We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap ('lens') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with semi-spherical shape. The Hamiltonian for a carrier confined in the quantum lens is correspondingly mapped into an equivalent operator and its eigenvalues and eigenfunctions for the corresponding Dirichlet problem are analyzed. A modified Rayleigh-Schrödinger perturbation theory is presented to obtain analytical expressions for the energy levels and wavefunctions as a function of the spherical cap height b and radius a of the circular cross section. Calculations for a hard wall confinement potential are presented, and the effect of decreasing symmetry on the energy values and eigenfunctions of the lens-shape quantum dot is studied. As the degeneracies of a semi-circular geometry are broken for b = a, our perturbation approach allows tracking of the split states. Energy states and electronic wavefunctions with m = 0 present the most pronounced influence on the reduction of the lens height. The analytical expressions presented here can be used to better parameterize the states in realistic self-assembled quantum dots.

In this paper we discuss the conduction of heat in solids excited by a periodically time-dependent source, commonly encountered in photothermal experiments. In the analysis, we take into account the relaxation time necessary for the onset of the heat flux which leads to a second time derivative in the heat diffusion equation. It is shown that there exists a critical modulation frequency at which the heat flux changes its diffusive character to a wave propagation process with the velocity of sound. Evidence is provided for the possibility of detecting second sound in solids by means of a photothermal experiment.

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A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of the group and phase velocity are analyzed.

We obtain an analytic representation for the pro le of the surge wave in the sea, due to a tropical storm at a low latitude. The results reproduce the known experimental data adequately. In the calculations we take i n to account the in uence of Rossby's second parameter and we analyse its contribution to the surge wave, which is proved to be su ciently small to be neglected in higher latitudes. The obtained analytical solution allows us to study in detail the surge wave formation in the presence of such a storm. To solve the problem, Laplace method and Green functions are used. This allows us to improve previous results obtained by Evsa in 1989. I IntroductionIn the last years the interest of studying non-periodic oscillations of sea level has grown. In particular, it is of interest the study of those oscillations excited by pressure elds and strong winds in the tropical storm. It is possible to nd previous information about this theme in the work of Jelesniansky 1 and more recently, Johns et al. 2 , Fandry et al. 3 , Jerome et al. 4 , Signorini 5 , Davies et al. 6 and Lardner et al. 7 and 8 . The majority of these papers employ n umerical methods or qualitative analysis of the solution of the mathematical model. In the present paper we obtain an analytic solution of the problem, similar to the one formulated by Evsa 9 . In this work, there is an incorrect expresion for the Green function of the problem. Therefore, for the analytic solution, Evsa does not take account of the multi-valuated character of the complex variable function in the path integrations. In the present paper we make correct use of the Green function method and the integral transform techniques. We also analyze the inuence of Rossby's second parameter, which is usually neglected at high latitudes by other authors because of its smallness with respect to Rossby's rst parameter and because it allows to simplify the calculation. We check that Rossby's second parameter is small enough to be neglected at low latitudes. II Formulation of the problemLet us consider a tropical cyclone TC which causes a perturbation of the sea surface in an ocean region distant from any coast. The interaction region has a characteristic deepness less than the storm horizontal size by t wo orders of magnitude. Therefore, we can use the shalow w ater approximation. We also consider a quasistationary regime for the storm, in order to keep a xed coordinate center. Due to the axial symmetry of this problem, we use a cylindrical system of coordinates with center on the axis of the cyclone. The Navier-Stokes equations in the cilindrical system of coordinates including the Coriolis terms are given by c