Search results for "Exact solution"
showing 10 items of 77 documents
Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor
2016
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-sim…
Exact solution of the soft-clustered vehicle-routing problem
2020
Abstract The soft-clustered vehicle-routing problem (SoftCluVRP) extends the classical capacitated vehicle-routing problem by one additional constraint: The customers are partitioned into clusters and feasible routes must respect the soft-cluster constraint, that is, all customers of the same cluster must be served by the same vehicle. In this article, we design and analyze different branch-and-price algorithms for the exact solution of the SoftCluVRP. The algorithms differ in the way the column-generation subproblem, a variant of the shortest-path problem with resource constraints (SPPRC), is solved. The standard approach for SPPRCs is based on dynamic-programming labeling algorithms. We s…
Thin obstacle problem : Estimates of the distance to the exact solution
2018
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution and any function that satisfies the boundary condition and is admissible with respect to the obstacle condition (i.e., they are valid for any approximation regardless of the method by which it was found). Computation of the estimates does not require knowledge of the exact solution and uses only the problem data and an approximation. The estimates provide guaranteed upper bounds of the error (error majorants) and vanish if and only if the approximation c…
Spatially limited diffusion coupled with ohmic potential drop and/or slow interfacial exchange: a new method to determine the diffusion time constant…
2004
Abstract We have analyzed chronoamperometric curves, I ( t ), after small-amplitude potential steps Δ E (PITT technique) for the model of linear diffusion of a species inside an electroactive film, taking into account ohmic effects in the external media (solution and electrode) as well as a finite rate of the interfacial exchange. For its short-time interval, t ≪ τ d ( τ d is the diffusion time constant, corresponding to unlimited diffusion from the interface), three approximate analytical expressions have been proposed. One of these represents an interpolation formula between the value of the current at the start of the diffusion process, I (0)=Δ E / R ext (after the end of the EDL chargin…
A model for multilayered beams undergoing end loads
2013
A formulation for layered beams undergoing end loads, namely axial, shear and bending actions, is developed and presented in this paper. A layer-wise kinematical model is first derived so that the point-wise balance relationships are fulfilled at the layer level. Successively, by enforcing the interface continuity conditions and taking the traction–free conditions on the top and bottom surfaces of the laminate into account, the layer-wise kinematical quantities are written in terms of generalized kinematical variables representative of the beam displacements field. The beam problem is then formulated in terms of these generalized variables leading to a model that shows the positive characte…
A Theory of Laminated Beams Subjected to Axial, Bending and Shear Load
2013
A theory of laminated beams subjected to axial, bending and shear loads is presented in this paper. The kinematical model employed to describe the laminated beam displacement field is layer-wise in nature. Moreover it is such that the equilibrium equations and the continuity of the stress components at plies interfaces are satisfied. By using the whole set of interface continuity conditions in conjunction with the traction –free conditions on the beam top and bottom surfaces the layer-wise kinematical quantities are written in terms of the mechanical primary variables pertaining to one layer only, which are then expressed in terms of the laminated generalized displacements. The solution for…
A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm
2014
Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.
Quantum critical point in a periodic Anderson model
2000
We investigate the symmetric Periodic Anderson Model (PAM) on a three-dimensional cubic lattice with nearest-neighbor hopping and hybridization matrix elements. Using Gutzwiller's variational method and the Hubbard-III approximation (which corresponds to the exact solution of an appropriate Falicov-Kimball model in infinite dimensions) we demonstrate the existence of a quantum critical point at zero temperature. Below a critical value $V_c$ of the hybridization (or above a critical interaction $U_c$) the system is an {\em insulator} in Gutzwiller's and a {\em semi-metal} in Hubbard's approach, whereas above $V_c$ (below $U_c$) it behaves like a metal in both approximations. These prediction…
Theoretical investigation of the self-trapped hole in alkali halides. I. Long-range effects within the model hamiltonian approach
1994
A small-radius polaron model of the self-trapped hole (Vk-center) in alkali halide crystals is presented. Along with the usual contributions, the electronic polarization is also included in accordance with the electronic polaron theory of Toyozawa. It is shown that the exact solution of the problem within the Landau-Pekar approximation leads to multi-hole quantum states accompanied by the relevant electronic and lattice polarizations. As an example the KCl crystal is considered, for which the Vk-center structure as well as the self-trapping energy are computed. While solving our equations, the local symmetry of the defect is taken into account allowing us to consider a comparatively spread …
Thickness scaling of space-charge-limited currents in organic layers with field- or density-dependent mobility
2006
An exact solution is provided for the current density-voltage (J –V) characteristics of space-charge limited transport of a single carrier in organic layers with field-dependent mobility of the type μ (E) = μ0 exp (γ √E. The general scaling relationship for field-dependent mobility occurs in terms of the variables JL and V /L. For the density-dependence of the mobility found in organic field-effect transistor measurements, the thickness scaling occurs in terms of different variables, J1/βL and V /L. The proposed scaling is a useful test for distinguishing field- and carrier density-dependent mobility in disordered organic semiconductors. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)