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

Phage displayed peptides/antibodies recognizing growth factors and their tyrosine kinase receptors as tools for anti-cancer therapeutics.

The basic idea of displaying peptides on a phage, introduced by George P. Smith in 1985, was greatly developed and improved by McCafferty and colleagues at the MRC Laboratory of Molecular Biology and, later, by Barbas and colleagues at the Scripps Research Institute. Their approach was dedicated to building a system for the production of antibodies, similar to a naïve B cell repertoire, in order to by-pass the standard hybridoma technology that requires animal immunization. Both groups merged the phage display technology with an antibody library to obtain a huge number of phage variants, each of them carrying a specific antibody ready to bind its target molecule, allowing, later on, rare phage (one in a million) to be isolated by affinity chromatography. Here, we will briefly review the basis of the technology and the therapeutic application of phage-derived bioactive molecules when addressed against key players in tumor development and progression: growth factors and their tyrosine kinase receptors

1D modelling and preliminary analysis of the coupled DYNASTY–eDYNASTY natural circulation loop

In the continuous strive to improve the safety of current-generation and next-generation nuclear power plants, natural circulation can be used to design passive safety systems to remove the decay heat during the shutdown. The Molten Salt Fast Reactor (MSFR) is a peculiar type of Gen-IV nuclear facility, where the fluid fuel is homogeneously mixed with the coolant. This design leads to natural circulation in the presence of an internally distributed heat source during the shutdown. Furthermore, to shield the environment from the highly radioactive fuel, an intermediate loop between the primary and the secondary loops, able to operate in natural circulation, is required. To analyze the natural circulation with a distributed heat source and to study the natural circulation of coupled systems and the influence of the intermediate loop on the behaviour of the primary, Politecnico di Milano designed and built the DYNASTY-eDYNASTY facility. The two facilities are coupled with a double-pipe heat exchanger, which siphons heat from DYNASTY and delivers it to the eDYNASTY loop. This work focuses on modelling the coupled DYNASTY-eDYNASTY natural circulation loops using DYMOLA2023((R)), an integrated development environment based on the Modelica Object-Oriented a-causal simulation language. The 1D Modelica approach allows for building highly reusable and flexible models easing the design effort on a complex system such as the DYNASTY-eDYNASTY case without the need to rewrite the whole model from scratch. The coupled models were developed starting from the already-validated single DYNASTY model and the double-pipe heat exchanger coupling. The models were tested during the whole development process, studying the influence of the numerical integration algorithm on the simulation behaviour. A preliminary analysis of both the adiabatic and the heat loss models analyzed the effect of the secondary natural circulation loop on the behaviour of the DYNASTY loop. The simulation results showed that the eDYNASTY loop dampens the behaviour of the primary DYNASTY loop. Furthermore, a parametric analysis of the DYNASTY and the eDYNASTY coolers highlighted the influence of the cooling configuration on the facility's behaviour. Finally, the simulation results identified the most critical aspects of the models in preparation for an experimental comparison

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

β-decay systematic trends of nuclei beyond 208Pb

n/

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

Existence of weak solution for compressible fluid models of Korteweg type

This work is devoted to prove existence of global weak solutions for a general isothermal model of capillary fluids derived by J.- E Dunn and J. Serrin (1985) [6], which can be used as a phase transition model. We improve the results of [5] by showing the existence of global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant capillarity coefficient. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with large initial data in the energy space

Agata : in-beam spectroscopy with relativistic beams

An analysis of the capabilities of AGATA for in-beam γ -ray spectroscopy at relativistic energies is presented. AGATA’s ability to determine the position of γ -ray interaction points in the Germanium crystal provides the crucial ingredient for attaining high γ -ray energy resolution when the emitting nucleus is traveling at more than half the speed of light. This is the typical velocity of exotic nuclei exiting the SuperFRS spectrometer at the future FAIR facility, where AGATA will be deployed as part of the high-resolution in-beam spectroscopy project, HISPEC. A discussion of different experimental techniques using AGATA under these conditions is presented, including analysis of the different Doppler-based methods for lifetime determination. The properties of the key reaction mechanisms expected to be applied for in-beam γ -ray spectroscopy at FAIR are discussed, along with the aspects of those reactions that can be exploited by the advanced capabilities of the AGATA array

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