Integral balance methods applied to non-classical Stefan problems

We consider two different Stefan problems for a semi-infinite material for the non-classical heat equation with a source that depends on the heat flux at the fixed face. One of them, with constant temperature at the fixed face, was already studied in literature and the other, with a convective boundary condition at the fixed face, is presented in this work. Due to the complexity of the exact solution it is of interest to compare with approximate solutions obtained by applying heat balance integral methods, assuming a quadratic temperature profile in space. A dimensionless analysis is carried out by using the parameters: Stefan number and the generalized Biot number. In addition it is studied the case when Biot number goes to infinity, recovering the approximate solutions when a Dirichlet condition is imposed at the fixed face. Some numerical simulations are provided in order to verify the accuracy of the approximate methods.

Integral methods of solving heat-conduction problems: a new concept (Dirichlet condition)

On the basic of consideration of the heat-conduction problem for a semi-bounded space with a temperature profile defined by a parabola with an exponent n, a new concept of construction of constitutive involves the introduction of a local function for a heat flow or for the temperature, with is determined from the heat-conduction equation. The approach proposed made it possible to obtain a number of new integral relation: an improved integral for the temperature momentum, an integral of a quadratic heat flow, and an integral of a quadratic temperature function. Two Schemes of optimizing the exponent n with the use of the error norms E1 and are proposed. As compared to the Langford norm, the indicated error norms made it possible to substantially increase the approximation accuracy of solutions of the problem posed.

Parametric Level Set-Based Multimaterial Topology Optimization of Heat Conduction Structures

This paper presents a parametric level set-based method (PLSM) for multimaterial topology optimization of heat conduction structures with volume constraints. A parametric level set-based optimization model of heat conduction structures is built with multimaterial level set (MM-LS) model, which describes the boundaries of different materials by the combination of all level set functions. The heat dissipation efficiency which means the quadratic temperature gradient is conducted as the objective function. The adjoint method is utilized to calculate the sensitivities of the objective function with respect to expansion coefficients of the compactly supported radial basis functions (CSRBFs). The optimal configuration is achieved by updating the expansion coefficients gradually with the method of moving asymptotes (MMA). Several numerical examples are discussed to demonstrate effectiveness of the proposed method for multimaterial topology optimization of heat conduction structures.

Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa2Cu4O8

Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that, inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations [Doiron-Leyraud N, et al. (2007)Nature447(7144):565–568], optical conductivity [Mirzaei SI, et al. (2013)Proc Natl Acad Sci USA110(15):5774–5778], and the validity of Wiedemann–Franz law [Grissonnache G, et al. (2016)Phys Rev B93:064513] point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field–induced normal state of underdoped YBa2Cu4O8that are consistent with aT2resistivity extending down to 1.5 K. The magnitude of theT2coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket.

Quadratic temperature dependence of electronic heat capacities in the κ-type organic superconductors

We carried out a systematic measurement and data analysis of low-temperature heat capacities of three BEDT-TTF-based superconductive compounds with [Formula: see text]-type structure, where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene so as to compare the character of the quasi-particle excitations reflected in the electronic heat capacity. We used an original relaxation calorimetry cell with much reduced addenda heat capacity as compared with previous works. The three compounds, [Formula: see text]-(BEDT-TTF)2Cu(NCS)2, [Formula: see text]-(BEDT-TTF)2Ag(CN)2H2O, [Formula: see text]-(BEDT-TTF)4Hg[Formula: see text]Br8 show distinct quadratic temperature dependence in their electronic heat capacity obtained by subtracting normal states data obtained by applying magnetic fields from the 0 T data. The line-nodal gap due to [Formula: see text]-wave pairing symmetry is suggested as common phenomena of the superconductivity of the [Formula: see text]-type compounds.