Closed Abrikosov Vortices in a Superconducting Cylinder

The new type of solutions of the London equation for type-II superconductors is obtained to describe the ring-shaped (toroidal) Abrikosov vortices. The specific feature of these solutions is the self-consistent localization of both the supercurrent and the magnetic field, enabling one to construct compact magnetic structures inside a superconductor. The torus vortex contraction caused by the vortex instability leads to the destruction of the Cooper pairing and the formation of a normal electron stream in the vicinity of the torus axis. The thermodynamic condition for the excitation of a small closed vortex by a bunch of charged particles contains the fine-structure constant as a determining parameter.Comment: LaTex using revtex, 12 pages. 5 Figures available upon request from [email protected] Accepted for publication in Physica

Identification of Boundary Conditions Using Natural Frequencies

The present investigation concerns a disc of varying thickness of whose flexural stiffness $D$ varies with the radius $r$ according to the law $D=D_0 r^m$, where $D_0$ and $m$ are constants. The problem of finding boundary conditions for fastening this disc, which are inaccessible to direct observation, from the natural frequencies of its axisymmetric flexural oscillations is considered. The problem in question belongs to the class of inverse problems and is a completely natural problem of identification of boundary conditions. The search for the unknown conditions for fastening the disc is equivalent to finding the span of the vectors of unknown conditions coefficients. It is shown that this inverse problem is well posed. Two theorems on the uniqueness and a theorem on stability of the solution of this problem are proved, and a method for establishing the unknown conditions for fastening the disc to the walls is indicated. An approximate formula for determining the unknown conditions is obtained using first three natural frequencies. The method of approximate calculation of unknown boundary conditions is explained with the help of three examples of different cases for the fastening the disc (rigid clamping, free support, elastic fixing). Keywords: Boundary conditions, a disc of varying thickness,inverse problem, Plucker condition.Comment: 19 page

On the role of the magnetic dipolar interaction in cold and ultracold collisions: Numerical and analytical results for NH(3Σ−^3\Sigma^-) + NH(3Σ−^3\Sigma^-)

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important \textit{below} a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.Comment: Accepted by Eur. Phys. J. D for publication in Special Issue on Cold Quantum Matter - Achievements and Prospects (2011

Andreev reflections in the pseudogap state of cuprate supercondcutors

We propose that, if the pseudogap state in the cuprate superconductors can be described in terms of the phase-incoherent preformed pairs, there should exist Andreev reflection from these pairs even above the superconducting transition temperature, $T_c$. After giving qualitative arguments for this effect, we present more quantitative calculations based on the Bogoliubov--de Gennes equation. Experimental observations of the effects of Andreev reflections above $T_c$---such as an enhanced tunneling conductance below the gap along the copper oxide plane---could provide unambiguous evidence for the preformed pairs in the pseudogap state.Comment: 5 pages, 1 figur

Time Variations in the Scale of Grand Unification

We study the consequences of time variations in the scale of grand unification, $M_U$, when the Planck scale and the value of the unified coupling at the Planck scale are held fixed. We show that the relation between the variations of the low energy gauge couplings is highly model dependent. It is even possible, in principle, that the electromagnetic coupling $\alpha$ varies, but the strong coupling $\alpha_3$ does not (to leading approximation). We investigate whether the interpretation of recent observations of quasar absorption lines in terms of time variation in $\alpha$ can be accounted for by time variation in $M_U$. Our formalism can be applied to any scenario where a time variation in an intermediate scale induces, through threshold corrections, time variations in the effective low scale couplings.Comment: 14 pages, revtex4; Updated observational results and improved statistical analysis (section IV); added reference

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.Comment: 9 pages, 6 figure

Genetic variation at MECOM, TERT, JAK2 and HBS1L-MYB predisposes to myeloproliferative neoplasms

Clonal proliferation in myeloproliferative neoplasms (MPN) is driven by somatic mutations in JAK2, CALR or MPL, but the contribution of inherited factors is poorly characterized. Using a three-stage genome-wide association study of 3,437 MPN cases and 10,083 controls, we identify two SNPs with genome-wide significance in JAK2V617F-negative MPN: rs12339666 (JAK2; meta-analysis P=1.27 × 10−10) and rs2201862 (MECOM; meta-analysis P=1.96 × 10−9). Two additional SNPs, rs2736100 (TERT) and rs9376092 (HBS1L/MYB), achieve genome-wide significance when including JAK2V617F-positive cases. rs9376092 has a stronger effect in JAK2V617F-negative cases with CALR and/or MPL mutations (Breslow–Day P=4.5 × 10−7), whereas in JAK2V617F-positive cases rs9376092 associates with essential thrombocythemia (ET) rather than polycythemia vera (allelic χ2 P=7.3 × 10−7). Reduced MYB expression, previously linked to development of an ET-like disease in model systems, associates with rs9376092 in normal myeloid cells. These findings demonstrate that multiple germline variants predispose to MPN and link constitutional differences in MYB expression to disease phenotype