Second-order moment-closure for tighter epidemic thresholds

Second-order moment-closure for tighter epidemic thresholds

In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infectedsusceptible (SIS) stochastic spreading process. A precise quantification of this decay rate is crucial for designing efficient strategies to contain epidemic outbreaks. Ho...

Modelling transonic flows with second-moment closure

It is now generally accepted that statistical turbulence models are unlikely, ever, to enable highfidelity predictions of massively-separated flows, especially if separation occurs from curved three-dimensional surfaces. In such circumstances, even the most elaborate turbulence models are ill-equipped to capture the dynamics associated with highly-unsteady and intense large-scale motions that a...

Second Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum

This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright}‎ where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...

Vanishing Moment Method and Moment Solutions for Fully Nonlinear Second Order Partial Differential Equations

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...

Second-order scheme for quadrature-based velocity high order moment methods for disperse two-phase flows