The Midpoint Rule as a Variational--Symplectic Integrator. I. Hamiltonian Systems

Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the foundation for such applications. The midpoint rule for Hamilton's equations is examined from the perspectives of variational and symplectic integrators. It is shown that the midpoint rule preserves the symplectic form, conserves Noether charges, and exhibits excellent long--term energy behavior. The energy behavior is explained by the result, shown here, that the midpoint rule exactly conserves a phase space function that is close to the Hamiltonian. The presentation includes several examples.Comment: 11 pages, 8 figures, REVTe

Three-dimensional numerical simulation of 1GeV/Nucleon U92+ impact against atomic hydrogen

The impact of 1GeV/Nucleon U92+ projectiles against atomic hydrogen is studied by direct numerical resolution of the time-dependent wave equation for the atomic electron on a three-dimensional Cartesian lattice. We employ the fully relativistic expressions to describe the electromagnetic fields created by the incident ion. The wave equation for the atom interacting with the projectile is carefully derived from the time-dependent Dirac equation in order to retain all the relevant terms.Comment: 12 pages and 7 figures included in the tex

Contribution of the magnetic resonance to the third harmonic generation from a fishnet metamaterial

We investigate experimentally and theoretically the third harmonic generated by a double-layer fishnet metamaterial. To unambiguously disclose most notably the influence of the magnetic resonance, the generated third harmonic was measured as a function of the angle of incidence. It is shown experimentally and numerically that when the magnetic resonance is excited by pump beam, the angular dependence of the third harmonic signal has a local maximum at an incidence angle of {\theta} \simeq 20{\deg}. This maximum is shown to be a fingerprint of the antisymmetric distribution of currents in the gold layers. An analytical model based on the nonlinear dynamics of the electrons inside the gold shows excellent agreement with experimental and numerical results. This clearly indicates the difference in the third harmonic angular pattern at electric and magnetic resonances of the metamaterial.Comment: 7 pages, 5 figure

Excitation of weakly bound Rydberg electrons by half-cycle pulses

The interaction of a weakly bound Rydberg electron with an electromagnetic half-cycle pulse (HCP) is described with the help of a multidimensional semiclassical treatment. This approach relates the quantum evolution of the electron to its underlying classical dynamics. The method is nonperturbative and is valid for arbitrary spatial and temporal shapes of the applied HCP. On the basis of this approach angle- and energy-resolved spectra resulting from the ionization of Rydberg atoms by HCPs are analyzed. The different types of spectra obtainable in the sudden-impact approximation are characterized in terms of the appearing semiclassical scattering phenomena. Typical modifications of the spectra originating from finite pulse effects are discussed.Comment: Submitted to Phys. Rev.

Ion Collisions in Very Strong Electric Fields

A Classical Trajectory Monte Carlo (CTMC) simulation has been made of processes of charge exchange and ionization between an hydrogen atom and fully stripped ions embedded in very strong static electric fields ($O(10^{10}$ V/m$)$), which are thought to exist in cosmic and laser--produced plasmas. Calculations show that the presence of the field affects absolute values of the cross sections, enhancing ionization and reducing charge exchange. Moreover, the overall effect depends upon the relative orientation between the field and the nuclear motion. Other features of a null-field situation, such as scaling laws, are revisited.Comment: Latex, 13 pages, 11 figures (available upon request), to be published in Journal of Physics

Toll-like receptor 4 in experimental kidney transplantation: early mediator of endogenous danger signals

The role of toll-like receptors (TLRs) has been described in the pathogenesis of renal ischemia/reperfusion injury, but data on the expression and function of TLR4 during renal allograft damage are still scarce. We analyzed the expression of TLR4 in an experimental rat model 6 and 28 days after allogeneic kidney transplantation in comparison to control rats and rats after syngeneic transplantation. On day 6, a significant induction in TLR4 expression - restricted to the glomerular compartment - was found in acute rejecting allografts only. TLR4 expression strongly correlated with renal function, and TLR4 induction was accompanied by a significant increase in CC chemokine expression within the graft as well as in urinary CC chemokine excretion. TLR4 induction may be caused by an influx of macrophages as well as TLR4-expressing intrinsic renal cells. Fibrinogen deposition in renal allografts correlated with renal TLR4 expression and may act as a potent stimulator of chemokine release via TLR4 activation. This study provides, for the first time, data about the precise intrarenal localization and TLR4 induction after experimental kidney transplantation. It supports the hypothesis that local TLR4 activation by endogenous ligands may be one pathological link from unspecific primary allograft damage to subsequent chemokine release, infiltration and activation of immune cells leading to deterioration of renal function and induction of renal fibrosis. Copyright (c) 2012 S. Karger AG, Base

On the absence of bound-state stabilization through short ultra-intense fields

We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect on the atom. For short pulses we find almost complete ionization as the field strength increases.Comment: 34 pages Late