Newly Discovered Global Temperature Structures in the Quiet Sun at Solar Minimum

Magnetic loops are building blocks of the closed-field corona. While active region loops are readily seen in images taken at EUV and X-ray wavelengths, quiet Sun loops are seldom identifiable and therefore difficult to study on an individual basis. The first analysis of solar minimum (Carrington Rotation 2077) quiet Sun (QS) coronal loops utilizing a novel technique called the Michigan Loop Diagnostic Technique (MLDT) is presented. This technique combines Differential Emission Measure Tomography (DEMT) and a potential field source surface (PFSS) model, and consists of tracing PFSS field lines through the tomographic grid on which the Local Differential Emission Measure (LDEM) is determined. As a result, the electron temperature Te and density Ne at each point along each individual field line can be obtained. Using data from STEREO/EUVI and SOHO/MDI, the MLDT identifies two types of QS loops in the corona: so-called "up" loops in which the temperature increases with height, and so-called "down" loops in which the temperature decreases with height. Up loops are expected, however, down loops are a surprise, and furthermore, they are ubiquitous in the low-latitude corona. Up loops dominate the QS at higher latitudes. The MLDT allows independent determination of the empirical pressure and density scale heights, and the differences between the two remain to be explained. The down loops appear to be a newly discovered property of the solar minimum corona that may shed light on the physics of coronal heating. The results are shown to be robust to the calibration uncertainties of the EUVI instrument.Comment: Accepted for publication in The Astrophysical Journal, waiting for the full biblio inf

High-accuracy two-loop computation of the critical mass for Wilson fermions

We test an algebraic algorithm based on the coordinate-space method, evaluating with high accuracy the critical mass for Wilson fermions in lattice QCD at two loops. We test the results by using different types of infrared regularization.Comment: Lattice2001(improvement): 3 page

A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal have been found to be isotopic invariant relative to a special type of isotopism or the other. Presently, there are two outstanding open problems on universality of loops: semi automorphic inverse property loops(1999) and Osborn loops(2005). Smarandache isotopism(S-isotopism) was originally introduced by Vasantha Kandasamy in 2002. But in this work, the concept is re-restructured in order to make it more explorable. As a result of this, the theory of Smarandache isotopy inherits the open problems as highlighted above for isotopy. In this short note, the question 'Under what type of S-isotopism will a pair of S-quasigroups(S-loops) form any variety?' is answered by presenting a pair of specially S-isotopic S-quasigroups(loops) that both belong to the same variety of S-quasigroups(S-loops). This is important because pairs of specially S-isotopic S-quasigroups(e.g Smarandache cross inverse property quasigroups) that are of the same variety are useful for applications(e.g cryptography).Comment: 10 page

d dimensional SO(d)-Higgs Models with Instanton and Sphaleron: d=2,3

The Abelian Higgs model and the Georgi-Glashow model in 2 and 3 Euclidean dimensions respectively, support both finite size instantons and sphalerons. The instantons are the familiar Nielsen-Oleson vortices and the 't Hooft-Polyakov monopole solutions respectively. We have constructed the sphaleron solutions and calculated the Chern-Simons charges N_cs for sphalerons of both models and have constructed two types of noncontractible loops between topologically distinct vacuua. In the 3 dimensional model, the sphaleron and the vacuua have zero magnetic and electric flux while the configurations on the loops have non vanishing magnetic flux.Comment: 24 pages, 3 figures, LaTe

Exact conjectured expressions for correlations in the dense O(1)(1) loop model on cylinders

We present conjectured exact expressions for two types of correlations in the dense O$(n=1)$ loop model on $L\times \infty$ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by $m$ loops and the probability that $k$ consecutive points on a row are on the same or on different loops. The dense O$(n=1)$ loop model is equivalent to the bond percolation model at the critical point. The former probability can be interpreted in terms of the bond percolation problem as giving the probability that a vertex is on a cluster that is surrounded by \floor{m/2} clusters and \floor{(m+1)/2} dual clusters. The conjectured expression for this probability involves a binomial determinant that is known to give weighted enumerations of cyclically symmetric plane partitions and also of certain types of families of nonintersecting lattice paths. By applying Coulomb gas methods to the dense O$(n=1)$ loop model, we obtain new conjectures for the asymptotics of this binomial determinant.Comment: 17 pages, replaced by version accepted by JSTA

Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.Comment: 8 pages, 7 figure

Enhanced entrainability of genetic oscillators by period mismatch

Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We investigated the advantageous effect of this period mismatch in terms of a synchronization response to external stimuli. Specifically, we considered two fundamental models of genetic circuits: smooth- and relaxation oscillators. Using phase reduction and Floquet multipliers, we numerically analyzed their entrainability under different coupling strengths and period ratios. We found that a period mismatch induces better entrainment in both types of oscillator; the enhancement occurs in the vicinity of the bifurcation on their limit cycles. In the smooth oscillator, the optimal period ratio for the enhancement coincides with the experimentally observed ratio, which suggests biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often explained as a passive mechanism to ensure robustness against perturbation, we study the active benefits of the period mismatch, which include increasing the efficiency of the genetic oscillators. Our findings show a qualitatively different perspective for both the inherent advantages of multiple loops and their essentiality.Comment: 28 pages, 13 figure