The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

The gravity-driven flow of a thin liquid film down a uniformly heated vertical fiber is considered. This is an unstable open flow that exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the variation of surface tension induced by temperature disturbance at the interface. A linear stability analysis and a nonlinear simulation are performed to investigate the dynamic of axisymmetric disturbances. The results showed that the Marangoni instability and the Rayleigh-Plateau instability reinforce each other. With the increase of the thermocapillary effect, the fiber flow has a tendency to break up into smaller droplets.

The shear viscosity coefficient of the one-component plasma is calculated with unprecedented accuracy using equilibrium molecular dynamics simulations and the Green-Kubo relation. Numerical and statistical uncertainties and their mitigation for improving accuracy are analyzed. In the weakly coupled regime, our results agree with the Landau-Spitzer prediction. In the moderately and strongly coupled regimes, our results are found in good agreement with recent results obtained for the Yukawa one-component plasma using nonequilibrium molecular dynamics. A practical formula is provided for evaluating the viscosity coefficient across coupling regimes, from the weakly coupled regime to solidification threshold. The results are used to test theoretical predictions of the viscosity coefficients found in the literature.

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete ${\mathrm{Hirota}}^{-}$ equation and the nonintegrable semidiscrete ${\mathrm{Hirota}}^{+}$ equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete ${\mathrm{Hirota}}^{-}$ equation and the nonintegrable semidiscrete ${\mathrm{Hirota}}^{+}$ equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.

We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function $c\left(t\right)$ can always be expanded in a series of (complex) exponential functions of time when its Laplace transform $\tilde{C}\left(z\right)$ has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades. Our method is based on a different projection technique in the Hilbert space S of the system and shows that appropriate approximations of the exponential series are related to the contraction of S to a finite, usually small, number of dimensions. The time dependence of correlation functions is always described in detail by a multiple-exponential functionality also at long times. This result is therefore also valid for correlation functions of many-body Hamiltonian systems for which a power-law dependence, observed in restricted time ranges and predicted to be the asymptotic one, can be considered at most as a useful approximate modeling of long-time behavior.

Motivated by fundamental issues in nonequilibrium statistical mechanics, we study the venerable susceptible-infected-susceptible (SIS) model of disease spreading in an idealized, simple setting. Using Monte Carlo and analytic techniques, we consider a fully connected, unidirectional network of odd number of nodes, each having an equal number of in- and out-degrees. With the standard SIS dynamics at high infection rates, this system settles into an active nonequilibrium steady state. We find the exact probability distribution and explore its implications for nonequilibrium statistical mechanics, such as the presence of persistent probability currents.

The process of dynamical arrest, leading to formation of different arrested states such as glasses and gels, along with the closely related process of aging, is central for both basic research and technology. Here we report on a study of the time-dependent structural evolution of two aqueous Laponite clay suspensions at different weight concentrations. Neutron diffraction experiments have been performed with the near and intermediate range order diffractometer (NIMROD) that allows studies of the structure of liquids and disordered materials over a continuous length scale ranging from 1 to 300 Å, i.e., from the atomistic to the mesoscopic scales. NIMROD is presently a unique diffractometer, bridging the length scales traditionally investigated by small angle neutron scattering or small angle x-ray scattering with that accessible by traditional diffractometers for liquids. Interestingly, we have unveiled a signature of aging of both suspensions in the length scale region of NIMROD. This phenomenon, ascribed to sporadic contacts between Laponite platelets at long times, has been observed with the sample arrested as gel or as repulsive glass. Moreover, water molecules within the layers closest to Laponite platelets surface show orientational and translational order, which maps into the crystalline structure of Laponite.

Lattice-based Monte Carlo simulations are performed to study a confined liquid crystal system with a topological disclination line entangling a colloidal nanoparticle. In our microscopic study the disclination line is stretched by moving the colloid, as in laser tweezing experiments, which results in a restoring force attempting to minimize the disclination length. From constant-force simulations we extract the corresponding disclination line tension, estimated as $\sim 50$ pN, and observe its decrease with increasing temperature.

I develop a kinetic mechanism to explain chain folding in polymer crystallization which is based on the competition between the formation of stems, which is due to frequent occupations of trans states along the chains in the supercooled polymer melt, and the random coil structure of the polymer chains. Setting equal the average formation time of stems of length $d_l$ with the Rouse time of a piece of polymer of the same arc length $d_l$ yields a lower bound for the thickness of stems and bundles. The estimated lamellar thickness is inversely proportional to the supercooling. The present approach emphasizes the importance of repulsive interactions in polymer crystallization, which are expected to be responsible for the logarithmic lamellar thickening and the increase of lamellar thickness with pressure. An expression for the growth rate for formation and deposition of stems is derived by considering the growth as a dynamic multistage process.

We consider the adaptation dynamics of an asexual population that walks uphill on a rugged fitness landscape which is endowed with a large number of local fitness peaks. We work in a parameter regime where only those mutants that are a single mutation away are accessible, as a result of which the population eventually gets trapped at a local fitness maximum and the adaptive walk terminates. We study how the number of adaptive steps taken by the population before reaching a local fitness peak depends on the initial fitness of the population, the extreme value distribution of the beneficial mutations, and correlations among the fitnesses. Assuming that the relative fitness difference between successive steps is small, we analytically calculate the average walk length for both uncorrelated and correlated fitnesses in all extreme value domains for a given initial fitness. We present numerical results for the model where the fitness differences can be large and find that the walk length behavior differs from that in the former model in the Fréchet domain of extreme value theory. We also discuss the relevance of our results to microbial experiments.

The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising “rock-paper-scissors” interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allow us to clarify when spatial “rock-paper-scissors” competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility.

The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations (“hot spots”) and occasional series of such fluctuations through space and time (“rogue fluctuations”) are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.

Chimera states, that is, dynamical regimes characterized by the existence of a symmetry-broken solution where a coherent domain and an incoherent one coexist, have been theoretically demonstrated and numerically found in networks of homogeneously coupled identical oscillators. In this work we experimentally investigate the behavior of a closed and an open chain of electronic circuits with neuron-like spiking dynamics and first neighbor connections. Experimental results show the onset of a regime that we call chimera states with quiescent and synchronous domains, where synchronization coexists with spatially patterned oscillation death. The whole experimental bifurcation scenario, showing how disordered states, synchronization, chimera states with quiescent and synchronous domains, and oscillatory death states emerge as coupling is varied, is presented.

We deduce rigorous conditions for the onset of amplitude death (AD) and oscillation death (OD) in a system of identical coupled paradigmatic Stuart-Landau oscillators. A nonscalar coupling and high frequency are beneficial for the onset of AD. In strong contrast, scalar diffusive coupling and low intrinsic frequency are in favor of the emergence of OD. Our finding contributes to clearly distinguish intrinsic geneses for AD and OD, and further substantially corroborates that AD and OD are indeed two dynamically distinct oscillation quenching phenomena due to distinctly different mechanisms.

Inspired by the classical Kepler and Rutherford problem, we investigate an analogous setup in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First, we identify new steady bound states in the swirl flow and analyze their stability. Second, we study the dynamics of a self-propelled swimmer heading towards the vortex center, and we observe the subsequent capturing and scattering dynamics. We distinguish between two major types of swimmers, those that tend to elongate perpendicularly to the propulsion direction and those that pursue a parallel elongation. While the first ones can get caught by the swirl, the second ones were always observed to be scattered, which proposes a promising escape strategy. This offers a route to design artificial microswimmers that show the desired behavior in complicated flow fields. It should be straightforward to verify our results in a corresponding quasi-two-dimensional experiment using self-propelled droplets on water surfaces.

Many biological processes are regulated by molecular devices that respond in an ultrasensitive fashion to upstream signals. An important question is whether such ultrasensitivity improves or limits its ability to read out the (noisy) input stimuli. Here, we develop a simple model to study the statistical properties of ultrasensitive signaling systems. We demonstrate that the output sensory noise is always bounded, in contrast to earlier theories using the small noise approximation, which tends to overestimate the impact of noise in ultrasensitive pathways. Our analysis also shows that the apparent sensitivity of the system is ultimately constrained by the input signal-to-noise ratio. Thus, ultrasensitivity can improve the precision of biochemical sensing only to a finite extent. This corresponds to a new limit for ultrasensitive signaling systems, which is strictly tighter than the Berg-Purcell limit.

We present the results of direct numerical simulations of Rayleigh-Bénard convection in the presence of a uniform vertical magnetic field near instability onset. We have done simulations in boxes with square as well as rectangular cross sections in the horizontal plane. We have considered the horizontal aspect ratio $\eta =L_y/L_x=1$ and 2. The onset of the primary and secondary instabilities are strongly suppressed in the presence of the vertical magnetic field for $\eta =1$. The Nusselt number $\mathrm{Nu}$ scales with the Rayleigh number $\mathrm{Ra}$ close to the primary instability as ${\left[\{\text{Ra}-{\text{Ra}}_c\left(Q\right)\}/{\text{Ra}}_c\left(Q\right)\right]}^{0.91}$, where ${\text{Ra}}_c\left(Q\right)$ is the threshold for onset of stationary convection at a given value of the Chandrasekhar number $Q$. $\mathrm{Nu}$ also scales with $\text{Ra}/Q$ as ${\left(\text{Ra}/Q\right)}^{\mu }$. The exponent $\mu$ varies in the range $0.39\le \mu \le 0.57$ for $\text{Ra}/Q\ge 25$. The primary instability is stationary as predicted by Chandrasekhar. The secondary instability is temporally periodic for $\mathrm{Pr}=0.1$ but quasiperiodic for $\mathrm{Pr}=0.025$ for moderate values of $Q$. Convective patterns for higher values of $\mathrm{Ra}$ consist of periodic, quasiperiodic, and chaotic wavy rolls above the onset of the secondary instability for $\eta =1$. In addition, stationary as well as time-dependent cross rolls are observed, as $\mathrm{Ra}$ is further raised. The ratio $r_o/\mathrm{Pr}$ is independent of $Q$ for smaller values of $Q$. The delay in the onset of the oscillatory instability is significantly reduced in a simulation box with $\eta =2$. We also observe inclined stationary rolls for smaller values of $Q$ for $\eta =2$.

We experimentally investigate the Poiseuille flows in nanochannels. It is found that the flow rate undergoes a transition between two linear regimes as the shear rate is varied. The transition indicates that the nonslip boundary condition is valid at low shear rate. When the shear rate is larger than a critical value, slip takes place and the slip length increases linearly with increasing shear rate before approaching a constant value. The results reported in this work can help advance the understanding of flow slip in nanochannels.

Naturally occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the peculiar phenomenon of autoacoustic compaction—nonmonotonic variation of shear band volume with shear rate in angular particles—recently observed in experiments. Our approach is based on the notion that the volume of a granular material is determined by an effective-disorder temperature known as the compactivity. Noise sources in a driven granular material couple its various degrees of freedom and the environment, causing the flow of entropy between them. The grain-scale dynamics is described by the shear-transformation-zone theory of granular flow, which accounts for irreversible plastic deformation in terms of localized flow defects whose density is governed by the state of configurational disorder. To model the effects of grain shape and frictional characteristics, we propose an Ising-like internal variable to account for nearest-neighbor grain interlocking and geometric frustration and interpret the effect of friction as an acoustic noise strength. We show quantitative agreement between experimental measurements and theoretical predictions and propose additional experiments that provide stringent tests on the new theoretical elements.