Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na, $^{39}$K, and $^{87}$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 $^{3}$He-A. Current estimates of scattering lengths suggest that the ground states of $^{23}$Na and $^{87}$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: 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

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

Similarity solutions of Reaction-Diffusion equation with space- and time-dependent diffusion and reaction terms

We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction-diffusion systems. Several representative examples of exactly solvable reaction-diffusion equations are presented.Comment: 11 pages, 4 figure

The Human Right to Science and Foundational Technologies

Feeney et al. (2018) make a valid argument for restrictions on the exclusivity of foundational technologies such as CRISPR. The issue of balancing intellectual property right with access to scientific and technological advancements is certainly not new. In our commentary, we argue that the human right to science offers a more concrete basis for governments to balance their competing commitments in promoting scientific development on the one hand, and ensuring benefit-sharing on the other, in ways that advance social justice under non-ideal conditions

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 $p$ and the gas with exclusion coefficient $g=1/p$ at very low temperatures is noted. These two systems become exactly equivalent at $T=0$. 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