Stochastic flow simulation and particle transport in a 2D layer of random porous medium

A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.researc

Stochastic analysis of an elastic 3D half-space respond to random boundary displacements : exact results and Karhunen-Loéve expansion

A stochastic response of an elastic 3D half-space to random displacement excitations on the boundary plane is studied. We derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary. Solutions to this elasticity problem are random fields which appear to be horizontally homogeneous but inhomogeneous in the vertical direction. This enables us to construct explicitly the Karhunen-Loève (K-L) series expansion by solving the eigen-value problem for the correlation operator. Simulation results are presented and compared with the exact representations derived for the displacement correlation tensor. This paper is a complete 3D generalization of the 2D case study we presented in J. Stat. Physics, v.132 (2008), N6, 1071-1095

Checking Interaction-Based Declassification Policies for Android Using Symbolic Execution

Mobile apps can access a wide variety of secure information, such as contacts and location. However, current mobile platforms include only coarse access control mechanisms to protect such data. In this paper, we introduce interaction-based declassification policies, in which the user's interactions with the app constrain the release of sensitive information. Our policies are defined extensionally, so as to be independent of the app's implementation, based on sequences of security-relevant events that occur in app runs. Policies use LTL formulae to precisely specify which secret inputs, read at which times, may be released. We formalize a semantic security condition, interaction-based noninterference, to define our policies precisely. Finally, we describe a prototype tool that uses symbolic execution to check interaction-based declassification policies for Android, and we show that it enforces policies correctly on a set of apps.Comment: This research was supported in part by NSF grants CNS-1064997 and 1421373, AFOSR grants FA9550-12-1-0334 and FA9550-14-1-0334, a partnership between UMIACS and the Laboratory for Telecommunication Sciences, and the National Security Agenc

Analysis of relative dispersion of two particles by Lagrangian stochastic models and DNS methods

Comparisons of the Q1D against the known Lagrangian stochastic well-mixed quadratic form models and the moments approximation models are presented. In the case of modestly large Reynolds numbers turbulence (Re λ ⋍ 240) the comparison of the Q1D model with the DNS data is made. Being in a qualitatively agreemnet with the DNS data, the Q1D model predicts higher rate of separation. Realizability of Q1D model extracted from the transport equation with a quadratic form of the conditional acceleration is shown

Self-regulated radius of spontaneously formed GaN nanowires in molecular beam epitaxy

We investigate the axial and radial growth of GaN nanowires upon a variation of the Ga flux during molecular beam epitaxial growth. An increase in the Ga flux promotes radial growth without affecting the axial growth rate. In contrast, a decrease in the Ga flux reduces the axial growth rate without any change in the radius. These results are explained by a kinetic growth model that accounts for both the diffusion of Ga adatoms along the side facets towards the nanowire tip and the finite amount of active N available for the growth. The model explains the formation of a new equilibrium nanowire radius after increasing the Ga flux and provides an explanation for two well known but so far not understood experimental facts: the necessity of effectively N-rich conditions for the spontaneous growth of GaN nanowires and the increase in nanowire radius with increasing III/V flux ratios

Generalized differential privacy: regions of priors that admit robust optimal mechanisms

International audienceDifferential privacy is a notion of privacy that was initially designed for statistical databases, and has been recently extended to a more general class of domains. Both differential privacy and its generalized version can be achieved by adding random noise to the reported data. Thus, privacy is obtained at the cost of reducing the data's accuracy, and therefore their utility. In this paper we consider the problem of identifying optimal mechanisms for gen- eralized differential privacy, i.e. mechanisms that maximize the utility for a given level of privacy. The utility usually depends on a prior distribution of the data, and naturally it would be desirable to design mechanisms that are universally optimal, i.e., optimal for all priors. However it is already known that such mechanisms do not exist in general. We then characterize maximal classes of priors for which a mechanism which is optimal for all the priors of the class does exist. We show that such classes can be defined as convex polytopes in the priors space. As an application, we consider the problem of privacy that arises when using, for instance, location-based services, and we show how to define mechanisms that maximize the quality of service while preserving the desired level of geo- indistinguishability