1,325 research outputs found
Abstract polymer models with general pair interactions
A convergence criterion of cluster expansion is presented in the case of an
abstract polymer system with general pair interactions (i.e. not necessarily
hard core or repulsive). As a concrete example, the low temperature disordered
phase of the BEG model with infinite range interactions, decaying polynomially
as with , is studied.Comment: 19 pages. Corrected statement for the stability condition (2.3) and
modified section 3.1 of the proof of theorem 1 consistently with (2.3). Added
a reference and modified a sentence at the end of sec. 2.
Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
We present a set of well-posed constraint-preserving boundary conditions for
a first-order in time, second-order in space, harmonic formulation of the
Einstein equations. The boundary conditions are tested using robust stability,
linear and nonlinear waves, and are found to be both less reflective and
constraint preserving than standard Sommerfeld-type boundary conditions.Comment: 18 pages, 7 figures, accepted in CQ
Invariant measure in hot gauge theories
We investigate properties of the invariant measure for the gauge field
in finite temperature gauge theories both on the lattice and in the continuum
theory. We have found the cancellation of the naive measure in both cases. The
result is quite general and holds at any finite temperature. We demonstrate,
however, that there is no cancellation at any temperature for the invariant
measure contribution understood as Z(N) symmetrical distribution of gauge field
configurations. The spontaneous breakdown of Z(N) global symmetry is entirely
due to the potential energy term of the gluonic interaction in the effective
potential. The effects of this measure on the effective action, mechanism of
confinement and condensation are discussed.Comment: Latex file, 65.5kB, no figure
Fermionic Determinant of the Massive Schwinger Model
A representation for the fermionic determinant of the massive Schwinger
model, or , is obtained that makes a clean separation between the
Schwinger model and its massive counterpart. From this it is shown that the
index theorem for follows from gauge invariance, that the Schwinger
model's contribution to the determinant is canceled in the weak field limit,
and that the determinant vanishes when the field strength is sufficiently
strong to form a zero-energy bound state
Cosmological Implications of the Tetron Model of Elementary Particles
Based on a possible solution to the tetron spin problem, a modification of
the standard Big Bang scenario is suggested, where the advent of a spacetime
manifold is connected to the appearance of tetronic bound states. The metric
tensor is constructed from tetron constituents and the reason for cosmic
inflation is elucidated. Furthermore, there are natural dark matter candidates
in the tetron model. The ratio of ordinary to dark matter in the universe is
calculated to be 1:5.Comment: 23 page
Automated diffeomorphic registration of anatomical structures with rigid parts: application to dynamic cervical MRI.
International audienceWe propose an iterative two-step method to compute a diffeomorphic non-rigid transformation between images of anatomical structures with rigid parts, without any user intervention or prior knowledge on the image intensities. First we compute spatially sparse, locally optimal rigid transformations between the two images using a new block matching strategy and an efficient numerical optimiser (BOBYQA). Then we derive a dense, regularised velocity field based on these local transformations using matrix logarithms and M-smoothing. These two steps are iterated until convergence and the final diffeomorphic transformation is defined as the exponential of the accumulated velocity field. We show our algorithm to outperform the state-of-the-art log-domain diffeomorphic demons method on dynamic cervical MRI data
Absolute conservation law for black holes
In all 2d theories of gravity a conservation law connects the (space-time
dependent) mass aspect function at all times and all radii with an integral of
the matter fields. It depends on an arbitrary constant which may be interpreted
as determining the initial value together with the initial values for the
matter field. We discuss this for spherically reduced Einstein-gravity in a
diagonal metric and in a Bondi-Sachs metric using the first order formulation
of spherically reduced gravity, which allows easy and direct fixations of any
type of gauge. The relation of our conserved quantity to the ADM and Bondi mass
is investigated. Further possible applications (ideal fluid, black holes in
higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.
Mediterranean springs: Keystone ecosystems and biodiversity refugia threatened by global change
Mediterranean spring ecosystems are unique habitats at the interface between surface water and groundwater. These ecosystems support a remarkable array of biodiversity and provide important ecological functions and ecosystem services. Spring ecosystems are influenced by abiotic, biotic, and anthropogenic factors such as the lithology of their draining aquifers, their climate, and the land use of their recharge area, all of which affect the water chemistry of the aquifer and the spring discharges. One of the most relevant characteristics of spring ecosystems is the temporal stability of environmental conditions, including physicochemical features of the spring water, across seasons and years. This stability allows a wide range of species to benefit from these ecosystems (particularly during dry periods), fostering an unusually high number of endemic species. However, global change poses important threats to these freshwater ecosystems. Changes in temperature, evapotranspiration, and precipitation patterns can alter the water balance and chemistry of spring water. Eutrophication due to agricultural practices and emergent pollutants, such as pharmaceuticals, personal care products, and pesticides, is also a growing concern for the preservation of spring biodiversity. Here, we provide a synthesis of the main characteristics and functioning of Mediterranean spring ecosystems. We then describe their ecological value and biodiversity patterns and highlight the main risks these ecosystems face. Moreover, we identify existing knowledge gaps to guide future research in order to fully uncover the hidden biodiversity within these habitats and understand the main drivers that govern them. Finally, we provide a brief summary of recommended actions that should be taken to effectively manage and preserve Mediterranean spring ecosystems for future generations. Even though studies on Mediterranean spring ecosystems are still scarce, our review shows there are sufficient data to conclude that their future viability as functional ecosystems is under severe threat.Mediterranean spring ecosystems are unique habitats supporting a remarkable array of biodiversity and providing important ecological functions and ecosystem services. However, global change poses important threats to these freshwater ecosystems, such as changes in climate patterns and increasing human pressures like overexploitation and pollution. We provide a synthesis of the main characteristics and functioning of Mediterranean spring ecosystems and their threats due to global change.imag
The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma
We elucidate the close connection between the repulsive lattice gas in
equilibrium statistical mechanics and the Lovasz local lemma in probabilistic
combinatorics. We show that the conclusion of the Lovasz local lemma holds for
dependency graph G and probabilities {p_x} if and only if the independent-set
polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore,
we show that the usual proof of the Lovasz local lemma -- which provides a
sufficient condition for this to occur -- corresponds to a simple inductive
argument for the nonvanishing of the independent-set polynomial in a polydisc,
which was discovered implicitly by Shearer and explicitly by Dobrushin. We also
present some refinements and extensions of both arguments, including a
generalization of the Lovasz local lemma that allows for "soft" dependencies.
In addition, we prove some general properties of the partition function of a
repulsive lattice gas, most of which are consequences of the alternating-sign
property for the Mayer coefficients. We conclude with a brief discussion of the
repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity.
To be published in J. Stat. Phy
Adaptive Mesh Refinement for Characteristic Grids
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when
numerically solving partial differential equations with wave-like solutions,
using characteristic (double-null) grids. Such AMR algorithms are naturally
recursive, and the best-known past Berger-Oliger characteristic AMR algorithm,
that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on
individual "diamond" characteristic grid cells. This leads to the use of
fine-grained memory management, with individual grid cells kept in
2-dimensional linked lists at each refinement level. This complicates the
implementation and adds overhead in both space and time.
Here I describe a Berger-Oliger characteristic AMR algorithm which instead
recurses on null \emph{slices}. This algorithm is very similar to the usual
Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory
management, allowing entire null slices to be stored in contiguous arrays in
memory. The algorithm is very efficient in both space and time.
I describe discretizations yielding both 2nd and 4th order global accuracy.
My code implementing the algorithm described here is included in the electronic
supplementary materials accompanying this paper, and is freely available to
other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are
viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3
document class, includes C++ source code. Changes from v1: revised in
response to referee comments: many references added, new figure added to
better explain the algorithm, other small changes, C++ code updated to latest
versio
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