28,040 research outputs found
Asymptotic analysis of a system of algebraic equations arising in dislocation theory
The system of algebraic equations given by\ud
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\ud
\ud
appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole.\ud
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We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n -> ∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment but, up to corrections of logarithmic order, it also leads to a differential equation.\ud
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The continuum approximation is only valid for i not too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem
Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity
The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and , the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of for which it is close to the primary bifurcation from the normal state. These values of form a curve in the -plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]
Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
A class of Brownian dynamics algorithms for stochastic reaction-diffusion
models which include reversible bimolecular reactions is presented and
analyzed. The method is a generalization of the --\newrho model for
irreversible bimolecular reactions which was introduced in [arXiv:0903.1298].
The formulae relating the experimentally measurable quantities (reaction rate
constants and diffusion constants) with the algorithm parameters are derived.
The probability of geminate recombination is also investigated.Comment: 16 pages, 13 figures, submitted to SIAM Appl Mat
Analysis of Brownian dynamics simulations of reversible biomolecular reactions
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the λ-rho model for irreversible bimolecular reactions which was introduced in [11]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated
Quantifying fusion born ion populations in magnetically confined plasmas using ion cyclotron emission
Ion cyclotron emission (ICE) offers unique promise as a diagnostic of the
fusion born alpha-particle population in magnetically confined plasmas.
Pioneering observations from JET and TFTR found that ICE intensity
scales approximately linearly with the measured neutron flux from fusion
reactions, and with the inferred concentration, , of fusion-born
alpha-particles confined within the plasma. We present fully nonlinear
self-consistent kinetic simulations that reproduce this scaling for the first
time. This resolves a longstanding question in the physics of fusion
alpha-particle confinement and stability in MCF plasmas. It confirms the
magnetoacoustic cyclotron instability (MCI) as the likely emission mechanism
and greatly strengthens the basis for diagnostic exploitation of ICE in future
burning plasmas
Real-Time Cavity QED with Single Atoms
The combination of cold atoms and large coherent coupling enables investigations in a new regime in cavity QED with single-atom trajectories monitored in real time with high signal-to-noise ratio. The underlying “vacuum-Rabi” splitting is clearly reflected in the frequency dependence of atomic transit signals recorded atom by atom, with evidence for mechanical light forces for intracavity photon number <1. The nonlinear optical response of one atom in a cavity is observed to be in accord with the one-atom quantum theory but at variance with semiclassical predictions
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