The outer solar atmosphere, the corona, contains plasma at temperatures of more than a million K, more than 100 times hotter that solar surface. How this gas is heated is a fundamental question tightly interwoven with the structure of the magnetic fi
eld in the upper atmosphere. Conducting numerical experiments based on magnetohydrodynamics we account for both the evolving three-dimensional structure of the atmosphere and the complex interaction of magnetic field and plasma. Together this defines the formation and evolution of coronal loops, the basic building block prominently seen in X-rays and extreme ultraviolet (EUV) images. The structures seen as coronal loops in the EUV can evolve quite differently from the magnetic field. While the magnetic field continuously expands as new magnetic flux emerges through the solar surface, the plasma gets heated on successively emerging fieldlines creating an EUV loop that remains roughly at the same place. For each snapshot the EUV images outline the magnetic field, but in contrast to the traditional view, the temporal evolution of the magnetic field and the EUV loops can be different. Through this we show that the thermal and the magnetic evolution in the outer atmosphere of a cool star has to be treated together, and cannot be simply separated as done mostly so far.
The $2$-cell embeddings of graphs on closed surfaces have been widely studied. It is well known that ($2$-cell) embedding a given graph $G$ on a closed orientable surface is equivalent to cyclically ordering the edges incident to each vertex of $G$.
In this paper, we study the following problem: given a genus $g$ embedding $mathbb{E}$ of the graph $G$, if we randomly rearrange the edges around a vertex, i.e., re-embedding, what is the probability of the resulting embedding $mathbb{E}$ having genus $g+Delta g$? We give a formula to compute this probability. Meanwhile, some other known and unknown results are also obtained. For example, we show that the probability of preserving the genus is at least $frac{2}{deg(v)+2}$ for re-embedding any vertex $v$ of degree $deg(v)$ in a one-face embedding; and we obtain a necessary condition for a given embedding of $G$ to be an embedding with the minimum genus.
In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These problems are ver
y important in the study of the evolution of genomes. We give a general formulation for lower bounds of the transposition and block-interchange distance from which the existing lower bounds obtained by Bafna and Pevzner, and Christie can be easily derived. As to the reversal distance of signed permutations, we translate it into a block-interchange distance problem of permutations so that we obtain a new lower bound. Furthermore, studying distance problems via our framework motivates several interesting combinatorial problems related to product of permutations, some of which are studied in this paper as well.
In this paper, we introduce plane permutations, i.e. pairs $mathfrak{p}=(s,pi)$ where $s$ is an $n$-cycle and $pi$ is an arbitrary permutation, represented as a two-row array. Accordingly a plane permutation gives rise to three distinct permutations:
the permutation induced by the upper horizontal ($s$), the vertical $pi$) and the diagonal ($D_{mathfrak{p}}$) of the array. The latter can also be viewed as the three permutations of a hypermap. In particular, a map corresponds to a plane permutation, in which the diagonal is a fixed point-free involution. We study the transposition action on plane permutations obtained by permuting their diagonal-blocks. We establish basic properties of plane permutations and study transpositions and exceedances and derive various enumerative results. In particular, we prove a recurrence for the number of plane permutations having a fixed diagonal and $k$ cycles in the vertical, generalizing Chapuys recursion for maps filtered by the genus. As applications of this framework, we present a combinatorial proof of a result of Zagier and Stanley, on the number of $n$-cycles $omega$, for which the product $omega(1~2~cdots ~n)$ has exactly $k$ cycles. Furthermore, we integrate studies on the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. Plane permutations allow us to generalize and recover various lower bounds for transposition and block-interchange distances and to connect reversals with block-interchanges.
In this paper we generalize permutations to plane permutations. We employ this framework to derive a combinatorial proof of a result of Zagier and Stanley, that enumerates the number of $n$-cycles $omega$, for which $omega(12cdots n)$ has exactly $k$
cycles. This quantity is $0$, if $n-k$ is odd and $frac{2C(n+1,k)}{n(n+1)}$, otherwise, where $C(n,k)$ is the unsigned Stirling number of the first kind. The proof is facilitated by a natural transposition action on plane permutations which gives rise to various recurrences. Furthermore we study several distance problems of permutations. It turns out that plane permutations allow to study transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. Novel connections between these different distance problems are established via plane permutations.
Recently, the resistance saturation at low temperature in Kondo insulator SmB6, a long-standing puzzle in condensed matter physics, was proposed to originate from topological surface state. Here,we systematically studied the magnetoresistance of SmB6
at low temperature up to 55 Tesla. Both temperature- and angular-dependent magnetoresistances show a similar crossover behavior below 5 K. Furthermore, the angular-dependent magnetoresistance on different crystal face confirms a two-dimensional surface state as the origin of magnetoresistances crossover below 5K. Based on two-channels model consisting of both surface and bulk states, the field-dependence of bulk gap with critical magnetic field (Hc) of 196 T is extracted from our temperature-dependent resistance under different magnetic fields. Our results give a consistent picture to understand the low-temperature transport behavior in SmB6, consistent with topological Kondo insulator scenario.
The zero-field specific heat of LiFeAs was measured on several single crystals selected from a bulk sample. A sharp Delta Cp/Tc anomaly of approximately 20 mJ/(mole x K^2) was observed. The value appears to be between those of SmFeAs(O0.9F0.1) and (B
a0.6K0.4)Fe2As2, but bears no clear correlation with their Sommerfeld coefficients. The electronic specific heat below Tc further reveals a two-gap structure with the narrower one only on the order of 0.7 meV. While the results are in rough agreement with the Hc1(T) previously reported on both LiFeAs and (Ba0.6K0.4)Fe2As2, they are different from the published specific-heat data of a (Ba0.6K0.4)Fe2As2 single crystal.
We report the first comprehensive high-resolution angle-resolved photoemission measurements on CeFeAsO, a parent compound of FeAs-based high temperature superconductors with a mangetic/structural transition at $sim$150 K. In the magnetic ordering sta
te, four hole-like Fermi surface sheets are observed near $Gamma$(0,0) and the Fermi surface near M(+/-$pi$,+/-$pi$) shows a tiny electron-like pocket at M surrounded by four Dirac cone-like strong spots. The unusual Fermi surface topology deviates strongly from the band structure calculations. The electronic signature of the magnetic/structural transition shows up in the dramatic change of the quasiparticle scattering rate. A dispersion kink at $sim$ 25meV is for the first time observed in the parent compound of Fe-based superconductors.
Single Degenerate model is the most widely accepted progenitor model of type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from a main sequence or a slightly evolved star (WD +MS) to increase its
mass, and explodes when its mass approaches the Chandrasekhar mass limit. During the mass transfer phase between the two components, an optically thick wind may occur and the material lost as the wind may exist as circumstellar material (CSM). Searching the CSM around progenitor star is helpful to discriminate different progenitor models of SNe Ia. Meanwhile, the CSM is a source of color excess.The purpose of this paper is to study the color excess produced from the single-degenerate progenitor model with optically thick wind, and reproduce the distribution of color excesses of SNe Ia. Meng et al. (2009) systemically carried out binary evolution calculation of the WD +MS systems for various metallicities and showed the parameters of the systems before Roche lobe overflow and at the moment of supernova explosion in Meng & Yang (2009). With the results of Meng et al. (2009), we calculate the color excesses of SNe Ia at maximum light via a simple analytic method.We reproduces the distribution of color excesses of SNe Ia by our binary population synthesis approach if the velocity of the optically thick wind is taken to be of order of magnitude of 10 km s$^{rm -1}$. However, if the wind velocity is larger than 100 km s$^{rm -1}$, the reproduction is bad.
In order to evaluate $g_0$, the interaction strength of a pair of $^{52}$Cr atoms with total spin S=0, a specially designed s-wave scattering of the pair has been studied theoretically. Both the incident atom and the target atom trapped by a harmonic
potential are polarized previously but in reverse directions. Due to spin-flip, the outgoing atom may have spin component $mu$ ranging from -3 to 3. The outgoing channels are classified by $mu$. The effect of $g_{0}$ on the scattering amplitudes of each of these $mu-$channels has been predicted.
