Yu-Tung Chen

On kernel formulas and dispersionless Hirota equations of the extended dispersionless BKP hierarchy

We derive dispersionless Hirota equations of the extended dispersionless BKP(EdBKP) hierarchy proposed by Takasaki from the method of kernel formula provided by Carroll and Kodama. Moreover, we verify associativity equations (WDVV equations) in the EdBKP hierarchy from dispersionless Hirota equations and give a realization of associative algebra with structure constants expressed in terms of the residue formula.

Solving the dispersionless Dym equation by hodograph transformations

The method of hodograph transformation is used to find a class of exact solutions of the dispersionless Dym (dDym) equation and its reductions. In particular, we discuss hodograph solutions of one-variable and two-variable reductions of the dDym system and investigate their associated Lax as well as Hamiltonian formalism.

On the Dispersionless Dym Hierarchy: Dressing Formulation and Twistor Construction

We discuss the dressing formulation and twistor construction for the dispersionless Dym (dDym) hierarchy. In particular, we investigate one-variable and two-variables reductions of the dDym hierarchy to illustrate the formalism. We derive the associated string equations of the reduced dDym hierarchies and obtain their hodograph solutions.

NOVEL MAGNETISM AND SUPERCONDUCTIVITY IN A Ru-BASED DOUBLE PEROVSKITE

We report the observations, using magnetic susceptibility and specific heat measurements, of the coexistence of superconductivity and magnetic ordering at low temperatures in the Cu-doping double perovskites Sr2ARu1-xCuxO6, with A=Y or Ho, and x<0.2. The observed striking features can be understood in terms of a plausible theoretical model based on the double exchange mechanism, which occurs indirectly via Ru5+ spin coupling to itinerant electrons hopping from one Ru site to another.

A note on the dispersionless BKP hierarchy

We discuss the Miura map as well as the Poisson algebras associated with the dispersionless Dym hierarchy. Particularly, we study explicitly the bi-Hamiltonian structure of a truncated Dym system with two variables, in which a new hierarchy flow generated by logarithmic Hamiltonians appears. We then show that this new hierarchy emerges naturally from the topological recursion relation in the Landau–Ginzburg formulation.

Conformal covariantization of Moyal-Lax operators

A covariant approach to the conformal property associated with Moyal-Lax operators is given. By identifying the conformal covariance with the second Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the primary fields of one-parameter deformation of classical W-algebras.

Polytropic gas dynamics revisited

We investigate the Hamiltonian as well as Lax formulations of the polytropic gas dynamics which can be characterized by the polytropic exponent γ=1+h. We show that when h=1∕m with ∣m∣∊N⩾2, the resonant phenomena occur in bi-Hamiltonian formulation and logarithmic-type conserved charges emerge naturally. We provide a logarithmic Lax representation for conserved charges and the whole hierarchy flows, which coincides with the bi-Hamiltonian formulation constructed from a two-dimensional Frobenius manifold associated with the polytropic gas dynamics.

Magnetic and superconducting properties of single crystals of Sr2HoRu1−xCuxO6 grown from high temperature solutions

Single crystals of Sr2HoRu1−xCuxO6 (with x=0–0.2), measuring 2–3mm across have been grown from PbO–PbF2 based solutions in the temperature range of 1250–1150°C. The crystals exhibit octahedral morphology and belong to the monoclinic space group P21∕n. While Sr2HoRuO6 is found to be antiferromagnetic with weak ferromagnetism below 30K, the solid solutions containing Cu exhibit a diamagnetic transition at 31K which increases in magnitude and temperature with increasing Cu. Through a correlation of magnetic and calorimetric properties, these crystals are concluded to be spin-glass superconductors.

The -approach to the dispersionless (2+1)-Harry Dym hierarchy

A -approach is adopted to study the dispersionless Harry Dym (dHD) hierarchy. Moreover, this formulism is applied to construct some explicit solutions of the dHD hierarchy.

Nonlinear Thickness and Grain Size Effects on the Thermal Conductivity of CuFeSe2 Thin Films

A crucial issue in realizing the applications of high-density semiconductor devices is no more than heat dissipation, especially in the direction perpendicular to the substrate. For the past decades, crystallization effects on thermal conductivity have been intensively studied, whereas the quantitative analysis on this aspect is rare. In this study, a series of CuFeSe2 thin films with grain sizes 20-40 nm controlled by the thickness were fabricated for the quantitative study of the grain size effect on the thermal conductivity perpendicular to the subtract. The results reveal that larger grain sizes have higher thermal conductivity and the trend agreed well with the simplified theory of the phonon-grain boundary interaction. From the data of electrical conductivity and the Wiedemann-Franz law, the thermal conductivity is mainly contributed by the lattice thermal conductivity, and is nonlinearly dependent on the grain size and the thickness of the films. In addition, the ～ 2.6×10^(-8) K-m^2/W film-substrate interfacial thermal resistance (comparable to that of 200 nm films) is also a non-negligible factor and has to be taken into account.