Search results for "singularity."

Anharmonic effects on the dynamic behavior’s of Klein Gordon model’s

2021

Abstract This work completes and extends the Ref. Tchakoutio Nguetcho et al. (2017), in which we have focused our attention only on the dynamic behavior of gap soliton solutions of the anharmonic Klein-Gordon model immersed in a parameterized on-site substrate potential. We expand our work now inside the permissible frequency band. These considerations have crucial effects on the response of nonlinear excitations that can propagate along this model. Moreover, working in the allowed frequency band is not only interesting from a physical point of view, it also provides an extraordinary mathematical model, a new class of differential equations possessing vital parameters and vertical singular …

Analytic solutions and Singularity formation for the Peakon b--Family equations

2012

This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity a…

Spurious Singularities in Quasipotential Amplitudes

1973

Spatial multifractal properties of wave packets in the Anderson model of localization.

1993

The multifractal properties of electronic wave functions in disordered samples are investigated. In a given energy range all eigenstates are determined for the same disorder configuration in the Anderson model of localization. It is shown that the singularity spectrum and the generalized dimensions change only slowly with energy, aside from statistical fluctuations. More important, the wave packet constructed by linear combination of the eigenstates shows quantitatively the same multifractal properties. Consequences for the transport properties of electronic states in disordered systems are discussed.

RADIATION OF THE INNER HORIZON OF THE REISSNER–NORDSTRÖM BLACK HOLE

2005

Despite of over thirty years of research of the black hole thermodynamics our understanding of the possible role played by the inner horizons of Reissner-Nordstr\"om and Kerr-Newman black holes in black hole thermodynamics is still somewhat incomplete: There are derivations which imply that the temperature of the inner horizon is negative and it is not quite clear what this means. Motivated by this problem we perform a detailed analysis of the radiation emitted by the inner horizon of the Reissner-Nordstr\"om black hole. As a result we find that in a maximally extended Reissner-Nordstr\"om spacetime virtual particle-antiparticle pairs are created at the inner horizon of the Reissner-Nordstr…

Collision orbits in the oblate planet problem

1984

Some of the properties of the oblate planet problem are derived. We use the technique of blowing up the singularity to study the collision orbits. We define some families of them in terms of their asymptotic behavior.

Nonlinear Critical Layers in Barotropic Stability

1991

Abstract Applying the method of matched asymptotic expansions (MAE) to the shallow water equations on a rotating sphere, the structure of critical layers that occur in the linear and inviscid analysis of neutral disturbances of barotropic zonal flows is investigated, assuming that the critical layers are controlled by nonlinearity rather than viscosity or nonparallel flow effects. It turns out that nonlinearity is insufficient to resolve the critical layer singularity completely. It suffices however to connect linear and nondissipative solutions across critical latitudes.

Nonperturbative approach for the electronic Casimir-Polder effect in a one-dimensional semiconductor

2013

We present the electronic Casimir-Polder effect for a system consisting of two impurities on a one-dimensional semiconductor quantum wire. Due to the charge transfer from the impurity to a one-dimensional conduction band, the impurity states are dressed by a virtual cloud of the electron field. The attractive electronic Casimir force arises due to the overlap of the virtual clouds. The Van Hove singularity causes the persistent bound state (PBS) to appear below the band edge even when the bare impurity state energy is above the band edge. Since the decay rate of the virtual cloud of the PBS in space is small, the Casimir force can be of a very long range. While the overlap of the electronic…

Topological charge selection rule for phase singularities

2009

We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.

Symmetry breaking and singularity structure in Bose-Einstein condensates

2012

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the tra…