Topological model of soap froth evolution with deterministic T2-processes

We introduce a topological model for the evolution of 2d soap froth. The topological rearrangements (T2 processes) are deterministic (unlike the standard stochastic model): the final topology depends on the areas of the neighboring cells. The new model gives agreement with experiments in the transient regime, where the previous models failed qualitatively, and also improves agreement in the scaling state.Comment: latex, 12 pages, 2 figure

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

SUSY transformations with complex factorization constants. Application to spectral singularities

Supersymmetric (SUSY) transformation operators corresponding to complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. Obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of selfadjoint operators. A new regularization procedure for the resolution of the identity operator in terms of continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also shown that the continuous spectrum eigenfunction has zero binorm (in the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte

A priori estimates for the Hill and Dirac operators

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps \g_n,n\ge 1 with length |\g_n|\ge 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if \m_n^\pm are the effective masses associated with the gap \g_n=(\l_n^-,\l_n^+), then |\m_n^-+\m_n^+|\le C|\g_n|^2n^{-4} for some constant $C=C(q)$ and any $n\ge 1$. In order prove these results we use the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator. That makes possible to reformulate the problems for the differential operator as the problems of the conformal mapping theory. Then the proof is based on the analysis of the conformal mapping and the identities. Moreover, we obtain the similar estimates for the Dirac operator

Nitrogen and phosphorus limitation of oceanic microbial growth during spring in the Gulf of Aqaba

Bioassay experiments were performed to identify how growth of key groups within the microbial community was simultaneously limited by nutrient (nitrogen and phosphorus) availability during spring in the Gulf of Aqaba's oceanic waters. Measurements of chlorophyll a (chl a) concentration and fast repetition rate (FRR) fluorescence generally demonstrated that growth of obligate phototrophic phytoplankton was co-limited by N and P and growth of facultative aerobic anoxygenic photoheterotropic (AAP) bacteria was limited by N. Phytoplankton exhibited an increase in chl a biomass over 24 to 48 h upon relief of nutrient limitation. This response coincided with an increase in photosystem II (PSII) photochemical efficiency (F v /F m), but was preceded (within 24 h) by a decrease in effective absorption crosssection (σPSII) and electron turnover time (τ). A similar response for τ and bacterio-chl a was observed for the AAPs. Consistent with the up-regulation of PSII activity with FRR fluorescence were observations of newly synthesized PSII reaction centers via low temperature (77K) fluorescence spectroscopy for addition of N (and N + P). Flow cytometry revealed that the chl a and thus FRR fluorescence responses were partly driven by the picophytoplankton (æ10 μm) community, and in particular Synechococcus. Productivity of obligate heterotrophic bacteria exhibited the greatest increase in response to a natural (deep water) treatment, but only a small increase in response to N and P addition, demonstrating the importance of additional substrates (most likely dissolved organic carbon) in moderating the heterotrophs. These data support previous observations that the microbial community response (autotrophy relative to heterotrophy) is critically dependent upon the nature of transient nutrient enrichment. © Inter-Research 2009

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

The fastest unbound star in our Galaxy ejected by a thermonuclear supernova

Hypervelocity stars (HVS) travel with velocities so high, that they exceed the escape velocity of the Galaxy. Several acceleration mechanisms have been discussed. Only one HVS (US 708, HVS 2) is a compact helium star. Here we present a spectroscopic and kinematic analysis of US\,708. Travelling with a velocity of $\sim1200\,{\rm km\,s^{-1}}$, it is the fastest unbound star in our Galaxy. In reconstructing its trajectory, the Galactic center becomes very unlikely as an origin, which is hardly consistent with the most favored ejection mechanism for the other HVS. Furthermore, we discovered US\,708 to be a fast rotator. According to our binary evolution model it was spun-up by tidal interaction in a close binary and is likely to be the ejected donor remnant of a thermonuclear supernova.Comment: 16 pages report, 20 pages supplementary material

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure