Search results for "Boundary value problem"

Constrained control of a nonlinear two point boundary value problem, I

1994

In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.

Surface-directed spinodal decomposition in a thin-film geometry: A computer simulation

1994

The phase separation kinetics of a two-dimensional binary mixture at critical composition confined between (one-dimensional) straight walls which preferentially attract one component of the mixture is studied for a wide range of distancesD between the walls. Following earlier related work on semiinfinite systems, two choices of surface forces at the walls are considered, one corresponding to an incompletely wet state of the walls, the other to a completely wet state (forD→∞). The nonlinear Cahn-Hilliard-type equation, supplemented with appropriate boundary conditions which account for the presence of surfaces, is replaced by a discrete equivalent and integrated numerically. Starting from a …

Proposal for a running coupling JIMWLK equation

2014

In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.

Refined equivalent single layer formulations and finite elements for smart laminates free vibrations

2014

A family of 2D refined equivalent single layer models for multilayered and functionally graded smart magneto-electro-elastic plates is presented. They are based on variable kinematics and quasi-static behavior for the electromagnetic fields. First, the electromagnetic state of the plate is determined by solving the strong form of the electromagnetic governing equations coupled with the corresponding interface continuity conditions and external boundary conditions. The electromagnetic state is then condensed into the plate kinematics, whose governing equations can be written using the generalized principle of virtual displacements. The procedure identifies an effective elastic plate kinemati…

A fast BEM for the analysis of damaged structures with bonded piezoelectric sensors

2010

A fast boundary element method for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state-space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computationa…

Macroscopic and microscopic study of the planar vibrational mode coupling

1999

We investigate the planar vibrational modes (PVMs) of a structure consisting of two parallel slabs of a strange atom (X) inserted in a matrix of a binary material (AB). The study of the coupling of the PVMs has been undertaken with two different approaches. In the first model, the structure is described from a macroscopic point of view, characterizing the physical properties of the constitutive materials by their layer densities, dielectric constants and strain tensors. Adequate boundary conditions are imposed at the material interfaces to obtain the vibrational modes of the structure. In the second model, the study of the planar modes is undertaken from a microscopic point of view, by usin…

An equivalent single-layer approach for free vibrations analysis of smart laminated thick composite plates

2012

An equivalent single-layer model for the free vibration analysis of smart laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static and third-order in-plane kinematics is employed to adequately take the shear influence into account when the plate thickness increases. The model governing equations are the plate equations of motion written in terms of mechanical primary variables and effective stiffness coefficients, which take the multifield coupling effects into account. The model shows that the surfaces magneto-electric boundary conditions enter the definitions of the laminate forces and moments resultants. Moreover, it reveals that new stiffness terms,…

Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions

2010

Computational stability of an initially radial solution of a growth/dissolution problem in a nonradial implementation

1991

We consider a free boundary problem modelling the growth/dissolution of a crystal. The aim is to investigate the following question: Does the solution to the crystal growth problem posed in two dimensions with radially symmetric initial and boundary condition evolve as a radially symmetric solution?

Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type

2014

Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.