6,297 research outputs found
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 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 -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 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
- …