Order statistics for d-dimensional diffusion processes

We present results for the ordered sequence of first passage times of arrival of N random walkers at a boundary in Euclidean spaces of d dimensions

How `sticky' are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range $\lambda$ at a given packing fraction and reduced temperature can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter $\tau$. Such an equivalence cannot hold for the radial distribution function since this function has a delta singularity at contact in the SHS case, while it has a jump discontinuity at $r=\lambda$ in the SW case. Therefore, the equivalence is explored with the cavity function $y(r)$. Optimization of the agreement between y_{\sw} and y_{\shs} to first order in density suggests the choice for $\tau$. We have performed Monte Carlo (MC) simulations of the SW fluid for $\lambda=1.05$, 1.02, and 1.01 at several densities and temperatures $T^*$ such that $\tau=0.13$, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)]. Although, at given values of $\eta$ and $\tau$, some local discrepancies between y_{\sw} and y_{\shs} exist (especially for $\lambda=1.05$), the SW data converge smoothly toward the SHS values as $\lambda-1$ decreases. The approximate mapping y_{\sw}\to y_{\shs} is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y_{\shs} the solution of the Percus--Yevick equation as well as the rational-function approximation, the radial distribution function $g(r)$ of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.Comment: 14 pages, including 3 tables and 14 figures; v2: typo in Eq. (5.1) corrected, Fig. 14 redone, to be published in JC

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Fourth virial coefficients of asymmetric nonadditive hard-disc mixtures

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio ($0.05\leq q\leq 0.95$) and nonadditivity ($-0.5\leq \Delta\leq 0.5$) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio $q=0.7$ and two nonadditivities $\Delta=\pm 0.2$.Comment: 9 pages, 7 figures; v2: section on equation of state added; tables moved to supplementary material (http://jcp.aip.org/resource/1/jcpsa6/v136/i18/p184505_s1#artObjSF

Hot-Moments of Soil CO2 Efflux in a Water-Limited Grassland

The metabolic activity of water-limited ecosystems is strongly linked to the timing and magnitude of precipitation pulses that can trigger disproportionately high (i.e., hot-moments) ecosystem CO2 fluxes. We analyzed over 2-years of continuous measurements of soil CO2 efflux (Fs) under vegetation (Fsveg) and at bare soil (Fsbare) in a water-limited grassland. The continuous wavelet transform was used to: (a) describe the temporal variability of Fs; (b) test the performance of empirical models ranging in complexity; and (c) identify hot-moments of Fs. We used partial wavelet coherence (PWC) analysis to test the temporal correlation between Fs with temperature and soil moisture. The PWC analysis provided evidence that soil moisture overshadows the influence of soil temperature for Fs in this water limited ecosystem. Precipitation pulses triggered hot-moments that increased Fsveg (up to 9000%) and Fsbare (up to 17,000%) with respect to pre-pulse rates. Highly parameterized empirical models (using support vector machine (SVM) or an 8-day moving window) are good approaches for representing the daily temporal variability of Fs, but SVM is a promising approach to represent high temporal variability of Fs (i.e., hourly estimates). Our results have implications for the representation of hot-moments of ecosystem CO2 fluxes in these globally distributed ecosystems

Reliable and Elastic Propagation of Cortical Seizures In Vivo

Mapping the fine-scale neural activity that underlies epilepsy is key to identifying potential control targets of this frequently intractable disease. Yet, the detailed in vivo dynamics of seizure progression in cortical microcircuits remain poorly understood. We combine fast (30-Hz) two-photon calcium imaging with local field potential (LFP) recordings to map, cell by cell, the spread of locally induced (4-AP or picrotoxin) seizures in anesthetized and awake mice. Using single-layer and microprism-assisted multilayer imaging in different cortical areas, we uncover reliable recruitment of local neural populations within and across cortical layers, and we find layer-specific temporal delays, suggesting an initial supra-granular invasion followed by deep-layer recruitment during lateral seizure spread. Intriguingly, despite consistent progression pathways, successive seizures show pronounced temporal variability that critically depends on GABAergic inhibition. We propose an epilepsy circuit model resembling an elastic meshwork, wherein ictal progression faithfully follows preexistent pathways but varies flexibly in time, depending on the local inhibitory restraint

Altered Cortical Ensembles in Mouse Models of Schizophrenia

In schizophrenia, brain-wide alterations have been identified at the molecular and cellular levels, yet how these phenomena affect cortical circuit activity remains unclear. We studied two mouse models of schizophrenia-relevant disease processes: chronic ketamine (KET) administration and Df(16)A+/-, modeling 22q11.2 microdeletions, a genetic variant highly penetrant for schizophrenia. Local field potential recordings in visual cortex confirmed gamma-band abnormalities similar to patient studies. Two-photon calcium imaging of local cortical populations revealed in both models a deficit in the reliability of neuronal coactivity patterns (ensembles), which was not a simple consequence of altered single neuron activity. This effect was present in ongoing and sensory-evoked activity and was not replicated by acute ketamine administration or pharmacogenetic parvalbumin-interneuron suppression. These results are consistent with the hypothesis that schizophrenia is an ‘‘attractor’’ disease and demonstrate that degraded neuronal ensembles are a common consequence of diverse genetic, cellular, and synaptic alterations seen in chronic schizophrenia

Average shape of fluctuations for subdiffusive walks

We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a fractional diffusion approach. We find that, in contrast with processes where the waiting time between increments has finite variance, the fluctuation shape is no longer a semicircle: it tends to adopt a table-like form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.Comment: 4 pages, 6 figures. Accepted for publication Phys. Rev. E (Replaced for the latest version, in press.) Section II rewritte

Dynamics of unvisited sites in presence of mutually repulsive random walkers

We have considered the persistence of unvisited sites of a lattice, i.e., the probability $S(t)$ that a site remains unvisited till time $t$ in presence of mutually repulsive random walkers. The dynamics of this system has direct correspondence to that of the domain walls in a certain system of Ising spins where the number of domain walls become fixed following a zero termperature quench. Here we get the result that $S(t) \propto \exp(-\alpha t^{\beta})$ where $\beta$ is close to 0.5 and $\alpha$ a function of the density of the walkers $\rho$. The number of persistent sites in presence of independent walkers of density $\rho^\prime$ is known to be $S^\prime (t) = \exp(-2 \sqrt{\frac{2}{\pi}} \rho^\prime t^{1/2})$. We show that a mapping of the interacting walkers' problem to the independent walkers' problem is possible with $\rho^\prime = \rho/(1-\rho)$ provided $\rho^\prime, \rho$ are small. We also discuss some other intricate results obtained in the interacting walkers' case.Comment: 6 pages, 7 figure

On the joint residence time of N independent two-dimensional Brownian motions

We study the behavior of several joint residence times of N independent Brownian particles in a disc of radius $R$ in two dimensions. We consider: (i) the time T_N(t) spent by all N particles simultaneously in the disc within the time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N particles spend together in the disc within the time interval [0,t]; and (iii) the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend together in the disc within the time interval [0,t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t\to\infty.Comment: 8 page