Change in stability of solid solution at radiation influence

Stability of solid solution at radiation influence has been investigated. Expressions for diffusion streams of binary alloy components, which specify the existence of temperature interval in which the phenomenon of ascending diffusion of elements is observed, were received. Vacancy characters of diffusion, configuration entropy, and potential energy of atomic bonds were considered at derivation. The ascending diffusion testifies to stability infringement of homogeneous solid solution - stratification. Influence of radiation is connected with increase in concentration of vacancies which changes the energy of atomic bonds and, simultaneously, accelerates diffusion processes. The condition of alloy stability with regard to stratification at radiating influence was obtaine

Dispersionful analogues of Benney's equations and NN-wave systems

We recall Krichever's construction of additional flows to Benney's hierarchy, attached to poles at finite distance of the Lax operator. Then we construct a ``dispersionful'' analogue of this hierarchy, in which the role of poles at finite distance is played by Miura fields. We connect this hierarchy with $N$-wave systems, and prove several facts about the latter (Lax representation, Chern-Simons-type Lagrangian, connection with Liouville equation, $\tau$-functions).Comment: 12 pages, latex, no figure

Numerical studies of variable-range hopping in one-dimensional systems

Hopping transport in a one-dimensional system is studied numerically. A fast algorithm is devised to find the lowest-resistance path at arbitrary electric field. Probability distribution functions of individual resistances on the path and the net resistance are calculated and fitted to compact analytic formulas. Qualitative differences between statistics of resistance fluctuations in Ohmic and non-Ohmic regimes are elucidated. The results are compared with prior theoretical and experimental work on the subject.Comment: 12 pages, 12 figures. Published versio

Diagram of the equilibrium phase composition of the Fe – Cr – Si – B system

Isothermal sections of the phase composition diagram of the Fe – Si – Cr – B system in the temperature range of 300 – 3 000 K with a step of 200 K are constructed. The diagram is shown at a temperature of 1 900 K, which is typical for silicochromium at the outlet from the furnace. A mathematical model of the diagram has been created in the form of a system of linear equations connecting the chemical composition of the metal with its phase. A computer program has been developed for the numerical calculation of the number of formed phases. Silicochromium with 0,3 – 0,5 % boron is located in the crystallization field CrSi2 – Si – SiB4 – FeSi

Diagram of the equilibrium phase composition of the Fe – Cr – Si – B system

Isothermal sections of the phase composition diagram of the Fe – Si – Cr – B system in the temperature range of 300 – 3 000 K with a step of 200 K are constructed. The diagram is shown at a temperature of 1 900 K, which is typical for silicochromium at the outlet from the furnace. A mathematical model of the diagram has been created in the form of a system of linear equations connecting the chemical composition of the metal with its phase. A computer program has been developed for the numerical calculation of the number of formed phases. Silicochromium with 0,3 – 0,5 % boron is located in the crystallization field CrSi2 – Si – SiB4 – FeSi

Evolution of the eyes of vipers with and without infrared-sensing pit organs

We examined lens and brille transmittance, photoreceptors, visual pigments, and visual opsin gene sequences of viperid snakes with and without infrared-sensing pit organs. Ocular media transmittance is high in both groups. Contrary to previous reports, small as well as large single cones occur in pit vipers. Non-pit vipers differ from pit vipers in having a twotiered retina, but few taxa have been examined for this poorly understood feature. All vipers sampled express rh1, sws1 and lws visual opsin genes. Opsin spectral tuning varies but not in accordance with the presence/absence of pit organs, and not always as predicted from gene sequences. The visual opsin genes were generally under purifying selection, with positive selection at spectral tuning amino acids in RH1 and SWS1 opsins, and at retinal pocket stabilization sites in RH1 or LWS (and without substantial differences between pit and nonpit vipers). Lack of evidence for sensory trade-off between viperid eyes (in the aspects examined) and pit organs might be explained by the high degree of neural integration of vision and infrared detection; the latter representing an elaboration of an existing sense with addition of a novel sense organ, rather than involving the evolution of a wholly novel sensory system

Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation

The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop approximation and the RG series obtained are resummed using the Borel-Leroy transformation combined with the generalized Pad\'e approximant and conformal mapping techniques. For the cubic model, the RG flows for various N are investigated. For N=2 it is found that the continuous line of fixed points running from the XY fixed point to the Ising one is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta functions closer to each another. For the cubic model with N\geq 3, the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N>2 is an artifact of the perturbative analysis. For the quenched dilute O(M) models ($MN$ models with N=0) the results are compatible with a stable pure fixed point for M\geq1. For the MN model with M,N\geq2 all the non-perturbative results are reproduced. In addition a new stable fixed point is found for moderate values of M and N.Comment: 26 pages, 3 figure

Anisotropic fragmentation in low-energy dissociative recombination

On a dense energy grid reaching up to 75 meV electron collision energy the fragmentation angle and the kinetic energy release of neutral dissociative recombination fragments have been studied in a twin merged beam experiment. The anisotropy described by Legendre polynomials and the extracted rotational state contributions were found to vary on a likewise narrow energy scale as the rotationally averaged rate coefficient. For the first time angular dependences higher than 2$^{nd}$ order could be deduced. Moreover, a slight anisotropy at zero collision energy was observed which is caused by the flattened velocity distribution of the electron beam.Comment: 8 pages, 4 figures; The Article will be published in the proceedings of DR 2007, a symposium on Dissociative Recombination held in Ameland, The Netherlands (18.-23. July 2008); Reference 19 has been published meanwhile in S. Novotny, PRL 100, 193201 (2008

Wide operational windows of edge-localized mode suppression by resonant magnetic perturbations in the DIII-D tokamak

Edge-Localized-Mode (ELM) suppression by resonant magnetic perturbations (RMPs) generally occurs over very narrow ranges of the plasma current (or magnetic safety factor q95) in the DIII-D tokamak. However, wide q95 ranges of ELM suppression are needed for the safety and operational flexibility of ITER and future reactors. In DIII-D ITER Similar Shape (ISS) plasmas with n=3 RMPs, the range of q95 for ELM suppression is found to increase with decreasing electron density. Nonlinear two-fluid MHD simulations reproduce the observed q95 windows of ELM suppression and the dependence on plasma density, based on the conditions for resonant field penetration at the top of the pedestal. When the RMP amplitude is close to the threshold for resonant field penetration, only narrow isolated magnetic islands form near the top of the pedestal, leading to narrow q95 windows of ELM suppression. However, as the threshold for field penetration decreases with decreasing density, resonant field penetration can take place over a wider range of q95. For sufficiently low density (penetration threshold) multiple magnetic islands form near the top of the pedestal giving rise to continuous q95 windows of ELM suppression. The model predicts that wide q95 windows of ELM suppression can be achieved at substantially higher pedestal pressure in DIII-D by shifting to higher toroidal mode number (n=4) RMPs

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty