Equilibrium orbit analysis in a free-electron laser with a coaxial wiggler

An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and trajectories in the radially dependent wiggler. Simple analytical solutions are obtained in the radially-uniform-wiggler approximation and a formula for the derivative of the axial velocity $v_{\|}$ with respect to Lorentz factor $\gamma$ is derived. Results of numerical computations are presented and the characteristics of the equilibrium orbits are discussed. The third spatial harmonic of the coaxial wiggler field gives rise to group $III$ orbits which are characterized by a strong negative mass regime.Comment: 13 pages, 9 figures, to appear in phys. rev.

Drip and Mate Operations Acting in Test Tube Systems and Tissue-like P systems

The operations drip and mate considered in (mem)brane computing resemble the operations cut and recombination well known from DNA computing. We here consider sets of vesicles with multisets of objects on their outside membrane interacting by drip and mate in two different setups: in test tube systems, the vesicles may pass from one tube to another one provided they fulfill specific constraints; in tissue-like P systems, the vesicles are immediately passed to specified cells after having undergone a drip or mate operation. In both variants, computational completeness can be obtained, yet with different constraints for the drip and mate operations

How to detect level crossings without looking at the spectrum

We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians representable by matrices. This approach provides a pedagogical introduction to (avoided) crossings, is capable of handling realistic Hamiltonians analytically, and offers a way to visualize crossings which is sometimes superior to that provided by the spectrum. We illustrate the method using the Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground state hydrogen atom in a uniform magnetic field.Comment: Accepted for publication in the American Journal of Physic

Diffractive Vector Meson Photoproduction from Dual String Theory

We study diffractive vector meson photoproduction using string theory via AdS/CFT. The large $s$ behavior of the cross sections for the scattering of the vector meson $V$ on a proton is dominated by the soft Pomeron, $\sigma_V\sim s^{2\epsilon-2\alpha'_P/B}$, where from the string theory model of \cite{nastase2}, $\epsilon$ is approximately 1/7 below 10 GeV, and 1/11 for higher, but still sub-Froissart, energies. This is due to the production of black holes in the dual gravity. In $\phi$-photoproduction the mesonic Regge poles do not contribute, so that we deal with a pure Pomeron contribution. This allows for an experimental test. At the gauge theory "Planck scale" of about 1-2 GeV, the ratios of the soft Pomeron contributions to the photoproduction cross-sections of different vector mesons involve not only the obvious quark model factors, but also the Boltzmann factors $e^{-4 M_V/T_0}$, with $T_0$ the temperature of the dual black hole. The presence of these factors is confirmed in the experimental data for $\rho, \omega, \phi, J/\psi,$ and $\psi(2S)$ photoproduction and is compatible with the meager $\Upsilon$ photoproduction data. Throughout, we use vector meson dominance, and from the data we obtain $T_0$ of about $1.3 GeV$, i.e. the gauge theory "Planck scale," as expected. The ratio of the experimental soft Pomeron onset scale $\hat{E}_R\sim 9$ GeV and of the gauge theory Planck scale, $T_0 \sim 1.3$ GeV conforms to the theoretical prediction of $N_c^2/N_c^{1/4}$.Comment: 17 pages, 1 figure, late

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

Dynamic ductile to brittle transition in a one-dimensional model of viscoplasticity

We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow above a well defined yield stress. In this paper, we describe a first step in exploring the implications of these models for theories of fracture and related phenomena. We consider a one dimensional problem of decohesion from a substrate of a membrane that obeys the viscoplastic constitutive equations that we have constructed. We find that, quite generally, when the yield stress becomes smaller than some threshold value, the energy required for steady decohesion becomes a non-monotonic function of the decohesion speed. As a consequence, steady state decohesion at certain speeds becomes unstable. We believe that these results are relevant to understanding the ductile to brittle transition as well as fracture stability.Comment: 10 pages, REVTeX, 12 postscript figure

Dynamic stability of crack fronts: Out-of-plane corrugations

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.Comment: 5 pages, 2 figures + supplementary informatio

Learning from Minimum Entropy Queries in a Large Committee Machine

In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization error decreases exponentially with the number of training examples, providing a significant improvement over the algebraic decay for random examples. The connection between entropy and generalization error in multi-layer networks is discussed, and a computationally cheap algorithm for constructing queries is suggested and analysed.Comment: 4 pages, REVTeX, multicol, epsf, two postscript figures. To appear in Physical Review E (Rapid Communications

Growth and electronic and magnetic structure of iron oxide films on Pt(111)

Ultrathin (111)-oriented polar iron oxide films were grown on a Pt(111) single crystal either by the reactive deposition of iron or oxidation of metallic iron monolayers. These films were characterized using low energy electron diffraction, scanning tunneling microscopy and conversion electron Mossbauer spectroscopy. The reactive deposition of Fe led to the island growth of Fe3O4, in which the electronic and magnetic properties of the bulk material were modulated by superparamagnetic size effects for thicknesses below 2 nm, revealing specific surface and interface features. In contrast, the oxide films with FeO stoichiometry, which could be stabilized as thick as 4 nm under special preparation conditions, had electronic and magnetic properties that were very different from their bulk counterpart, w\"ustite. Unusual long range magnetic order appeared at room temperature for thicknesses between three and ten monolayers, the appearance of which requires severe structural modification from the rock-salt structure.Comment: 17 pages, 6 figures, 50 reference

Frictional sliding without geometrical reflection symmetry

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.Comment: 14 pages, 5 figures + Supplementary Material. Minor change in the title, extended analysis in the second par