403 research outputs found
Spectral methods in time for hyperbolic equations
A pseudospectral numerical scheme for solving linear, periodic, hyperbolic problems is described. It has infinite accuracy both in time and in space. The high accuracy in time is achieved without increasing the computational work and memory space which is needed for a regular, one step explicit scheme. The algorithm is shown to be optimal in the sense that among all the explicit algorithms of a certain class it requires the least amount of work to achieve a certain given resolution. The class of algorithms referred to consists of all explicit schemes which may be represented as a polynomial in the spatial operator
The eigenvalues of the pseudospectral Fourier approximation to the operator sin (2x) d/dx
It is shown that the eigenvalues Z sub i of the pseudospectral Fourier approximation to the operator sin(2x) curly d/curly dx satisfy (R sub e) (Z sub i) = + or - 1 or (R sub e)(Z sub I) = 0. Whereas this does not prove stability for the Fourier method, applied to the hyperbolic equation U sub t = sin (2x)(U sub x) - pi x pi; it indicates that the growth in time of the numerical solution is essentially the same as that of the solution to the differential equation
New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation
A propagation method for the time dependent Schr\"odinger equation was
studied leading to a general scheme of solving ode type equations. Standard
space discretization of time-dependent pde's usually results in system of ode's
of the form u_t -Gu = s where G is a operator (matrix) and u is a
time-dependent solution vector. Highly accurate methods, based on polynomial
approximation of a modified exponential evolution operator, had been developed
already for this type of problems where G is a linear, time independent matrix
and s is a constant vector. In this paper we will describe a new algorithm for
the more general case where s is a time-dependent r.h.s vector. An iterative
version of the new algorithm can be applied to the general case where G depends
on t or u. Numerical results for Schr\"odinger equation with time-dependent
potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page
A pseudospectral Legendre method for hyperbolic equations with an improved stability condition
A new pseudospectral method is introduced for solving hyperbolic partial differential equations. This method uses different grid points than previously used pseudospectral methods: in fact the grid are related to the zeroes of the Legendre polynomials. The main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points 1/N rather than to 1/n(2) (as in the case of other pseudospectral methods applied to mixed initial boundary value problems). A highly accurate time discretization suitable for these spectral methods is discussed
An efficient scheme for numerical simulations of the spin-bath decoherence
We demonstrate that the Chebyshev expansion method is a very efficient
numerical tool for studying spin-bath decoherence of quantum systems. We
consider two typical problems arising in studying decoherence of quantum
systems consisting of few coupled spins: (i) determining the pointer states of
the system, and (ii) determining the temporal decay of quantum oscillations. As
our results demonstrate, for determining the pointer states, the
Chebyshev-based scheme is at least a factor of 8 faster than existing
algorithms based on the Suzuki-Trotter decomposition. For the problems of
second type, the Chebyshev-based approach has been 3--4 times faster than the
Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide
spectrum of systems, with different spin baths and different Hamiltonians.Comment: 8 pages (RevTeX), 3 EPS figure
Evolution of low-mass metal-free stars including effects of diffusion and external pollution
We investigate the evolution of low-mass metal-free Population III stars.
Emphasis is laid upon the question of internal and external sources for
CNO-elements, which - if present in sufficient amounts in the hydrogen-burning
regions - lead to a strong modification of the stars' evolutionary behavior.
For the production of carbon due to nuclear processes inside the stars, we use
an extended nuclear network, demonstrating that hot pp-chains do not suffice to
produce enough carbon or are less effective than the triple3-alpha-process. As
an external source of CNO-elements we test the efficiency of pollution by a
nearby massive star combined with particle diffusion. For all cases
investigated, the additional metals fail to reach nuclear burning regions
before deep convection on the Red Giant Branch obliterates the previous
evolution. The surface abundance history of the polluted Pop III stars is
presented. The possibilities to discriminate between a Pop II and a polluted
Pop III field star are also discussed.Comment: Accepted for publication in Ap
Quantum Dynamics of Spin Wave Propagation Through Domain Walls
Through numerical solution of the time-dependent Schrodinger equation, we
demonstrate that magnetic chains with uniaxial anisotropy support stable
structures, separating ferromagnetic domains of opposite magnetization. These
structures, domain walls in a quantum system, are shown to remain stable if
they interact with a spin wave. We find that a domain wall transmits the
longitudinal component of the spin excitations only. Our results suggests that
continuous, classical spin models described by LLG equation cannot be used to
describe spin wave-domain wall interaction in microscopic magnetic systems
Conserved Quantities and Electroweak Phase Transitions
Some cosmological consequences of including the adequate conserved quantities
in the density matrix of the electroweak theory are investigated. Several
arguments against including the charges associated to the spontaneously broken
symmetry are presented. Special attention is focused on the phenomenon of
-boson condensation and its interplay with the phase transition for the
symmetry restoration is considered. The emerging cosmological implications,
such as on the baryon and lepton number densities, are of interest.Comment: 9 pages, Latex, HU-SEFT R 1994-0
The Many Faces of a Character
We prove an identity between three infinite families of polynomials which are
defined in terms of `bosonic', `fermionic', and `one-dimensional configuration'
sums. In the limit where the polynomials become infinite series, they give
different-looking expressions for the characters of the two integrable
representations of the affine algebra at level one. We conjecture yet
another fermionic sum representation for the polynomials which is constructed
directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9
An Assessment of Dynamical Mass Constraints on Pre-Main Sequence Evolutionary Tracks
[abridged] We have assembled a database of stars having both masses
determined from measured orbital dynamics and sufficient spectral and
photometric information for their placement on a theoretical HR diagram. Our
sample consists of 115 low mass (M < 2.0 Msun) stars, 27 pre-main sequence and
88 main sequence. We use a variety of available pre-main sequence evolutionary
calculations to test the consistency of predicted stellar masses with
dynamically determined masses. Despite substantial improvements in model
physics over the past decade, large systematic discrepancies still exist
between empirical and theoretically derived masses. For main-sequence stars,
all models considered predict masses consistent with dynamical values above 1.2
Msun, some models predict consistent masses at solar or slightly lower masses,
and no models predict consistent masses below 0.5 Msun but rather all models
systematically under-predict such low masses by 5-20%. The failure at low
masses stems from the poor match of most models to the empirical main-sequence
below temperatures of 3800 K where molecules become the dominant source of
opacity and convection is the dominant mode of energy transport. For the
pre-main sequence sample we find similar trends. There is generally good
agreement between predicted and dynamical masses above 1.2 Msun for all models.
Below 1.2 Msun and down to 0.3 Msun (the lowest mass testable) most
evolutionary models systematically under-predict the dynamically determined
masses by 10-30% on average with the Lyon group models (e.g. Baraffe et al.
1998) predicting marginally consistent masses *in the mean* though with large
scatter.Comment: accepted for publication in ApJ (2004
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