656 research outputs found
Truncation error analysis of multipole expansion
The multilevel fast multipole algorithm is based on the multipole expansion, which has numerical error sources such as truncation of the addition theorem, numerical integration, and interpolation/anterpolation. Of these, we focus on the truncation error and discuss its control precisely. The conventional selection rule fails when the buffer size is small compared to the desired numerical accuracy. We propose a new approach and show that the truncation error can be controlled and predicted regardless of the number of buffer sizes.published_or_final_versio
Error minimization of multipole expansion
In this paper, we focus on the truncation error of the multipole expansion for the fast multipole method and the multilevel fast multipole algorithm. When the buffer size is large enough, the error can be controlled and minimized by using the conventional selection rules. On the other hand, if the buffer size is small, the conventional selection rules no longer hold, and the new approach which we have recently proposed is needed. However, this method is still not sufficient to minimize the error for small buffer cases. We clarify this fact and show that the information about the placement of true worst-case interaction is needed. A novel algorithm to minimize the truncation error is proposed. © 2005 Society for Industrial and Applied Mathematics.published_or_final_versio
Microstructural Change and Mechanical Property of Neutron Irradiated Ti-Ni Shape Memory Alloy
Microstructural change and mechanical property of Ti-Ni shape memory alloy after neutron irradiation have been studied. The neutron doses were from 1.4Ă10^ to 1.2Ă10^n/cm^2, and the irradiation temperature was under 423K. A halo ring was observed after the irradiation of 1.2Ă10^n/cm^2, which means that amorphous phase was induced by the neutron irradiation. In stress-strain curve, the critical point (Ï_M) increased as the dose increased. At the highest dose, the stress-strain curve lost pseudoelasticity. These results indicate that such mechanical properties strongly depend on the amorphous formation
Spin Hall effect of Photons in a Static Gravitational Field
Starting from a Hamiltonian description of the photon within the set of
Bargmann-Wigner equations we derive new semiclassical equations of motion for
the photon propagating in static gravitational field. These equations which are
obtained in the representation diagonalizing the Hamiltonian at the order
, present the first order corrections to the geometrical optics. The
photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling.
However, even for a torsionless space-time, photons do not follow the usual
null geodesic as a consequence of an anomalous velocity term. This term is
responsible for the gravitational birefringence phenomenon: photons with
distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page
Pairing of Parafermions of Order 2: Seniority Model
As generalizations of the fermion seniority model, four multi-mode
Hamiltonians are considered to investigate some of the consequences of the
pairing of parafermions of order two. 2-particle and 4-particle states are
explicitly constructed for H_A = - G A^+ A with A^+}= 1/2 Sum c_{m}^+ c_{-m}^+
and the distinct H_C = - G C^+ C with C^+}= 1/2 Sum c_{-m}^+ c_{m}^+, and for
the time-reversal invariant H_(-)= -G (A^+ - C^+)(A-C) and H_(+) = -G
(A^+dagger + C^+)(A+C), which has no analogue in the fermion case. The spectra
and degeneracies are compared with those of the usual fermion seniority model.Comment: 18 pages, no figures, no macro
Wigner quantum oscillators. Osp(3/2) oscillators
The properties of the three-dimensional noncanonical osp(3/2) oscillators,
introduced in J.Phys. A: Math. Gen. {\bf 27} (1994) 977, are further studied.
The angular momentum M of the oscillators can take at most three values
M=p-1,p,p+1, which are either all integers or all half-integers. The
coordinates anticommute with each other. Depending on the state space the
energy spectrum can coincide or can be essentially different from those of the
canonical oscillator. The ground state is in general degenerated.Comment: TeX, Preprint INRNE-TH-94/3, 17
Bell-states diagonal entanglement witnesses for relativistic and non-relativistic multispinor systems in arbitrary dimensions
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are
constructed by using the algebra of Dirac matrices in the space-time
of arbitrary dimension , where the first kind can detect some BSD
relativistic and non-relativistic -partite multispinor bound entangled
states in Hilbert space of dimension , including the
bipartite Bell-type and iso-concurrence type states in the four-dimensional
space-time (). By using the connection between Hilbert-Schmidt measure and
the optimal EWs associated with states, it is shown that as far as the spin
quantum correlations is concerned, the amount of entanglement is not a
relativistic scalar and has no invariant meaning. The introduced EWs are
manipulated via the linear programming (LP) which can be solved exactly by
using simplex method. The decomposability or non-decomposability of these EWs
is investigated, where the region of non-decomposable EWs of the first kind is
partially determined and it is shown that, all of the EWs of the second kind
are decomposable. These EWs have the preference that in the bipartite systems,
they can determine the region of separable states, i.e., bipartite
non-detectable density matrices of the same type as the EWs of the first kind
are necessarily separable. Also, multispinor EWs with non-polygon feasible
regions are provided, where the problem is solved by approximate LP, and in
contrary to the exactly manipulatable EWs, both the first and second kind of
the optimal approximate EWs can detect some bound entangled states.
Keywords: Relativistic entanglement, Entanglement Witness, Multispinor,
Linear Programming, Feasible Region. PACs Index: 03.65.UdComment: 62 page
Grand canonical partition functions for multi level para Fermi systems of any order
A general formula for the grand canonical partition function for a para Fermi
system of any order and of any number of levels is derived.Comment: 9 pages, latex, no figure
Canonical Partition Functions for Parastatistical Systems of any order
A general formula for the canonical partition function for a system obeying
any statistics based on the permutation group is derived. The formula expresses
the canonical partition function in terms of sums of Schur functions. The only
hitherto known result due to Suranyi [ Phys. Rev. Lett. {\bf 65}, 2329 (1990)]
for parasystems of order two is shown to arise as a special case of our general
formula. Our results also yield all the relevant information about the
structure of the Fock spaces for parasystems.Comment: 9 pages, No figures, Revte
Einstein-Podolsky-Rosen correlation in gravitational field
For quantum communication in a gravitational field, the properties of the
Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of
general relativity. Acceleration and gravity are shown to deteriorate the
perfect anti-correlation of an EPR pair of spins in the same direction, and
apparently decrease the degree of the violation of Bell's inequality. To
maintain the perfect EPR correlation and the maximal violation of Bell's
inequality, observers must measure the spins in appropriately chosen different
directions. Which directions are appropriate depends on the velocity of the
particles, the curvature of the spacetime, and the positions of the observers.
Near the event horizon of a black hole, the appropriate directions depend so
sensitively on the positions of the observers that even a very small
uncertainty in the identification of the observers' positions leads to a fatal
error in quantum communication, unless the observers fall into the black hole
together with the particles.Comment: 22 pages, 3 figures, several minor revisions are mad
- âŠ