Search results for "Boundary value problem"
showing 10 items of 551 documents
On Different Type Solutions of Boundary Value Problems
2016
We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].
Wavelet-based efficient simulation of electromagnetic transients in a lightning protection system
2003
In this paper, a wavelet-based efficient simulation of electromagnetic transients in a lightning protection systems (LPS) is presented. The analysis of electromagnetic transients is carried out by employing the thin-wire electric field integral equation in frequency domain. In order to easily handle the boundary conditions of the integral equation, semiorthogonal compactly supported spline wavelets, constructed for the bounded interval [0,1], have been taken into account in expanding the unknown longitudinal currents. The integral equation is then solved by means of the Galerkin method. As a preprocessing stage, a discrete wavelet transform is used in order to efficiently compress the Fouri…
BIEM-based variational principles for elastoplasticity with unilateral contact boundary conditions
1998
The structural step problem for elastic-plastic internal-variable materials is addressed in the presence of frictionless unilateral contact conditions. Basing on the BIEM (boundary integral equation method) and making use of deformation-theory plasticity (through the backward-difference method of computational plasticity), two variational principles are shown to characterize the solution to the step problem: one is a stationarity principle having as unknowns all the problem variables, the other is a saddle-point principle having as unknowns the increments of the boundary tractions and displacements, along with the plastic strain increments in the domain. The discretization by boundary and i…
Method of Lines and Finite Difference Schemes with Exact Spectrum for Solving Some Linear Problems of Mathematical Physics
2013
In this paper linear initial-boundary-value problems of mathematical physics with different type boundary conditions BCs and periodic boundary conditions PBCs are studied. The finite difference scheme FDS and the finite difference scheme with exact spectrum FDSES are used for the space discretization. The solution in the time is obtained analytically and numerically, using the method of lines and continuous and discrete Fourier methods.
Non-Monotonic Concentration Dependence of the Electro-Phoretic Mobility of Charged Spheres in Realistic Salt Free Suspensions
2020
Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the opti-cally accessible range of concentrations in experiments on colloidal electro-kinetics. We here meas-ured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic con-centration dependence of the mobility for a single particle species. Our observations reconcile previ-ous experimental observations made on other species over restricted concentration ranges. We com-par…
How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non-viscous SPH simulations
2009
Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one protopla…
Layer-wise and equivalent single layer models for smart multilayered plates
2014
Layer-wise and equivalent single layer plate models for magneto-electro-elastic multiphysics laminates are presented in a unified framework. They are based on variable kinematics and quasi-static behavior of the electromagnetic fields. The electromagnetic state of each single layer is preliminary determined by solving the corresponding governing equations coupled with the proper interface continuity and external boundary conditions. By so doing, the electromagnetic state is condensed into the plate kinematics and the layer governing equations are inferred by the principle of virtual displacements. This approach identifies effective mechanical layers, which are kinematically equivalent to th…
An augmented MFS approach for brain activity reconstruction
2017
Abstract Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving rise to electric and magnetic fields, which can be modeled by the quasi-stationary approximation of Maxwell’s equations. Electroencephalography (EEG) and magnetoencephalography (MEG) techniques allow for reconstructing the cerebral electrical currents and thus investigating the neuronal activity in the human brain in a non-invasive way. This is a typical electromagnetic inverse problem which can be addressed in two stages. In the first one a physical and geometrical representation of the head is used to find the relation between a given source mo…
Experimental demonstration of the physics of resonant cavities
2005
We describe an undergraduate experiment that demonstrates the physics of cavity resonators. A mobile wall lets students alter the position of the nodes, thus changing the mode pattern. The nodal structure is made apparent by placing a metallic plate at different positions inside the cavity. A technique for dielectric characterization also is introduced, which helps students understand the boundary conditions in dielectrics, as well as highlighting the characteristics of fields in cavities.
Field fluctuations near a conducting plate and Casimir-Polder forces in the presence of boundary conditions
2006
We consider vacuum fluctuations of the quantum electromagnetic field in the presence of an infinite and perfectly conducting plate. We evaluate how the change of vacuum fluctuations due to the plate modifies the Casimir-Polder potential between two atoms placed near the plate. We use two different methods to evaluate the Casimir-Polder potential in the presence of the plate. They also give new insights on the role of boundary conditions in the Casimir-Polder interatomic potential, as well as indications for possible generalizations to more complicated boundary conditions.