Lognormal statistical distributions are observed in a variety of scientific fields. The widths of these distributions in the log scale are often similar, but the underlying mechanism that maintains these widths within a small range has not been well explained. We show that a stochastic process of halving followed by addition can yield a stationary distribution that resembles the universal lognormal distribution with a certain width. The mechanism that we propose here would provide insight into the essence of why lognormal-like distributions in many systems have a common width.

We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track of the relative weight of phase-space trajectories generated by the modified and the original dynamics one can obtain the required probabilities. The algorithm is tested on two model systems of steady-state particle and heat transport where we find a huge improvement from direct simulation methods.

We describe experimental observations of fully developed, large-amplitude bars under the action of a shearing fluid. The experiments were performed in an annular tank filled with water and sheared above by a steady motor source. The same steady shearing flow can produce a variety of different erodible bed manifestations: advective or precessive bars, which refer to bar structures with global regularity and a near-steady precession velocity; interactive bars, the structure of which depends on local rearrangements, which are in turn a response to complex background topography; and dispersive bars, which are created when an initially isolated mound of sand evolves into a train of sand ripples. Of these, the most amenable to analysis are the precessive bars. For precession bars, we find that the skin depth, which is the nondimensionalized mean-field transport rate, grows exponentially as a function of the shear velocity. From this, we arrive at an analytical expression that approximates the precession speed of the bars as a function of shear velocity. We use this to obtain a formula for sediment transport rate. However, in intense flows, the bars can get large engendering boundary layer separation, leading to a different dynamic for bar formation and evolution. Numerical flow calculations over an experimentally obtained set of precessive bars are presented and show that classical parametrizations of mass flux in terms of bottom gradients have shortcomings. Within the range of shear rates considered, a quantity that does not change appreciably in time is the aspect ratio, which is defined as the ratio of the average bar amplitude, with respect to a mean depth, to the average bar length.

In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009).]. This Brief Report presents a modest though more insightful extension of their arguments. We discuss the implications of their results on the cluster-size distribution and deduce that, under general conditions, the percolation transition will be explosive if the mean number of nodes per cluster diverges in the thermodynamic limit and prior to the transition threshold. In other words, if upon increase of the network size $n$ the amount of clusters in the network does not grow proportionally to $n$, the percolation transition is explosive. Simulations and analytical calculations on various models support our findings.

A step-by-step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDFs) of well-known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into the evolution of the PDF, for example, allowing the calculation of its relaxation times. Their equilibrium PDFs can also be calculated by finding its stationary solutions. This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others. This should provide some guidance into the type of PDFs that can be derived from particular economic agent exchange rules or, for that matter, any other kinetic model of gases with particular collision physics.

This paper investigates the robust stability of a steady state in network systems with dynamic connections. A linear stability analysis reveals that the odd number property holds for any network topology. It is shown that the stability of the steady state in network systems with topological uncertainty is governed by the interval family of real characteristic polynomials. A parametric approach, which plays an important role in the field of robust control theory, allows us to analyze the robust stability against the network topological uncertainty. The stability of the steady state, which is valid for any arbitrary topology, can be evaluated by examining at most four characteristic polynomials. These analytical results are applied to coupled Rössler oscillators on a small-world network.

We show that the distance dependence of the source-to-target mean-first-passage time (MFPT) on a finite network with $M$ links is approximately given by $2M$ times the target-to-shell resistance. For networks on which a random walker is transient the long-range MFPT is well approximated by the site-dependent resistance from the target to infinity. The result extends a recent scaling result for the MFPT to site-inhomogeneous lattices where the MFPT depends on the location of the source and targets and can be highly source-target asymmetric.

The stationary points of the potential energy function $V$ of the classical $\mathit{XY}$ chain with power-law pair interactions (i.e., interactions decaying like $r^{-\alpha }$ with the distance) are analyzed. For a class of “spinwave-type” stationary points, the asymptotic behavior of the Hessian determinant of $V$ is computed analytically in the limit of large system size. The computation is based on the Toeplitz property of the Hessian and makes use of a Szegö-type theorem. The results serve to illustrate a recently discovered relation between phase transitions and the properties of stationary points of classical many-body potentials. In agreement with this relation, the exact phase transition potential energy of the model can be read off from the behavior of the Hessian determinant for exponents $\alpha$ between zero and one. For $\alpha$ between one and two, the phase transition is not manifest in the behavior of the determinant, and it might be necessary to consider larger classes of stationary points.

Doppler-shift optical coherence tomography with infrared light was used to probe the velocity profiles of concentrated solutions of complex fluids with samples experiencing steady-state shear flow. The apparatus is sensitive to a velocity range of 0.7–330 mm/s probing very small volumes of material (quasicylindrical volume elements of 9-μm length and 11-μm radius with 3.4-picoliter volumes) inside a plate-plate rheometer with a total sample volume of ∼100–1000 μL. The technique can scan the flow in the plane perpendicular to the shear direction, building up a two-dimensional map of the velocity flow field. The use of a coherence gate with a broad-band infrared source (9-μm coherence length, 1300-nm wavelength) allows opaque specimens, such as concentrated colloidal suspensions (2% w/w) and margarine, to be probed. We observe the phenomena of wall slip (margarine) and shear banding (polyacrylamide, a linear flexible polyelectrolyte) using this technique.

Coherent diffractive imaging using x-ray free-electron lasers (XFELs) may provide a unique opportunity for high-resolution structural analysis of single particles sprayed from an aqueous solution into the laser beam. As a result, diffraction images are measured from randomly oriented objects covered by a water layer. We analyze theoretically how the thickness of the covering water layer influences the structural and orientational information contained in the recorded diffraction images. This study has implications for planned experiments on single-particle imaging with XFELs.

Human DNA shows a complex structure with compositional features at many scales; the isochores—long DNA segments ($~{10}^5$ bp) of relatively homogeneous guanine-cytosine (G + C) content—are the largest well-documented and well-analyzed compositional structures. However, we report here on the existence of a high-level compositional organization of isochores in the human genome. By using a segmentation algorithm incorporating the long-range correlations existing in human DNA, we find that every chromosome is composed of a few huge segments ($~$ ${10}^7$ bp) of relatively homogeneous G + C content, which become the largest compositional organization of the genome. Finally, we show evidence of the biological relevance of these superstructures, pointing to a large-scale functional organization of the human genome.

We investigate the statistics and dynamics of failure in a two-dimensional load-bearing network with branching hierarchical structure, and its variants. The variants strengthen the original lattice by using connectivity strategies which add new sites to the maximal cluster in top-to-bottom or bottom-to-top versions. We study the load-bearing capacity and the failure tolerance of all versions, as well as that of the strongest realization of the original lattice, the V lattice. The average number of failures as a function of the test load shows power-law behavior with power $5/2$ for the V lattice, but sigmoidal behavior for all other versions. Thus the V lattice turns out to be the critical case of the load-bearing lattices. The distribution of failures is Gaussian for the original lattice, the V lattice, and the bottom-to-top strategy, but is non-Gaussian for the top-to-bottom one. The bottom-to-top strategy leads to stable and strong lattices, and can resist failure even when tested with weights which greatly exceed the capacity of its backbone. We also examine the behavior of asymmetric lattices and discover that the mean failure rates are minimized if the probability of connection $p$ is symmetric with respect to both neighbors. Our results can be of relevance in the context of realistic networks.

The global stability of the steady jetting mode of liquid jets focused by coaxial gas streams is analyzed both theoretically and experimentally. Numerical simulations allow one to identify the physical mechanisms responsible for instability in the low viscosity and very viscous regimes of the focused liquid. The characteristic flow rates for which global instability takes place are estimated by a simple scaling analysis. These flow rates do not depend on the pressure drop (energy) applied to the system to produce the microjet. Their dependencies on the liquid viscosity are opposite for the two extremes studied: the characteristic flow rate increases (decreases) with viscosity for very low (high) viscosity liquids. Experiments confirmed the validity of these conclusions. The minimum flow rates below which the liquid meniscus becomes unstable are practically independent of the applied pressure drop for sufficiently large values of this quantity. For all the liquids analyzed, there exists an optimum value of the capillary-to-orifice distance for which the minimum flow rate attains a limiting value. That limiting value represents the lowest flow rate attainable with a given experimental configuration in the steady jetting regime. A two-dimensional stability map with a high degree of validity is plotted on the plane defined by the Reynolds and capillary numbers based on the limiting flow rate.

Rayleigh instability is investigated in a Hall thruster under the effect of finite temperature and density gradient of the plasma species. The instability occurs only when the frequency of the oscillations $\omega$ falls within a frequency band described by $k_y{u}_0+\frac{1}{k_y}\frac{\partial {}^2{u}_0}{\partial x^2}+\frac{\Omega }{k_y{n}_0}\frac{\partial n_0}{\partial x}\ll \omega <\sqrt{\frac{Y_i{T}_i{k}_y^2}{M}+\frac{{{\omega }_p}_i^2({\Omega }^2+Y_e{T}_e{k}_y^2/Y_e{T}_e{k}_y^{2}mm)}{({{\omega }_p}_e^2+{\Omega }^2+Y_e{T}_e{k}_y^2/Y_e{T}_e{k}_y^{2}mm)}}$, where $u_0$ is the drift velocity of the electrons, $\Omega$ is their gyration frequency under the effect of the magnetic field, $k_y$ is the wave propagation constant, $n_0$ is the plasma density together with $\partial n_0/\partial n_0\partial x\partial x$ as the density gradient, and $T_i(T_e)$, $M(m)$, $Y_i(Y_e)$, and ${{\omega }_p}_i({{\omega }_p}_e)$ are the temperature, mass, specific heat ratio, and plasma frequency of the ions (electrons), respectively. A relevant Rayleigh equation is derived and solved numerically using the fourth-order Runge-Kutta method for investigating the perturbed potential under the effect of electron drift velocity, channel length, magnetic field, ion temperature, and electron temperature. The instability grows faster because of the magnetic field, ion temperature, and drift velocity of the electrons but its growth rate is reduced because of the electron temperature, channel length, and also its far distances from the anode.

By the use of two-dimensional particle-in-cell simulations, we clarify the terahertz (THz) radiation mechanism from a plasma filament formed by an intense femtosecond laser pulse. The nonuniform plasma density of the filament leads to a net radiating current for THz radiation. This current is mainly located within the pulse and the first cycle of the wakefield. As the laser pulse propagates, a single-cycle and radially polarized THz pulse is constructively built up forward. The single-cycle shape is mainly due to radiation damping effect.

We study the effects of passive dendritic properties on the dynamics of neuronal oscillators. We find that the addition of a passive dendrite can sometimes have counterintuitive effects on firing frequency. Specifically, the addition of a hyperpolarized passive dendritic load can either increase, decrease, or have negligible effects on firing frequency. We use the theory of weak coupling to derive phase equations for “ball-and-stick” model neurons and two-compartment model neurons. We then develop a framework for understanding how the addition of passive dendrites modulates the frequency of neuronal oscillators. We show that the average value of the neuronal oscillator’s phase response curves measures the sensitivity of the neuron’s firing rate to the dendritic load, including whether the addition of the dendrite causes an increase or decrease in firing frequency. We interpret this finding in terms of to the slope of the neuronal oscillator’s frequency-applied current curve. We also show that equivalent results exist for constant and noisy point-source input to the dendrite. We note that the results are not specific to neurons but are applicable to any oscillator subject to a passive load.

Time-delay chaotic systems have some very interesting properties, and their parameter estimation has received increasing interest in the recent years. It is well known that parameter estimation of a chaotic system is a nonlinear, multivariable, and multimodal optimization problem for which global optimization techniques are required in order to avoid local minima. In this work, a seeker-optimization-algorithm (SOA)-based method is proposed to address this issue. In the SOA, search direction is based on the empirical gradients by evaluating the response to the position changes, and step length is based on uncertainty reasoning by using a simple fuzzy rule. The performance of the algorithm is evaluated on two typical test systems. Moreover, two state-of-the-art algorithms (i.e., particle swarm optimization and differential evolution) are also considered for comparison. The simulation results show that the proposed algorithm is better than or at least as good as the other two algorithms and can effectively solve the parameter estimation problem of time-delay chaotic systems.

We report a finding of spontaneous flow reversals of roll-like patterns in liquid gallium Rayleigh-Bénard convection. The vessel has a square geometry with an aspect ratio of 5, and a horizontal magnetic field is applied to align the rolls. The flow patterns were visualized by ultrasonic velocity measurements, and the processes of the reversal were clearly observed. The basic flow pattern observed in the vessel is a four-roll structure with its axis parallel to the magnetic field. Emergence of a new circulation at a corner of the vessel causes flow reversal with reorganization of the whole pattern. The flow keeps relatively steady four-roll structure for most of the duration, while the reversal of it is over in a short time. The reversals of the flow occur randomly with the interval time between reversals being much longer than the circulation time.

Laboratory experiments point out the existence of patterns made of alternately laminar and turbulent oblique bands in plane Couette flow (PCF) on its way to or from turbulence as the Reynolds number $R$ is varied. Many previous theoretical and numerical works on the problem have considered small-aspect-ratio systems subjected to periodic boundary conditions, while experiments correspond to the opposite limit of large aspect ratio. Here, by means of fully resolved direct numerical simulations of the Navier-Stokes equations at decreasing $R$, we scrutinize the transition from temporal to spatiotemporal behavior in systems of intermediate sizes. We show that there exists a streamwise crossover size of order $L_x~70$–80$h$ (where $2h$ is the gap between the plates driving the flow) beyond which the transition to or from turbulence in PCF is undoubtedly a spatiotemporal process, with typical scenario turbulent flow$\to$riddled regime$\to$oblique pattern$\to$ laminar flow, whereas below that size it is more a temporal process describable in terms of finite-dimensional dynamical systems with the scenario chaotic flow$\to$laminar flow (via chaotic transients). In the crossover region, the oblique pattern stage is skipped, which leads us to suggest that an appropriate rendering of the patterns observed in experiments needs a faithful account of streamwise correlations at scales at least of the order of that crossover size.

Applying Hirota's binary operator approach to the (2$+$1)-dimensional nonlinear Schrödinger equation with the radially variable diffraction and nonlinearity coefficients, we derive a variety of exact solutions to the equation. Based on the solitary wave solutions derived, we obtain some special soliton structures, such as the embedded, conical, circular, breathing, dromion, ring, and hyperbolic soliton excitations. For some specific choices of diffraction and nonlinearity coefficients, we discuss features of the (2$+$1)-dimensional multisolitonic solutions.