61,531 research outputs found
Spinor Bose Condensates in Optical Traps
In an optical trap, the ground state of spin-1 Bosons such as Na,
K, and Rb can be either a ferromagnetic or a "polar" state,
depending on the scattering lengths in different angular momentum channel. The
collective modes of these states have very different spin character and spatial
distributions. While ordinary vortices are stable in the polar state, only
those with unit circulation are stable in the ferromagnetic state. The
ferromagnetic state also has coreless (or Skyrmion) vortices like those of
superfluid He-A. Current estimates of scattering lengths suggest that the
ground states of Na and Rb condensate are a polar state and a
ferromagnetic state respectively.Comment: 11 pages, no figures. email : [email protected]
Hierarchical interpolative factorization for elliptic operators: differential equations
This paper introduces the hierarchical interpolative factorization for
elliptic partial differential equations (HIF-DE) in two (2D) and three
dimensions (3D). This factorization takes the form of an approximate
generalized LU/LDL decomposition that facilitates the efficient inversion of
the discretized operator. HIF-DE is based on the multifrontal method but uses
skeletonization on the separator fronts to sparsify the dense frontal matrices
and thus reduce the cost. We conjecture that this strategy yields linear
complexity in 2D and quasilinear complexity in 3D. Estimated linear complexity
in 3D can be achieved by skeletonizing the compressed fronts themselves, which
amounts geometrically to a recursive dimensional reduction scheme. Numerical
experiments support our claims and further demonstrate the performance of our
algorithm as a fast direct solver and preconditioner. MATLAB codes are freely
available.Comment: 37 pages, 13 figures, 12 tables; to appear, Comm. Pure Appl. Math.
arXiv admin note: substantial text overlap with arXiv:1307.266
Hierarchical interpolative factorization for elliptic operators: integral equations
This paper introduces the hierarchical interpolative factorization for
integral equations (HIF-IE) associated with elliptic problems in two and three
dimensions. This factorization takes the form of an approximate generalized LU
decomposition that permits the efficient application of the discretized
operator and its inverse. HIF-IE is based on the recursive skeletonization
algorithm but incorporates a novel combination of two key features: (1) a
matrix factorization framework for sparsifying structured dense matrices and
(2) a recursive dimensional reduction strategy to decrease the cost. Thus,
higher-dimensional problems are effectively mapped to one dimension, and we
conjecture that constructing, applying, and inverting the factorization all
have linear or quasilinear complexity. Numerical experiments support this claim
and further demonstrate the performance of our algorithm as a generalized fast
multipole method, direct solver, and preconditioner. HIF-IE is compatible with
geometric adaptivity and can handle both boundary and volume problems. MATLAB
codes are freely available.Comment: 39 pages, 14 figures, 13 tables; to appear, Comm. Pure Appl. Mat
Boson Mott insulators at finite temperatures
We discuss the finite temperature properties of ultracold bosons in optical
lattices in the presence of an additional, smoothly varying potential, as in
current experiments. Three regimes emerge in the phase diagram: a
low-temperature Mott regime similar to the zero-temperature quantum phase, an
intermediate regime where MI features persist, but where superfluidity is
absent, and a thermal regime where features of the Mott insulator state have
disappeared. We obtain the thermodynamic functions of the Mott phase in the
latter cases. The results are used to estimate the temperatures achieved by
adiabatic loading in current experiments. We point out the crucial role of the
trapping potential in determining the final temperature, and suggest a scheme
for further cooling by adiabatic decompression
A fast semi-direct least squares algorithm for hierarchically block separable matrices
We present a fast algorithm for linear least squares problems governed by
hierarchically block separable (HBS) matrices. Such matrices are generally
dense but data-sparse and can describe many important operators including those
derived from asymptotically smooth radial kernels that are not too oscillatory.
The algorithm is based on a recursive skeletonization procedure that exposes
this sparsity and solves the dense least squares problem as a larger,
equality-constrained, sparse one. It relies on a sparse QR factorization
coupled with iterative weighted least squares methods. In essence, our scheme
consists of a direct component, comprised of matrix compression and
factorization, followed by an iterative component to enforce certain equality
constraints. At most two iterations are typically required for problems that
are not too ill-conditioned. For an HBS matrix with
having bounded off-diagonal block rank, the algorithm has optimal complexity. If the rank increases with the spatial dimension as is
common for operators that are singular at the origin, then this becomes
in 1D, in 2D, and
in 3D. We illustrate the performance of the method on
both over- and underdetermined systems in a variety of settings, with an
emphasis on radial basis function approximation and efficient updating and
downdating.Comment: 24 pages, 8 figures, 6 tables; to appear in SIAM J. Matrix Anal. App
Two-dimensional gases of generalized statistics in a uniform magnetic field
We study the low temperature properties of two-dimensional ideal gases of
generalized statistics in a uniform magnetic field. The generalized statistics
considered here are the parafermion statistics and the exclusion statistics.
Similarity in the behaviours of the parafermion gas of finite order and the
gas with exclusion coefficient at very low temperatures is noted. These
two systems become exactly equivalent at . Qumtum Hall effect with these
particles as charge carriers is briefly discussed.Comment: Latex file, 14 pages, 5 figures available on reques
Influence of high gas production during thermophilic anaerobic digestion in pilot-scale and lab-scale reactors on survival of the thermotolerant pathogens Clostridium perfringens and Campylobacter jejuni in piggery wastewater
Safe reuse of animal wastes to capture energy and nutrients, through anaerobic digestion processes, is becoming an increasingly desirable solution to environmental pollution. Pathogen decay is the most important safety consideration and is in general, improved at elevated temperatures and longer hydraulic residence times. During routine sampling to assess pathogen decay in thermophilic digestion, an inversely proportional relationship between levels of Clostridium perfringens and gas production was observed. Further samples were collected from pilot-scale, bench-scale thermophilic reactors and batch scale vials to assess whether gas production (predominantly methane) could be a useful indicator of decay of the thermotolerant pathogens C. perfringens and Campylobacter jejuni. Pathogen levels did appear to be lower where gas production and levels of methanogens were higher. This was evident at each operating temperature (50, 57, 65 °C) in the pilot-scale thermophilic digesters, although higher temperatures also reduced the numbers of pathogens detected. When methane production was higher, either when feed rate was increased, or pH was lowered from 8.2 (piggery wastewater) to 6.5, lower numbers of pathogens were detected. Although a number of related factors are known to influence the amount and rate of methane production, it may be a useful indicator of the removal of the pathogens C. perfringens and C. jejuni
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