PHYSICAL REVIEW E

Online ISSN: 2470-0045
Publications
Article
Under the influence of an ac electric field, electrolytes on planar microelectrodes exhibit fluid flow. The nonuniform electric field generated by the electrodes interacts with the suspending fluid through a number of mechanisms, giving rise to body forces and fluid flow. This paper presents the detailed experimental measurements of the velocity of fluid flow on microelectrodes at frequencies below the charge relaxation frequency of the electrolyte. The velocity of latex tracer particles was measured as a function of applied signal frequency and potential, electrolyte conductivity, and position on the electrode surface. The data are discussed in terms of a linear model of ac electroosmosis: the interaction of the nonuniform ac field and the induced electrical double layer.
 
Article
Frequency-dependent fluid flow in electrolytes on microelectrodes subjected to ac voltages has recently been reported. The fluid flow is predominant at frequencies of the order of the relaxation frequency of the electrode-electrolyte system. The mechanism responsible for this motion has been termed ac electro-osmosis: a continuous flow driven by the interaction of the oscillating electric field and the charge at the diffuse double layer on the electrodes. This paper develops the basis of a theoretical approach to this problem using a linear double layer analysis. The theoretical results are compared with the experiments, and a good correlation is found.
 
The empirically determined equilibrium value of nc/(1 − nc) as a function of the initial gas density, Ng(0)/L 2 , for systems of size L = 128, 256, and 512. The solid line is the mean field prediction. Note that the error bars are the same size as the points.
Two growth clusters of the same mass, N c ∼ 8270. (a) A cluster grown via the RA model, pictured at time t = τ T , 
The number of aggregate particles contained in a box of length l, as a function of l. The slope of the line is the fractal dimension. The top curve is for parallel DLA clusters of mass Nc ≃ 8270. The bottom curve is for the RA clusters sampled at t = τT. Examples of these clusters are pictured in Fig. 3.
A growth cluster grown via the RA model, pictured at time t = 80 τ T . The fractal dimension for this cluster 
The average fractal dimension of the RA growth clusters as a function of time into the simulation, for all three system sizes.
Article
We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible diffusion limited aggregation model (DLA) in contact with a heat bath. Particles release latent heat when aggregating, while singly connected cluster members can absorb heat and evaporate. The heat bath is initially empty, hence we observe the flow of entropy from the aggregating gas of particles into the heat bath, which is being populated by diffusing heat tokens. Before the population of the heat bath stabilizes, the cluster morphology (quantified by the fractal dimension) is similar to a standard DLA cluster. The cluster then gradually anneals, becoming more tenuous, until reaching configurational equilibrium when the cluster morphology resembles a quenched branched random polymer. As the microscopic dynamics is invertible, we can reverse the evolution, observe the inverse flow of heat and entropy, and recover the initial condition. This simple system provides an explicit example of how macroscopic dissipation and self-organization can result from an underlying microscopically reversible dynamics. We present a detailed description of the dynamics for the model, discuss the macroscopic limit, and give predictions for the equilibrium particle densities obtained in the mean field limit. Empirical results for the growth are then presented, including the observed equilibrium particle densities, the temperature of the system, the fractal dimension of the growth clusters, scaling behavior, finite size effects, and the approach to equilibrium. We pay particular attention to the temporal behavior of the growth process and show that the relaxation to the maximum entropy state is initially a rapid nonequilibrium process, then subsequently it is a quasistatic process with a well defined temperature.
 
Article
We have investigated the onset of avalanches in fine, cohesive granular materials. In our experiments shear stress is generated by tilting an initialized bed of powder and increasing the angle of tilt until the powder avalanches. We find that the angle alpha of the avalanche decreases with increasing bed width. The avalanche depth increases with the bed width and, in all cases, is of the order of several millimeters, which is much greater than the particle size. We carry out a macroscopic analysis of the avalanche process based on Coulomb's method of wedges. This analysis shows the fundamental role played by powder cohesion and boundary conditions on avalanches in fine cohesive powders. This behavior contrasts with the behavior of noncohesive grains, such as dry sand, where avalanches consist of superficial layers of about ten grains. The reason behind this is that for our experimental powders (particle diameter approximately 10 &mgr;m) the van der Waals interparticle adhesive force exceeds several orders of magnitude particle weight. Adhesive forces oppose gravity, and as a result fine cohesive powders settle in very open structures as compared to noncohesive granular materials. Because of the dominance of adhesive forces over particle weight, our materials behave more like wet sand.
 
Article
The settling of inertial particles in 2D vertical flows is investigated in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The generic case of recirculation cells bounded by a set of separatrix streamlines forming a heteroclinic cycle of fluid points' dynamics is considered. The (weak) unsteadiness of the flow generally induces a chaotic tangle near the heteroclinic cycle, leading to the apparent diffusion of fluid elements through the boundary. For inertial particles this complex motion can also exist in spite of inertia and sedimentation, provided the Stokes number is below some critical value $St_c$. It is shown that $St_c= Pe^{-1}/|Fr^{-1}\pm u_{0c}^2|$, where $Pe$ is an effective Peclet number related to the diffusion of fluid points through the boundary, $Fr$ is the Froude number based on the horizontal distance between the end points of the separatrix streamline, and $u_0^2$ is the non-dimensional curvature-weighted average of the squared velocity of the steady fluid flow along this separatrix. The $\pm$ sign is positive if gravity and centrifugation act in the same direction, and negative otherwise. When $St < St_c$, particles moving near the separatrix streamline can enter and exit the cell in a complex manner. When $St > St_c$ a regular motion takes place. Trapping can still exist in this case, since particles can be driven towards the interior of the cell in a regular manner, under the effect of either gravity or curvature, or both.
 
Article
Information flow or information transfer the widely applicable general physics notion can be rigorously derived from first principles, rather than axiomatically proposed as an ansatz. Its logical association with causality is firmly rooted in the dynamical system that lies beneath. The principle of nil causality that reads, an event is not causal to another if the evolution of the latter is independent of the former, which transfer entropy analysis and Granger causality test fail to verify in many situations, turns out to be a proven theorem here. Established in this study are the information flows among the components of time-discrete mappings and time-continuous dynamical systems, both deterministic and stochastic. They have been obtained explicitly in closed form, and put to applications with the benchmark systems such as the Kaplan-Yorkemap, R¨ossler system, baker transformation, H´enon map, and stochastic potential flow. Besides unraveling the causal relations as expected from the respective systems, some of the applications show that the information flow structure underlying a complex trajectory pattern could be tractable. For linear systems, the resulting remarkably concise formula asserts analytically that causation implies correlation, while correlation does not imply causation, providing a mathematical basis for the long-standing philosophical debate over causation versus correlation.
 
Avalanche spike statistics in the sparsely connected integrate-and-fire model [13] with N = 5 000 neurons in the SI and AI states. (A) Raster plot of the SI together with the firing rate (below). (B) Raster plot in the AI state: spiking is asynchronous and faster (notice that the time window is shorter compared to A for legibility): no silence period arises. In the SI states, (C) avalanche size and (D) avalanche duration scale as power law (dashed line is the maximum likelihood fit), and averaged avalanche size scales as a power law with the duration avalanche duration according to the universal scaling law [14] (E). Average avalanche shapes collapse onto the same curve (F,G) very accurately. 
Avalanche analysis defined from the macroscopic variable VLF P of a network of integrate-and-fire neurons with exponential synapses. Networks displaying an AI state (left), its stochastic surrogate (middle) or a SI state (right), all show similar macroscopic power-law statistics with a universal exponent close to-3/2, and plots are indistinguishable.
Article
Critical states are usually 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. Power-law statistics are also seen when the units are replaced by independent stochastic surrogates, and thus 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.
 
Article
Molecular motors and cytoskeletal filaments mostly work collectively under opposing forces. This opposing force may be due to cargo carried by motors, or resistance coming from cell membrane pressing against the cytoskeletal filaments. Certain recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of stall force for individual filaments or motors. To understand this phenomena of excess or deficit collective force generation, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, i.e., the stall force of N filaments(motors) is N times the stall force of one filament (motor), when the system is in equilibrium at stall. Consequently, we show that this additivity typically does not hold when the system departs from equilibrium at stall. We thus present a novel and unified understanding of existing models exhibiting such non- addivity, and generalize our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to provide a simple understanding of deviation from stall-force additivity for filament and motor collectives.
 
Polynomial energy growth in ergodic regime. We change parameters so that the frozen system remains chaotic, with no visible stability islands. The ensemble averaged energy versus time is shown. In the inset the rates r(n) = 1
Article
Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time, the energy is no longer conserved, which makes the acceleration possible. One of the main problems is how to generate a sustained and robust energy growth. We show that the non-ergodicity of any chaotic Hamiltonian system must universally lead to the exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of a Geometric Brownian Motion with a positive drift, and relate it to the entropy increase.
 
Article
Single component pseudo-potential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many research, it has been claimed that this model can be stable for density ratios larger than 1000, however, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in present work show that, by applying the contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with the new contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.
 
Sketch of a 2d amorphous material upon bi-axial loading. (a) The mesh is deformed according to the displacement. The associated strain has a reversible elastic contribution and an irreversible plastic contribution. The latter is represented according to the color scale. (b) The plastic strain field (colors) is represented on the un-deformed reference frame. (c) The plastic strain field can be represented as a d -dimensional manifold moving in a d + 1 space. 
Top: Strain variance (equivalently interface width) vs cumulated plastic strain ε pl for 5 different propagators: GQ, Ga (a = 10 −1 , 10 −2 , 10 −3 ), GMF. Bottom: Maps of plastic strain field obtained for a mere quadrupolar elastic interaction (b), and with a positive (a) and a negative (c) MF contribution a = ±10 −2 for ε pl ≈ 5, past the transient regime. The same color scale has been used in the three cases.
Spectrum of eigenvalues of elastic propagators: Mean-Field (MF), quadrupolar interaction and MF-weighted quadrupolar interactions. The introduction of a fraction a of MF opens a gap between the translational mode having a null eigenvalue and the other modes λ < 0. The evolution of the gap is zoomed in the inset. 
Article
A mesoscopic model of amorphous plasticity is discussed in the wider context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be controlled by the existence of soft modes of the quadrupolar interaction, the consequence of which is discussed in the context of depinning.
 
Article
Plastic events in amorphous solids can be much more than just "shear transformation zones" when the positional degrees of freedom are coupled non-trivially to other degrees of freedom. Here we consider magnetic amorphous solids where mechanical and magnetic degrees of freedom interact, leading to rather complex plastic events whose nature must be disentangled. In this paper we uncover the anatomy of the various contributions to some typical plastic events. These plastic events are seen as Barkhausen Noise or other "serrated noises". Using theoretical considerations we explain the observed statistics of the various contributions to the considered plastic events. The richness of contributions and their different characteristics imply that in general the statistics of these "serrated noises" cannot be universal, but rather highly dependent on the state of the system and on its microscopic interactions.
 
Article
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of delta-functions, treated as a statistical-mechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous sampling methods. The key development is the suppression of entropy by constraining the spectral weight to within identifiable optimal bounds and imposing a set number of peaks. As a test case, the dynamic structure factor of the S=1/2 Heisenberg chain is computed. Very good agreement is found with Bethe Ansatz results in the ground state (including a sharp edge) and with exact diagonalization of small systems at elevated temperatures.
 
Article
Nonlinear localized magnetic excitations in one dimensional magnonic crystal is investigated under periodic magntic field. The governing Landau-Lifshitz equation is transformed into variable coefficient nonlinear Schrodinger equation(VCNLS) using sterographic projection. The VCNLS equation is in general nonintegrable, by using painleve analysis necessary conditions for the VCNLS equation to pass Weiss-Tabor-Carnevale (WTC) Painleve test are obtained. A sufficient integrability condition is obtained by further exploring a transformation, which can map the VCNLS equation into the well-known standard nonlinear Schrodinger equation. The transformation built a systematic connection between the solution of the standard nonlinear Schrodinger equation and VC-NLS equation. The results shows the excitation of magnetization in the form of soliton has spatialperiod exists on the background of spin Bloch waves. Such solution exisits only certain constrain conditions on the coefficient of the VCNLS equation are satisfied. The analytical results suggest a way to control the dynamics of magnetization in the form of solitons by an appropriate spatial modulation of the nonlinearity coefficient in the governing VCNLS equation which is determined by the ferromagnetic materials which forms the magnonic crystal.
 
Article
Time reversal mirrors have been widely used to achieve wave focusing in acoustics and electromagnetics. A typical time reversal experiment requires that a transmitter be initially present at the target focusing point, which limits the application of this technique. In this letter, we propose a method to focus waves at an arbitary location inside a complex enclosure using a numerically calculated wave signal. We use a semi-classical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location. The quaility of the reconstruction is quantified in three different ways and the values of these metrics can be predicted by the statistics of the scattering-parameter $|S_{21}|^2$ between the transceiver and target points in the enclosure. We experimentally demonstrate the method using a flat microwave billiard and quantify the reconstruction quality as a function of enclosure loss, port coupling and other considerations.
 
Article
A novel mechanism for the transport of microscale particles in viscous fluids is demonstrated. The mechanism exploits the trapping of such particles by rotational streaming cells established in the vicinity of an oscillating cylinder, recently analyzed in previous work. The present work explores a strategy of transporting particles between the trapping points established by multiple cylinders undergoing oscillations in sequential intervals. It is demonstrated that, by controlling the sequence of oscillation intervals, an inertial particle is effectively and predictably transported between the stable trapping points. Arrays of cylinders in various arrangements are investigated, revealing a quite general technique for constructing arbitrary particle trajectories. The timescales for transport are also discussed.
 
(Color online) The AT model on a mono-layer network may be regarded as a two-species-of-Ising-spin model with an inter-layer interaction (dashed lines) on a doublelayer network.
[color online] Plots of the order parameters m and M as a function of temperature in each regime of phase transitions, which are obtained from different values of x = K4/K2 and the degree exponent λ.  
[color online] Susceptibility χm as a function of T. It diverges for T > Ts, whereas it becomes finite for T < Ts.
Article
Recently, diverse phase transition (PT) types have been obtained in multiplex networks, such as discontinuous, continuous, and mixed-order PTs. However, they emerge from individual systems, and there is no theoretical understanding of such PTs in a single framework. Here, we study a spin model called the Ashkin-Teller (AT) model in a mono-layer scale-free network; this can be regarded as a model of two species of Ising spin placed on each layer of a double-layer network. The four-spin interaction in the AT model represents the inter-layer interaction in the multiplex network. Diverse PTs emerge depending on the inter-layer coupling strength and network structure. Especially, we find that mixed-order PTs occur at the critical end points. The origin of such behavior is explained in the framework of Landau-Ginzburg theory.
 
Article
We investigate scaling of work output and efficiency of a photonic Carnot engine with the number of quantum coherent resources. Specifically, we consider a generalization of the "phaseonium fuel" for the photonic Carnot engine, which was first introduced as a three-level atom with two lower states in a quantum coherent superposition by [M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther, Science {\bf 299}, 862 (2003)], to the case of $N+1$ level atoms with $N$ coherent lower levels. Deriving a multilevel mesoscopic master equation for the system, we evaluate the harvested work by the engine, and its efficiency. We find that efficiency and extracted work scale quadratically with the number of quantum coherent levels. Quantum coherence boost to the specific energy (work output per unit mass of the resource) is a profound fundamental difference of quantum fuel from classical resources. Besides, we examine the dependence of cavity loss on the number of atomic levels and find that multilevel phaseonium fuel can be utilized to beat the decoherence due to cavity loss. Our results bring the photonic Carnot engines much closer to the capabilities of current resonator technologies.
 
Article
Using numerical simulations we examine colloids with a long-range Coulomb interaction confined in a two-dimensional trough potential undergoing dynamical compression. As the depth of the confining well is increased, the colloids move via elastic distortions interspersed with intermittent bursts or avalanches of plastic motion. In these avalanches, the colloids rearrange to minimize their colloid-colloid repulsive interaction energy by adopting an average lattice constant that is isotropic despite the anisotropic nature of the compression. The avalanches take the form of shear banding events that decrease or increase the structural order of the system. At larger compressions, the avalanches are associated with a reduction of the number of rows of colloids that fit within the confining potential, and between avalanches the colloids can exhibit partially crystalline or even smectic ordering. The colloid velocity distributions during the avalanches have a non-Gaussian form with power law tails and exponents that are consistent with those found for the velocity distributions of gliding dislocations. We observe similar behavior when we subsequently decompress the system, and find a partially hysteretic response reflecting the irreversibility of the plastic events.
 
Article
Small-scale heat exchanges have recently been modeled with resource theories intended to extend thermodynamics to the nanoscale and quantum regimes. We generalize these theories to exchanges of quantities other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with "grand-potential" theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law and from resource-theory principles, the grand-canonical form of the free states is derived. States are shown to form a quasiorder characterized by free operations, d-majorization, the hypothesis-testing entropy, and rescaled Lorenz curves. We calculate the work distillable from, and we bound the work cost of creating, a state. These work quantities can differ but converge to the grand potential in the thermodynamic limit. Extending thermodynamic resource theories beyond heat baths, we open diverse realistic systems to modeling with one-shot statistical mechanics. Prospective applications such as electrochemical batteries are hoped to bridge one-shot theory to experiments.
 
Examples of the different dynamical regimes and comparison with the variational approach [20]. The density plots show the evolution of the norms |ψn|2 of initially Gaussian wave packets (3). The insets on the left show the time traces of the maximum local norm N [Eq. (6)]. (a) Strongly diffusive regime. In contrast, the variational approach predicts self-trapping. The parameters are α0=1, cos(p0)=0.88, and λ=2.5. (b) Moving breather regime. The variational approach predicts diffusion. The parameters are α0=1, cos(p0)=0.88, and λ=1.5. (c) The DB solution for the parameters α0=1, cos(p0)=−1, and λ=3. (d) Breather of higher order with asymmetric shape for the parameters α0=4, cos(p0)=−0.6, and λ=8.9. It corresponds to a drop in Hthrs. The examples are indicated by (a) △, (b) ◯, (c) ⋄ (in Fig. 2), and (d) * (in Fig. 6).
Peierls Nabarro energy barrier for n = 1 corresponding to λP N = 1.3 calculated as the difference between the energies of a bright central peak breather located around a single site (cp) and a central bond breather located between two lattice sites (cb).
Article
We study the mean field dynamics of self-trapping in Bose-Einstein condensates loaded in deep optical lattices with Gaussian initial conditions. We calculate a detailed dynamical phase diagram accurately describing the different dynamical regimes (such as diffusion and self-trapping) that markedly differs from earlier predictions based on variational dynamics. The phase diagram exhibits a very complex structure which could readily be tested in current experiments. We derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings.
 
Illustration of enclaves—clusters fully surrounded by other clusters. In this example the enclaves are marked by dashed boundaries and non enclaves by solid boundaries. 
An illustration of the influence of steric interactions on the collapsed state properties. The initial state presented in (a) without steric interactions collapses to two clusters with masses 3 and 9, as show in (b). Due to steric interactions the enclave is trapped in its surroundings, leading to a collapsed state with one cluster of mass 12, as shown in (c).
An example of the collapse process of a small ( M = 10 × 12 ) network. (a) initial state of the network. Dashed lines indicate first three springs that have been broken. (b) state of the network after first three breaks. (c) final state of the collapsed network. Note, that during the process the total mass (total number of nodes) is conserved. In the final state of the network all the mass is concentrated in 11 clusters. 
(a,b) Modelling of the collapse. The final state of ruptured collapsed network with M = 400 × 400 nodes, without (a) and with (b) steric interactions. Each point contains the nodes of a collapsed cluster. (c) The final state (converted to binary picture) of the collapse in the experiment (see cap- tion of Fig. 2 for experimental conditions). Note the large voids in the case of the modelling with steric interactions (b) and the experiment (c). 
Article
We report analytical and numerical modelling of active elastic networks, motivated by experiments on crosslinked actin networks contracted by myosin motors. Within a broad range of parameters, the motor-driven collapse of active elastic networks leads to a critical state. We show that this state is qualitatively different from that of the random percolation model. Intriguingly, it possesses both euclidean and scale-free structure with Fisher exponent smaller than $2$. Remarkably, an indistinguishable Fisher exponent and the same euclidean structure is obtained at the critical point of the random percolation model after absorbing all enclaves into their surrounding clusters. We propose that in the experiment the enclaves are absorbed due to steric interactions of network elements. We model the network collapse, taking into account the steric interactions. The model shows how the system robustly drives itself towards the critical point of the random percolation model with absorbed enclaves, in agreement with the experiment.
 
Article
A general lattice Boltzmann (LB) model is proposed for solving nonlinear partial differential equations with the form $\partial_t \phi+\sum_{k=1}^{m} \alpha_k \partial_x^k \Pi_k (\phi)=0$, where $\alpha_k$ are constant coefficients, and $\Pi_k (\phi)$ are the known differential functions of $\phi$, $1\leq k\leq m \leq 6$. The model can be applied to the common nonlinear evolutionary equations, such as (m)KdV equation, KdV-Burgers equation, K($m,n$) equation, Kuramoto-Sivashinsky equation, and Kawahara equation, etc. Unlike the existing LB models, the correct constraints on moments of equilibrium distribution function in the proposed model are given by choosing suitable \emph{auxiliary-moments}, and how to exactly recover the macroscopic equations through Chapman-Enskog expansion is discussed in this paper. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies. Comment: 18 pages, 4 figures
 
Experimental results 
Article
We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula that decides whether short-term chaos (damage spreading) will happen. We provide a formal proof for this formula, and empirically show that its predictions are accurate. Previous work only works for special cases of balanced families. It has been observed that these characterizations fail for unbalanced families, yet such families are widespread in real biological networks.
 
Article
Parameterization of reaction rates for thermal desorption are often analyzed using the Arrhenius equation. Data analysis procedures typically impose the empirical constraint of compensation, such that the different parameters in the equation balance each other out thereby leading to an implicitly assumed constant reaction rate for a wide range of thermally activated processes. However, the compensation effect has not been generally demonstrated and its origins are not completely understood. Using kinetic Monte Carlo simulations on a model interface, we explore how site and adsorbate interactions influence surface coverage during a typical desorption process. We find that the traditional criterion for the existence of a compensation effect for interacting species breaks down and the time characterizing desorption increases with increasing interaction strength due to an increase in the effective activation energy. At the molecular-site level these changes are the result of enhanced site correlations with increasing adsorbate interaction strength suppressing the onset of desorption. Our results show that the parameters vary as a result of interactions, however they do not offset or compensate each other completely as predicted with traditional methods of analysis.
 
Patterns produced from larger perturbations of the ground state in cases (a)-(f) with D = 0.65, ε = 0.005, τ = 0.075, and parameter values (4). The initial condition is the same in all cases and consists of random disturbances of the ground state with maximal amplitude 20ε = 0.1. The colour scale is identical in all cases.
Dependence of patterns on the ratio of diffusions D and the strength of the unilateral source τ for the nonsmooth unilateral termˆgtermˆ termˆg(v) = τ v −. Each box corresponds to the indicated values of D and τ and to parameter values (4).
Dependence of patterns on D and τ for the linear approximation of the unilateral term from the left, i.e. ˆ g(v) = −τ v. Each box corresponds to the indicated values of D and τ and to parameter values (4).
Typical coat patterns of cheetah (left) and king cheetah (right).
Article
We consider a classical reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. The nonsmooth positively homogeneous unilateral term $\tau v^-$ has favourable properties in spite of the fact that the standard linear stability analysis cannot be performed. We illustrate the importance of the nonsmoothness by a numerical case study, which shows that the Turing instability can considerably change if we replace this term by its arbitrarily precise smooth approximation. However, the nonsmooth unilateral term and all its approximations yield qualitatively same patterns although not necessarily developing from arbitrarily small disturbances of the spatially homogeneous steady state. Further, we show that inserting the unilateral source into a classical system breaks the approximate symmetry and regularity of the classical patterns and yields asymmetric and irregular patterns. Moreover, a given system with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same system without any unilateral term. Biologically, these findings can contribute to the understanding of symmetry breaking during morphogenesis.
 
Article
The classical theory of Brownian dynamics follows from coarse-graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally non-isothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the non-isothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.
 
Basic flows and perturbation scheme in the x-y physical plane. A Cartesian reference frame is adopted, with unit vectors e1, e2, e3 in the x, y, z directions, respectively. The base flow profiles are qualitatively represented in black with arrows. A generic perturbation wave is represented in red. k=αe1+γe3 is the wavenumber vector, ϕ is its angle with respect to the basic flow U=U(y)e1. In the physical domain, the longitudinal space variable is unbounded for the channel flow and positive for the wake flow. However, due to the adoption of the near-parallel flow approximation, see section 2, the domain for the plane wake is also seen as unbounded. The spanwise coordinate is unbounded for both flows. Note that the transversal computational domain width is defined through the parameter yf. For the channel flow yf=±1, while for the wake flow yf is defined so that the numerical solution be insensitive to further extensions of the computational domain (yf=20 for short waves and yf up to 100 for long waves).
Temporal evolution of perturbations in terms of the phase velocity c (a),(e), the amplification factor G (b),(f), and the temporal growth rate r (c),(g), for different initial conditions. The eigenvalues spectra are shown in panels (d) and (h). Left column: channel flow with Re=6000, ϕ=π/4, and k=1. Right column: wake flow with Re=100, ϕ=π/6, and k=0.7. The phase velocity is computed at y0=0.5 for the channel and at y0=1 for the wake flow (note that the reference lengths are the channel half width and the cylinder diameter). The quantity Tc, see (a) and (e), indicates the temporal periodicity of the phase-velocity fluctuations observed in the early and intermediate terms and corresponds to the ratio Tc=2π/[σrmax−σrmin], as shown in panels (d) and (h).
Qualitative scheme for the phase-velocity transients. Left column: type of transient; the black lines represent the phase-velocity evolution over time (refer to Figs. 4– 7 in the paper), while the red sketches indicate the presence of self-similar perturbation profiles, in the intermediate term, for the wake case (please refer to Fig. 7). Middle column: wake flow; in each cell the conditions under which the corresponding kind of transient realizes are indicated, in terms of initial condition type (SI = symmetric in-wake, AI = antisymmetric in wake, SO = symmetric out-of-wake, AO = antisymmetric out-of-wake) and the wave-number value, namely k<kd or k>kd. Right column: channel flow. (SC = symmetric central, AC = antisymmetric central, SW=symmetric lateral, AW = antisymmetric lateral). With the blue sketches we represent, for each case, the shape of the perturbation in the long term (temporal asymptotic conditions). The green star is to remind that, even for k<kd, the least stable antisymmetric mode belongs to the right branch of the spectrum and it is nondispersive.
Article
In this study we analyze the phase and group velocity of three-dimensional linear traveling waves in two sheared flows: the plane channel and the wake flows. This was carried out by varying the wave number over a large interval of values at a given Reynolds number inside the ranges 20–100, 1000–8000, for the wake and channel flow, respectively. Evidence is given about the possible presence of both dispersive and nondispersive effects which are associated with the long and short ranges of wavelength. We solved the Orr-Sommerfeld and Squire eigenvalue problem and observed the least stable mode. It is evident that, at low wave numbers, the least stable eigenmodes in the left branch of the spectrum behave in a dispersive manner. By contrast, if the wave number is above a specific threshold, a sharp dispersive-to-nondispersive transition can be observed. Beyond this transition, the dominant mode belongs to the right branch of the spectrum. The transient behavior of the phase velocity of small three-dimensional traveling waves was also considered. Having chosen the initial conditions, we then show that the shape of the transient highly depends on the transition wavelength threshold value. We show that the phase velocity can oscillate with a frequency which is equal to the frequency width of the eigenvalue spectrum. Furthermore, evidence of intermediate self-similarity is given for the perturbation field.
 
Article
Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks which sets in at characteristic packing fraction $\phi_d$. Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event driven molecular dynamics simulations and the time dependent dynamical length scale extracted. It increases with time and on the equilibration time scale is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above $\phi_d$. The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer matrix approach.
 
x-t plot of Pp, P + ν , and Dν . The characteristic structure around x ∼ 25 corresponds to the vortex ejection processes.
A schematic view of the ejection-jet cycle.
The growth of the vortex pair. Three figures display different parts of the same snapshot. Regions ζ > 3 ( ζ < − 3) are colored by the same color of ζ = 3 ( ζ = − 3) to emphasize the bulk vorticity, though the vorticity field ζ ( x, y ) reaches its maximum ζ max 25 around x 24. 
Article
An iterface structure between turbulence and laminar flow is investigated in two-dimensional channel flow. This spatially localized structure not only sustains itself, but also converts laminar state into turbulence actively. In other words, this coherent structure has a functionality to generate inhomogeneity by its inner dynamics. The dynamics of this functional coherent structure is isolated using the filtered simulation, and a physical perspective of its dynamics is summarized in a phenomenological model called an "ejection-jet" cycle, which includes multiscale interaction process.
 
Article
We propose a novel approach for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. In contrast to the existing schemes, the selection of the optimum value of the threshold $\epsilon$ in our scheme is done empirically. We show that the range of $\epsilon$ values that we choose for each embedding dimension $M$ map the optimum information from the time series to the constructed network and this range is approximately the same for all the standard low dimensional chaotic systems. This provides us a general framework for non-subjective comparison of the measures derived from the recurrence networks of various chaotic attractors. By using the optimum recurrence network constructed in this way, we compute all the important statistical measures associated with the underlying attractor as function of $M$ and the number of nodes $N$. We show explicitly that the degree distribution of the optimum recurrence network from a chaotic attractor is a characteristic measure of the structure of the attractor and display statistical scale invariance with respect to increase in $N$. The practical utility of our scheme is also made clear by applying it to a time series from the real world. Finally, we look at the recurrence network from a complex network perspective by comparing its properties with that of a synthetically generated scale free network.
 
Inference of couplings in the CW model with N = 100 and two different values of the number M of input configurations. We see that the nMF method with all the input data is good only for β < βc = 1. For β > βc the phase space separates in 2 states and the nMF method with 2 clusters give much better performance (although it fails badly at high temperature). Inference methods, like PLM and nMF with density clustering, that take correctly into account the clustering of input configurations provide the best estimate in the entire temperature range, both above and below the transition temperature. In the left inset, we show how the inferred magnetic field at β = 1.6 decreases when increasing the number of samples (M ∈ [10 3 , 10 6 ]) used for the inference process via nMF with K-means clustering and K = 2. In the right inset the same inferred magnetic field is plotted versus β, for M = 10 4 , 10 5 . 
Article
In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is many states are present. The clustering of the phase space can occur for many reasons, e.g. when a system undergoes a phase transition. Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may led to very bad inference (for instance in the low temperature phase of the Curie-Weiss model). In the present work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of the new method on different clustered structures (low temperature phases of Curie-Weiss and Hopfield models).
 
Article
The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation. Comment: 17 pages, 3 figures. Submitted to Phys Rev B
 
Result of the integration of Eq. (130), with ν=1,tf−ti=0.5,ϕi=15. The black circle has radius ϕf=3.6614, obtained by integrating the drift term ∂tϕt=−ϕt2+ϕt+t/2. The color codes the number of splittings, from yellow over green, cyan, blue, magenta to red. (Thus a red point has 2−5 times the weight of a yellow point.)
Result for pfCGSEM(n) in Eq. (136), after integrating Eqs. (137) (real noise, green circles) and (138) (imaginary noise, blue diamonds) for ai=15,tf−ti=0.025. One sees that real noise leads to a broadening of the distribution, while imaginary noise leads to a narrowing.
A coarse-grained lattice with box size ℓ=4. The yellow box contains n=4 particles.
Article
We derive and study two different formalisms used for non-equilibrium processes: The coherent-state path integral, and an effective, coarse-grained stochastic equation of motion. We first study the coherent-state path integral and the corresponding field theory, using the annihilation process $A+A\to A$ as an example. The field theory contains counter-intuitive quartic vertices. We show how they can be interpreted in terms of a first-passage problem. Reformulating the coherent-state path integral as a stochastic equation of motion, the noise generically becomes imaginary. This renders it not only difficult to interpret, but leads to convergence problems at finite times. We then show how alternatively an effective coarse-grained stochastic equation of motion with real noise can be constructed. The procedure is similar in spirit to the derivation of the mean-field approximation for the Ising model, and the ensuing construction of its effective field theory. We finally apply our findings to stochastic Manna sandpiles. We show that the coherent-state path integral is inappropriate, or at least inconvenient. As an alternative, we derive and solve its mean-field approximation, which we then use to construct a coarse-grained stochastic equation of motion with real noise.
 
Article
In a recent paper Arita et al. [Phys. Rev. E 90, 052108 (2014)] consider the transport properties of a class of generalized exclusion processes. Analytical expressions for the transport-diffusion coefficient are derived by ignoring correlations. It is claimed that these expressions become exact in the hydrodynamic limit. In this Comment, we point out that (i) the influence of correlations upon the diffusion does not vanish in the hydrodynamic limit, and (ii) the expressions for the self- and transport diffusion derived by Arita et al. are special cases of results derived in [Phys. Rev. Lett. 111, 110601 (2013)].
 
Article
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows. This establishes a new link between the exact invariant solutions and the theory of turbulent flow and provides new evidence of the former's continuing organising importance in that regime.
 
Description of experimental procedure. (a) Schematic of the data collected about each 
Article
The mean size of exponentially dividing E. coli cells cultured at a fixed temperature but different nutrient conditions is known to depend on the mean growth rate only. The quantitative relation between these two variables is typically explained in terms of cell cycle control. Here, we measure the fluctuations around the quantitative laws relating cell size, doubling time and individual growth rate. Our primary result is a predominance of cell individuality: single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Additionally, the population and the individual-cell growth rate differ in their dependencies on division time, so that individuals with the same interdivision time but coming from colonies in different growth conditions grow at different rates. An interesting crossover in this cell individuality separates fast- and slow-growth conditions, possibly relating these findings to genome replication control. Secondly, extending previous findings focused on a single growth condition, we also establish that the spread in both size and doubling times is a linear function of the population means of these variables. By contrast, the fluctuations in single-cell growth rates do not show the same universality. Estimates of the division rate as a function of the measurable parameters imply a link between the universal and individual trends followed by single cells and a cell division control process which is sensitive to cell size as well as to additional variables, but which encodes a single intrinsic length-scale.
 
Article
Networks of biofilaments are essential for the formation of cellular structures and they support various biological functions. Previous studies have largely investigated the collective dynamics of rod-like biofilaments; however, the shapes of actual subcelluar componensts are often more elaborate. In this study, we investigated an active object composed of two active filaments, which represents a progression from rod-like biofilaments to complex-shaped biofilaments. Specifically, we numerically assessed the collective behaviors of these active objects and observed several types of dynamics depending on the density and the angle of the two filaments as shape parameters of the object. Among the observed collective dynamics, moving density bands that we named 'moving smectic' are reported here for the first time. By using statistical analyses of the orbits of individual objects and the interactions among them, the mechanisms underlying the rise of these dynamics patterns in the system were determined. This study demonstrated how interactions among active biofilaments with complex shapes produce collective dynamics in a non-trivial manner.
 
Article
We introduce a general contagion-like model for competing opinions that includes dynamic resistance to alternative opinions. We show that this model can describe candidate vote distributions, spatial vote correlations, and a slow approach to opinion consensus with sensible parameter values. These empirical properties of large groups, previously understood using distinct models, may be different aspects of human behavior that can be captured by a more unified model, such as the one introduced in this paper.
 
Article
We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs). The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant mathematical formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. We then utilize the one-to-one correspondence between V and the T-matrix of the problem, T. An iterative process is formulated for the T-matrix in which we seek T that is (i) compatible with the data and (ii) corresponds to an interaction potential V that is as diagonally-dominated as possible but not necessarily strictly diagonal. We refer to this algorithm as to the data-compatible T-matrix completion (DCTMC).
 
(a) Representation of a triangle as a cell complex by three 0-cells, three 1-cells, and one 2-cell. (b) Representation of a triangle as a graph with seven vertices, nine edges, and three vertex types.
Components of the model dislocation network around (a) a node along a dislocation, and (b) a vertex joining three dislocations. (c) The continuous version of (a).
Distances of several simulations to the reference condition. Error bars show the standard deviation of the distance of a steady-state configuration with the indicated number of edges to the reference condition.
Relative rates of topological changes throughout a simulation with a random graph initial condition.
Article
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by the analysis of particular physical systems and do not necessarily apply to general situations. The central concepts in this paper---the swatch and the cloth---provide a description of the local topology of a cell complex that is general (any physical system that may be represented as a cell complex is admissible) and complete (any statistical question about the local topology may be answered from the cloth). Furthermore, this approach allows a distance to be defined that measures the similarity of the local topology of two cell complexes. The distance is used to identify a steady state of a model dislocation network evolving by energy minimization, and then to rigorously quantify the approach of the simulation to this steady state.
 
Proportion of nodes in the largest component as a function of time for a functional network deduced from the electrocorticogram of a single patient with epilepsy during a seizure (see [27] for details). The weighted functional networks have been binarized by conducting independent hypothesis tests on the maximum absolute values of the cross correlations over 0.5-s windows with 50% overlap and after correcting for multiple comparisons. The black trace is a smoothed version of this process. Seizure onset was clinically estimated to occur at the vertical dotted line.
Birth and death steps for the product rule (PR) in the Achlioptas' model of percolation. In this example, edge e2 was born before edge e1, since |C11||C12|>|C21||C22|. Therefore, when e1 and e2 are selected during a death step, e2 is discarded after e1. This death step specification ensures that births and deaths constitute genuine reverse PR operations.
Percentage of vertices in the giant connected component (GCC) in the main window, and the corresponding sizes of the second-largest component (SLC) in inset, for a birth rate of p=1 and death rate of q=0, for the ER (black) and PR (gray) percolation models, for Nv=100; in which the x axis denotes the number of steps in the process divided by Nv. In bold, these results are reported for a noise-free model, whereas the thin lines represent noisy simulations with type-I and type-II error rates of α=0.0075, β=0. The details of the algebraic relationship between the type-I and type-II error rates and the graph process is described in Appendix, for the case of the ER model. Observe that the ER and PR models are nearly indistinguishable once a small amount of noise is added to these percolation processes.
Densities of the QD(.05, .75) of the first component's size in the main window, and densities of the maximal size of the second component (inset) are reported for the ER (blue) and PR (red) percolation models, based on 1,000 draws from the distributions of these two (noise-free) models. Note that the difference in scales of the density values of the y-axes in these two figures is due to the difference in scales of the x-axes.
Receiver operating characteristic (ROC) curves based on the QD of the first component's size (bold lines) and on the maximal size of the second component (thin lines). Each curve was produced using 1,000 simulations from each percolation model. In inset, the areas under the curves (AUCs) of these different ROC curves are compared for different choices of the birth rate, p, with the blue and purple bars denoting the ER and PR models, respectively.
Article
We consider the problem of distinguishing classical (Erd\H{o}s-R\'{e}nyi) percolation from explosive (Achlioptas) percolation, under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent and an observed non-stationary process, where the observed graph process is corrupted by Type I and Type II errors. This produces a hidden Markov graph model. We show that for certain choices of parameters controlling the noise, the classical (ER) percolation is visually indistinguishable from the explosive (Achlioptas) percolation model. In this setting, we compare two different criteria for discriminating between these two percolation models, based on a quantile difference (QD) of the first component's size and on the maximal size of the second largest component. We show through data simulations that this second criterion outperforms the QD of the first component's size, in terms of discriminatory power. The maximal size of the second component therefore provides a useful statistic for distinguishing between the ER and Achlioptas models of percolation, under physically motivated conditions for the birth and death of edges, and under noise. The potential application of the proposed criteria for percolation detection in clinical neuroscience is also discussed.
 
Article
We study the reversible crossover between stable and bistable phases of an over-damped Brownian bead inside an optical piston. The interaction potentials are solved developing a method based on Kramers' theory that exploits the statistical properties of the stochastic motion of the bead. We evaluate precisely the energy balance of the crossover. We show that the deformation of the optical potentials induced by the compression of the piston is related to a production of heat which measures the non-adiabatic character of the crossover. This reveals how specific thermodynamic processes can be designed and controlled with a high level of precision by tailoring the optical landscapes of the piston.
 
Article
Using Wilson renormalization group, we show under commonly accepted assumptions that scale invariance implies conformal invariance in dimension three for the Ising and O(N) models.
 
Article
We study the dependence of the static dielectric constant of aqueous electrolyte solutions upon the concentration of salt in the solution and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, the ionic response to an applied field, and the effect of thermal fluctuations. The analysis suggests that the formation of ion pairs by a small fraction of disassociated ions can have a significant effect on the static dielectric constant. The model predicts the dielectric has the functional dependence $\varepsilon(c)=\varepsilon_w-\beta L(3\alpha c/\beta)$ where $L$ is the Langevin function, $c$ is the salt concentration, $\varepsilon_w$ is the dielectric of the pure water, $\alpha$ is the total excess polarization of the ions and $\beta$ is the relative difference between the water dipole moment and the effective dipole moment of ion pairs as weighted by the density of ion pairs and their structural rigidity. The functional form gives an extremely accurate prediction of the dielectric constant for a variety of salts and a wide range of concentrations by fitting only the parameter $\beta$.
 
Article
Analyzing the physical and chemical properties of single DNA based molecular machines such as polymerases and helicases often necessitates to track stepping motion on the length scale of base pairs. Although high resolution instruments have been developed that are capable of reaching that limit, individual steps are oftentimes hidden by experimental noise which complicates data processing. Here, we present an effective two-step algorithm which detects steps in a high bandwidth signal by minimizing an energy based model (Energy based step-finder, EBS). First, an efficient convex denoising scheme is applied which allows compression to tupels of amplitudes and plateau lengths. Second, a combinatorial optimization algorithm formulated on a graph is used to assign steps to the tupel data while accounting for prior information. Performance of the algorithm was tested on poissonian stepping data simulated based on published kinetics data of RNA Polymerase II (Pol II). Comparison to existing step-finding methods shows that EBS is superior both in speed and precision. Moreover, the capability to detect backtracked intervals in experimental data of Pol II as well as to detect stepping behavior of the Phi29 DNA packaging motor is demonstrated.
 
Article
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The dynamic non-linear susceptibility is quantitatively well described by the inhomogeneous version of the Mode-Coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by a sharp geometric transition and large energy barriers, as expected from the lack of activated, hopping dynamics. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically realistic, three-dimensional model.
 
Article
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of transitions induced by interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in a vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of stable eigenstates from which particles cannot escape due to the binding energy. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N-particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in different sectors, in contrast to the Gibbs ensemble. We argue that the emergence of the Boltzmann distribution is rooted in a regular dependence of transition rates between eigenstates of the system on the transition energy.
 
Article
We consider paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models, and show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can get more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins -- for classical and quantum correlations -- is related to the quantum critical point in the corresponding ordered system.
 
Examples of different types of disordered chains. A: Anderson model; RDM1: random dimer model 1; and RDM2: random dimer model 2. The vertical dashed lines are visual guides to separate adjacent dimers from each other.
Schematic of a homogeneous system with (a) one and (b) two impurities. The incident wave is (i), the reflected wave is (r), and the transmitted wave is (t). We label the identities of the particles with integers. We calculate the parameters Bij = 3 2 A 2/3 ij F 1/3 0 from the static load and the interactions between consecutive particles.
Inverse participation ratio (averaged over 100 chain configurations) as a function of the ratio of radii R2/R1 = ξ and mode number for different types of disordered chains and different values of the probability parameters q. The black regions are associated with delocalized waves.
Examples of linear modes and the position of their frequencies inside of the linear spectrum for the Anderson model. The red dots indicate examples of isolated modes and their corresponding frequencies in the linear spectrum.
Article
We study spreading processes of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements). For all three types of disorder, the long-time asymptotic behavior of the second moment $\tilde{m}_2$ and the inverse participation ratio $P^{-1}$ satisfy the following scaling relations: $\tilde{m}_2\sim t^{\gamma}$ and $P^{-1}\sim t^{-\eta}$. For the Anderson-like uncorrelated disorder, we find a transition from subdiffusive ($\gamma<1$) to superdiffusive ($\gamma>1$) dynamics that depends on the amount of precompression in the chain. By contrast, for the correlated disorders, we find that the dynamics is superdiffusive for all precompression levels that we consider. Additionally, for strong precompression, the inverse participation ratio decreases slowly (with $\eta<0.1$) for all three types of disorder, and the dynamics leads to a partial localization around the leading edge of the wave. This localization phenomenon does not occur in the sonic-vacuum regime, which yields the surprising result that the energy is no longer contained in strongly nonlinear waves but instead is spread across many sites. In this regime, the exponents are very similar (roughly $\gamma\approx 1.7$ and $\eta\approx 1$) for all three types of disorder.
 
Top-cited authors
Antonio Ramos
  • Universidad de Sevilla
Antonio Castellanos
  • Universidad de Sevilla
Antonio González
  • Universidad de Sevilla
Nicolas G Green
  • University of Southampton
Hywel Morgan
  • University of Southampton