Search results for "continuum"

Fractional mechanical model for the dynamics of non-local continuum

2009

In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both…

The Vlasov Limit for a System of Particles which Interact with a Wave Field

2008

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.

Cross-sections for (e, 3e) collisions on helium: the DS6C wavefunction

2006

A dynamically screened product of six pairwise Coulomb functions (DS6C) is used as an analytic approximation to describe the four-body Coulomb continuum state produced by electron-impact full fragmentation of helium. Good agreement is obtained with experimental data close to threshold, where four-body effects are expected to be important. Even for the high impact energy of 640 eV, four-body effects still play a role in deciding the shape of multi-differential cross-sections.

Modeling electron dynamics coupled to continuum states in finite volumes with absorbing boundaries

2015

arXiv:1409.1689v1

Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover w…

2013

The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-d…

Isomorphic controllers and Dynamic Tuning: invariant fingering over a tuning continuum

2007

Andrew Milne, William Sethares, and James Plamondon *Department of Music University of Jyvaskyla Finland andymilne@tonalcentre.org **Department of Electrical and Computer Engineering University of Wisconsin-Madison Madison, WI 53706 USA sethares@ece.wisc.edu †Thumtronics Inc. 6911 Thistle Hill Way Austin, TX 78754 USA jim@thumtronics.com Isomorphic Controllers and Dynamic Tuning: Invariant Fingering over a Tuning Continuum

Controlling ionization products through laser-induced continuum structure

1998

Simultaneous uvbyβ Photometry and Hα Spectroscopy of Be Stars in Open Clusters

1994

The usual methods of spectral clasification, equivalent widths of Balmer lines or photometric calibrations are not suitable for the determination of the astrophysical parameters of the underlying star in Be-type objects. The spectrum is distorted by the circumstellar envelope lines, while the contribution of the envelope continuum radiation contaminates the photometric indices.

Theory of bound polarons in oxide compounds

2001

We present a multilateral theoretical study of bound polarons in oxide compounds MgO and \alpha-Al_2O_3 (corundum). A continuum theory at arbitrary electron-phonon coupling is used for calculation of the energies of thermal dissociation, photoionization (optically induced release of an electron (hole) from the ground self-consistent state), as well as optical absorption to the non-relaxed excited states. Unlike the case of free strong-coupling polarons, where the ratio \kappa of the photoionization energy to the thermal dissociation energy was shown to be always equal to 3, here this ratio depends on the Froehlich coupling constant \alpha and the screened Coulomb interaction strength \beta.…

Simultaneous Measurement ofβ−Decay to Bound and Continuum Electron States

2005

We report the first measurement of a ratio {lambda}{sub {beta}{sub b}}/{lambda}{sub {beta}{sub c}} of bound-state ({lambda}{sub {beta}{sub b}}) and continuum-state ({lambda}{sub {beta}{sub c}}) {beta}{sup -}-decay rates for the case of bare {sup 207}Tl{sup 81+} ions. These ions were produced at the GSI fragment separator FRS by projectile fragmentation of a {sup 208}Pb beam. After in-flight separation with the B{rho}-{delta}E-B{rho} method, they were injected into the experimental storage-ring ESR at an energy of 400.5A MeV, stored, and electron cooled. The number of both the {sup 207}Tl{sup 81+} ions and their bound-state {beta}{sup -}-decay daughters, hydrogenlike {sup 207}Pb{sup 81+} ion…