5,787 research outputs found
A SVD accelerated kernel-independent fast multipole method and its application to BEM
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of
almost linear complexity. In the original KIFMM the time-consuming M2L
translations are accelerated by FFT. However, when more equivalent points are
used to achieve higher accuracy, the efficiency of the FFT approach tends to be
lower because more auxiliary volume grid points have to be added. In this
paper, all the translations of the KIFMM are accelerated by using the singular
value decomposition (SVD) based on the low-rank property of the translating
matrices. The acceleration of M2L is realized by first transforming the
associated translating matrices into more compact form, and then using low-rank
approximations. By using the transform matrices for M2L, the orders of the
translating matrices in upward and downward passes are also reduced. The
improved KIFMM is then applied to accelerate BEM. The performance of the
proposed algorithms are demonstrated by three examples. Numerical results show
that, compared with the original KIFMM, the present method can reduce about 40%
of the iterating time and 25% of the memory requirement.Comment: 19 pages, 4 figure
Nanoparticle enhanced evaporation of liquids: A case study of silicone oil and water
Evaporation is a fundamental physical phenomenon, of which many challenging
questions remain unanswered. Enhanced evaporation of liquids in some occasions
is of enormous practical significance. Here we report the enhanced evaporation
of the nearly permanently stable silicone oil by dispersing with nanopariticles
including CaTiO3, anatase and rutile TiO2. The results can inspire the research
of atomistic mechanism for nanoparticle enhanced evaporation and exploration of
evaporation control techniques for treatment of oil pollution and restoration
of dirty water
Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
In this paper we revisit the relation between the Friedmann equations and the
first law of thermodynamics. We find that the unified first law firstly
proposed by Hayward to treat the "outer"trapping horizon of dynamical black
hole can be used to the apparent horizon (a kind of "inner" trapping horizon in
the context of the FRW cosmology) of the FRW universe. We discuss three kinds
of gravity theorties: Einstein theory, Lovelock thoery and scalar-tensor
theory. In Einstein theory, the first law of thermodynamics is always satisfied
on the apparent horizon. In Lovelock theory, treating the higher derivative
terms as an effective energy-momentum tensor, we find that this method can give
the same entropy formula for the apparent horizon as that of black hole
horizon. This implies that the Clausius relation holds for the Lovelock theory.
In scalar-tensor gravity, we find, by using the same procedure, the Clausius
relation no longer holds. This indicates that the apparent horizon of FRW
universe in the scalar-tensor gravity corresponds to a system of
non-equilibrium thermodynamics. We show this point by using the method
developed recently by Eling {\it et al.} for dealing with the gravity.Comment: v2: revtex, 23 pages, references added, minor changes, to appear in
PR
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