A new viewpoint on theory of the scaling-law heat conduction process

In this article, we suggest a new model for the heat-conduction problem by us?ing the scaling-law vector calculus with Mandelbrot scaling law. The linear and non-linear scaling-law heat conduction equations are considered as analogues to the work of Fourier, Laplace, and Burgers. The obtained results are considered as typical examples to deal with the Mandelbrots scaling-law phenomena in heat transport system.

SYNTHESIS OF ZONAL CONTROL OF LUMPED SOURCES FOR THE HEAT CONDUCTION PROCESS

The paper studies the problem of synthesis of control of lumped sources for an object with distributed parameters based on discrete observation of the phase state at specific object points. We propose an approach in which the whole phase space at the observed points is preliminarily divided in some way into given subsets (zones). The synthesized controls are selected from the class of piecewise-constant functions, and their current values are determined by a subset of the phase space containing the population of current states of the object at the observed points, at which controls take constant values. Such synthesized controls are called zonal. We give a numerical technique for obtaining optimal values of zonal controls using efficient first-order optimization methods. To this purpose, we derive formulas for the gradient of the objective function in the space of zonal controls.

Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system

The heat conduction process in composite medium can be modeled by a parabolic equation with discontinuous radiative coefficient. To detect the composite medium characterized by such a non-smooth coefficient from measurable information about the heat distribution, we consider a nonlinear inverse problem for parabolic equation, with the average measurement of temperature field in some time interval as the inversion input. We firstly establish the uniqueness for this nonlinear inverse problem, based on the property of the direct problem and the known uniqueness result for linear inverse source problem. To solve the inverse problem from a nonlinear operator equation, the differentiability and the tangential condition of this nonlinear map is analyzed. An iterative process called two-point gradient method is proposed by minimizing data-fit term and the penalty term alternatively, with rigorous convergence analysis in terms of the tangential condition. Numerical simulations are presented to illustrate the effectiveness of the proposed method.

Dynamic Error Correction of Filament Thermocouples with Different Structures of Junction based on Inverse Filtering Method

Since filament thermocouple is limited by its junction structure and dynamic characteristics, the actual heat conduction process cannot be reproduced during the transient thermal shock. In order to solve this problem, we established a thermocouple dynamic calibration system with laser pulse as excitation source to transform the problem of the restoring excitation source acting on the surface temperature of thermocouple junction into the problem of solving the one-dimensional (1D) inverse heat conduction process, proposed a two-layer domain filtering kernel regularization method for double conductors of thermocouple, analyzed the factors causing unstable two-layer domain solution, and solved the regular solution of two-layer domain by the filtering kernel regularization strategy. By laser narrow pulse calibration experiment, we obtained experimental samples of filament thermocouples with two kinds of junction structures, butt-welded and ball-welded; established error estimation criterion; and obtained the optimal filtering kernel parameters by the proposed regularization strategy, respectively. The regular solutions solved for different thermocouples were very close to the exact solution under the optimal strategy, indicating that the proposed regularization method can effectively approach the actual surface temperature of the thermocouple junction.

Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations

Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The uniqueness and conditional stability for this inverse problem are established by using the properties of a parabolic equation and the representation of solution after reforming the equation. By combining the least squares method with the regularization technique, the inverse problem is transformed into an optimal control problem. Based on the existence and uniqueness of the minimizer of the cost functional, an alternative iteration process is built to solve this optimizing problem by the variational adjoint method. The negative gradient direction is selected as the first search direction. For further iterations, the alternative iteration algorithm is used for the initial field and heat source identification. The efficiency of the proposed scheme is tested by the numerical simulation experiments.

Information filtering based on eliminating redundant diffusion and compensating balance

In statistical physics, researchers concentrate on mass diffusion and heat conduction-based information filtering models, which effectively facilitate recommendation accuracy and diversity. There are many improved methods combining mass diffusion with heat conduction theories. Research results show that the best results are achieved when the combination of mass diffusion and heat conduction reaches equilibrium. With elaborative analysis, we find that similarity redundancies derive from the attribute correlations of objects, and deduce the similarity estimation deviation. Considering the former deficiencies, we propose a novel model through eliminating redundant diffusion and compensating balance (shortly ERD-CB), which symmetrically combines mass diffusion with heat conduction process through balance compensation. Three benchmark datasets from Movielens, Amazon and Netflix are used in our extensive experiments. Experiment results show that the ERD-CB model outperforms the benchmarkbaselines for accuracy, diversity and novelty.

Research on the dissipative characteristics of unsteady heat conduction for the one-dimensional sphere

In this paper, the dissipative characteristics of unsteady heat conduction process for the one-dimensional sphere is studied. The dissipation function can be regarded as a Lyapunov function for the heat conduction system, which determines the evolution direction of the system and the stability of the steady state. By use of the vector formula, the relationship between the thermal potential and dissipation function is derived, and its similarity with the dissipation system of mechanical energy is shown. The expression of dissipation function is obtained when the boundary temperature is fixed. In addition, an example for optimization of heat conduction process is discussed based on the entransy dissipation extremum principle.