Search results for "Multiple integral"
showing 6 items of 16 documents
Formulation and test of an ice aggregation scheme for two-moment bulk microphysics schemes
2013
A simple formulation of aggregation for 2-moment bulk microphysical models is de-rived. The solution involves the evaluation of a double integral of the collection kernelweighted with the crystal size (or mass) distribution. This quantity is to be inserted intothe differential equation for the crystal number concentration which has classical form. The double integrals are evaluated numerically for log-normal size distributions overa large range of geometric mean masses. A polynomial fit of the results is given thatyields good accuracy. Various tests of the new parameterization are described: aggre-gation as stand-alone process, in a box-model, and in 2-D simulations of a cirrostratuscloud. …
Weighted estimates for diffeomorphic extensions of homeomorphisms
2019
Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$
Stochastic response of MDOF wind-excited structures by means of Volterra series approach
1998
Abstract The role played by the quadratic term of the forcing function in the response statistics of multi-degree-of-freedom (MDOF) wind-excited linear-elastic structures is investigated. This is accomplished by modeling the structural response as a Volterra series up to the second order and neglecting the wind-structure interaction. In order to reduce the computational effort due to the calculation of a large number of multiple integrals, required by the used approach, a recent model of the wind stochastic field is adopted.
Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
2016
We analyze the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to their form factor expansion. Its explicit form is obtained from a saddle-point analysis of the corresponding double integral. It describes the propagation of a wave front with velocity $v_{c_1}$ which is found to be the maximal possible group velocity. Like in wave propagation in dispersive media the wave front is preceded by a precursor running ahead with velocity $v_{c_2}$. As a special case we obta…
Erratum to “Simulation of BSDEs with jumps by Wiener Chaos expansion” [Stochastic Process. Appl. 126 (2016) 2123–2162]
2017
Abstract We correct Proposition 2.9 from “Simulation of BSDEs with jumps by Wiener Chaos expansion” published in Stochastic Processes and their Applications, 126 (2016) 2123–2162. The proposition which provides an expression for the expectation of products of multiple integrals (w.r.t. Brownian motion and compensated Poisson process) requires a stronger integrability assumption on the kernels than previously stated. This does not affect the remaining results of the article.
A symmetric Galerkin BEM for plate bending analysis
2009
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…