Search results for "Values"
showing 10 items of 1365 documents
On the geometry of Killing and conformal tensors
2006
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues, the condition to be a Killing or a conformal tensor is characterized in terms of its underlying almost-product structure. A canonical expression for the metrics admitting these kinds of symmetries is also presented. The space-time cases 1+3 and 2+2 are analyzed in more detail. Starting from this approach to Killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum Petrov-Bel type…
Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
2010
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as…
Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well
2015
Nonlocal Hamiltonian-type operators, like e.g. fractional and quasirelativistic, seem to be instrumental for a conceptual broadening of current quantum paradigms. However physically relevant properties of related quantum systems have not yet received due (and scientifically undisputable) coverage in the literature. In the present paper we address Schr\"{o}dinger-type eigenvalue problems for $H=T+V$, where a kinetic term $T=T_m$ is a quasirelativistic energy operator $T_m = \sqrt{-\hbar ^2c^2 \Delta + m^2c^4} - mc^2$ of mass $m\in (0,\infty)$ particle. A potential $V$ we assume to refer to the harmonic confinement or finite well of an arbitrary depth. We analyze spectral solutions of the per…
Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk…
2019
A deformation of a disk D of radius r is described as follows: Let two disks D1 and D2 have the same radius r, and let the distance between the two disk centers be 2a, 0 ≤ a ≤ r. The deformation transforms D into the intersection D1 ∩ D2. This deformation is parametrized by e = a/r. For e = 0, there is no deformation, and the deformation starts when e, starting from 0, increases, transforming the disk into a lens. Analytic results are obtained for the eigenvalues of Helmholtz equation with zero Dirichlet boundary condition to the lowest order in e for this deformation. These analytic results are obtained via a Hamiltonian method for solving the Helmholtz equation with zero Dirichlet boundar…
Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems
1991
In order to describe the type of nonlinear eigenvalue problems we are going to discuss, consider a densely defined closed linear operator T in a real Hilbert space H and let H1 be the Hilbert space which consists of the domain of T together with the graph norm. Also, let H 1 * be the dual space of H1 and denote the dual operator corresponding to T: H1 → H by T’:H → H 1 * . Since H1 is dense in H, we may view H as a subspace of H1, and then the scalar product (·,·) on H and the dual pairing on H1 × H 1 * coincide on H1 × H.
Random polarisations of the dipoles
2012
We extend the dipole formalism for massless and massive partons to random polarisations of the external partons. The dipole formalism was originally formulated for spin-summed matrix elements and later extended to individual helicity eigenstates. For efficiency reasons one wants to replace the spin sum by a smooth integration over additional variables. This requires the extension of the dipole formalism to random polarisations. In this paper we derive the modified subtraction terms. We only modify the real subtraction terms, the integrated subtraction terms do not require any modifications.
Confinement of Lévy flights in a parabolic potential and fractional quantum oscillator
2018
We study L\'evy flights confined in a parabolic potential. This has to do with a fractional generalization of an ordinary quantum-mechanical oscillator problem. To solve the spectral problem for the fractional quantum oscillator, we pass to the momentum space, where we apply the variational method. This permits one to obtain approximate analytical expressions for eigenvalues and eigenfunctions with very good accuracy. The latter fact has been checked by a numerical solution to the problem. We point to the realistic physical systems ranging from multiferroics and oxide heterostructures to quantum chaotic excitons, where obtained results can be used.
Some analytical considerations on two-scale relations
1994
Scaling functions that generate a multiresolution analysis (MRA) satisfy, among other conditions, the so-called «two-scale relation» (TSR). In this paper we discuss a number of properties that follow from the TSR alone, independently of any MRA: position of zeros (mainly for continuous scaling functions), existence theorems (using fixed point and eigenvalue arguments) and orthogonality relation between integer translates. © 1994 Società Italiana di Fisica.
Effect of Topological Structure and Coupling Strength in Weighted Multiplex Networks
2018
Algebraic connectivity (second smallest eigenvalue of the supra-Laplacian matrix of the underlying multilayer network) and inter-layer coupling strength play an important role in the diffusion processes on the multiplex networks. In this work, we study the effect of inter-layer coupling strength, topological structure on algebraic connectivity in weighted multiplex networks. The results show a remarkable transition in the value of algebraic connectivity from classical cases where the inter-layer coupling strength is homogeneous. We investigate various topological structures in multiplex networks using configuration model, the Barabasi-Albert model (BA) and empirical data-set of multiplex ne…
Towards a quantitative comparison between global and local stability analysis
2017
A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed spher…