Minimal stochastic model for Fermi's acceleration.

Asymptotic analysis of the high field semiconductor Boltzmann equation

Estimating the Signal to Noise Ratio (SNR) of the Primary Users' (PUs) signals over a wideband spectrum accurately is crucial in order to fully exploit an under-utilized primary spectrum using underlay Cognitive Radio (CR) techniques. In this context, we study an SNR estimation problem for a wideband CR under practical correlated scenarios in compressive settings. We carry out detailed theoretical analysis for the considered scenarios and then derive the expressions for the asymptotic eigenvalue probability distribution function (aepdf) of the measured signal's covariance matrix using asymptotic Random Matrix Theory. Subsequently, based on the derived aepdfs, we present a technique to estimate the PU SNR over a wideband spectrum with compressive measurements. The performance of the proposed technique is evaluated in terms of normalized Mean Square Error (MSE) and it is shown that the SNR of the PU signals over the wideband spectrum can be reliably estimated using the proposed technique.

A sequence of independent vectors with correlated components is considered. It is supposed that there is one change point in the mean of each component and changes need not occur simultaneously. The asymptotic distribution of the change point estimators is studied. If the true change points are well separated, the explicit asymptotic distribution of the change point estimators is presented. In the case the true change points coincide, it is shown that the limit distribution of properly standardized change points estimates exists. It depends not only on the underlying time series dependence structure, but also on the ratio of the sizes of the changes. The asymptotic distribution function is not known, but due to the invariance principle it can be obtained by simulations.

Heating by Fermi acceleration offers a unifying explanation of several disparate properties of solar wind ions. Inside 1 AU, undamped Alfvén wave amplitudes, δB, decrease less rapidly than the field magnitude, maintaining |δB|/B≳1 and forming wave fronts about a proton gyroradius thick. Fermi acceleration in the compressible medium heats ions to a thermal speed about equal to the Alfvén wave amplitude, |δVA|; the heating mechanism is ion reflection from the wave fronts. Because |δVA|∼ρ1/4, the heating results in a proton polytropic index of 3/2 (while the adiabatic index is 5/3 for a fully ionized gas with three degrees of freedom), consistent with observational results and the observed entropy increase of protons in fast wind between 0.3 and 1 AU. Because ions are heated to a thermal speed that is independent of mass, ion temperature is proportional to mass in accord with observations. Helium and heavy ions, with larger gyroradii than protons, are more efficiently reflected by the wave fronts and cross them with difficulty; they are therefore carried by the wave and have differential velocities with respect to protons of about the Alfvén velocity, also in agreement with observations. The Fermi acceleration mechanism is inapplicable to the inner corona where |δB|/B≪1 but offers a plausible explanation of an inference by S. Olbert of a temperature maximum in the outer corona near the Alfvén critical point where the wave amplitude is maximum.

We investigate the electron acceleration behind dipolarization fronts (DFs) in the magnetotail from −25 R E to −10R E through the examination of the energetic electron energy flux (>30 keV) with the observations from THEMIS satellites. Statistical results of 133 DF events are presented based on the dataset from January to April of the years 2008 and 2009. As the DFs propagate earthward, the acceleration of energetic electrons behind the DFs is found to take place over several R E along the tail. The increase in energetic electron energy flux can reach 2∼4 orders of magnitude. The dominant acceleration mechanisms are different in the mid-tail (X GSM ≤−15R E ) and the near-Earth region (−15 GSM ≤−10R E ). In the mid-tail, the majority of DF events show that the dominant electron acceleration mechanism is betatron acceleration. In the near-Earth region, betatron acceleration is dominant in ∼46% DF events while Fermi acceleration is dominant in ∼39% DF events.

In this paper, we treat the inverse problem of determining the scattering coefficient and the absorption coefficient appearing in the linear Boltzmann equation via boundary measurements. We show that the gauge-equivalent of the coefficients yields the same albedo operator. The albedo operator is defined as the mapping from the incoming boundary conditions to the outgoing transport solution at the boundary of a bounded and convex domain. We study the stability of the absorption coefficient up to a gauge transformation from the albedo operator, and we prove that the scattering time-dependent coefficient can be uniquely determined in a precise subset of domain, from the albedo operator.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation R. Kallenbach, K. Bamert, R. F. Wimmer‐Schweingruber; Charge‐to‐mass Fractionation of Suprathermal Ions Associated with Interplanetary CMEs. AIP Conf. Proc. 2 September 2003; 679 (1): 672–675. https://doi.org/10.1063/1.1618684 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

On continuous-time threshold ARMA processes

Based on the asymptotic spectral distribution of sample covariance matrix, a new low probability of interception (LPI) signal detection method for multi-antenna intercept receiver is proposed via reforming the noise sequence into a Wishart matrix. The authors deduce the asymptotic cumulative distribution function (CDF) of eigenvalues of sample covariance matrix. Also a numerical Kullback–Leibler divergence of the empirical spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. By comparing with other signal detection methods, simulation results show the new LPI signal detection method is superior and robust.

Traditionally, uncertainties in activity durations have been modelled as random variables with corresponding probability distribution functions. These latter are assumed to be known a priori. In reality estimates of activities’ “remaining work cbntents” as well as their duration vary dynamically over time, with divergent variability as the planning horizon extends into the future. To capture this dynamic nature of the estimates, we model the activity as diffusion processes.

An iterative method is proposed for solving the homogeneous (i.e., critical) or inhomogeneous (i.e., source) linear irtegral Boltzmann equation for general geometry. By using successive approximations, these two classes of problems are shown to be mathematically equivalent. For the homogeneous problem, constraints on the algorithm regarding the existence of eigenvalues and the initial approximation are investigated. The algorithm is as the elementary interaction causing the pinning). For higher defect densities, the agreement with the experiments on niobium is better than with the previous theory. This method of correlations seemed suitable for studying the effect of cutting-off'' the small elementary intenactions and for the replacement of the Gauss distribution function by the Poisson distribution function for the number of defects in the elementary volumes. Both these give negative results with respect to the experiments; so far wrte are therefore not able to explain quartitatively the large please delete the above 9 lines======= applied to isotropically scattering slabs and spheres, and is compared with previously published results as well as an independent extrapolation method. For the inhomogeneous problem, an improvement over the normal successive collision method via the use of a Neumann series expansion is used to allow economic parametric studies. Constraintsmore » on the algorithm and methods of efficiently terminating the infinite Neumann series are investigated. The solution via the proposed method as applied to isotropically scattering slabs and spheres is provided in a compact form for a range of multiplication factors and optical dimensions. The shape of the scalar flux distribution is expiained. Extensions of the method to more complex problems are outlined; in particular, the solution to an energy-dependent problem in general geometry is obtained, and the implications of the results are discussed. (7 figures, 2 tables) (auth)« less

Value-distribution of cubic Hecke L-functions

We obtain the large deviation function for entropy production of the medium and its distribution function for the two-site totally asymmetric simple exclusion process (TASEP) and the three-state unicyclic network. Since such systems are described through microscopic irreversible transitions, we obtain time-dependent transition rates by sampling the states of these systems at a regular short time interval τ. These transition rates are used to derive the large deviation function for the entropy production in the nonequilibrium steady state and its asymptotic distribution function. The shapes of the large deviation function and the distribution function depend on the value of the mean entropy production rate which has a non-trivial dependence on the particle injection and withdrawal rates in the case of TASEP. Further, it is argued that in case of a TASEP, the distribution function tends to be like a Poisson distribution for smaller values of particle injection and withdrawal rates.

The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a composite medium with optically thin inclusions in an optically thick background medium. The equation governing the evolution of the approximate particle density coincides with the limit of the diffusion equation with infinite diffusion coefficient in the optically thin inclusions.

This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to investigate the case where a given acceleration field is present. The main result of this paper shows that for an appropriate scaling of the acceleration field, the usual fractional diffusion equation is supplemented by an advection term. Both the critical and supercritical case are considered.