Transient diffusion and thermal processes in a finite one-dimensional harmonic crystal.

In this paper, an instant homogeneous thermal perturbation in the periodic one-dimensional harmonic crystal is studied. The exact solution for thermal and diffusive characteristics is obtained, namely, particle velocity dispersion (kinetic temperature) and particle displacement dispersion. It is found that thermal and diffusion processes demonstrate a quasi-periodic recurrence. The recurrence interval is equal to the time it takes the sound wave to travel the half-length of the crystal. The 'thermal echo' (sharp peaks in kinetic temperature) occurs in the system with the specified periodicity. Diffusion characteristics reveal large-scale time changes with a nearly complete return to the initial state at each quasi-period. It is also shown that the spatial mean squared displacements of particles are significantly different from the ensemble mean squared displacements.

Transition to thermal equilibrium in a crystal subjected to instantaneous deformation.

An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the particles have random displacements and random velocities corresponding to uniform initial temperature distributions. An instantaneous change in the parameters of the chain initiates a transitional process. Analytical expressions for the chain temperature as a function of time are obtained from statistical analysis of the dynamic equations. It is shown that the transition process is oscillatory and that the temperature converges non-monotonically to a new equilibrium state, in accordance with what is usually unexpected for thermal processes. The analytical results are supplemented by numerical simulations.

Geometrically nonlinear dynamic model for a hexagonal lattice.

It is shown that angular stiffness in the hexagonal lattice model plays a significant role in the geometrical nonlinear terms in the equations of the continuum limit. A geometrically nonlinear discrete model is formulated for the hexagonal lattice by considering the interaction of two sublattices. An asymptotic procedure is developed in order to obtain the nonlinear coupled equations of motion in the continuum limit of the discrete model. An interaction of longitudinal and shear plane strain waves is studied by using the solutions of the obtained equations.

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 t^{-3/2} in the case of the potential energy and to t^{-5/2} 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.

Thermal echo in a finite one-dimensional harmonic crystal.

An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude described by the Bessel function of the first kind. In the present paper it is shown that in the finite crystal this behavior is observed only until a certain period of time when a sharp increase of the oscillation amplitude is realized. This phenomenon, further referred to as the thermal echo, occurs periodically, with the period proportional to the crystal length. The amplitude for each subsequent echo is lower than for the previous one. It is obtained analytically that the time-dependence of the kinetic temperature can be described by an infinite sum of the Bessel functions with multiple indices. It is also shown that the thermal echo in the thermodynamic limit is described by the Airy function.

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. The motion of each particle is governed by a single scalar equation and therefore the notion 'scalar lattice' is used. The 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 the 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 t by [Formula: see text]. 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.

[Genetically determined lipid metabolism disorders due to oral intake of technogenic hyperchlorination products].

The study covered genetically determined lipid metabolism disorders due to oral intake of technogenic hyperchlorination drinkable water products. Findings are that overweight and obese children in a main group appeared to have serum chloroform level 2.3 times higher than that in a reference group. In oral intake of hyperchlorination drinkable water products, the study revealed main genes having polymorphism associated with endocrine disorders: overweight and obesity--APOE, PPARG, HTR2A, characterizing antioxidant system state--SOD2 and detoxication--SULTA. Polymorphism of candidate genes HTR2A and SOD2 was characterized by increased occurrence of mutant homo-- and heterozygous genotype, relative risk of pathologic allele presence in population exceeded the refrence group values. Probability of increased serum serotonin and lower Cu/Zn in children with mutant homozygous genotype HTR2A and SOD2 is 1.2-1.3 times higher than in those with heterozygous and normal homozygous genotypes.

[Immune and genetic changes in workers exposed to industrial noise and dust].

Comparative analysis covered immune genetic parameters in nonferrous metallurgy workers. The authors demonstrated differences in immune genetic profile between male and female workers, under exposure to combination of occupational hazards: noise and dust. Analysis of gene polymorphism revealed predominant disorders in the female workers, concerning criterion of prevalence for minor allele of genes in 1 and 2 phases of detoxication, neuro-endocrine regulation, lipid and energy metabolism, genes of immune regulation and apoptosis.