arXiv subjects
Publications and source records attributed to Alexander Goncharov.
We give an example of Cantor type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in Stahl-Totik sense.
A time domain finite element numerical study of impedance spectroscopy in composite electroceramics is presented. The simulations take into account the complexity of the realistic three dimensional granular structure including grains and grain boundaries. Two types of finite elements are used to represent the bulk (tetrahedrons) and the grain boundary (prisms) phases, which allow using extremely high bulk to grain boundary ratios. Simulations at various frequencies reveal a strong influence of the grain shape on the impedance data of the sample, both at low and at high frequencies.
In this paper we numerically conduct micromagnetic modelling with an expended micromagnetic model that includes the spin torque term and an impedance model to investigate methods to replace external field sources with internal ones and to investigate its tuneability on nanopillar geometries. We present results for three methods: interlayer coupling, large perpendicular anisotropy and magnetostatic coupling. The internal field sources are evaluated as function of frequency shift with current, its dependency on temperature and are tested against analytical predictions.
In this paper we numerically conduct micromagnetic modelling to optimize computational boundaries of magnetic thin-film elements applicable to single and double point contact spin torque nano-oscillators. Different boundary conditions have been introduced to compensate spin waves reflections at boundaries that are based on extended layers, absorbing boundaries, and focal point methods and are compared with a technique based on scattering theory. A surface roughness boundary model is presented which is modelled according to the Rayleigh criterion to minimize specular reflections at computational boundaries. It is shown that the surface roughness model disperses the reflected spin waves and improves the signal to background noise ratio. The model is tested in comparison to conventional approaches such as extended layer systems, variable damping constant and focal point methods for double point contacts. The surface roughness model gives solutions that are stable in time, in qualitative agreement with experiments and capable to reproduce phenomena such as phase locking in double point contacts.
We report the discovery of a new class of molecular phases of solid nitrogen at high pressures and temperatures by Raman and infrared spectroscopy and powder x-ray diffraction. Unlike the molecular phases consisting of disk- and sphere-like molecular disorder ($δ$-, $ε$- and $ζ$-N$_2$) and reportedly stable over a wide P-T range, one of the new phases ($ι$) is diatomic with disk-like molecules. A second new phase (the higher pressure $θ$-phase) is characterized by strong intermolecular interactions and infrared vibron absorption. Both phases exhibit wide P-T ranges of stability and metastability.
I compute explicitly the regulator map on $K_4(X)$ for an arbitrary curve $X$ over a number field. Using this and Beilinson's theorem about regulators for modular curves ([B2]) I prove a formula expressing the value of the $L$-function $L(E,s)$ of a modular elliptic curve $E$ over $\Bbb Q$ at $s=3$ by the double Eisenstein-Kronecker series.
Two different constructions of an invariant of an odd dimensional hyperbolic manifold in the K-group $K_{2n-1}(\bar \Bbb Q)\otimes \Bbb Q$ are given. The volume of the manifold is equal to the value of the Borel regulator on that element. The scissor congruence groups in non euclidian geometries are studied and their relationship with algebraic K-theory of the field of complex numbers is discussed.