Search results for "Exact solutions in general relativity"
showing 10 items of 70 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…
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)
Non-Markovian master equation for the XX central spin model
2008
The non-Markovian correlated projection operator technique is applied to the model of a central spin coupled to a spin bath through non uniform XX Heisenberg coupling. The second order results of the Nakajima-Zwanzig and of the time-convolutionless methods are compared with the exact solution considering a fully polarized initial bath state.
Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering
2017
Abstract The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.
Exact solution of generalized Tavis - Cummings models in quantum optics
1996
Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogen…