Domain wall dynamics in a two-layer uniaxial film

Numerical solution of the Slonczewski equations were used to study the motion of an individual domain wall in a two-layer uniaxial film in which the damping parameter and the gyromagnetic ratio depend on the specific layer.     

Dynamics of a domain wall in two-layer uniaxial magnetic films with gyromagnetic ratios of different signs in the layers

Motion of an isolated domain wall in two-layer uniaxial magnetic films with gyromagnetic ratios of different signs in the layers is first investigated by solving numerically the Slonczewski equations. The mode of stationary domain wall motion with the angle of magnetization vector departure from the wall plane exceeding π is established. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 50–53, May, 2007.     

Domain wall dynamics in a double-layer uniaxial magnetic film with different magnetic anisotropy in the layers

Motion of an isolated domain wall in a double-layered magnetic film is investigated through solving the Slonczewski equations by a numerical method for the same gyromagnetic ratio and different anisotropy constants in the layers. Dependences of the threshold field and the limiting velocity of disruption of the steady state motion of the film on the magnetic anisotropy constant in one of the layers are obtained. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 3–7, August, 2007.     

Prediction of molecular properties including symmetry from quantum-based molecular structural formulas, VIF

Structurally covariant valency interaction formulas, VIF, gain chemical significance by comparison with resonance structures and natural bond orbital, NBO, bonding schemes and at the same time allow for additional prediction such as symmetry of ring systems and destabilization of electron pairs with respect to reference energy of -1/2 Eh. Comparisons are based on three chemical interpretations of Sinano?lu's theory of structural covariance: (1) sets of structurally covariant quantum structural formulas, VIF, are interpreted as the same quantum operator represented in linearly related basis frames; (2) structurally covariant VIF pictures are interpreted as sets of molecular species with similar energy; and (3) the same VIF picture can be interpreted as different quantum operators, one-electron density or Hamiltonian; for example. According to these three interpretations, bond pair, lone pair, and free radical electrons understood in terms of a localized orbital representation are recognized as having energies above, below, or equal to a predetermined reference, frequently-1/2 Eh. The probable position of electron pairs and radical electrons is predicted. The selectivity of concerted ring closures in allyl anion and cation is described. Symmetries of conjugated ring systems are predicted according to their numbers of pi-electrons and spin-multiplicity. The pi-distortivity of benzene is predicted.The 3c/2e- H-bridging bonds in diborane are derived in a natural way according to the notion that the bridging bonds will have delocalizing interactions between them consistent with results of the NBO method. Key chemical bonding motifs are described using VIF. These include 2c/1e-, 2c/2e-, 2c/3e-, 3c/2e-, 3c/3e-,3c/4e-, 4n antiaromatic, and 4n+2 aromatic bonding systems. Some common organic functional groups are represented as VIF pictures and because these pictures can be interpreted simultaneously as one-electron density and Hamiltonian operators, the valence shell electron pair repulsion method is applied toward understanding the energies of valence NBOs with respect to the reference energy of -1/2Eh.     

Domain wall dynamics in a double-layer uniaxial magnetic film with different intensity of saturation magnetization of the layers

Motion of an isolated domain wall in a double-layered magnetic film, whose layers differ in their saturation magnetization intensity only, is investigated through solving the Slonczewski equations by a numerical method. Dependences of the threshold field and the limiting velocity of disruption of the steady state motion of the film on the saturation magnetization are obtained. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 37–42, July, 2007.     

Transformation of three-dimensional regions onto rectangular regions by elliptic systems

Summary A transformation method is developed which may be used to solve various types of boundary value problems on three-dimensional regions with an arbitrary boundary. The implementation of the method is illustrated in the solution of a potential flow problem. All computations are performed on a cubic mesh in a rectangular region.This report was prepared as a result of work performed under NASA Contract No. NAS1-14101 while the first author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665, USA     

Dynamics of a domain wall in two-layer uniaxial magnetic films with the same gyromagnetic ratios in the layers

Motion of an isolated domain wall in two-layer uniaxial magnetic films with the same gyromagnetic ratios in the layers is investigated by solving the Slonczewski equations using a numerical method. The steady-state motion regimes are established for the domain with the angle of magnetization vector departure from the wall plane exceeding π. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 76–82, April, 2007.     

Stability conditions for abstract functional differential equations in Hilbert space

Stability conditions for functional differential equations of the form: du(t)/dt = Au(t) + bAu(t ? h) + (a* Au)(t) are studied, where A is the infinitesimal generator of an analytic semigroup in a Hilbert space, b ≠ 0 and the convolution term contains a square integrable real function a ≠ 0. Norm discontinuity of the solution semigroup of the equation with discrete delay is avoided by studying the inverse of the characteristic operator. Sufficient and necessary conditions for the uniform exponential stability of the solution semigroup are obtained. The results are applied to a retarded partial integrodifferential equation.     

Discrete–time delta hedging and the Black–Scholes model with transaction costs

The paper deals with the problem of discrete–time delta hedging and discrete-time option valuation by the Black–Scholes model. Since in the Black–Scholes model the hedging is continuous, hedging errors appear when applied to discrete trading. The hedging error is considered and a discrete-time adjusted Black–Scholes–Merton equation is derived. By anticipating the time sensitivity of delta in many cases the discrete-time delta hedging can be improved and more accurate delta values dependent on the length of the rebalancing intervals can be obtained. As an application the discrete-time trading with transaction costs is considered. Explicit solution of the option valuation problem is given and a closed form delta value for a European call option with transaction costs is obtained.     

Elliptic systems and numerical transformations

Properties of a transformation method which has been developed for solving fluid dynamic problems on general two-dimensional regions are discussed. These include the error in the construction of the transformation and applications to mesh generation. An error and stability analysis for the numerical solution of a model parabolic problem is also presented.