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 $f(R)$ gravity.Comment: v2: revtex, 23 pages, references added, minor changes, to appear in PR