Search results for "Computational Mathematic"
showing 10 items of 987 documents
Erratum: An Inverse Backscatter Problem for Electric Impedance Tomography
2011
We fix an incorrect statement from our paper [M. Hanke, N. Hyvonen, and S. Reusswig, SIAM J. Math. Anal., 41 (2009), pp. 1948–1966] claiming that two different perfectly conducting inclusions necessarily have different backscatter in impedance tomography. We also present a counterexample to show that this kind of nonuniqueness does indeed occur.
An inverse problem for the fractional Schrödinger equation in a magnetic field
2020
This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrodinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely many measurements of solutions taken in arbitrary open subsets of the exterior. The proof is based on Alessandrini's identity and the Runge approximation property, thus generalizing some previous works on the fractional Laplacian. Moreover, we show with a simple model that the FMSE relates to a long jump random walk with weights.
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…
Corrective meshless particle formulations for time domain Maxwell's equations
2007
AbstractIn this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell's curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consiste…
Ab initio calculations for the F-center transfer and R centers in SrF2
2013
We have simulated the F-center transfer and R center in SrF2 crystal by using density functional theory (DFT) with a hybrid B3PW description of exchange and correlation. Our calculations show that the F-center diffusion barrier is equal to 1.84 eV. During the F-center transfer, the trapped electron is more delocalized than that in the regular F-center case, and the gap between defect level and conduction bands (CB) in the a-spin state decreases. The formation energy calculations of R center show the trend of F centers to aggregate in SrF2. During the F-center aggregation, a considerable covalency forms between two neighboring fluorine vacancies with trapped electrons. Three incompletely pai…
Nature of the ring-closure process along the rearrangement of octa-1,3,5,7-tetraene to cycloocta-1,3,5-triene from the perspective of the electron lo…
2011
We analyze the behavior of the energy profile of the ring-closure process for the transformation of (3Z,5Z)-octa-1,3,5,7-tetraene 5 to (1Z,3Z,5Z)-cycloocta-1,3,5-triene 6 through a combination of electron localization function (ELF) and catastrophe theory (CT). From this analysis, concepts such as bond breaking/forming processes, formation/annihilation of lone pairs, and other electron pair rearrangements arise naturally through the reaction progress simply in terms of the different ways of pairing up the electrons. A relationship between the topology and the nature of the bond breaking/forming processes along this rearrangement is reported. The different domains of structural stability of …
A two-scale approach to electron correlation in multiconfigurational perturbation theory.
2014
We present a new approach for the calculation of dynamic electron correlation effects in large molecular systems using multiconfigurational second-order perturbation theory (CASPT2). The method is restricted to cases where partitioning of the molecular system into an active site and an environment is meaningful. Only dynamic correlation effects derived from orbitals extending over the active site are included at the CASPT2 level of theory, whereas the correlation effects of the environment are retrieved at lower computational costs. For sufficiently large systems, the small errors introduced by this approximation are contrasted by the substantial savings in both storage and computational de…
High order normal form construction near the elliptic orbit of the Sitnikov problem
2011
We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form up to 40th order in Cartesian coordinates.
Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)
2017
Let be a bounded smooth domain in RN. We prove a general existence result of least energy solutions and least energy nodal ones for the problem −u = f(x, u) in u = 0 on ∂ (P) where f is a Carathéodory function. Our result includes some previous results related to special cases of f . Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type f(x, u) = λ|u| s−2u − μ|u| r−2u, with s, r ∈ (1, 2) and λ,μ > 0.
Singular quasilinear elliptic systems involving gradient terms
2019
Abstract In this paper we establish the existence of at least one smooth positive solution for a singular quasilinear elliptic system involving gradient terms. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem.