Search results for "Formula"

Translationally invariant coupled cluster method in coordinate space for nuclei

2002

We study a formulation of the translationally invariant coupled cluster method in coordinate space for finite nuclei. The new formulation remedies convergence problems that plagued previous calculations in configuration space. The method is applied to light nuclei using semi-realistic central interactions.

Effects of damage on the response of Euler-Bernoulli beams traversed by a moving mass

2003

The perturbation induced by damage in the dynamic response of Euler-Bernoulli beams traversed by a moving mass is investigated. The structure is discretized into segments of constant bending stiffness, connected together by elastic hinges representing damaged sections. The beam-moving mass interaction force is modelled in the most accurate way by taking into account the effective structural mass distribution and the convective acceleration terms, often omitted in similar studies. The analytical response is obtained through a series expansion of the unknown deflection in a basis of the beam eigenfunctions. The results of experimental tests, performed on a small-scale model of a prototype bri…

Special Section on Fractional Operators in the Analysis of Mechanical Systems Under Stochastic Agencies

2017

Quantized adiabatic quantum pumping due to interference

2002

Recent theoretical calculations, demonstrating that quantized charge transfer due to adiabatically modulated potentials in mesoscopic devices can result purely from the interference of the electron wave functions (without invoking electron-electron interactions) are reviewed: (1) A new formula is derived for the pumped charge Q (per period); It reproduces the Brouwer formula without a bias, and also yields the effect of the modulating potential on the Landauer formula in the presence of a bias. (2) For a turnstile geometry, with time-dependent gate voltages V_L(t) and V_R(t), the magnitude and sign of Q are determined by the relative position and orientation of the closed contour traversed …

Gravitational waves from oscillating accretion tori: Comparison between different approaches

2005

Quasi-periodic oscillations of high density thick accretion disks orbiting a Schwarzschild black hole have been recently addressed as interesting sources of gravitational waves. The aim of this paper is to compare the gravitational waveforms emitted from these sources when computed using (variations of) the standard quadrupole formula and gauge-invariant metric perturbation theory. To this goal we evolve representative disk models using an existing general relativistic hydrodynamics code which has been previously employed in investigations of such astrophysical systems. Two are the main results of this work: First, for stable and marginally stable disks, no excitation of the black hole quas…

GENERALIZED GAUGE TRANSFORMATIONS AND HIDDEN SYMMETRY IN THE STANDARD MODEL

1992

A recently proposed, new construction of the Standard Model based on the graded Lie algebra SU (2|1) is analyzed in some depth. The essential ingredient is an algebraic superconnection which incorporates both the gauge fields and the Higgs fields and whose curvature automatically leads to a spontaneously broken realization of the theory. The mechanism of hiding the original algebraic structure is unorthodox and is due to the specific, "noncommutative" realization of SU (2|1). The model is characterized by a constant background supercurvature which is invariant under arbitrary, constant SU (2|1) gauge transformations. This background field whose effect is analogous to the action of a consta…

Interior spacetimes of stars in Palatinif(R)gravity

2006

We study the interior spacetimes of stars in the Palatini formalism of f(R) gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation for a static, spherically symmetric star. We show that matching the interior solution with the exterior Schwarzschild-De Sitter solution in general gives a relation between the gravitational mass and the density profile of a star, which is different from the one in General Relativity. These modifications become neglible in models for which $\delta F(R) \equiv \partial f/\partial R - 1$ is a decreasing function of R however. As a result, both Solar System constraints and stellar dynamics are perfectly consistent with $f(R) = R - \mu^4/R$.

Axisymmetric core collapse simulations using characteristic numerical relativity

2003

We present results from axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allo…

Measure dependence of 2D simplicial quantum gravity

1995

We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.

Covariant phase space quantization of the Jackiw-Teitelboim model of two-dimensional gravity

1992

Abstract On the basis of the covariant phase space formulation of field theory we analyze the Jackiw-Teitelboim model of two-dimensional gravity on a cylinder. We compute explicitly the symplectic structure showing that the (reduced) phase space is the cotangent bundle of the space of conjugacy classes of the PSL(2, R ) group. This makes it possible to quantize the theory exactly. The Hilbert space is given by the character functions of the PSL (2, R ) group. As a byproduct, this implies the complete equivalence with the PSL (2, R )-topological gravity model.