Boundary Condition in the Oscillating Turbulent Boundary Layer for the Simulation of Wave Breaking

In this paper a new numerical model for the simulation of the wave breaking is proposed. In order to represent the complex geometry of coastal regions, the three-dimensional equations of motion are expressed in integral contravariant form and are solved on a curvilinear boundary conforming grid. A time-dependent transformation of the vertical coordinate that is a function of the oscillation of the turbulent wave boundary layer is proposed. New boundary condition bottom for the equations of motion expressed in contravariant form are proposed. In order to correctly simulate the height of the breaking waves, the importance of the correct positioning, inside the oscillating turbulent boundary layer, of the centre of the calculation grid cell closest to the bottom, is demonstrated

New Two-Dimensional Quantum Models with Shape Invariance

Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional SUSY Quantum Mechanics. They are obtained using the expressions for known one-dimensional shape invariant potentials. The constructed Hamiltonians are integrable with symmetry operators of fourth order in momenta, and they are not amenable to the conventional separation of variables.Comment: 16 p.p., a few new references adde

A 3D numerical model for turbidity currents

A numerical model that solves two-phase flow motion equations to reproduce turbidity currents that occur in reservoirs, is proposed. Three formalizations of the two-phase flow motion equations are presented: the first one can be adopted for high concentration values; the second one is valid under the hypothesis of diluted concentrations; the third one is based on the assumption that the particles are in translational equilibrium with the fluid flow. The proposed numerical model solves the latter formalization of two-phase flow motion equations, in order to simulate turbidity currents. The motion equations are presented in an integral form in time-dependent curvilinear coordinates, with the vertical coordinate that varies in order to follow the free surface movements. The proposed numerical model is validated against experimental data and is applied to a practical engineering case study of a reservoir, in order to evaluate the possibility of the formation of turbidity currents

Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction

We study a quantum model with non-isotropic two-dimensional oscillator potential but with additional quadratic interaction $x_1x_2$ with imaginary coupling constant. It is shown, that for a specific connection between coupling constant and oscillator frequences, the model {\it is not} amenable to a conventional separation of variables. The property of shape invariance allows to find analytically all eigenfunctions and the spectrum is found to be equidistant. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of the identity must include also the corresponding associated functions. These functions are constructed explicitly, and their properties are investigated. The problem of $R-$separation of variables in two-dimensional systems is discussed.Comment: 20 pages; minor corrections were made; new Appendix was adde

Pseudohermitian Hamiltonians, time-reversal invariance and Kramers degeneracy

A necessary and sufficient condition in order that a (diagonalizable) pseudohermitian operator admits an antilinear symmetry T such that T^{2}=-1 is proven. This result can be used as a quick test on the T-invariance properties of pseudohermitian Hamiltonians, and such test is indeed applied, as an example, to the Mashhoon-Papini Hamiltonian.Comment: 6 page

Numerical simulation of 3D free surface flows in time dependent curvilinear coordinates

We propose a three dimensional non-hydrostatic shock-capturing numerical model for the simulation of wave propagation, transformation and breaking, which is based on an original integral formulation of the contravariant Navier-Stokes equations, devoid of Christoffel symbols, in general time-dependent curvilinear coordinates

Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must include also the corresponding associated functions. In the specific case of anharmonic second-plus-fourth order interaction, expressions for the wave functions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wave functions is given.Comment: 17 p.

The ππ\pi \pi S-Wave in the 1 to 2 GeV Region from a ππ\pi \pi, KˉK\bar{K}K and ρρ\rho \rho(ωω\omega \omega) Coupled Channel Model

A simple $\pi \pi$, $\bar{K}K$, and $\rho \rho$($\omega \omega$) fully coupled channel model is proposed to predict the isoscalar S-wave phase shifts and inelasticities for $\pi \pi$ scattering in the 1.0 to 2.0 GeV region. The S-matrix is required to exhibit poles corresponding to the established isoscalar J$^{\pi}$ = 0$^+$ resonances f$_0$(975), f$_0$(1400), and f$_0$(1710). A dominant feature of the experimental $\pi \pi$ inelasticity is the clear opening of the $\bar{K}K$ channel near 1 GeV, and the opening of another channel in the 1.4 - 1.5 GeV region. The success of our model in predicting this observed dramatic energy dependence indicates that the effect of multi-pion channels is adequately described by the $\pi \pi$ coupling to the $\bar{K}K$ channel, the $\rho \rho$(4$\pi$) and $\omega \omega$(6$\pi$) channels.Comment: 11 pages (Revtex 3.0), 4 figs. avail. upon request, RU946

A Flexible and Robust Large Scale Capacitive Tactile System for Robots

IEEE Sensor Journal, Vol. 13, Issue 10, 2013Capacitive technology allows building sensors that are small, compact and have high sensitivity. For this reason it has been widely adopted in robotics. In a previous work we presented a compliant skin system based on capacitive technology consisting of triangular modules interconnected to form a system of sensors that can be deployed on non-flat surfaces. This solution has been successfully adopted to cover various humanoid robots. The main limitation of this and all the approaches based on capacitive technology is that they require to embed a deformable dielectric layer (usually made using an elastomer) covered by a conductive layer. This complicates the production process considerably, introduces hysteresis and limits the durability of the sensors due to ageing and mechanical stress. In this paper we describe a novel solution in which the dielectric is made using a thin layer of 3D fabric which is glued to conductive and protective layers using techniques adopted in the clothing industry. As such, the sensor is easier to produce and has better mechanical properties. Furthermore, the sensor proposed in this paper embeds transducers for thermal compensation of the pressure measurements. We report experimental analysis that demonstrates that the sensor has good properties in terms of sensitivity and resolution. Remarkably we show that the sensor has very low hysteresis and effectively allows compensating drifts due to temperature variations