scholarly journals Spin driven motion in intense spacetime wave geometries

2002 ◽  
pp. 77-92 ◽  
Author(s):  
D.A. Burton ◽  
R.W. Tucker ◽  
C. Wang
Keyword(s):  
Plane Wave ◽  
Compact Support ◽  
Dynamical Behavior ◽  
Massive Particle ◽  
Multipole Expansion ◽  
Dipole Approximation ◽  
First Order ◽  
Einstein Vacuum ◽  
Plane Wave Background ◽  
Arbitrary Intensity

The motion of a massive particle with intrinsic spin in a gravitational Einstein vacuum plane wave background is explored using the pole-dipole approximation to the Dixon multipole expansion for matter with compact support. Motivated by application to astrophysical processes the dynamical behavior of the spin and particle motion is described by numerically solving a system of non-linear first order ordinary differential equations. Some results are displayed in a reference frame adapted to the transverse nature of a monochromatic polarised gravitational wave of arbitrary intensity. .

scholarly journals QUANTUM LARMOR RADIATION FROM A MOVING CHARGE IN AN ELECTROMAGNETIC PLANE WAVE BACKGROUND

2012 ◽  
Vol 27 (24) ◽  
pp. 1250142 ◽  
Author(s):  
GEN NAKAMURA ◽  
KAZUHIRO YAMAMOTO
Keyword(s):  
Plane Wave ◽  
Quantum Effect ◽  
Radiation Energy ◽  
Theoretical Formula ◽  
Total Radiation ◽  
Electromagnetic Plane Wave ◽  
First Order ◽  
Total Radiation Energy ◽  
Plane Wave Background ◽  
Electromagnetic Plane

We extend our previous work [Phys. Rev. D83, 045030 (2011)], which investigated the first-order quantum effect in the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field. Specifically, we investigate the quantum Larmor radiation from a moving charge in a monochromatic electromagnetic plane wave background based on the scalar quantum electrodynamics at the lowest order of the perturbation theory. Using the in–in formalism, we derive the theoretical formula of the total radiation energy from a charged particle in the initial states being at rest and being in a relativistic motion. Expanding the theoretical formula in terms of the Planck constant ℏ, we obtain the first-order quantum effect on the Larmor radiation. The quantum effect generally suppresses the total radiation energy compared with the prediction of the classical Larmor formula, which is a contrast to the previous work. The reason is explained by the fact that the radiation from a moving charge in a monochromatic electromagnetic plane wave is expressed in terms of the inelastic collisions between an electron and photons of the background electromagnetic waves.

scholarly journals An overview of branes in the plane wave background

2003 ◽  
Vol 20 (12) ◽  
pp. S567-S573 ◽  
Author(s):  
Kostas Skenderis ◽  
Marika Taylor
Keyword(s):  
Plane Wave ◽  
Plane Wave Background

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

scholarly journals Excitation of Atomic Hydrogen by Proton Impact in the Presence of a Resonant Laser Field Using the First Order Magnus Approximation

1992 ◽  
Vol 45 (1) ◽  
pp. 47 ◽  
Author(s):  
Bhupat Sharma ◽  
Man Mohan
Keyword(s):  
Laser Beam ◽  
Computer Time ◽  
Dipole Approximation ◽  
Collision Dynamics ◽  
Hydrogen Atoms ◽  
Close Coupling ◽  
First Order ◽  
Resonant Laser ◽  
Atom Interaction ◽  
Transverse Polarisation

We consider proton collisions from hydrogen atoms in the presence of a laser beam (taken in the electric dipole approximation) that resonantly (or nearly resonantly) excites the hydrogen atoms from the Is to the 2p state. The laser beam is linearly polarised with polarisation either parallel (longitudinal) or perpendicular (transverse) to the direction of incidence of the proton. A non-perturbative quasi-energy approach is used to describe the laser-atom interaction, while the first-order Magnus approximation is used to describe the collision dynamics in the presence of the nearly resonant laser beam. We have calculated the integrated cross section o-(2s} for the excitation of the 2s state. It is found that 0-(2s} is small for longitudinal polarisation, as compared with transverse polarisation. We have also compared our field-free results obtained by using the first-order Magnus approximation to that obtained by the close-coupling approximation. Although both methods give excellent results, the former method is quite demanding in terms of computer time.

scholarly journals Exact and approximate reflection/transmission responses from a layer containing vertical fractures

2020 ◽  
Vol 222 (1) ◽  
pp. 260-288
Author(s):  
Song Jin ◽  
Alexey Stovas
Keyword(s):  
Plane Wave ◽  
Layer Thickness ◽  
Finite Thickness ◽  
Subsurface Layer ◽  
Symmetry Plane ◽  
Middle Layer ◽  
Second Order ◽  
First Order ◽  
Background Medium ◽  
Vertical Fractures

SUMMARY Analyses of vertical fractures are of great interest in characterizing the fluid flow and minimum in situ stress direction in reservoirs. Long-wavelength equivalent orthorhombic (ORT) media typically characterize the anisotropy induced by a set of vertical parallel fractures or two sets of vertical and mutually orthogonal fractures embedded into a transversely isotropic medium with a vertical symmetry axis (VTI). Reflection and transmission (R/T) responses quantify wave amplitude variations in 1-D media and help to reveal the model property enclosing the heterogeneity. Conventionally, the R/T responses are analysed for an interface bounded by two half-spaces. However, for a plane wave travelling through a subsurface layer, the wave scattering effects at the top and bottom of the layer interact with each other. For a continuous infinite ORT space cut in two halves along the horizontal symmetry plane, we focus on the plane wave R/T responses from an ORT layer that is placed between the two halves, where the azimuths of the vertical symmetry plane in the layer and in the upper and lower half-spaces are identical. The R/T coefficient modelling method can be found in many publications for the ORT layer with an arbitrary finite thickness. We decompose the exact R/T coefficients into series expansions that correspond to different orders of intrabed multiples in the ORT layer. Under the weak-contrast assumption for the ORT half-spaces and the ORT layer, we use the anisotropic background medium to obtain the first-order R/T coefficient approximations and second-order reflectivity approximations. There is no constraint for the middle layer thickness in the obtained first-order reflectivity approximations. In the proposed first-order transmissivity approximations and second-order reflectivity approximations, the layer thickness is assumed to be thin to obtain appropriate approximations for a few wave modes. The isotropic background medium is also considered for weakly anisotropic models to obtain simpler approximations that facilitate parametric analyses. For the ORT layer with its thickness much smaller than the propagating wave's wavelength, the influences of the layer thickness on R/T coefficients can be inspected conveniently from the derived approximations. Particularly, the R/T coefficients are analysed for the model which would be a homogeneous VTI medium, if the vertical parallel fractures were absent from the middle layer. Numerical tests demonstrate that the proposed R/T coefficient approximations perform well for the thin ORT layer. The approximation accuracy decreases when the thin layer thickness increases.

NEW FORMULATION FOR NON-EQUILIBRIUM SOLVATION: SPECTRAL SHIFTS AND CAVITY RADII OF 6-PROPANOYL-2-(N,N-DIMETHYLAMINO) NAPHTHALENE AND 4-(N,N-DIMETHYLAMINO) BENZONITRILE

2006 ◽  
Vol 05 (spec01) ◽  
pp. 355-374 ◽  
Author(s):  
YAO HUANG ◽  
XIANG-YUAN LI ◽  
KE-XIANG FU ◽  
QUAN ZHU
Keyword(s):  
Density Functional ◽  
Multipole Expansion ◽  
Dipole Approximation ◽  
Point Dipole ◽  
Functional Theory ◽  
Spectral Shifts ◽  
Point Dipole Approximation ◽  
Accessible Surface ◽  
New Formulation ◽  
Solvent Accessible Surface

In the present work, the new formulations describing spectral shifts by the authors have been introduced and employed to investigate two dye molecules, 6-propanoyl-2-(N,N-dimethylamino) naphthalene and 4-(N,N-dimethylamino) benzonitrile. From the viewpoints of the authors, the cavity radii were overestimated owing to the errors existing in the traditional models. Slightly differing from the results by other authors in the past, this work fits the cavity radii to the values of ~4.5 Å for 6-propanoyl-2-(N,N-dimethylamino) naphthalene and ~3.2 Å for 4-(N,N-dimethylamino) benzonitrile. In the fittings, both point dipole approximation and multipole expansion methods are employed. The calculations of the excited states are performed by means of the time-dependent density functional theory. Comparing the fitted cavity radii from the experimental spectra with those estimated from the molecular volumes by some well-known procedures such as COSMO and PCM, we find that the new formulations give fairly satisfactory results. By taking an atomic ion as an example, the authors argue that the Onsager radii recommended by some popular procedures are greatly exaggerated. The cavity radius derived simply from the volume encompassed by the solvent-accessible surface, without any addition of other parts, is suggested for application.

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