218 research outputs found
A heat transfer with a source: the complete set of invariant difference schemes
In this letter we present the set of invariant difference equations and
meshes which preserve the Lie group symmetries of the equation
u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the
symmetry group admitted by the differential equation are considered. This paper
completes the paper [J. Phys. A: Math. Gen. 30, no. 23 (1997) 8139-8155], where
a few invariant models for heat transfer equations were presented.Comment: arxiv version is already officia
The higher order C_n dispersion coefficients for the alkali atoms
The van der Waals coefficients, from C_11 through to C_16 resulting from 2nd,
3rd and 4th order perturbation theory are estimated for the alkali (Li, Na, K
and Rb) atoms. The dispersion coefficients are also computed for all possible
combinations of the alkali atoms and hydrogen. The parameters are determined
from sum-rules after diagonalizing the fixed core Hamiltonian in a large basis.
Comparisons of the radial dependence of the C_n/r^n potentials give guidance as
to the radial regions in which the various higher-order terms can be neglected.
It is seen that including terms up to C_10/r^10 results in a dispersion
interaction that is accurate to better than 1 percent whenever the
inter-nuclear spacing is larger than 20 a_0. This level of accuracy is mainly
achieved due to the fortuitous cancellation between the repulsive (C_11, C_13,
C_15) and attractive (C_12, C_14, C_16) dispersion forces.Comment: 8 pages, 7 figure
Weak Transversality and Partially Invariant Solutions
New exact solutions are obtained for several nonlinear physical equations,
namely the Navier-Stokes and Euler systems, an isentropic compressible fluid
system and a vector nonlinear Schroedinger equation. The solution methods make
use of the symmetry group of the system in situations when the standard Lie
method of symmetry reduction is not applicable.Comment: 23 pages, preprint CRM-284
Symmetry-preserving discrete schemes for some heat transfer equations
Lie group analysis of differential equations is a generally recognized
method, which provides invariant solutions, integrability, conservation laws
etc. In this paper we present three characteristic examples of the construction
of invariant difference equations and meshes, where the original continuous
symmetries are preserved in discrete models. Conservation of symmetries in
difference modeling helps to retain qualitative properties of the differential
equations in their difference counterparts.Comment: 21 pages, 4 ps figure
Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis
Families of exact solutions are found to a nonlinear modification of the
Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM)
incorporates both transaction costs and the risk from a volatile portfolio.
Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM
equation. It gives us the possibility to describe an optimal system of
subalgebras and correspondingly the set of invariant solutions to the model. In
this way we can describe the complete set of possible reductions of the
nonlinear RAPM model. Reductions are given in the form of different second
order ordinary differential equations. In all cases we provide solutions to
these equations in an exact or parametric form. We discuss the properties of
these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages,
Symposium on Optimal Stopping in Abo/Turku 200
State-dependent, addressable subwavelength lattices with cold atoms
We discuss how adiabatic potentials can be used to create addressable
lattices on a subwavelength scale, which can be used as a tool for local
operations and readout within a lattice substructure, while taking advantage of
the faster timescales and higher energy and temperature scales determined by
the shorter lattice spacing. For alkaline-earth-like atoms with non-zero
nuclear spin, these potentials can be made state dependent, for which we give
specific examples with Yb atoms. We discuss in detail the limitations
in generating the lattice potentials, in particular non-adiabatic losses, and
show that the loss rates can always be made exponentially small by increasing
the laser power.Comment: replaced with the published version. 23 pages, 11 figure
Trapping of Neutral Mercury Atoms and Prospects for Optical Lattice Clocks
We report a vapor-cell magneto-optical trapping of Hg isotopes on the
intercombination transition. Six abundant isotopes, including
four bosons and two fermions, were trapped. Hg is the heaviest non-radioactive
atom trapped so far, which enables sensitive atomic searches for ``new
physics'' beyond the standard model. We propose an accurate optical lattice
clock based on Hg and evaluate its systematic accuracy to be better than
. Highly accurate and stable Hg-based clocks will provide a new
avenue for the research of optical lattice clocks and the time variation of the
fine-structure constant.Comment: 4 pages, 3 figure
Magpie: towards a semantic web browser
Web browsing involves two tasks: finding the right web page and then making sense of its content. So far, research has focused on supporting the task of finding web resources through ‘standard’ information retrieval mechanisms, or semantics-enhanced search. Much less attention has been paid to the second problem. In this paper we describe Magpie, a tool which supports the
interpretation of web pages. Magpie offers complementary knowledge sources, which a reader can call upon to quickly gain access to any background knowledge relevant to a web resource. Magpie automatically associates an ontologybased
semantic layer to web resources, allowing relevant services to be invoked within a standard web browser. Hence, Magpie may be seen as a step towards a semantic web browser. The functionality of Magpie is illustrated using examples of how it has been integrated with our lab’s web resources
On asymptotic nonlocal symmetry of nonlinear Schr\"odinger equations
A concept of asymptotic symmetry is introduced which is based on a definition
of symmetry as a reducibility property relative to a corresponding invariant
ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle
Schr\"odinger equation, discovered by Fushchych and Segeda in 1977, can be
extended to Galilei-invariant equations for free particles with arbitrary spin
and, with our definition of asymptotic symmetry, to many nonlinear
Schr\"odinger equations. An important class of solutions of the free
Schr\"odinger equation with improved smoothing properties is obtained
A symmetry classification for a class of (2+1)-nonlinear wave equation
In this paper, a symmetry classification of a -nonlinear wave equation
where is a smooth function on , using
Lie group method, is given. The basic infinitesimal method for calculating
symmetry groups is presented, and used to determine the general symmetry group
of this -nonlinear wave equation
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