Search results for "classical"

Influence of a Magnetic Field on Liquid Metal Free Convection in an Internally Heated Cubic Enclosure

2002

The buoyancy‐driven magnetohydrodynamic flow in a cubic enclosure was investigated by three‐dimensional numerical simulation. The enclosure was volumetrically heated by a uniform power density and cooled along two opposite vertical walls, all remaining walls being adiabatic. A uniform magnetic field was applied orthogonally to the gravity vector and to the temperature gradient. The Prandtl number was 0.0321 (characteristic of Pb–17Li at 300°C), the Rayleigh number was 104, and the Hartmann number was made to vary between 0 and 2×103. The steady‐state Navier–Stokes equations, in conjunction with a scalar transport equation for the fluid's enthalpy and with the Poisson equation for the electr…

TRANSIENT DYNAMICS AND ASYMPTOTIC POPULATIONS IN A DRIVEN METASTABLE QUANTUM SYSTEM

2013

The transient dynamics of a periodically driven metastable quantum system, interacting with a heat bath, is investigated. The time evolution of the populations, within the framework of the Feynman–Vernon influ- ence functional and in the discrete variable representation, is analyzed by varying the parameters of the external driving. The results display strong non-monotonic behaviour of the populations with respect to the driving frequency.

Linear response theory: many-body formulation

2013

On the unification of electroweak interactions with gravity

1982

It is shown that the electroweak interactions in the Salam-Weinberg model can be described by a space-time connection form which preserves the space-time metric multiplied by a conformal factor. In addition, one needs an extraSO(2)-connection form. The Dirac field in this formalism is described (after making a certain regularity assumption) by a vierbein field for the space-time metric and a complex scalar field.

One pendulum to run them all

2013

The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.

A physically based connection between fractional calculus and fractal geometry

2014

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalous dimension of such geometry, as well as to the m…

Nonlocal Fractional Dynamics for Different Terminal Densities

2018

We study the effect of confining potentials, generated by different equilibrium (long-time asymptotic or terminal) probability densities, on nonGaussian stochastic processes, described by Lévy–Schrödinger semigroup dynamics. The former densities belong to the family of so-called M-Wright functions of index ν. Using analytical and numerical arguments, we demonstrate that properly tailored confining potentials can generate the Gaussian distribution (which is also a member of M-Wright family at ν = 1/2) at final stages of time evolution. This means that the Gaussian distribution (and other sufficiently fast decaying distributions like exponential one) can emerge in the differential equation wi…

Quantization as a consequence of the group law

1982

A method of gemetric quantization which solely makes use of the structure of the symmetry group of the dynamical system is proposed; the classical limit is discussed along similar lines. The method is applied to two examples, the free particle and the harmonic oscillator.

Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system

2000

The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approxi…

Non-equilibrium thermodynamics analysis of rotating counterflow superfluid turbulence

2010

In two previous papers two evolution equations for the vortex line density $L$, proposed by Vinen, were generalized to rotating superfluid turbulence and compared with each other. Here, the already generalized alternative Vinen equation is extended to the case in which counterflow and rotation are not collinear. Then, the obtained equation is considered from the viewpoint of non-equilibrium thermodynamics. According with this formalism, the compatibility between this evolution equation for $L$ and that one for the velocity of the superfluid component is studied. The compatibility condition requires the presence of a new term dependent on the anisotropy of the tangle, which indicates how the…