Search results for "classical mechanics"

Onset of convection in a vertical porous cylinder with a permeable and conducting side boundary

2015

Abstract The onset of natural convection in a vertical porous cylinder saturated by a fluid is studied. The lateral confinement of the porous cylinder is due to an external porous medium having a permeability much smaller than that of the cylinder. Thus, the vertical side boundary of the cylinder is permeable and constrained by given pressure and temperature distributions. The lower and upper plane boundaries of the cylinder are impermeable walls. The lower wall is subject to a uniform heat flux, while the upper wall has a uniform temperature. The basic motionless state displays a uniform and vertical temperature gradient oriented downward. The linear stability analysis is carried out by us…

Kinematically corrected correlation functions for inclusive reactions

1972

Signorini problem with Coulomb's law of friction. Shape optimization in contact problems

1992

Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation

2000

We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …

Effective hamiltonian approach to the non-Markovian dynamics in a spin-bath

2010

We investigate the dynamics of a central spin that is coupled to a bath of spins through a non-uniform distribution of coupling constants. Simple analytical arguments based on master equation techniques as well as numerical simulations of the full von Neumann equation of the total system show that the short-time damping and decoherence behaviour of the central spin can be modelled accurately through an effective Hamiltonian involving a single effective coupling constant. The reduced short-time dynamics of the central spin is thus reproduced by an analytically solvable effective Hamiltonian model.

Coupling Mechanics of Antikythera Gearwheels

2012

This paper discusses the gear coupling mechanics of the ancient Antikythera mechanism, among whose distinctive characteristics was the triangular shaping of the teeth. The engagement of the tooth pairs is analyzed in detail, estimating the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. The admissibility of the theoretical contact points is carefully checked, and the magnitude of the successive tooth collisions is calculated together with the energy losses arising from the particular nature of the coupling. Some interesting results are that only one tooth pair turns out to be active at each time instant and the real path may belong on…

Macroscopic and microscopic study of the planar vibrational mode coupling

1999

We investigate the planar vibrational modes (PVMs) of a structure consisting of two parallel slabs of a strange atom (X) inserted in a matrix of a binary material (AB). The study of the coupling of the PVMs has been undertaken with two different approaches. In the first model, the structure is described from a macroscopic point of view, characterizing the physical properties of the constitutive materials by their layer densities, dielectric constants and strain tensors. Adequate boundary conditions are imposed at the material interfaces to obtain the vibrational modes of the structure. In the second model, the study of the planar modes is undertaken from a microscopic point of view, by usin…

Nodes of entangledN-particle wave functions

2006

In a recent paper [Bressanini et al. Phys. Rev. Lett. 95, 110201 (2005)] it was pointed out that ``the nodes of even simple wave functions are largely unexplored.'' Here we show that for $N$-particle wave functions nodal surfaces arise from the spin and orbital entanglement of constituent two-particle wave functions and derive, for two-electron atoms, 11 exact nodal rules applicable in $LS$ coupling. In addition, the ``higher symmetry'' identified numerically in the above paper is shown to be an approximate dynamical symmetry described by a molecular model or a classical unstable periodic orbit. We show that the analysis is readily extended to four-particle wave functions and consider the c…

Quantum Non-Markovian Collision Models from Colored-Noise Baths

2019

A quantum collision model (CM), also known as repeated interactions model, can be built from the standard microscopic framework where a system S is coupled to a white-noise bosonic bath under the rotating wave approximation, which typically results in Markovian dynamics. Here, we discuss how to generalize the CM construction to the case of frequency-dependent system–bath coupling, which defines a class of colored-noise baths. This leads to an intrinsically non-Markovian CM, where each ancilla (bath subunit) collides repeatedly with S at different steps. We discuss the illustrative example of an atom in front of a mirror in the regime of non-negligible retardation times.

Observation of Kuznetsov-Ma soliton dynamics in optical fibre

2012

International audience; The nonlinear Schro¨dinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important serie…