutenberg-Richter distribution, unless the process is essentially subcritical (branching ratio less than 1) or the magnitude dependence between the parent event and the direct offspring is weak.

The observation of two polarity-sensitive electrical responses found in the low-frequency (<1 Hz) regime of a square wave field is reported for an achiral rodlike smectic-$C$ liquid crystal with negative dielectric and conductivity anisotropies and in the 90°-twisted configuration. The first involves a transient director modulation appearing at each polarity reversal and vanishing under steady field conditions. The instability is polarity sensitive, with the maximum distortion localized near the negative electrode instead of the sample midplane. This is inferred from the wave-vector orientation alternating in the two halves of the driving cycle between the alignment directions at the two substrates. Various electro-optic characteristics of this temporal phenomenon are also described. Following a similar observation in nematic liquid crystals, we associate the transient periodic order with the Carr-Helfrich mechanism assisted by quadrupolar flexoelectric polarization obtaining under electric field gradients. The second polarity-sensitive effect manifests in the relative shift of the periodic Fréedericksz pattern upon field reversal. The shift, which is linear in field for low fields, tends to saturate for large fields. It is interpreted as due to flexoelectric polarization associated primarily with the c director twist about the layer normal. A model involving a periodic wedgelike band, which has the twist localized within it and is flanked by two uniformly and transversely aligned regions, accounts for the flexoelectric shift of the optical pattern.

Crosslinkers play an essential role in determining the physical properties of gels. We synthesized a new type of crosslinker with three vinyl groups [trisacrylaminomethan (TRI), which joins six polymer chains per single molecule]. We found that $N$-isopropylacrylamide (NIPA) gels crosslinked with the new crosslinker gel at a much lower fraction of crosslinker than the gel crosslinked with popular N,N′-methylenebisacrylamide (BIS). We also found that the NIPA gels with TRI crosslinker displayed larger discrete volume changes at the volume phase transition. We discuss the effects of the average length of NIPA chains between two crosslinkers on the volume phase transition as well as the effects of inhomogeneity in gels caused by a low fraction of crosslinker.

The membrane components of cellular organelles have been shown to segregate into domains as the result of biochemical maturation. We propose that the dynamical competition between maturation and lateral segregation of membrane components regulates domain formation. We study a two-component fluid membrane in which enzymatic reaction irreversibly converts one component into another and phase separation triggers the formation of transient membrane domains. The maximum domain size is shown to depend on the maturation rate as a power law similar to the one observed for domain growth with time in the absence of maturation, despite this time dependence not being verified in the case of irreversible maturation. This control of domain size by enzymatic activity could play a critical role in regulating exchange between organelles or within compartmentalized organelles such as the Golgi apparatus.

Mutational escape from vaccine-induced immune responses has thwarted the development of a successful vaccine against AIDS, whose causative agent is HIV, a highly mutable virus. Knowing the virus' fitness as a function of its proteomic sequence can enable rational design of potent vaccines, as this information can focus vaccine-induced immune responses to target mutational vulnerabilities of the virus. Spin models have been proposed as a means to infer intrinsic fitness landscapes of HIV proteins from patient-derived viral protein sequences. These sequences are the product of nonequilibrium viral evolution driven by patient-specific immune responses and are subject to phylogenetic constraints. How can such sequence data allow inference of intrinsic fitness landscapes? We combined computer simulations and variational theory á la Feynman to show that, in most circumstances, spin models inferred from patient-derived viral sequences reflect the correct rank order of the fitness of mutant viral strains. Our findings are relevant for diverse viruses.

We present an algebraic approach to reveal attractor transitions in Boolean networks under single control based on the recently developed matrix semitensor product theory. In this setting, the reachability of attractors is estimated by the state transition matrices. We then propose procedures that compute the shortest control sequence and the result of each step of input (control) exactly. The general derivation is exemplified by numerical simulations for two kinds of gene regulation networks, the protein-nucleic acid interactions network and the cAMP receptor of Dictyostelium discoideum network.

Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.

We explore how nonlinear coherent waves localized in a few wells of a periodic potential can act analogously to a chain of coupled oscillators. We identify the small-amplitude oscillation modes of these “coupled wave oscillators” and find that they can be extended into the large amplitude regime, where some “ring” for long times. We also reveal the appearance of complex behavior such as the breakdown of Josephson-like oscillations, the destabilization of fundamental oscillation modes, and the emergence of chaotic oscillations for large amplitude excitations. We show that the dynamics may be accurately described by a discrete model with nearest-neighbor coupling, in which the lattice oscillators bear an effective mass.

An experimental and theoretical study of the flow of liquid films around a stationary horizontal cylinder is reported. The film presents two different behaviors: The flow is stable in the upper zone (up to $\sim {150}^{\circ }$ with the vertical) and Rayleigh-Taylor-like instabilities appear in the lower zone. For the stable region, film thickness evolution could be described by numerically integrating an evolution equation obtained using a lubrication approximation. For the unstable region, a linear stability analysis allows us to determine the maximum growth wavelength for the Rayleigh-Taylor instability. Approximate analytical solutions were obtained for generatrices at an angle with the vertical $\theta =0$ (stable region) and $\theta =\pi$ (where the instability appears).

We prove that, for an object with a finitefold rotational symmetry (except for a twofold one) around an axis and mirror symmetries (such as a square rod or pentagonal slab, etc.), dynamics of the symmetry axis in low Reynolds number shear flow exactly follows the same form as that of a uniaxial object (e.g., a circular rod or symmetric ellipsoid) as the so-called Jeffery orbits. We use the formulation in which the dynamics of the rigid body follows first-order ordinary differential equations in time [Phys. Rev. E 84, 056309 (2011)]. Interaction between the object and the shear flow enters through a set of scalar coefficients, and the flow field does not need to be solved dynamically. Results of numerical simulations for general-shaped objects also are discussed. In the second part, Brownian dynamics of a uniaxial object is studied numerically. With $D$ as the rotational diffusion constant, $\alpha$ as a parameter characterizing the aspect ratio, and $\gamma$ as the shear rate, the object starts to align with the flow when the value of $D/\left(\gamma \alpha \right)$ decreases near 1. At large $\alpha$ (the long object limit), the results suggest much lower flow alignment when $D/\left(\gamma \alpha \right)>1$.

We present a generalization of inertial coupling (IC) [Balboa Usabiaga et al., J. Comput. Phys. 235, 701 (2013)], which permits the resolution of radiation forces on small particles with arbitrary acoustic contrast factor. The IC method is based on a Eulerian-Lagrangian approach: particles move in continuum space while the fluid equations are solved in a regular mesh (here we use the finite volume method). Thermal fluctuations in the fluid stress, important below the micron scale, are also taken into account following the Landau-Lifshitz fluid description. Each particle is described by a minimal cost resolution which consists of a single small kernel (bell-shaped function) concomitant to the particle. The main role of the particle kernel is to interpolate fluid properties and spread particle forces. Here, we extend the kernel functionality to allow for an arbitrary particle compressibility. The particle-fluid force is obtained from an imposed “no-slip” constraint which enforces similar particle and kernel fluid velocities. This coupling is instantaneous and permits the capture of the fast, nonlinear effects underlying the radiation forces on particles. Acoustic forces arise because of an excess either in particle compressibility (monopolar term) or in mass (dipolar contribution) over the fluid values. Comparison with theoretical expressions shows that the present generalization of the IC method correctly reproduces both contributions. Due to its low computational cost, the present method allows for simulations with many [$O\left({10}^4\right)$] particles using a standard graphical processor unit.

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.