Nonlinear surface waves on the plasma-vacuum interface

In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagate along the plasma-vacuum interface, when it is linearly weakly stable. Following the approach of Ali and Hunter, we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive a blow up criterion.Comment: arXiv admin note: text overlap with arXiv:1305.5327 by other author

Co-periodic stability of periodic waves in some Hamiltonian PDEs

International audienceThe stability theory of periodic traveling waves is much less advanced than for solitary waves, which were first studied by Boussinesq and have received a lot of attention in the last decades. In particular, despite recent breakthroughs regarding periodic waves in reaction-diffusion equations and viscous systems of conservation laws [Johnson–Noble–Rodrigues–Zumbrun, Invent math (2014)], the stability of periodic traveling wave solutions to dispersive PDEs with respect to 'arbitrary' perturbations is still widely open in the absence of a dissipation mechanism. The focus is put here on co-periodic stability of periodic waves, that is, stability with respect to perturbations of the same period as the wave, for KdV-like systems of one-dimensional Hamiltonian PDEs. Fairly general nonlinearities are allowed in these systems, so as to include various models of mathematical physics, and this precludes complete integrability techniques. Stability criteria are derived and investigated first in a general abstract framework, and then applied to three basic examples that are very closely related, and ubiquitous in mathematical physics, namely, a quasilinear version of the generalized Korteweg–de Vries equation (qKdV), and the Euler–Korteweg system in both Eulerian coordinates (EKE) and in mass Lagrangian coordinates (EKL). Those criteria consist of a necessary condition for spectral stability , and of a sufficient condition for orbital stability. Both are expressed in terms of a single function, the abbreviated action integral along the orbits of waves in the phase plane, which is the counterpart of the solitary waves moment of instability introduced by Boussinesq. However, the resulting criteria are more complicated for periodic waves because they have more degrees of freedom than solitary waves, so that the action is a function of N + 2 variables for a system of N PDEs, while the moment of instability is a function of the wave speed only once the endstate of the 1 solitary wave is fixed. Regarding solitary waves, the celebrated Grillakis–Shatah– Strauss stability criteria amount to looking for the sign of the second derivative of the moment of instability with respect to the wave speed. For periodic waves, stability criteria involve all the second order, partial derivatives of the action. This had already been pointed out by various authors for some specific equations, in particular the generalized Korteweg–de Vries equation — which is special case of (qKdV) — but not from a general point of view, up to the authors' knowledge. The most striking results obtained here can be summarized as: an odd value for the difference between N and the negative signature of the Hessian of the action implies spectral instability, whereas a negative signature of the same Hessian being equal to N implies orbital stability. Furthermore, it is shown that, when applied to the Euler–Korteweg system, this approach yields several interesting connexions between (EKE), (EKL), and (qKdV). More precisely, (EKE) and (EKL) share the same abbreviated action integral, which is related to that of (qKdV) in a simple way. This basically proves simultaneous stability in both formulations (EKE) and (EKL) — as one may reasonably expect from the physical point view —, which is interesting to know when these models are used for different phenomena — e.g. shallow water waves or nonlinear optics. In addition, stability in (EKE) and (EKL) is found to be linked to stability in the scalar equation (qKdV). Since the relevant stability criteria are merely encoded by the negative signature of (N + 2) × (N + 2) matrices, they can at least be checked numerically. In practice, when N = 1 or 2, this can be done without even requiring an ODE solver. Various numerical experiments are presented, which clearly discriminate between stable cases and unstable cases for (qKdV), (EKE) and (EKL), thus confirming some known results for the generalized KdV equation and the Nonlinear Schrödinger equation, and pointing out some new results for more general (systems of) PDEs

Stiff Stability of the Hydrogen atom in dissipative Fokker electrodynamics

We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) timescale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics (QED) agree with the prediction of our resonance condition within one percent average deviation.Comment: 1 figure, Notice that Eq. (34) of the Phys. Rev. E paper has a typo; it is missing the square Brackets of eq. (33), find here the correct e

On the amplitude equation of approximate surfacewaves on the plasma-vacuum interface

In this paper we present a recent result about the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagate along the plasma-vacuum interface, when it is linearly weakly stable. Following the approach of Alì and Hunter, we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive the regularity of the first order corrections of the asymptotic expansion

GDR Feeding of the Highly-Deformed Band in 42Ca

The gamma-ray spectra from the decay of the GDR in the compound nucleus reaction 18O+28Si at bombarding energy of 105 MeV have been measured in an experiment using the EUROBALL IV and HECTOR arrays. The obtained experimental GDR strength function is highly fragmented, with a low energy (10 MeV) component, indicating a presence of a large deformation and Coriolis effects. In addition, the preferential feeding of the highly-deformed band in 42Ca by this GDR low energy component is observed.Comment: 6 pages, 2 figures, Proceedings of the Zakopane2004 Symposium, to be published in Acta Phys. Pol. B36 (2005

β-Decay Half-Lives of 110 Neutron-Rich Nuclei across the N = 82 Shell Gap: Implications for the Mechanism and Universality of the Astrophysical r Process

The β-decay half-lives of 110 neutron-rich isotopes of the elements from 37Rb to 50Sn were measured at the Radioactive Isotope Beam Factory. The 40 new half-lives follow robust systematics and highlight the persistence of shell eff

Crossover from Isotropic to Directed Percolation

Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic scaling behavior (``self--affinity''). Taking advantage of the fact that both isotropic and directed bond percolation (with one preferred direction) may be mapped onto corresponding variants of (Reggeon) field theory, we discuss the crossover between self--similar and self--affine scaling. This has been a long--standing and yet unsolved problem because it is accompanied by different upper critical dimensions: $d_c^{\rm I} = 6$ for isotropic, and $d_c^{\rm D} = 5$ for directed percolation, respectively. Using a generalized subtraction scheme we show that this crossover may nevertheless be treated consistently within the framework of renormalization group theory. We identify the corresponding crossover exponent, and calculate effective exponents for different length scales and the pair correlation function to one--loop order. Thus we are able to predict at which characteristic anisotropy scale the crossover should occur. The results are subject to direct tests by both computer simulations and experiment. We emphasize the broad range of applicability of the proposed method.Comment: 19 pages, written in RevTeX, 12 figures available upon request (from [email protected] or [email protected]), EF/UCT--94/2, to be published in Phys. Rev. E (May 1994

Cryptic species and host specificity in the bryozoan-associated hydrozoan Zanclea divergens (Hydrozoa, Zancleidae)

: Zanclea divergens is a tropical hydrozoan living in symbiotic association with bryozoans and currently reported from Papua New Guinea, Indonesia, and Maldives. Here, we used an integrative approach to assess the morpho-molecular diversity of the species across the Indo-Pacific. Phylogenetic and species delimitation analyses based on seven mitochondrial and nuclear loci revealed four well-supported molecular lineages corresponding to cryptic species, and representing a Pacific clade, an Indian clade, and two Red Sea clades. Since the general polyp morphology was almost identical in all samples, the nematocyst capsules were measured and analysed to search for possible fine-scale differences, and their statistical treatment revealed a significant difference in terms of length and width among the clades investigated. All Zanclea divergens specimens were specifically associated with cheilostome bryozoans belonging to the genus Celleporaria. The Pacific and Indian clades were associated with Celleporaria sp. and C. vermiformis, respectively, whereas both Red Sea lineages were associated with C. pigmentaria. Nevertheless, the sequencing of host bryozoans revealed that one of the Red Sea hydrozoan clades is associated with two morphologically undistinguishable, but genetically divergent, bryozoan species. Overall, our results show that Z. divergens is a species complex composed of morphologically cryptic lineages showing partially disjunct distributions and host specificity. The presence of two sympatric lineages living on the same host species reveal complex dynamics of diversification, and future research aimed at understanding their diversification process will likely improve our knowledge on the mechanisms of speciation among currently sympatric cryptic species

Computational Modeling of the Seismic Response of Tensegrity Dissipative Devices Incorporating Shape Memory Alloys

Infrastructures and buildings must have sufficient protection for design level earthquake excitations while minimizing major damage to comply with existing seismic design criteria. This paper explores the computational modeling of a tensegrity based brace, which helps dissipate energy while preventing inter-story drifts. The proposed brace integrates a D-bar tensegrity structure, shaped like a rhombus, with Shape-Memory Alloy (SMA) cables or tendons. These tendons grow austenitic-martensiticaustenetic (solid to solid) transformations, which make them more susceptible to mechanical stress when taking strain, and amplifying the stress into broad superelastic hysteresis, even after repeated mechanical cycles that require strains of up to 6% 8%. In addition in this article two special classes of the tensegrities are discussed namely 2D and 3D braces. 3D braces have been proven more efficient because of an enhaced capacity of energy dissipation, and also due to their improved safety against buckling. The effectiveness of the planned bracing paves the way to the development of innovative systems of seismic energy dissipation that combine tensegrity concepts with superelasticity

Strong Deformation Effects in Hot Rotating 46Ti

Exotic-deformation effects in 46Ti nucleus were investigated by analysing the high-energy gamma-ray and the alpha-particle energy spectra. One of the experiments was performed using the charged-particle multi-detector array ICARE together with a large volume (4"x4") BGO detector. The study focused on simultaneous measurement of light charged particles and gamma-rays in coincidence with the evaporation residues. The experimental data show a signature of very large deformations of the compound nucleus in the Jacobi transition region at the highest spins. These results are compared to data from previous experiments performed with the HECTOR array coupled to the EUROBALL array, where it was found that the GDR strength function is highly fragmented, strongly indicating a presence of nuclei with very large deformation.Comment: 10 pages, 6 figures, Proceedings of the Zakopane Conference on Nuclear Physics, to be published in Acta Phys. Pol. B (2007