Tatyana Belozerova

Stability of plane-parallel vibrational flow in a two-layer system

Abstract The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillations. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved for both (a) inviscid and (b) viscous fluids. A transformation is found which reduces the linear stability problem under the inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.

Collective effects due to dipolar fields as the origin of the extremely random behavior in hyperpolarized NMR maser: a theoretical and numerical study.

Numerical simulations based on microscopic approach are used to explore the spin dynamics encountered in the recently reported hyperpolarized (129)Xe NMR maser [D. J. Y. Marion, G. Huber, P. Berthault, and H. Desvaux, ChemPhysChem 9, 1395-1401 (2008)] where series of amplitude modulated rf emissions are observed. The integration of the dynamic features of the electronic detection circuit in the present simulations, based on non-linear Maxwell-Bloch differential equations with dipole-dipole interactions, allows us to prove that the experimentally observed extremely random amplitude modulations crucially require the long-distance dipolar couplings between the nuclear spins with the feedback field acting as an amplifier. The massive dipolar couplings act, when the magnetization is largely tilted off the longitudinal axis, as an apparent transverse self-relaxation mechanism which destroys coherence. This, in particular, explains why the final magnetization after emissions can still be opposite to the magnetic field direction, i.e., being in an unstable state.

SPIN-WAVE APPROACH TO THE 2D PARAMAGNETIC UNDER THE MAGNETIC FIELD

We study the possibility of collective spin excitations in 2D paramagnetic crystal with the dipole-dipole interaction and without the exchange interaction. The crystal is under uniform constant magnetic field. All the magnetic moments are oriented along the magnetic field at the saturation. Using the Holstein–Primakoff transformation, we describe the properties of paramagnetic in terms of the spin waves at the low-temperature limit. We obtain the dispersion relations for spin waves at the square and hexagonal flat lattices. It is shown the wavelength of the collective excitations and their bandwidth are determined by the external magnetic field direction. The long-wave perturbations have the lowest energy when the magnetic field is orthogonal to the lattice plane, and the short-wave perturbations are the most preferable when the field is parallel to the lattice. We provide the direct numerical simulation of the group of interacting magnetic moments under the constant external field with different orientation to the lattice. The total transversal spin and dipole energy evolution in time and their Fourier-spectrum are considered. The numerical results match the analytical calculation in spin-wave approach. Received 22.08.2016; accepted 31 .0 8 .2016

Ordinary and partial differential equations

Ordinary Differential Equations, Boundary Value Problems, Fourier Series, and the Introduction to Integral Equations First-Order Differential Equations Second-Order Differential Equations Systems of Differential Equations Boundary Value Problems for Second-Order ODE and Sturm-Liouville Theory Qualitative Methods and Stability of ODE Solutions Method of Laplace Transforms for ODE Integral Equations Series Solutions of ODEs and Bessel and Legendre Equations Fourier Series Partial Differential Equations Introduction to PDE One-Dimensional Hyperbolic Equations Two-Dimensional Hyperbolic Equations One-Dimensional Parabolic Equations Two-Dimensional Parabolic Equations Elliptic Equations Appendix 1: Eigenvalues and Eigenfunctions of One-Dimensional Sturm-Liouville Boundary Value Problem for Different Types of Boundary Conditions Appendix 2: Auxiliary Functions, w(x,t), for Different Types of Boundary Conditions Appendix 3: Eigenfunctions of Sturm-Liouville Boundary Value Problem for the Laplace Equation in a Rectangular Domain for Different Types of Boundary Conditions Appendix 4: A Primer on the Matrix Eigenvalue Problems and the Solution of the Selected Examples in Sec. 5.2 Appendix 5: How to Use the Software Associated with the Book Bibliography

Wavelet analysis of data in particle physics: Vector mesons in e + e − annihilation

AbstractThe advantages that wavelet analysis (WA) provides for resolving the structures in experimental data are demonstrated. Due to good scaling properties of the wavelets, one can consider data with various resolutions, which allows the resonances to be separated from the background and from each other. The WA is much less sensitive to noise than any other analysis and allows the role of statistical errors to be substantially reduced. The WA is applied to the e+e− annihilation into hadron states with quantum numbers of ρ and ω mesons, and to p-wave ππ scattering. Distinguishing the resonance structures from an experimental noise and the background allows us to make more reliable conclusions about the ρ′ and ω′ states. The WA yields a useful set of starting conditions for analysis of ω′ states with the multiresonance Breit-Wigner method preserving unitarity in the case of overlapping resonances. We also apply the WA for the ratio

Application of wavelet analysis to the spectrum of \(\omega'\) states and ratio R e+e-

R_{e^ + e^ - }

The quantum mechanics correspondence principle for spin systems and its application for some magnetic resonance problems

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Using wavelet analysis to compare the QCD prediction and experimental data on R_{e^+e^-} and to determine parameters of the charmonium states above the D\bar{D} threshold

We use the wavelet analysis to separate noise and resonances contributions for some e+e− → hadrons data. With these “cleaned up” data as output, we find ρ′ and ω′ parameters using the generalized Breit‐Wigner method that preserves unitarity in the case of overlapping states.