Search results for "Mathematical analysis"

Markovian Connection, Curvature and Weitzenböck Formula on Riemannian Path Spaces

2001

Abstract We shall consider on a Riemannian path space P m o ( M ) the Cruzeiro–Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbock formula will be established. To this end, we shall introduce an “inner product” between the tangent processes and simple vector fields.

Graded metrics adapted to splittings

1997

Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul, are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry: It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion an…

The Bochner and Riesz integral representations for the Radon transform

1984

A non-stationary one-ring scattering model

2013

This paper introduces a non-stationary one-ring scattering model in which the mobile station (MS) can move along a straight line from the ring's center to the border of the ring. This movement results in a time-variant angle-of-arrival (AOA), which is modeled by a stochastic process. We derive the first-order density of the AOA process in closed form. Subsequently, a closed-form expression is provided for the local power spectral density (PSD) of the channel. We also formulate the local autocorrelation function (ACF) of the complex channel gain in integral form, from which a highly accurate closed-form approximation is derived. Furthermore, the average Doppler shift and the Doppler spread o…

NUMERICAL SIMULATION OF MAGNETIC DROPLET DYNAMICS IN A ROTATING FIELD

2013

Dynamics and hysteresis of an elongated droplet under the action of a rotating magnetic field is considered for mathematical modelling. The shape of droplet is found by regularization of the ill-posed initial–boundary value problem for nonlinear partial differential equation (PDE). It is shown that two methods of the regularization – introduction of small viscous bending torques and construction of monotonous continuous functions are equivalent. Their connection with the regularization of the ill-posed reverse problems for the parabolic equation of heat conduction is remarked. Spatial discretization is carried out by the finite difference scheme (FDS). Time evolution of numerical solutions …

Mathematical modelling of an elongated magnetic droplet in a rotating magnetic field

2012

Dynamics of an elongated droplet under the action of a rotating magnetic field is considered by mathematical modelling. The actual shape of a droplet is obtained by solving the initial-boundary value problem of a nonlinear singularly perturbed partial differential equation (PDE). For the discretization in space the finite difference scheme (FDS) is applied. Time evolution of numerical solutions is obtained with MATLAB by solving a large system of ordinary differential equations (ODE).

Internal spring distribution for quasi brittle fracture via Symmetric Boundary Element Method

2009

Abstract In this paper the symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials . The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method . The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation σ − Δ u that describes the interaction between mechanical and kinematical quantities…

On the stability of the localized single-valued extension property under commuting perturbations

2013

This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators.

Diagonalization of indefinite saddle point forms

2020

We obtain sufficient conditions that ensure block diagonalization (by a direct rotation) of sign-indefinite symmetric sesquilinear forms as well as the associated operators that are semi-bounded neither from below nor from above. In the semi-bounded case, we refine the obtained results and, as an example, revisit the block Stokes operator from fluid dynamics.

CVBEM for solving De Saint-Venant solid under shear forces

2013

Abstract Evaluation of shear stresses distribution due to external shear forces applied to De Saint-Venant beams has been solved through Complex Variable Boundary Element Method properly extended, to benefit from advantages of this method, so far widely used for twisted solids. Extending the above method, further simplifications have been introduced such as those of performing line integrals only, instead of domain integrals. Numerical applications confirm accuracy and efficiency of the proposed extended version of the method, since the good agreement with results proposed in literature.