Effective Hamiltonian approach to kinetic Ising models: Application to an infinitely long-range Husimi-Temperley model.

The probability distribution (PD) of spin configurations in kinetic Ising models has been cast in the form of the canonical Boltzmann PD with a time-dependent effective Hamiltonian (EH). It has been argued that in systems with extensive energy EH depends linearly on the number of spins N leading to the exponential dependence of PD on the system size. In macroscopic systems the argument of the exponential function may reach values of the order of the Avogadro number which is impossible to deal with computationally, thus making unusable the linear master equation (ME) governing the PD evolution. To overcome the difficulty, it has been suggested to use instead the nonlinear ME (NLME) for the EH density per spin. It has been shown that in spatially homogeneous systems NLME contains only terms of order unity even in the thermodynamic limit. The approach has been illustrated with the kinetic Husimi-Temperley model (HTM) evolving under the Glauber dynamics. At finite N the known numerical results has been reproduced and extended to broader parameter ranges. In the thermodynamic limit an exact nonlinear partial differential equation of the Hamilton-Jacobi type for EH has been derived. It has been shown that the average magnetization in HTM evolves according to the conventional kinetic mean field equation.

Universality and scaling in two-step epitaxial growth in one dimension.

Irreversible one-dimensional (1D) epitaxial growth at small coverages via the recently suggested two-step growth protocol [Tokar and Dreyssé, Surf. Sci. 637-638, 116 (2015)] has been studied with the use of the kinetic Monte Carlo and the rate-equation techniques. It has been found that similar to the two-dimensional (2D) case the island capture zones could be accurately approximated with the Gamma probability distribution (GD). Coverage independence of the average island sizes grown at the first step that was also found in two dimensions was observed. In contrast to 2D case, the shape parameter of the GD was also found to be coverage-independent. Using these two constants as the input, an analytical approach that allowed for the description of the commonly studied statistical distributions to the accuracy of about 2% has been developed. Furthermore, it was established that the distributions of the island sizes and the interisland gaps grown via the two-step protocol were about 50% narrower than in the case of nucleation on random defects, which can be of practical importance. Equivalence between the GD shape of the island size distribution in the scaling regime and the linear dependence of the capture numbers on the island size in the rate-equation approach has been proved.

Nucleation of size calibrated three-dimensional nanodots in atomistic model of strained epitaxy: a Monte Carlo study.

We introduce a simple model of strained epitaxy to study the growth of coherent several-monolayers-high nanoislands at low coverage. The size mismatch between the substrate (which is assumed to be rigid and passive) and the growing overlayer is modelled by the hard-sphere interaction between the adatoms. In the case of positive misfit the sphere diameter is larger than the substrate lattice parameter. Elastic interactions are described within the harmonic approximation to the substrate potential in the vicinity of the deposition sites. With additional attractive interaction between the nearest neighbour atoms the model exhibited the growth of miniature nanoislands of several morphologies with their kinetics similar to those found in real quantum dot (QD) systems. The 3D QDs exhibited narrow distributions of their heights, diameters and volumes in qualitative agreement with experimental observations.

Accelerated kinetic Monte Carlo algorithm for diffusion-limited kinetics.

If a stochastic system during some periods of its evolution can be divided into noninteracting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo algorithms. As an illustrative example, the simulation of irreversible growth of extended one-dimensional islands is considered. The approach allowed us to simulate the systems characterized by parameters superior to those used in previous simulations.

Exact solution of a one-dimensional model of strained epitaxy on a periodically modulated substrate.

We consider a one-dimensional lattice gas model of strained epitaxy with the elastic strain accounted for through a finite number of cluster interactions comprising contiguous atomic chains. Interactions of this type arise in the models of strained epitaxy based on the Frenkel-Kontorova model. Furthermore, the deposited atoms interact with the substrate via an arbitrary periodic potential of period L. This model is solved exactly with the use of an appropriately adopted technique developed recently in the theory of protein folding. The advantage of the proposed approach over the standard transfer-matrix method is that it reduces the problem to finding the largest eigenvalue of a matrix of size L instead of 2(L-1), which is vital in the case of nanostructures where L may measure in hundreds of interatomic distances. Our major conclusion is that the substrate modulation always facilitates the size calibration of self-assembled nanoparticles in one- and two-dimensional systems.

Analytical solution of a one-dimensional lattice gas model with an infinite number of multiatom interactions.

We consider a one-dimensional lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next-nearest-neighbor pairwise interaction. All interactions are of arbitrary strength. An analytical expression for the size distribution of atomic chain lengths is obtained in the framework of the canonical ensemble formalism. Application of the exact solution to the problems of self-assembly and self-organization is briefly discussed.

[Chronic effect of fluorides on the status of the pancreatic insular apparatus of workers]. / Khronicheskoe vliianie ftoridov na sostoianie ostrovkovogo apparata podzheludochnoi zhelezy u rabochikh.

Decreasing of the insulin concentration and increasing of the C-peptide level in blood serum of 72 workers of cryolytes industries detected by radioimmunological method. These changes were caused by the fluorine intoxication of workers.

[The function of the pancreatic islet cells during prolonged hypokinesia]. / Funktsional'noe sostoianie ostrovkovykh kletok podzheludochnoi zhelezy pri dlitel'noi gipokinezii.

The content of insulin, C-peptide, glucagon, somatostatin, and glucose was studied in the blood of animals experiencing 3, 10, 30, 70, and 140-day hypokinesia (HK) and the cAMP content--in their liver and renal cortex. It was found that in 3-day HK insulin production and catabolism are sharply stimulated, the glucagon and glucose content is increased, the somatostatin level is reduced, and cAMP content in the liver and kidneys is reduced. Ten-day HK is characterized by hyperglycemia, an almost normal hormone content, and increased cAMP level in the renal cortex. In 30-day HK the blood insulin and glucagon content, the content of cAMP in the liver and renal cortex are sharply increased, and the level of somatostatin and glucose is reduced. In 70-day HK the content of glucose and hormones in the blood is reduced, the cAMP level in both organs does not differ from that in the controls. In 140-day HK the concentration of insulin and glucagon in the blood of the animals increases significantly and the level of glycemia normalizes, evidently through increase of cAMP in the liver and kidneys.

[Mathematical evaluation of methods of determining the fibrinolytic activity of whole blood]. / Matematicheskaia otsenka metodov opredeleniia fibrinoliticheskoi aktivnosti tsel'noi krovi.

Mathematical analysis of the adequacy of laboratory tests for estimation of blood fibrinolytic activity, routinely used in practical obstetrics, has shown that any of the known methods may be used in healthy nonpregnant and pregnant women for the diagnosis of fibrinolysis system abnormalities. To diagnose such conditions in women with pathologic pregnancy two laboratory tests should be employed with due consideration for their impact.

[Chronic effects of fluorides on the pituitary-thyroid system in industrial workers]. / Khronicheskoe vliianie ftoridov na sistemu gipofiz--shchitovidnaia zheleza u promyshlennykh rabochikh.

Radioimmunologic study of thyrotropin and thyroid hormones in the blood of those engaged in fluorine production showed moderate functional changes of the hypophysis-thyroid gland system, not accompanied by clinical manifestations of hypo- or hyperthyreosis and caused by disorders of the regulatory chain and fluorine impact on thyroid hormones' metabolism at the level of target cells. Elevation of calcitonin concentration in workers' blood indicated stimulation of thyroid gland parafollicular cells. Phase states in the hypophysis-thyroid gland system were detected along with the dependence of some hormones' concentration on the duration of workers' contact with fluorine compounds and the stage of fluorosis.

[Effect of chorionic gonadotropin on estrogen excretion in healthy men and in fluorosis patients]. / Vliianie khorionicheskogo gonadotropina na ékskretsiiu éstrogenov u zdorovykh muzhchin i bol'nykh fliuorosom.

Estrogen excretion was studied by fractions in the urine of 10 healthy men and in 11 men suffering from fluorosis before and after the chorionic gonadotropin (CG) load. The response to the CG administration was expressed in increased urinary estrogens excretion in the healthy men and in the patients with fluorosis; the hyperexcretion intensity depended on the dose of the hormone administered. In comparison with healthy men, patients with fluorosis displayed specific temporary shifts in the maximal estrogen excretion peaks, and also a significant increase in estriol concentration in the urine. A conclusion was drawn that changes in the estrogen concentration in the urine of patients with fluorosis were connected with disturbed metabolism of these steroids, and not with elevation of their production in the testes.

[Effect of inorganic fluorine compounds on the functional state of the pituitary-testis system]. / Vliianie neorganicheskikh soedinenii ftora na funktsional'noe sostoianie sistemy gipofiz--semenniki.

The radioimmunological method was applied to the study of blood testosterone, LH, and FSH content in 41 men suffering from fluorosis, aged from 33 to 45 years. Nineteen men who had no contact with fluorine compounds served as control. In comparison with healthy individuals testosterone content proved to be decreased and FSH content elevated in patients with fluorosis. Blood LH content was increased only in those patients with fluorosis who had long contact with fluorine compounds (over 15 years). The changes in the blood hormone concentration were connected with disturbances of the hormonal, and, possibly, of the germenative function of the testes. The hypophysis proved to suffer less, and the changes of its function were apparently secondary in character.