Search results for "Boundary value problem"
showing 10 items of 551 documents
Time-dependent Maxwell field operators and field energy density for an atom near a conducting wall
2009
We consider the time evolution of the electric and magnetic field operators for a two-level atom, interacting with the electromagnetic field, placed near an infinite perfectly conducting wall. We solve iteratively the Heisenberg equations for the field operators and obtain the electric and magnetic energy density operators around the atom (valid for any initial state). Then we explicitly evaluate them for an initial state with the atom in its bare ground state and the field in the vacuum state. We show that the results can be physically interpreted as the superposition of the fields propagating directly from the atom and the fields reflected on the wall. Relativistic causality in the field …
Optimization of the domain in elliptic variational inequalities
1988
This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.
Filling defects in a ceramics forming process
1997
Publisher Summary This paper presents a simple semi-heuristic method to predict mold filling defects in a porcelain forming process. It involves both a mechanical modelling of this process as a squeezing flow, and a postprocessing calculus that unable a defects prediction as soon as the shape and the size of artistic reliefs are known. This shape analysis is carried out with a multi resolution wavelet analysis. The chapter models the filling stage and to propose a criterium to avoid any filling defect that could waste the quality of the drawings. It illustrates a simplified modelling of the process during which the “turning” stage is approximated by the deformation under pressure of a Norto…
Thermo-mechanical post-buckling analysis of variable angle tow composite plate assemblies
2017
peer-reviewed The increasing use of composite materials for lightweight structural applications and the extended tailoring capabilities offered by variable stiffness laminates requires rapid and robust analysis tools that adequately describe the mechanical behaviour of such structures. In this work, a Rayleigh–Ritz solution for generally restrained multilayered stiffened variable angle tow plates in the post-buckling regime is presented. The plate model is based on first-order shear deformation theory and accounts for geometrical nonlinearity through von Kármán’s assumptions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed…
Prediction of flow fields in a dual-impeller stirred vessel
1999
Numerical simulations were connected for the flow field in a baffled tank stirred by a dual Rushton impeller. For this geometry, LDV measurements show a characteristic dependence of the flow patterns upon the position of the impellers. Two advanced modeling approaches were tested. In the first, the vessel was divided info two concentric blocks, coupled by, a sliding grin technique, and simulations were conducted in time-dependent mode. In the second approach, the vessel was modeled as two partially over-lapping I regions, the inner one rotating with the impeller and rite outer one stationary simulations were run in steady-state mode for each of the two regions, while information was iterati…
Experimental Investigation of the Outflow Process over a Triangular Labyrinth-Weir
2012
In this paper, the outflow process from a sharp-crested triangular labyrinth weir is studied. Applying dimensional analysis and the Π theorem, five dimensionless groups, describing the outflow process, are deduced. The measurements, carried out by using sharp-crested weirs placed in a flume, allowed to establish a dimensionless stage-discharge relation. According to this equation, the flow magnification is affected by either the length magnification ratio or head to one cycle width ratio. The proposed equation, which also satisfies two theoretical boundary conditions, was finally tested by using experimental measurements of different reservoir hydraulic models.
Assessment of seismic resistance of masonry structures including boundary conditions
2002
The paper is devoted to the investigation of seismic response of the masonry structure and describes experiences with modelling of boundary conditions during the test of large heavy model on 6DOF shaking table. The main aim of the research was how to increase dynamic resistance capacity of old masonry buildings including the medium and strong seismic effects. The results of theoretical and numerical analyses are compared including initial forecasting calculations made before any test started. The emphasis is given to the boundary conditions reached during the excitation of the large masonry model via shaking table. Strengthening and retrofitting procedures and their effects are discussed wh…
A shoreline boundary condition for a highly nonlinear Boussinesq model for breaking waves
2012
Abstract A physically based strategy was used to model swash zone hydrodynamics forced by breaking waves within a Boussinesq type of model. The position and the velocity of the shoreline were determined continuously in space by solving the physically-based equations of the shoreline motion; moreover, a fixed grid method, with a wet–dry interface, was adopted for integrating the Boussinesq model. The numerical stability of the model was improved by means of an extrapolation method. To validate the proposed methodology, the classical analytical solution for the shoreline motion of a monochromatic wave train over a plane beach was considered. The comparison between the analytical and numerical…
A shallow water SPH model with PML boundaries
2015
Abstract We focus on the study and implementation of Smoothed Particle Hydrodynamics (SPH) numerical code to deal with non-reflecting boundary conditions, starting from the Perfect Matched Layer (PML) approach. Basically, the method exploits the concept of a physical damping which acts on a fictitious layer added to the edges of computational domain. In this paper, we develop the study of time dependent shallow waves propagating on a finite 2D-XY plane domain and their behavior in the presence of circular and, more generic, rectangular boundary absorbing layers. In particular, an analysis of variation of the layer׳s thickness versus the absorbing efficiency is conducted. In our model, the m…
Planar systems with critical points: multiple solutions of two-point nonlinear boundary value problems
2005
Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. First, we consider the planar systems equivalent to equation x ″ = f ( x ) , where f ( x ) has multiple zeros and the respective system has centers and saddle points in various combinations. Estimations of the number of solutions are given. Then results are extended to nonautonomous equations which have superlinear behavior at infinity.