Search results for "equation"
showing 10 items of 4219 documents
Minimum main sequence mass in quadratic Palatini f(R) gravity
2019
General relativity yields an analytical prediction of a minimum required mass of roughly $\ensuremath{\sim}0.08--0.09\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for a star to stably burn sufficient hydrogen to fully compensate photospheric losses and, therefore, to belong to the main sequence. Those objects below this threshold (brown dwarfs) eventually cool down without any chance to stabilize their internal temperature. In this work we consider quadratic Palatini $f(\mathcal{R})$ gravity and show that the corresponding Newtonian hydrostatic equilibrium equation contains a new term whose effect is to introduce a weakening/strengthening of the gravitational interaction inside astrophysical…
Three-state quantum systems: A procedure for the solution
1989
An iterative method to obtain a solution of the differential equation $$i\dot a = \hat H(t)a$$ , with Ĥ a 3×3 Hermitian matrix anda the unknown vector, is proposed. The procedure is particularly suitable for computer implementation and, as an example, has been applied to find the excitation probability of a three-level atom after the synchronous passage of two laser pulses each almost resonant with a pair of atomic levels.
Laser driven structured quantum rings
2015
In this work we study harmonic emission from structured quantum rings (SQRs). In SQRs, electrons trapped in two-dimensional structures are further confined by an external potential composed of N scattering centers arranged on a circle. We build a suitable one-dimensional model Hamiltonian describing this class of systems and analytically solve the associated Schödinger equation. We find that the solution can be expressed in terms of Mathieu functions and focus on the specific case of N = 6. By exactly solving the time-dependent Schödinger equation, we then show how the harmonic response to linearly polarized lasers strongly depends on the ring physical parameters. The results illustrate how…
Evidence of Nuclear Motion in H2-like Molecule by Means of High Order Harmonic Generation
2008
The dynamics of hydrogen-like molecules is investigated beyond the usual fixed nuclei approximation. The nuclear motion introduces in the familiar spectrum of emitted radiation additional regular lines whose separation is essentially given by the vibrational frequency of nuclear motion. A wavelet analysis of the emitted spectrum shows that the intensity of the harmonic lines is modulated with the same period of the nuclear motion; this suggests the possibility of the real-time control of the nuclear dynamics.
The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics
2000
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multidimensional relativistic hydrodynamic codes (of Godunov type) is discussed.
General Solution for Self-Gravitating Spherical Null Dust
1997
We find the general solution of equations of motion for self-gravitating spherical null dust as a perturbative series in powers of the outgoing matter energy-momentum tensor, with the lowest order term being the Vaidya solution for the ingoing matter. This is done by representing the null-dust model as a 2d dilaton gravity theory, and by using a symmetry of a pure 2d dilaton gravity to fix the gauge. Quantization of this solution would provide an effective metric which includes the back-reaction for a more realistic black hole evaporation model than the evaporation models studied previously.
Constraints on Area Variables in Regge Calculus
2000
We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
2009
[EN] We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance
Numerical study of the primitive equations in the small viscosity regime
2018
In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.
Singular behavior of a vortex layer in the zero thickness limit
2017
The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.