Bayesian inference for solving a class of heat conduction problems

The Monte-Carlo algorithm is an effective method to study the Curie temperature of a ferromagnetic system related to its exchange constant, magnetic moment, and co-ordination number. Curie temperatures of the three types of ferromagnetic systems are calculated, e.g., the hexagonal crystal system, the tetragonal sys-tem, and the orthorhombic system. In order to make the calculated magnetic moment-temperature curve fit a steep slope, the size of the supercell of the ferro-magnetic system is selected as small as possible, and Monte-Carlo steps are per-formed 5000000 times at each temperature. The calculation reveals a significant result: the Curie temperature scales with the exchange constant and the square of the magnetic moment.

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“…1(a), the lattice constant a = b, γ = 60°, and the co-ordination number Z = 6. The Hamiltonian describing the system is [12,[19][20][21]:…”

Section: Monte-carlo Algorithmmentioning

confidence: 99%

Research on the curie temperature of ferromagnetic system by Monte-Carlo algorithm

Dong

Yan

2022

THERM SCI

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“…There are alternative methods for nonlinear oscillators; some famous ones include the variational iteration method, [74][75][76][77][78][79] the exp-function method, [80][81][82][83] the variational theory, [82][83][84] the G'/G-expansion method, 85 the Bayesian inference method, 86 the barycentric rational interpolation collocation method, 87 and others. 88 This section focuses itself on a simple method to find the frequency-amplitude relationship of a nonlinear oscillator using He's frequency formulation, [89][90][91] which represents a genius idea in converting a nonlinear equation into a linear equation.…”

Section: Quasi-exact Solution Based On He's Frequency Formulamentioning

confidence: 99%

“…Ex19: Solve the following fractional damping Duffing equation using He’s frequency formula 102 In terms of the restoring forcethe fractional Duffing equation (276) becomesBased on He’s frequency formula, equation (278) can be written in the formwhere the Duffing frequency ω2 is estimated as 86 Now, equation (279) has a linear form with the fractional order. It can be solved using the modified homotopy technique.…”

Section: Quasi-exact Solution Based On He’s Frequency Formulamentioning

confidence: 99%

A heuristic review on the homotopy perturbation method for non-conservative oscillators

El‐Dib

2021

Journal of Low Frequency Noise, Vibration and Active Control

112

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The homotopy perturbation method (HPM) was proposed by Ji-Huan. He was a rising star in analytical methods, and all traditional analytical methods had abdicated their crowns. It is straightforward and effective for many nonlinear problems; it deforms a complex problem into a linear system; however, it is still developing quickly. The method is difficult to deal with non-conservative oscillators, though many modifications have appeared. This review article features its last achievement in the nonlinear vibration theory with an emphasis on coupled damping nonlinear oscillators and includes the following categories: (1) Some fallacies in the study of non-conservative issues; (2) non-conservative Duffing oscillator with three expansions; (3)the non-conservative oscillators through the modified homotopy expansion; (4) the HPM for fractional non-conservative oscillators; (5) the homotopy perturbation method for delay non-conservative oscillators; and (6) quasi-exact solution based on He’s frequency formula. Each category is heuristically explained by examples, which can be used as paradigms for other applications. The emphasis of this article is put mainly on Ji-Huan He’s ideas and the present authors’ previous work on the HPM, so the citation might not be exhaustive.

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Numerical simulation of radiative heat transfer in a binary-size granular bed

et al. 2022

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The radiative heat transfer in a high-temperature granular bed of binary-size mixture was explored in this paper. The effective view factor between particles decreases exponentially with the increase in particle interval, increases with the increase in the size of the absorption particle but is hardly affected by the volume ratio of the mixture. The effective thermal conductivity of granular bed was further deduced basing on the characteristic of the effective view factor. It is indicated that the thermal conductivity is proportional to the particle size and temperature cubed, and increases with the increase in the particle size ratio and volume ratio. Finally, modified calculation correlations of the effective view factor and effective thermal conductivity were developed for binary-size bed based on the simulation results, and good accuracy of less than 0.01 and 10% had been achieved, respectively.

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Bayesian inference for solving a class of heat conduction problems

Cited by 4 publications

References 26 publications

Research on the curie temperature of ferromagnetic system by Monte-Carlo algorithm

Research on the curie temperature of ferromagnetic system by Monte-Carlo algorithm

A heuristic review on the homotopy perturbation method for non-conservative oscillators

Numerical simulation of radiative heat transfer in a binary-size granular bed

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