A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes

We describe a finite-volume method for solving the Poisson equation on oct-tree adaptive meshes using direct solvers for individual mesh blocks. The method is a modified version of the method presented by Huang and Greengard (2000), which works with finite-difference meshes and does not allow for shared boundaries between refined patches. Our algorithm is implemented within the FLASH code framework and makes use of the PARAMESH library, permitting efficient use of parallel computers. We describe the algorithm and present test results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor revisions in response to referee's comments; added char

The hyperfine structure in the rotational spectrum of CF+

Context. CF+ has recently been detected in the Horsehead and Orion Bar photo-dissociation regions. The J=1-0 line in the Horsehead is double-peaked in contrast to other millimeter lines. The origin of this double-peak profile may be kinematic or spectroscopic. Aims. We investigate the effect of hyperfine interactions due to the fluorine nucleus in CF+ on the rotational transitions. Methods. We compute the fluorine spin rotation constant of CF+ using high-level quantum chemical methods and determine the relative positions and intensities of each hyperfine component. This information is used to fit the theoretical hyperfine components to the observed CF+ line profiles, thereby employing the hyperfine fitting method in GILDAS. Results. The fluorine spin rotation constant of CF+ is 229.2 kHz. This way, the double-peaked CF+ line profiles are well fitted by the hyperfine components predicted by the calculations. The unusually large hyperfine splitting of the CF+ line therefore explains the shape of the lines detected in the Horsehead nebula, without invoking intricate kinematics in the UV-illuminated gas.Comment: 2 pages, 1 figure, Accepted for publication in A&

Photon inner product and the Gauss linking number

It is shown that there is an interesting interplay between self-duality, loop representation and knots invariants in the quantum theory of Maxwell fields in Minkowski space-time. Specifically, in the loop representation based on self-dual connections, the measure that dictates the inner product can be expressed as the Gauss linking number of thickened loops.Comment: 18 pages, Revtex. No figures. To appear in Class. Quantum Gra

Gauss Linking Number and Electro-magnetic Uncertainty Principle

It is shown that there is a precise sense in which the Heisenberg uncertainty between fluxes of electric and magnetic fields through finite surfaces is given by (one-half $\hbar$ times) the Gauss linking number of the loops that bound these surfaces. To regularize the relevant operators, one is naturally led to assign a framing to each loop. The uncertainty between the fluxes of electric and magnetic fields through a single surface is then given by the self-linking number of the framed loop which bounds the surface.Comment: 13 pages, Revtex file, 3 eps figure

A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases

Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases have been given in several papers (see [2,3,7,8]). In the course of evaluation, the sigh (or unit root) ambiguities are unavoidably occurred. This paper presents another method, different from [7] and [8], to determine the sigh (unit root) ambiguities of Gauss sums in the index 2 case, as well as the ones with odd order in the non-cyclic index 4 case. And we note that the method in this paper are more succinct and effective than [8] and [7]

The interplay of Hrd3 and the molecular chaperone system ensures efficient degradation of malfolded secretory proteins

Misfolded proteins of the secretory pathway are extracted from the endoplasmic reticulum (ER), polyubiquitylated by a protein complex termed the Hmg-CoA reductase degradation ligase (HRD-ligase) and degraded by cytosolic 26S proteasomes. This process is termed ER-associated protein degradation (ERAD). We previously showed that the membrane protein Der1, which is a subunit of the HRD-ligase, is involved in the export of aberrant polypeptides from the ER. Unexpectedly, we also uncovered a close spatial proximity of Der1 and the substrate receptor Hrd3 in the ER lumen. We report here on a mutant Hrd3KR, which is selectively defective for ERAD of soluble proteins. Hrd3KR displays subtle structural changes that affect its positioning toward Der1. Furthermore, increased quantities of the ER-resident Hsp70 type chaperone Kar2 and the Hsp40 type cochaperone Scj1 bind to Hrd3KR. Noteworthy, deletion of SCJ1 impairs ERAD of model substrates and causes the accumulation of client proteins at Hrd3. Our data imply a function of Scj1 in the removal of malfolded proteins from the receptor Hrd3, which facilitates their delivery to downstream acting components like Der1

Proposal of a population wide genome-based testing for Covid-19

Our lives (and deaths) have by now been dominated for two years by COVID-19, a pandemic that has caused hundreds of millions of disease cases, millions of deaths, trillions in economic costs, and major restrictions on our freedom. Here we suggest a novel tool for controlling the COVID-19 pandemic. The key element is a method for a population-scale PCR-based testing, applied on a systematic and repeated basis. For this we have developed a low cost, highly sensitive virus-genome-based test. Using Germany as an example, we demonstrate by using a mathematical model, how useful this strategy could have been in controlling the pandemic. We show using real-world examples how this might be implemented on a mass scale and discuss the feasibility of this approach

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017