1,416 research outputs found
On Unsteady Heat Conduction in a Harmonic Crystal
An analytical model of unsteady heat transfer in a one-dimensional harmonic
crystal is presented. A nonlocal temperature is introduced as a generalization
of the kinetic temperature. A closed equation determining unsteady thermal
processes in terms of the nonlocal temperature is derived. For an instantaneous
heat perturbation a time-reversible equation for the kinetic temperature is
derived and solved. The resulting constitutive law for the heat flux in the
considered system is obtained. This law significantly differs from Fourier's
law and it predicts a finite velocity of the heat front and independence of the
heat flux on the crystal length. The analytical results are confirmed by
computer simulations.Comment: 5 pages, 3 figure
On heat transfer in a thermally perturbed harmonic chain
Unsteady heat transfer in a harmonic chain is analyzed. Two types of thermal
perturbations are considered: 1) initial instant temperature perturbation, 2)
external heat supply. Closed equations describing the heat propagation are
obtained and their analytical solution is constructed
G1-Renewal Process as Repairable System Model
This paper considers a point process model with a monotonically decreasing or
increasing ROCOF and the underlying distributions from the location-scale
family, known as the geometric process (Lam, 1988). In terms of repairable
system reliability analysis, the process is capable of modeling various
restoration types including "better-than-new", i.e., the one not covered by the
popular G-Renewal model (Kijima & Sumita, 1986). The distinctive property of
the process is that the times between successive events are obtained from the
underlying distributions as the scale parameter of each is monotonically
decreasing or increasing. The paper discusses properties and maximum likelihood
estimation of the model for the case of the Exponential and Weibull underlying
distributions.Comment: 11 pages, 1 table, 7 figure
Enhanced vector-based model for elastic bonds in solids
A model (further referred to as the enhanced vector-based model or EVM) for
elastic bonds in solids, composed of bonded particles is presented. The model
can be applied for a description of elastic deformation of rocks, ceramics,
concrete, nanocomposites, aerogels and other materials with structural elements
interacting via forces and torques. A material is represented as a set of
particles (rigid bodies) connected by elastic bonds. Vectors rigidly connected
with particles are used for description of particles orientations. Simple
expression for potential energy of a bond is proposed. Corresponding forces and
torques are calculated. Parameters of the potential are related to
longitudinal, transverse (shear), bending, and torsional stiffnesses of the
bond. It is shown that fitting parameters of the potential allows one to
satisfy any values of stiffnesses. Therefore, the model is applicable to bonds
with arbitrary length/thickness ratio. Bond stiffnesses are expressed in terms
of geometrical and elastic properties of the bonds using three models:
Bernoulli-Euler beam, Timoshenko beam, and short elastic cylinder. An approach
for validation of numerical implementation of the model is presented.
Validation is carried out by a comparison of numerical and analytical solutions
of four test problems for a pair of bonded particles. Benchmark expressions for
forces and torques in the case of pure tension/compression, shear, bending and
torsion of a single bond are derived. This approach allows one to minimize the
time required for a numerical implementation of the model.
Keywords: granular solid, elastic bond, torque interactions, V-model,
discrete element method, distinct element method, particle dynamics.Comment: 4 pages; 2 figure
Dissociation of Diatomic Molecule by Energy-Feedback Control
New method for dissociation of diatomic molecule based on nonperiodic
excitation generated by energy-feedback control mechanism is proposed. The
energy-feedback control uses frequency-energy (FE) relation of the natural
oscillations to fulfill the resonance conditions at any time of excitation.
Efficiency of the proposed method is demonstrated by the problem of
dissociation of hydrogen fluoride (HF) molecule. It is shown that new method is
more efficient then methods based on constant frequency and linear chirping
excitation.Comment: 9 pages, 8 figure
Discrete and Continuum Thermomechanics
In the present chapter, we discuss an approach for transition from discrete
to continuum description of thermomechanical behavior of solids. The transition
is carried out for several anharmonic systems: one-dimensional crystal,
quasi-one-dimensional crystal (a chain possessing longitudinal and transversal
motions), two- and tree-dimensional crystals with simple lattice. Macroscopic
balance equations are derived from equations of motion for particles.
Macroscopic parameters, such as stress, heat flux, deformation, thermal energy,
etc., are represented via parameters of the discrete system. Closed form
equations of state relating thermal pressure, thermal energy and specific
volume are derived. Description of the heat transfer in harmonic approximation
is discussed. Unsteady ballistic heat transfer in a harmonic one-dimensional
crystal is considered. The heat transfer equation for this system is rigorously
derived.Comment: 22 page
Thermal equilibration in a one-dimensional damped harmonic crystal
The features for the unsteady process of thermal equilibration ("the fast
motions") in a one-dimensional harmonic crystal lying in a viscous environment
(e.g., a gas) are under investigation. It is assumed that initially the
displacements of all the particles are zero and the particle velocities are
random quantities with zero mean and a constant variance, thus, the system is
far away from the thermal equilibrium. It is known that in the framework of the
corresponding conservative problem the kinetic and potential energies oscillate
and approach the equilibrium value that equals a half of the initial value of
the kinetic energy. We show that the presence of the external damping
qualitatively changes the features of this process. The unsteady process
generally has two stages. At the first stage oscillations of kinetic and
potential energies with decreasing amplitude, subjected to exponential decay,
can be observed (this stage exists only in the underdamped case). At the second
stage (which always exists), the oscillations vanish, and the energies are
subjected to a power decay. The large-time asymptotics for the energy is
proportional to in the case of the potential energy and to
in the case the kinetic energy. Hence, at large values of time the
total energy of the crystal is mostly the potential energy. The obtained
analytic results are verified by independent numerical calculations.Comment: Several misprints (Eqs. (10), (28), (31), (32) and below, (C21)) are
fixe
Fast and slow thermal processes in harmonic scalar lattices
An approach for analytical description of thermal processes in harmonic
lattices is presented. We cover longitudinal and transverse vibrations of
chains and out-of-plane vibrations of two-dimensional lattices with
interactions of an arbitrary number of neighbors. Motion of each particle is
governed by a single scalar equation and therefore the notion "scalar lattice"
is used. Evolution of initial temperature field in an infinite lattice is
investigated. An exact equation describing the evolution is derived.
Continualization of this equation with respect to spatial coordinates is
carried out. The resulting continuum equation is solved analytically. The
solution shows that the kinetic temperature is represented as the sum of two
terms, one describing short time behavior, the other large time behavior. At
short times, the temperature performs high-frequency oscillations caused by
redistribution of energy among kinetic and potential forms (fast process).
Characteristic time of this process is of order of ten periods of atomic
vibrations. At large times, changes of the temperature are caused by ballistic
heat transfer (slow process). The temperature field is represented as a
superposition of waves having the shape of initial temperature distribution and
propagating with group velocities dependent on the wave vector. Expressions
describing fast and slow processes are invariant with respect to substitution
by . However examples considered in the paper demonstrate that these
processes are irreversible. Numerical simulations show that presented theory
describes the evolution of temperature field at short and large time scales
with high accuracy.Comment: 26 pages, 7 figure
Localized heat perturbation in harmonic 1D crystals. Solutions for an equation of anomalous heat conduction
In this work exact solutions for the equation that describes anomalous heat
propagation in 1D harmonic lattices are obtained. Rectangular, triangular, and
sawtooth initial perturbations of the temperature field are considered. The
solution for an initially rectangular temperature profile is investigated in
detail. It is shown that the decay of the solution near the wavefront is
proportional to . In the center of the perturbation zone the decay
is proportional to . Thus the solution decays slower near the wavefront,
leaving clearly visible peaks that can be detected experimentally.Comment: 12 pages, 5 figure
Unsteady heat conduction processes in a harmonic crystal with a substrate potential
An analytical model of high frequency oscillations of the kinetic and
potential energies in a one-dimensional harmonic crystal with a substrate
potential is obtained by introducing the nonlocal energies [1]. A
generalization of the kinetic temperature (nonlocal temperature) is adopted to
derive a closed equation determining the heat propagation processes in the
harmonic crystal with a substrate potential
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