Tkachenko modes as sources of quasiperiodic pulsar spin variations

We study the long wavelength shear modes (Tkachenko waves) of triangular lattices of singly quantized vortices in neutron star interiors taking into account the mutual friction between the superfluid and the normal fluid and the shear viscosity of the normal fluid. The set of Tkachenko modes that propagate in the plane orthogonal to the spin vector are weakly damped if the coupling between the superfluid and normal fluid is small. In strong coupling, their oscillation frequencies are lower and are undamped for small and moderate shear viscosities. The periods of these modes are consistent with the observed ~100-1000 day variations in spin of PSR 1828-11.Comment: 7 pages, 3 figures, uses RevTex, v2: added discussion/references, matches published versio

Dissipationless Phonon Hall Viscosity

We study the acoustic phonon response of crystals hosting a gapped time-reversal symmetry breaking electronic state. The phonon effective action can in general acquire a dissipationless "Hall" viscosity, which is determined by the adiabatic Berry curvature of the electron wave function. This Hall viscosity endows the system with a characteristic frequency, \omega_v; for acoustic phonons of frequency \omega, it shifts the phonon spectrum by an amount of order (\omega/\omega_v)^2 and it mixes the longitudinal and transverse acoustic phonons with a relative amplitude ratio of \omega/\omega_v and with a phase shift of +/- \pi/2, to lowest order in \omega/\omega_v. We study several examples, including the integer quantum Hall states, the quantum anomalous Hall state in Hg_{1-y}Mn_{y}Te quantum wells, and a mean-field model for p_x + i p_y superconductors. We discuss situations in which the acoustic phonon response is directly related to the gravitational response, for which striking predictions have been made. When the electron-phonon system is viewed as a whole, this provides an example where measurements of Goldstone modes may serve as a probe of adiabatic curvature of the wave function of the gapped sector of a system.Comment: 14 page

Modeling of the process of oilseed meat cooking in a multi-vat cooker during processing of oil raw materials

Вивчені й проаналізовані процеси, що відбуваються при жарінні м’ятки масличної сировини в кожному чані багаточанної жаровні. Розроблено їх математична модель, що враховує гідродинаміку первинної і вторинної циркуляції, енергію зв'язку вологи з матеріалом. Чисельні рішення моделі дозволять обґрунтувати технологічні режими жаріння і конструктивні параметри жаровні. Складено і проаналізовано тепловий баланс кондуктивного і конвектівного тепло-, масопереносу при сушінні м’ятк

Vortex states of rapidly rotating dilute Bose-Einstein condensates

We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, $\Omega$, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.Comment: 4 pages, 2 figures, RevTex4. Version as published; discussion extended, some references added and update

Self-assembly of DNA-coded nanoclusters

We present a theoretical discussion of a self-assembly scheme which makes it possible to use DNA to uniquely encode the composition and structure of micro- and nanoparticle clusters. These anisotropic DNA-decorated clusters can be further used as building blocks for hierarchical self-assembly of larger structures. We address several important aspects of possible experimental implementation of the proposed scheme: the competition between different types of clusters in a solution, possible jamming in an unwanted configuration, and the degeneracy due to symmetry with respect to particle permutations.Comment: v2, 4 pages, 7 figures, added journal re

Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate

We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.Comment: 29 pages, 4 figures, changes in section

Least-squares deconvolution based analysis of stellar spectra

In recent years, astronomical photometry has been revolutionised by space missions such as MOST, CoRoT and Kepler. However, despite this progress, high-quality spectroscopy is still required as well. Unfortunately, high-resolution spectra can only be obtained using ground-based telescopes, and since many interesting targets are rather faint, the spectra often have a relatively low S/N. Consequently, we have developed an algorithm based on the least-squares deconvolution profile, which allows to reconstruct an observed spectrum, but with a higher S/N. We have successfully tested the method using both synthetic and observed data, and in combination with several common spectroscopic applications, such as e.g. the determination of atmospheric parameter values, and frequency analysis and mode identification of stellar pulsations.Comment: Proceedingspaper, 8 pages, 4 figures, appears in "Setting a New Standard in the Analysis of Binary Stars", Eds K. Pavlovski, A. Tkachenko, and G. Torres, EAS Publications Serie