On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Two sets of vectors, covariant Lyapunov vectors (CLVs) and orthogonal Lyapunov vectors (OLVs), are currently used to characterize the linear stability of chaotic systems. A comparison is made to show their similarity and difference, especially with respect to the influence on hydrodynamic Lyapunov modes (HLMs). Our numerical simulations show that in both Hamiltonian and dissipative systems HLMs formerly detected via OLVs survive if CLVs are used instead. Moreover, the previous classification of two universality classes works for CLVs as well, i.e., the dispersion relation is linear for Hamiltonian systems and quadratic for dissipative systems, respectively. The significance of HLMs changes in different ways for Hamiltonian and dissipative systems with the replacement of OLVs with CLVs. For general dissipative systems with nonhyperbolic dynamics the long-wavelength structure in Lyapunov vectors corresponding to near-zero Lyapunov exponents is strongly reduced if CLVs are used instead, whereas for highly hyperbolic dissipative systems the significance of HLMs is nearly identical for CLVs and OLVs. In contrast the HLM significance of Hamiltonian systems is always comparable for CLVs and OLVs irrespective of hyperbolicity. We also find that in Hamiltonian systems different symmetry relations between conjugate pairs are observed for CLVs and OLVs. Especially, CLVs in a conjugate pair are statistically indistinguishable in consequence of the microreversibility of Hamiltonian systems. Transformation properties of Lyapunov exponents, CLVs, and hyperbolicity under changes of coordinate are discussed in appendices.

In living organisms, branching structures are often observed in open systems. During the process of structure formation/deformation, signal propagation can be observed. Branching paths often deform depending on the history of signal propagation. To gain a better understanding of the process of pattern formation that results in characteristic geometrical paths, we adopt a system in which the dynamics of path formation are correlated with signal propagation. This model involves both branch-generation dynamics and signal-propagation dynamics, and we introduced positive feedback between these two dynamic processes. We studied the geometrical properties of path deformation and the pattern of signal propagation using a discretized reaction-diffusion model. The proposed model can qualitatively reproduce different branching patterns and means of signal propagation. One remarkable result is that the mutual interaction of these two dynamic processes leads to autonomous wave generation, similar to a pacemaker or the generation of spiral waves. Because the autonomous wave generation in the signal is spontaneous, the shapes of the branching paths become distorted. We discuss the correlation between path deformation and signal propagation as a first step in understanding signal processing for such complex deformable paths.

We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, and absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.

Rotational effects on the nonlinear sliding friction of a damped dimer moving over a substrate are studied within a largely one-dimensional model. The model consists of two masses connected rigidly, internally damped, and sliding over a sinusoidal (substrate) potential while being free to rotate in the plane containing the masses and the direction of sliding. Numerical simulations of the dynamics performed by throwing the dimer with an initial center of mass velocity along the substrate direction show a richness of phenomena including the appearance of three separate regimes of motion. The orientation of the dimer performs tiny oscillations around values that are essentially constant in each regime. The constant orientations form an intricate pattern determined by the ratio of the dimer length to the substrate wavelength as well as by the initial orientations chosen. Corresponding evolution of the center of mass velocity consists, respectively, of regular oscillations in the first and the third regimes, but a power law decay in the second regime; the center of mass motion is effectively damped in this regime because of the coupling to the rotation. Depending on the initial orientation of the dimer, there is considerable variation in the overall behavior. For small initial angles to the vertical, an interesting formal connection can be established to earlier results known in the literature for a vibrating, rather than rotating, dimer. But for large angles, on which we focus in the present paper, quite different evolution occurs. Some of the numerical observations are explained successfully on the basis of approximate analytical arguments but others pose puzzling problems.

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.

We consider a standard microscopic analysis of the transport coefficients, commonly used in nonequilibrium molecular dynamics techniques, and apply it to the smoothed particle hydrodynamics method in steady-shear flow conditions. As previously suggested by Posch et al. [Phys. Rev. E 52, 1711 (1995)], we observe the presence of nonzero microscopic (kinetic and potential) contributions to the total stress tensor in addition to its dissipative part coming from the discretization of the Navier-Stokes continuum equations. Accordingly, the dissipative part of the shear stress produces an output viscosity equal to the input model parameter. On the other hand, the nonzero atomistic viscosities can contribute significantly to the overall output viscosity of the method. In particular, it is shown that the kinetic part, which acts similarly to an average Reynolds-like stress, becomes dominant at very low viscous flows where large velocity fluctuations occur. Remarkably, in this kinetic regime the probability distribution function of the particle accelerations is in surprisingly good agreement with non-Gaussian statistics observed experimentally.

We study universality classes and crossover behaviors in non-Abelian directed sandpile models in terms of the metastable pattern analysis. The non-Abelian property induces spatially correlated metastable patterns, characterized by the algebraic decay of the grain density along the propagation direction of an avalanche. Crossover scaling behaviors are observed in the grain density due to the interplay between the toppling randomness and the parity of the threshold value. In the presence of such crossovers, we show that the broadness of the grain distribution plays a crucial role in resolving the ambiguity of the universality class. Finally, we claim that the metastable pattern analysis is important as much as the conventional analysis of avalanche dynamics.

In this paper, we have studied Brownian motion in multidimension phase space in presence of a magnetic field. The nonequilibrium behavior of thermodynamically inspired quantities along the individual component of motion has been studied in detail. Based on the Fokker-Planck description of the stochastic process and entropy balance equation, we have calculated information entropy production and entropy flux at nonequilibrium state. The dependence of these quantities on time, magnetic field, and thermal bath is studied. In this context, we have observed that there exists extremum behavior in the dynamics and the applied magnetic field breaks the equivalence in motion of the components in the nonequilibrium state.

We use molecular simulation to study the ability of excess entropy scaling relationships to describe the kinetic properties of a confined molecular system. We examine a model for a confined fluid consisting of dumbbell-shaped molecules that interact with atomistically detailed pore walls via a Lennard-Jones potential. We obtain kinetic, thermodynamic, and structural properties of the system at three wall-fluid interaction strengths and over a temperature range that includes sub- and super-critical conditions. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate scattering function. We carefully consider the reference state used to define the excess entropy of a confined fluid. Three ideal-gas reference states are considered, with the cases differentiated by the extent to which one-body spatial and orientational correlations are accounted for in the reference state. Our results indicate that a version of the excess entropy that includes information related to the one-body correlations in a confined fluid serves as the best scaling variable for dynamic properties. When adopting such a definition for the reference state, to a very good approximation, bulk and confined data for a specified dynamic property at a given temperature collapse onto a common curve when plotted against the excess entropy.

Using coarse-grained molecular-dynamics simulations, a generic styrene-block-butadiene-block-styrene triblock copolymer under lamellar conformation is used in order to investigate the mutual entanglement evolution when a structure of alternating glassy (S)/rubbery (B) layers is submitted to an imposed deformation. By varying the amount of loop chains between each phase, i.e., noncrossing chains, it is possible to generate different types of S/B interface definitions. A specific boundary driven tensile strain protocol has been developed in order to mimic “real” experiments and measure the stress-strain curve. The same protocol is also applied to a reference state consisting in a directed glassy homopolymers, as well as to an isotropic glassy polymer. The evolution of initial mutual entanglements from the undeformed samples during the whole deformation process is monitored. It is shown for all considered systems that initial entanglements mostly participate to the preyield regime of the stress-strain curve and that this network is debonded during the strain-hardening regime. For triblocks with a non-null amount of crossing chains, the lower the amount is, the longer the memory effect of the initial entanglement network in the postyield regime is. On the fly distributions of entanglements, which depart from the postyield regime, depict memory effects and long-time correlations during the strain-hardening regime. For triblocks, loop chains reinforce these effects.

A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as ${\text{Re}}_{\delta }\to \infty$, the dynamically defined boundary layer thickness $\delta \left(x\right)\propto x/{\text{ln}}^2{\text{Re}}_x$ and the skin friction $\lambda =\frac{2{\tau }_w}{\rho U_0^2}\propto 1/{\text{ln}}^2\delta \left(x\right)$. Here ${\tau }_w$ and $U_0$ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter $\frac{d\delta \left(x\right)}{dx}\to 0$ in the limit $x\to \infty$.

Properties of dynamical systems with dichotomous Markov noise which exhibit crises are investigated. We find numerically the dependence of the mean residence time on the precrisis attractor on the transition rate (or transition probability in the discrete-time case) of dichotomous Markov noise. To explain this dependence, we construct a simple Markov chain model, which allows us to find the mean residence time for the given transition rate with a good accuracy. Next, we find the distribution of residence times for a system driven by dichotomous Markov noise and also build a simple model to explain its properties.

We show that a nonlinear coupling with delayed feedback between two limit-cycle oscillators can lead to phase-locked, periodically modulated, and chaotic phase synchronization as well as to desynchronization. Parameter regions with stable phase-locked states attain the well-known form of the swallows or shrimps found and studied for nonlinear maps. We demonstrate that the swallow regions can be accompanied by a different bifurcation scenario where the periodic orbits of the phase-locked states undergo a torus bifurcation instead of a previously reported period-doubling bifurcation. This property has an impact on the spatial organization of the swallows in the parameter space. The swallow regions contribute to the synchronization domain of the considered system, and we analytically approximate the parameter synchronization threshold.

The effects of preplasma on lateral fast electron transport at front target surface, irradiated by ultraintense $\left(>{10}^{18}\text{W}/{\text{cm}}^2\right)$ laser pulses, are investigated by $K\alpha$ imaging technique. A large annular $K\alpha$ halo with a diameter of $\sim 560\mu \text{m}$ surrounding a central spot is observed. A specially designed steplike target is used to identify the possible mechanisms. It is believed that the halos are mainly generated by the lateral diffusion of fast electrons due to the electrostatic and magnetic fields in the preplasma. This is illustrated by simulated electron trajectories using a numerical model.

We address the heat flow study starting from microscopic models of matter: we develop an approach and investigate some anharmonic graded mass crystals, with weak interparticle interactions. We calculate the thermal conductivity, and show the existence of rectification and negative differential thermal resistance. Our formalism allows us to understand the mechanism behind the phenomena, and shows that the properties of graded materials make them genuine thermal diodes.

We consider an inextensible, semiflexible polymer or wormlike chain, with persistence length $P$ and contour length $L$, fluctuating in a cylindrical channel of diameter $D$. In the regime $D⪡P⪡L$, corresponding to a long, tightly confined polymer, the average length of the channel $⟨R_{\parallel }⟩$ occupied by the polymer and the mean-square deviation from the average vary as $⟨R_{\parallel }⟩=\left[1-{\alpha }_{\circ }{\left(D/P\right)}^{2/3}\right]L$ and $⟨\Delta R_{\parallel }^2⟩={\beta }_{\circ }\left(D^2/P\right)L$, respectively, where ${\alpha }_{\circ }$ and ${\beta }_{\circ }$ are dimensionless amplitudes. In earlier work we determined ${\alpha }_{\circ }$ and the analogous amplitude ${\alpha }_{◻}$ for a channel with a rectangular cross section from simulations of very long chains. In this paper, we estimate ${\beta }_{\circ }$ and ${\beta }_{◻}$ from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of $R_{\parallel }$ or radial distribution function, which is asymptotically exact for large $L$ and has the skewed shape seen experimentally.

We study MCF-7 breast cancer cell movement in a transwell apparatus. Various experimental conditions lead to a variety of monotone and nonmonotone responses which are difficult to interpret. We anticipate that the experimental results could be caused by cell-to-cell adhesion or volume exclusion. Without any modeling, it is impossible to understand the relative roles played by these two mechanisms. A lattice-based exclusion process random-walk model incorporating agent-to-agent adhesion is applied to the experimental system. Our combined experimental and modeling approach shows that a low value of cell-to-cell adhesion strength provides the best explanation of the experimental data suggesting that volume exclusion plays a more important role than cell-to-cell adhesion. This combined experimental and modeling study gives insight into the cell-level details and design of transwell assays.

The physical limit with which a cell senses external ligand concentration corresponds to the perfect absorber, where all ligand particles are absorbed and overcounting of same ligand particles does not occur. Here, we analyze how the lateral diffusion of receptors on the cell membrane affects the accuracy of sensing ligand concentration. Specifically, we connect our modeling to neurotransmission in neural synapses where the diffusion of glutamate receptors is already known to refresh synaptic connections. We find that receptor diffusion indeed increases the accuracy of sensing for both the glutamate $\alpha$-Amino-3-hydroxy-5-Methyl-4-isoxazolePropionic Acid (AMPA) and $N$-Methyl-D-aspartic Acid (NMDA) receptor, although the NMDA receptor is overall much noisier. We propose that the difference in accuracy of sensing of the two receptors can be linked to their different roles in neurotransmission. Specifically, the high accuracy in sensing glutamate is essential for the AMPA receptor to start membrane depolarization, while the NMDA receptor is believed to work in a second stage as a coincidence detector, involved in long-term potentiation and memory.

Perfect spike-to-spike synchrony is studied in all-to-all coupled networks of identical excitatory, current-based, integrate-and-fire neurons with delta-impulse coupling currents and Poisson spike-train external drive. This synchrony is induced by repeated cascading “total firing events,” during which all neurons fire at once. In this regime, the network exhibits nearly periodic dynamics, switching between an effectively uncoupled state and a cascade-coupled total firing state. The probability of cascading total firing events occurring in the network is computed through a combinatorial analysis conditioned upon the random time when the first neuron fires and using the probability distribution of the subthreshold membrane potentials for the remaining neurons in the network. The probability distribution of the former is found from a first-passage-time problem described by a Fokker-Planck equation, which is solved analytically via an eigenfunction expansion. The latter is found using a central limit argument via a calculation of the cumulants of a single neuronal voltage. The influence of additional physiological effects that hinder or eliminate cascade-induced synchrony are also investigated. Conditions for the validity of the approximations made in the analytical derivations are discussed and verified via direct numerical simulations.