Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

The Dynamics of a Rigid Body in Potential Flow with Circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte

Extended Classical Over-Barrier Model for Collisions of Highly Charged Ions with Conducting and Insulating Surfaces

We have extended the classical over-barrier model to simulate the neutralization dynamics of highly charged ions interacting under grazing incidence with conducting and insulating surfaces. Our calculations are based on simple model rates for resonant and Auger transitions. We include effects caused by the dielectric response of the target and, for insulators, localized surface charges. Characteristic deviations regarding the charge transfer processes from conducting and insulating targets to the ion are discussed. We find good agreement with previously published experimental data for the image energy gain of a variety of highly charged ions impinging on Au, Al, LiF and KI crystals.Comment: 32 pages http://pikp28.uni-muenster.de/~ducree

The role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials

We assert that the physics underlying the extraordinary light transmission (reflection) in nanostructured materials can be understood from rather general principles based on the formal scattering theory developed in quantum mechanics. The Maxwell equations in passive (dispersive and absorptive) linear media are written in the form of the Schr\"{o}dinger equation to which the quantum mechanical resonant scattering theory (the Lippmann-Schwinger formalism) is applied. It is demonstrated that the existence of long-lived quasistationary eigenstates of the effective Hamiltonian for the Maxwell theory naturally explains the extraordinary transmission properties observed in various nanostructured materials. Such states correspond to quasistationary electromagnetic modes trapped in the scattering structure. Our general approach is also illustrated with an example of the zero-order transmission of the TE-polarized light through a metal-dielectric grating structure. Here a direct on-the-grid solution of the time-dependent Maxwell equations demonstrates the significance of resonances (or trapped modes) for extraordinary light transmissioComment: 14 pages, 6 figures; Discussion in Section 4 expanded; typos corrected; a reference added; Figure 4 revise

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Microsecond Time-Resolved Absorption Spectroscopy Used to Study CO Compounds of Cytochrome bd from Escherichia coli

Cytochrome bd is a tri-heme (b558, b595, d) respiratory oxygen reductase that is found in many bacteria including pathogenic species. It couples the electron transfer from quinol to O2 with generation of an electrochemical proton gradient. We examined photolysis and subsequent recombination of CO with isolated cytochrome bd from Escherichia coli in oneelectron reduced (MV) and fully reduced (R) states by microsecond time-resolved absorption spectroscopy at 532-nm excitation. Both Soret and visible band regions were examined. CO photodissociation from MV enzyme possibly causes fast (t,1.5 ms) electron transfer from heme d to heme b595 in a small fraction of the protein, not reported earlier. Then the electron migrates to heme b558 (t,16 ms). It returns from the b-hemes to heme d with t,180 ms. Unlike cytochrome bd in the R state, in MV enzyme the apparent contribution of absorbance changes associated with CO dissociation from heme d is small, if any. Photodissociation of CO from heme d in MV enzyme is suggested to be accompanied by the binding of an internal ligand (L) at the opposite side of the heme. CO recombines with heme d (t,16 ms) yielding a transient hexacoordinate state (CO-Fe2+ -L). Then the ligand slowly (t,30 ms) dissociates from heme d. Recombination of CO with a reduced heme b in a fraction of the MV sample may also contribute to the 30-ms phase. In R enzyme, CO recombines to heme d (t,20 ms), some heme b558 (t,0.2–3 ms), and finally migrates from heme d to heme b595 (t,24 ms) in ,5% of the enzyme population. Data are consistent with the recent nanosecond study of Rappaport et al. conducted on the membranes at 640-nm excitation but limited to the Soret band. The additional phases were revealed due to differences in excitation and other experimental conditions

Tunneling mechanism of light transmission through metallic films

A mechanism of light transmission through metallic films is proposed, assisted by tunnelling between resonating buried dielectric inclusions. This is illustrated by arrays of Si spheres embedded in Ag. Strong transmission peaks are observed near the Mie resonances of the spheres. The interaction among various planes of spheres and interference effects between these resonances and the surface plasmons of Ag lead to mixing and splitting of the resonances. Transmission is proved to be limited only by absorption. For small spheres, the effective dielectric constant can be tuned to values close to unity and a method is proposed to turn the resulting materials invisible.Comment: 4 papges, 5 figure

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure