scholarly journals On the expansion coefficients of Tau-function of the BKP hierarchy

2016 ◽  
Vol 49 (29) ◽  
pp. 295201 ◽  
Author(s):  
Yoko Shigyo
2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Atsushi Nakayashiki ◽  
Soichi Okada ◽  
Yoko Shigyo

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Alexander Alexandrov

Abstract In their recent inspiring paper, Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar description for the Brézin-Gross-Witten tau-function. Moreover, we identify both tau-functions of the KdV hierarchy, which describe intersection numbers on the moduli spaces of punctured Riemann surfaces, with the hypergeometric solutions of the BKP hierarchy.


Author(s):  
Jipeng Cheng ◽  
Todor Milanov

Abstract It was proved in 2010 that the principal Kac–Wakimoto hierarchy of type $D$ is a reduction of the 2-component BKP hierarchy. On the other hand, it is known that the total descendant potential of a singularity of type $D$ is a tau-function of the principal Kac–Wakimoto hierarchy. We find explicitly the point in the Grassmannian of the 2-component BKP hierarchy (in the sense of Shiota) that corresponds to the total descendant potential. We also prove that the space of tau-functions of Gaussian type is parametrized by the base of the miniversal unfolding of the simple singularity of type $D$.


Author(s):  
Karren L. More

Beta-SiC is an ideal candidate material for use in semiconductor device applications. Currently, monocrystalline β-SiC thin films are epitaxially grown on {100} Si substrates by chemical vapor deposition (CVD). These films, however, contain a high density of defects such as stacking faults, microtwins, and antiphase boundaries (APBs) as a result of the 20% lattice mismatch across the growth interface and an 8% difference in thermal expansion coefficients between Si and SiC. An ideal substrate material for the growth of β-SiC is α-SiC. Unfortunately, high purity, bulk α-SiC single crystals are very difficult to grow. The major source of SiC suitable for use as a substrate material is the random growth of {0001} 6H α-SiC crystals in an Acheson furnace used to make SiC grit for abrasive applications. To prepare clean, atomically smooth surfaces, the substrates are oxidized at 1473 K in flowing 02 for 1.5 h which removes ∽50 nm of the as-grown surface. The natural {0001} surface can terminate as either a Si (0001) layer or as a C (0001) layer.


2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Marco Bertola

AbstractThe paper has two relatively distinct but connected goals; the first is to define the notion of Padé approximation of Weyl–Stiltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the Riemann surface and a measure on it, together with the additional datum of a local coordinate near a point and a divisor of degree g. The denominators of the resulting Padé-like approximation also satisfy an orthogonality relation and are sections of appropriate line bundles. A Riemann–Hilbert problem for a square matrix of rank two is shown to characterize these orthogonal sections, in a similar fashion to the ordinary orthogonal polynomial case. The second part extends this idea to explore its connection to integrable systems. The same data can be used to define a pairing between two sequences of line bundles. The locus in the deformation space where the pairing becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kadomtsev–Petviashvili hierarchy with respect to either deformation parameters, and a certain modification of the 2-Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is related to the Krichever construction of algebro-geometric solutions.


2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jean-Emile Bourgine

Abstract In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.


2013 ◽  
Vol 646 ◽  
pp. 59-66 ◽  
Author(s):  
Arcady Zhukov ◽  
Margarita Churyukanova ◽  
Lorena Gonzalez-Legarreta ◽  
Ahmed Talaat ◽  
Valentina Zhukova ◽  
...  

We studied the effect ofthe magnetoelastic ansitropy on properties of nanostructured glass-coated microwires with soft magnetic behaviour (Finemet-type microwires of Fe70.8Cu1Nb3.1Si14.5B10.6, Fe71.8Cu1Nb3.1Si15B9.1 and Fe73.8Cu1Nb3.1Si13B9.1 compositions) and with granular structure (Cu based Co-Cu microwires). The magnetoelastic energy originated from the difference in thermal expansion coefficients of the glass and metallic alloy during the microwires fabrication, affected the hysteresis loops, coercivity and heat capacity of Finemet-type microwires. Hysteresis loops of all as-prepared microwires showed rectangular shape, typical for Fe-rich microwires. As expected, coercivity, HC, of as-prepared microwires increases with decreasing of the ratio ρ defined as the ratio between the metallic nucleus diameter, d to total microwire diameter, D. On the other hand we observed change of heat capacity in microwires with different ratio ρ. In the case of Co-Cu microwires ρ- ratio affected the structure and the giant magneto-resistance of obtained microwires.


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