State-of-the-art oriented review of CIRCUS

Mathematical procedures for CIRCUS, digital computer program which is based on built-in model library and is capable of time domain analysis of certain circuit

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Modeling of primary dendrite arm spacing variations in thin-slab casting of low carbon and low alloy steels

Solidification structure of a High Strength Low Alloy (HSLA) steel, in terms of dendrite arm spacing distribution across the shell thickness, is studied in a breakout shell from a thin-slab caster at Tata Steel in IJmuiden. Columnar dendrites were found to be the predominant morphology throughout the shell with size variations across the shell thickness. Primary Dendrite Arm Spacing (PDAS) increases by increasing the distance from meniscus or slab surface. Subsequently, a model is proposed to describe the variation of the PDAS with the shell thickness (the distance from slab surface) under solidifiction conditions experienced in the primary cooling zone of thin-slab casting. The proposed relationship related the PDAS to the shell thickness and, hence, can be used as a tool for predicting solidifcation structure and optimizing the thin-slab casting of low alloy steels

Square-tiled cyclic covers

A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichm\"uller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichm\"uller curve with respect to the geodesic flow. This paper includes a new example (announced by G. Forni and C. Matheus in \cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover in a stratum of Abelian differentials in genus four with a maximally degenerate Kontsevich--Zorich spectrum (the only known example found previously by Forni in genus three also corresponds to a square-tiled cyclic cover \cite{ForniSurvey}). We present several new examples of Teichm\"uller curves in strata of holomorphic and meromorphic quadratic differentials with maximally degenerate Kontsevich--Zorich spectrum. Presumably, these examples cover all possible Teichm\"uller curves with maximally degenerate spectrum. We prove that this is indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments. In particular, a gap in the previous version was corrected. This file uses the journal's class file (jmd.cls), so that it is very similar to published versio

Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation

We show that for almost all points on any analytic curve on R^{k} which is not contained in a proper affine subspace, the Dirichlet's theorem on simultaneous approximation, as well as its dual result for simultaneous approximation of linear forms, cannot be improved. The result is obtained by proving asymptotic equidistribution of evolution of a curve on a strongly unstable leaf under certain partially hyperbolic flow on the space of unimodular lattices in R^{k+1}. The proof involves ergodic properties of unipotent flows on homogeneous spaces.Comment: 26 page

Spectral statistics for quantized skew translations on the torus

We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level--spacing distribution and other common spectral statistics, like the number variance, do not exist in the semiclassical limit.Comment: 7 pages. One figure, include

Effect of input power and temperature on the cavitation intensity during the ultrasonic treatment of molten aluminium

Experimental results of ultrasonic processing of liquid aluminium with a 5 kW magnetostrictive transducer and a 20 mm titanium sonotrode excited at 17 kHz are reported in this study. A unique high-temperature cavitometer sensor, placed at various locations in the liquid melt, measured cavitation activity at various acoustic power levels and different temperature ranges. The highest cavitation intensity in the liquid bulk is achieved below the surface of the sonotrode, at the lowest temperature and with an applied power of 3.5 kW. This two-fold mechanism is related to (a) acoustic shielding and (b) the tendency of liquid aluminium to release hydrogen when the temperature drops, thus promoting multiple cavitation events. Understanding these mechanisms in liquid metals can result in a major breakthrough for the optimization of ultrasound applications to liquid metal processing.This work is performed within the Ultramelt Project supported by the EPSRC Grants EP/K005804/1 and EP/K00588X/1

Linear Contraction Behavior of Low-Carbon, Low-Alloy Steels During and After Solidification Using Real-Time Measurements

A technique for measuring the linear contraction during and after solidification of low-alloy steel was developed and used for examination of two commercial low-carbon and low-alloy steel grades. The effects of several experimental parameters on the contraction were studied. The solidification contraction behavior was described using the concept of rigidity in a solidifying alloy, evolution of the solid fraction, and the microstructure development during solidification. A correlation between the linear contraction properties in the solidification range and the hot crack susceptibility was proposed and used for the estimation of hot cracking susceptibility for two studied alloys and verified with the real casting practice. The technique allows estimation of the contraction coefficient of commercial steels in a wide range of temperatures and could be helpful for computer simulation and process optimization during continuous casting. © 2013 The Minerals, Metals & Materials Society and ASM International

The physical-mechanical and electrical properties of cast aluminum-based alloys reinforced with diamond nanoparticles

The results obtained from investigations into the microstructure and physical-mechanical and electrical properties of cast aluminum-based alloys reinforced with nanodiamonds are presented. Addition of the diamond nanoparticles is shown to change the structural parameters and improve the mechanical properties of the materials.The work was financed by the Ministry of Education and Science of the Russian Federation within the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2014–2020 (Agreement № 14.578.21.0025, UID RFME157814X0025) and the Program to Improve the Competitiveness of Tomsk State University among the World Leading Research and Education Centers

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo