Spreading of Antarctic Bottom Water in the Atlantic Ocean

This paper describes the transport of bottom water from its source region in the Weddell Sea through the abyssal channels of the Atlantic Ocean. The research brings together the recent observations and historical data. A strong flow of Antarctic Bottom Water through the Vema Channel is analyzed. The mean speed of the flow is 30 cm/s. A temperature increase was found in the deep Vema Channel, which has been observed for 30 years already. The flow of bottom water in the northern part of the Brazil Basin splits. Part of the water flows through the Romanche and Chain fracture zones. The other part flows to the North American Basin. Part of the latter flow propagates through the Vema Fracture Zone into the Northeast Atlantic. The properties of bottom water in the Kane Gap and Discovery Gap are also analyzed

Phase behaviour of block copolymer melts with arbitrary architecture

The Leibler theory [L. Leibler, Macromolecules, v.13, 1602 (1980)] for microphase separation in AB block copolymer melts is generalized for systems with arbitrary topology of molecules. A diagrammatic technique for calculation of the monomeric correlation functions is developed. The free energies of various mesophases are calculated within the second-harmonic approximation. Model highly-branched tree-like structures are considered as an example and their phase diagrams are obtained. The topology of molecules is found to influence the spinodal temperature and asymmetry of the phase diagrams, but not the types of phases and their order. We suggest that all model AB block-copolymer systems will exhibit the typical phase behaviour.Comment: Submitted to J. Chem. Phys., see also http://rugmd4.chem.rug.nl/~morozov/research.htm

Stability of constant retrial rate systems with NBU input*

We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient stability conditions were obtained by Avrachenkov and Morozov (2014), which hold for a rather general retrial system. However, only in the case of Poisson input is an explicit expression provided; otherwise one has to rely on simulation. On the other hand, the stability criteria derived by Lillo (1996) can be easily computed but only hold for the case of exponential service times. We present new sufficient stability conditions, which are less tight than the ones obtained by Avrachenkov and Morozov (2010), but have an analytical expression under rather general assumptions. A key assumption is that interarrival times belongs to the class of new better than used (NBU) distributions. We illustrate the accuracy of the condition based on this assumption (in comparison with known conditions when possible) for a number of non-exponential distributions

Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (i) the spatial gradient of the growth rate is due to abiotic factors only, and (ii) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism.Comment: 2 figures; appendices available on request. To appear in the Bulletin of Mathematical Biolog

More Evidence for the WDVV Equations in N=2 SUSY Yang-Mills Theories

We consider 4d and 5d N=2 supersymmetric theories and demonstrate that in general their Seiberg-Witten prepotentials satisfy the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. General proof for the Yang-Mills models (with matter in the first fundamental representation) makes use of the hyperelliptic curves and underlying integrable systems. A wide class of examples is discussed, it contains few understandable exceptions. In particular, in perturbative regime of 5d theories in addition to naive field theory expectations some extra terms appear, like it happens in heterotic string models. We consider also the example of the Yang-Mills theory with matter hypermultiplet in the adjoint representation (related to the elliptic Calogero-Moser system) when the standard WDVV equations do not hold.Comment: LaTeX, 40 pages, no figure

Defect and degree of the Alexander polynomial

Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simons theory. We prove the conjecture that the defect can be alternatively described as the degree in $q^{\pm 2}$ of the fundamental Alexander polynomial, which formally corresponds to the case of no colors. We also pose a question if these Alexander polynomials can be arbitrary integer polynomials of a given degree. A first attempt to answer the latter question is a preliminary analysis of antiparallel descendants of the 2-strand torus knots, which provide a nice set of examples for all values of the defect. The answer turns out to be positive in the case of defect zero knots, what can be observed already in the case of twist knots. This proved conjecture also allows us to provide a complete set of $C$-polynomials for the symmetrically colored Alexander polynomials for defect zero. In this case, we achieve a complete separation of representation and knot variables.Comment: 21 page

The vanishing of two-point functions for three-loop superstring scattering amplitudes

In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen vanishes. Our proof uses the reformulation of ansatz in terms of even cosets, theta functions, and specifically the theory of the $\Gamma_{00}$ linear system on Jacobians introduced by van Geemen and van der Geer. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong, we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera