Asymptotic behavior of a hyperbolic system arising in ferroelectricity

We consider a coupled hyperbolic system which describes the evolution of the electromagnetic field inside a ferroelectric cylindrical material in the framework of the Greenberg-MacCamy-Coffman model. In this paper we analyze the asymptotic behavior of the solutions from the viewpoint of infinitedimensional dissipative dynamical systems. We first prove the existence of an absorbing set and of a compact global attractor in the energy phase-space. A sufficient condition for the decay of the solutions is also obtained. The main difficulty arises in connection with the study of the regularity property of the attractor. Indeed, the physically reasonable boundary conditions prevent the use of a technique based on multiplication by fractional operators and bootstrap arguments. We obtain the desired regularity through a decomposition technique introduced by Pata and Zelik for the damped semilinear wave equation. Finally we provide the existence of an exponential attractor

Attractors for semilinear damped wave equations with an acoustic boundary condition

In this paper, we study a semilinear weakly damped wave equation equipped with an acoustic boundary condition. The problem can be considered as a system consisting of the wave equation describing the evolution of an unknown function u = u(x, t), x is an element of Omega in the domain coupled with an ordinary differential equation for an unknown function delta = delta(x, t), x is an element of Gamma := partial derivative Omega on the boundary. A compatibility condition is also added due to physical reasons. This problem is inspired on a model originally proposed by Beale and Rosencrans (Bull Am Math Soc 80: 1276-1278, 1974). The goal of the paper is to analyze the global asymptotic behavior of the solutions. We prove the existence of an absorbing set and of the global attractor in the energy phase space. Furthermore, the regularity properties of the global attractor are investigated. This is a difficult issue since standard techniques based on the use of fractional operators cannot be exploited. We finally prove the existence of an exponential attractor. The analysis is carried out in dependence of two damping coefficients

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Magnetic Properties of a Superconductor with no Inversion Symmetry

We study the magnetic properties of a superconductor in a crystal without $z \to -z$ symmetry, in particular how the lack of this symmetry exhibits itself. We show that, though the penetration depth itself shows no such effect, for suitable orientation of magnetic field, there is a magnetic field discontinuity at the interface which shows this absence of symmetry. The magnetic field profile of a vortex in the $x-y$ plane is shown to be identical to that of an ordinary anisotropic superconductor except for a shift in the $-z$ direction by ${\tilde \kappa} \lambda_x$ (see errata). For a vortex along $z$, there is an induced magnetization along the radial direction.Comment: J. Low Temp. Physics, 140, 67 (2005); with Errat

Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi liquid behavior over the whole surface except at the Brillouin zone diagonal.Comment: 12 pages, 2 figures, revised version as publishe

GaAs Sub-Micron and Nano Islands by Droplet Epitaxy on Si

Merging the high effi?ciency light emitting III-V semiconductors with the state-of-the-art Silicon based electronics is of great interest for the realization of new optoelectronic devices. Unfortunately the heteroepitaxial growth of GaAs thin ?films on Si is a diffi?cult task because of the di?fference in the lattice constant, the polar/non-polar surface interaction and the di?fference in the thermal expansion coeffi?cients. We present for the ?first time the MBE growth of GaAs nanostructures on Si substrates by Droplet Epitaxy (DE) [1,2]. We believe this growth method to be promising for the growth of high quality GaAs nanoislands directly on Silicon. In the DE, the substrate is irradiated by a Ga molecular beam fl?ux ?first, leading to the formation of numerous fi?ne Ga droplets with uniform size, which are subsequently crystallized into GaAs nanostructures by an As molecular beam supply. By changing the Ga droplets deposition temperature is possible to change independently the size and the density of the droplets, while by varying the As ?flux for the crystallization we can change the fi?nal shape of the GaAs nanocrystals. We present the results for the growth of GaAs on Si by DE where the density of the GaAs nanoislands was changed by two orders of magnitude, while the size is varied from around 200 nm to around 20 nm. Measurements by X-ray microanalysis in the TEM con- fi?rmed the reaction between Ga and As with formation of GaAs. This has also seen by the presence of Moir? fringes in the TEM images taken in the two beam di?raction mode. The discontinuities of some Moir? fringes would suggest the presence of dislocations

Novel Pressure Phase Diagram of Heavy Fermion Superconductor CePt3_{3}Si Investigated by ac Calorimetry

The pressure dependences of the antiferromagnetic and superconducting transition temperatures have been investigated by ac heat capacity measurement under high pressures for the heavy-fermion superconductor CePt$_3$Si without inversion symmetry in the tetragonal structure. The N\'{e}el temperature $T_{\rm N}$ = 2.2 K decreases with increasing pressure and becomes zero at the critical pressure $P_{\rm AF}$ $\simeq$ 0.6 GPa. On the other hand, the superconducting phase exists in a wider pressure region from ambient pressure to about 1.5 GPa. The pressure phase diagram of CePt$_3$Si is thus very unique and has never been reported before for other heavy fermion superconductors.Comment: 4 pages and 3 figures. This paper will be published in the July issue of J. Phys. Soc. Jp

Critical Strain Region Evaluation of Self-Assembled Semiconductor Quantum Dots

A novel peak finding method to map the strain from high resolution transmission electron micrographs, known as the Peak Pairs method, has been applied to In(Ga) As/AlGaAs quantum dot (QD) samples, which present stacking faults emerging from the QD edges. Moreover, strain distribution has been simulated by the finite element method applying the elastic theory on a 3D QD model. The agreement existing between determined and simulated strain values reveals that these techniques are consistent enough to qualitatively characterize the strain distribution of nanostructured materials. The correct application of both methods allows the localization of critical strain zones in semiconductor QDs, predicting the nucleation of defects, and being a very useful tool for the design of semiconductor device