On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals

Loboda, O. S.; Podolskaya, E. A.; Tsvetkov, D.; Кривцов, А. М.

doi:10.1007/s00161-020-00921-0

Cited by 6 publications

(5 citation statements)

References 30 publications

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“…Formulas (55) are derived in Appendix A.3. The space distribution of mass forms a body of matter-a cloud of particles.…”

Section: Mass Dispersionmentioning

confidence: 99%

“…where the constant coefficients are defined by formulas (55) and can be expressed in the terms of initial conditions. Similar to the case of mass dispersion, at the moment of focusing (𝑡 = 𝑡 * ) the phantom reaches its minimum size described by 𝜌 min , for 𝑡 < 𝑡 * the phantom shrinks, afterwards it expands infinitely -see fig.…”

Section: Energy Dispersionmentioning

confidence: 99%

“…Wave energy transfer is responsible for heat transfer in crystalline solids, where nondiffusive ballistic and anomalous processes of heat energy transfer are common at micro/nanolevel, especially in low dimensions, which is shown by analytical [23][24][25][26][27][28][29][30][31][32][33][34][35][36] and experimental [3,[37][38][39][40][41][42][43][44] investigations. Recently an extensive research for description of unsteady ballistic heat transfer processes was performed by our scientific group [45][46][47][48][49][50][51][52][53][54][55][56], and the obtained results together with some ideas inspired by Zhilin [57] and Kunin [58] played a motivation role for this paper.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of matter and energy

Кривцов

2022

Z Angew Math Mech

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We propose and examine a potential analogy between mass transfer (in space) and energy transfer (in solids). We adapt classical equations of matter dynamics to describe the dynamics of energy transfer. Such fundamental quantities as the effective mass, momentum, moment of inertia and other quantities typical for bodies of matter are introduced for “bodies” of energy. Along with this, two new concepts of “carrier” and “phantom” are proposed. A carrier is a medium which enables energy transfer. A phantom is a virtual body of matter having its mass distribution equivalent to the energy distribution in the carrier. Using an inhomogeneous chain of particles as a sample system, we show that the phantom motion satisfies the Newton's second law of dynamics. For certain systems, we derive constitutive equations for the net force, which results in a closed system of dynamics equations. We further show that with the relevant properties of the chain it is possible to obtain the dynamics equation for the phantom motion in a gravitational field. We use similar methods to study energy dispersion. To analyze phantom evolution, we introduce the velocities of phantom transfer and dispersion. We show that, depending on the ratio of these velocities, the phantom can behave either as a wave or as a particle. Furthermore, we discuss potential application of energy dynamics to other branches of physics, such as quantum mechanics, electrodynamics and general relativity. We introduce the idea that a body of matter itself can be a phantom in some other carrier, which is a different entity than matter. Possible associations of the phantom/carrier model with current models of physical space are discussed. Based on the presented concept, we propose plausible qualitative answers to several open questions in modern physics.

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“…Formulas (55) are derived in Appendix A.3. The space distribution of mass forms a body of matter-a cloud of particles.…”

Section: Mass Dispersionmentioning

confidence: 99%

Section: Energy Dispersionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of matter and energy

Кривцов

2022

Z Angew Math Mech

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“…Здесь же отметим, что с ней ассоциируются имена Ньютона, Бернулли, Лагранжа, Коши, Гамильтона, Эйнштейна, Дебая, Шредингера и многих других выдающихся ученых. В текущее время интерес к этой модели связан в основном с проблемой аналитического обоснования закона теплопроводности Фурье [2][3][4][5].…”

Section: Introductionunclassified

The problem of vibrations in a harmonic chain with damping and anti-damping on the boundaries

Gudimenko,

Lihosherstov

2023

FEMJ

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The problem of oscillations in a finite homogeneous chain of coupled harmonic oscillators is considered under special boundary conditions that ensure a stable flow of energy from one end of the chain to the other. The problem covers, as special cases, the classical problem of oscillations in a chain with free and fixed ends, as well as the problem of oscillations in a chain with absorbing and anti-absorbing boundaries. Absorbing boundary conditions are used in numerical simulation of wave propagation to minimize the influence of non-physical boundaries. An exact analytical solution to the considered problem is obtained. The dynamical system of the problem is studied. In particular, a description of the invariant subspaces of the system is given. The oscillatory properties of the system are investigated. The phenomenon of a significant increase in the amplitude of low-frequency oscillations has been discovered and studied. The problem is solved in Schrodinger variables. The solution is presented both in terms of infinite series of Bessel functions and in terms of natural oscillations (eigenmodes) of the system.

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“…Особенно наглядно это проявляется в термоупругом эффекте [4][5][6], где изменение температуры при адиабатическом деформировании тела часто носит парадоксальный характер: температура уменьшается при растяжении тела, т. е. при совершении работы внешних сил. Указанные проблемы также связаны с проблемой термализации (достижения состояния теплового равновесия) в некоторых системах [7,8,9], которая в последнее время вызывает большой интерес [10,11,12].…”

Section: Introductionunclassified

О Термодинамических Параметрах Адиабатически Изолированного Тела

Горобей¹,

Лукьяненко²

2021

Физика Твердого Тела

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The definition of the main thermodynamic functions for an adiabatically isolated body with constant internal energy is proposed in the framework of the formalism of the covariant quantum theory with reparametrization invariance of proper time. The modification does not change the dynamic content of the theory at the classical level, but it allows one to define the unitary evolution operator in quantum theory. In this operator, proper time is a measure of the internal movement of the body. The transition to statistical mechanics is carried out by the Wick rotation of proper time in the complex plane. As a result, a representation of the partition function of an isolated body in the form of a Euclidean functional integral on the space of closed trajectories in the configuration space is obtained. For a given internal energy, the average return temperature and free energy are determined, which under lie the thermomechanics of an adiabatically isolated body.

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On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals

Cited by 6 publications

References 30 publications

Dynamics of matter and energy

Dynamics of matter and energy

The problem of vibrations in a harmonic chain with damping and anti-damping on the boundaries

О Термодинамических Параметрах Адиабатически Изолированного Тела

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