303 research outputs found
On infrared divergences in spin glasses
By studying the structure of infrared divergences in a toy propagator in the
replica approach to the Ising spin glass below , we suggest a possible
cancellation mechanism which could decrease the degree of singularity in the
loop expansion.Comment: 13 pages, Latex , revised versio
Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
The free energy of a multi-component scalar field theory is considered as a
functional W[G,J] of the free correlation function G and an external current J.
It obeys non-linear functional differential equations which are turned into
recursion relations for the connected Greens functions in a loop expansion.
These relations amount to a simple proof that W[G,J] generates only connected
graphs and can be used to find all such graphs with their combinatoric weights.
A Legendre transformation with respect to the external current converts the
functional differential equations for the free energy into those for the
effective energy Gamma[G,Phi], which is considered as a functional of the free
correlation function G and the field expectation Phi. These equations are
turned into recursion relations for the one-particle irreducible Greens
functions. These relations amount to a simple proof that Gamma[G,J] generates
only one-particle irreducible graphs and can be used to find all such graphs
with their combinatoric weights. The techniques used also allow for a
systematic investigation into resummations of classes of graphs. Examples are
given for resumming one-loop and multi-loop tadpoles, both through all orders
of perturbation theory. Since the functional differential equations derived are
non-perturbative, they constitute also a convenient starting point for other
expansions than those in numbers of loops or powers of coupling constants. We
work with general interactions through four powers in the field.Comment: 34 pages; abstract expanded; section IV.E about absorption of
tadpoles and one related reference added; eqs. (20) and (23) corrected;
further references added; some minor beautifications; to be published by
Phys.Rev.
MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting – Part 2: Numerical simulations and validations
Abstract. In this paper we use MEDSLIK-II, a Lagrangian marine surface oil spill model described in Part 1 (De Dominicis et al., 2013), to simulate oil slick transport and transformation processes for realistic oceanic cases, where satellite or drifting buoys data are available for verification. The model is coupled with operational oceanographic currents, atmospheric analyses winds and remote sensing data for initialization. The sensitivity of the oil spill simulations to several model parameterizations is analyzed and the results are validated using surface drifters, SAR (synthetic aperture radar) and optical satellite images in different regions of the Mediterranean Sea. It is found that the forecast skill of Lagrangian trajectories largely depends on the accuracy of the Eulerian ocean currents: the operational models give useful estimates of currents, but high-frequency (hourly) and high-spatial resolution is required, and the Stokes drift velocity has to be added, especially in coastal areas. From a numerical point of view, it is found that a realistic oil concentration reconstruction is obtained using an oil tracer grid resolution of about 100 m, with at least 100 000 Lagrangian particles. Moreover, sensitivity experiments to uncertain model parameters show that the knowledge of oil type and slick thickness are, among all the others, key model parameters affecting the simulation results. Considering acceptable for the simulated trajectories a maximum spatial error of the order of three times the horizontal resolution of the Eulerian ocean currents, the predictability skill for particle trajectories is from 1 to 2.5 days depending on the specific current regime. This suggests that re-initialization of the simulations is required every day
Eddy diffusivity derived from drifter data for dispersion model applications
Ocean transport and dispersion processes are at the present time simulated using Lagrangian stochastic models coupled with Eulerian circulation models that are supplying analyses and forecasts of the ocean currents at unprecedented time and space resolution. Using the Lagrangian approach, each particle displacement is described by an average motion and a fluctuating part. The first one represents the advection associated with the Eulerian current field of the circulation models while the second one describes the sub-grid scale diffusion. The focus of this study is to quantify the sub-grid scale diffusion of the Lagrangian models written in terms of a horizontal eddy diffusivity. Using a large database of drifters released in different regions of the Mediterranean Sea, the Lagrangian sub-grid scale diffusion has been computed, by considering different regimes when averaging statistical quantities. In addition, the real drifters have been simulated using a trajectory model forced by OGCM currents, focusing on how the Lagrangian properties are reproduced by the simulated trajectories
Absence of an equilibrium ferromagnetic spin glass phase in three dimensions
Using ground state computations, we study the transition from a spin glass to
a ferromagnet in 3-d spin glasses when changing the mean value of the spin-spin
interaction. We find good evidence for replica symmetry breaking up till the
critical value where ferromagnetic ordering sets in, and no ferromagnetic spin
glass phase. This phase diagram is in conflict with the droplet/scaling and
mean field theories of spin glasses. We also find that the exponents of the
second order ferromagnetic transition do not depend on the microscopic
Hamiltonian, suggesting universality of this transition.Comment: 4 pages, 5 figures, revte
Oil spill forecasting in the Mediterranean Sea
In this work sensitivity experiments to the coupled MFS (currents) and MEDSLIK (oil spill) input parameters will be shown and results will be compared with observations. In these experiments the drift angle, the drift factor, the currents depth, the type of oil, horizontal diffusivity and the horizontal and temporal current resolution were changed
Theory of disordered flux-line liquids
We study the equilibrium statics and nonequilibrium driven dynamics of flux
line liquids in presence of a random pinning potential. Under the assumption of
replica symmetry, we find in the static case using a replica Gaussian
variational method that the only effect of disorder is to increase the tilt
modulus and the confining "mass" of the internal modes of the flux lines, thus
decreasing their thermal wandering. In the nonequilibrium, driven case, we
derive the long scale, coarse-grained equation of motion of the vortices in
presence of disorder, which apart from new Kardar-Parisi-Zhang nonlinearities,
has the same form as the equation of motion for unpinned vortices, with
renormalized coefficients. This implies, in particular, that the structure
factor of a disordered vortex liquid has the same functional form as in the
absence of pinning, in disagreement with the results of previous hydrodynamic
methods. The expression of the static structure factor derived within our
approach is consistent both with experimental data and with the standard theory
of elasticity of vortex lattices.Comment: 27 pages, 1 figure; added a new Appendix; accepted for publication in
Phys. Rev.
Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons
A diagrammatic technique for two-particle vertex functions is used to
describe systematically the influence of spatial quantum coherence and
backscattering effects on transport properties of noninteracting electrons in a
random potential. In analogy with many-body theory we construct parquet
equations for topologically distinct {\em nonlocal} irreducible vertex
functions into which the {\em local} one-particle propagator and two-particle
vertex of the coherent-potential approximation (CPA) enter as input. To
complete the two-particle parquet equations we use an integral form of the Ward
identity and determine the one-particle self-energy from the known irreducible
vertex. In this way a conserving approximation with (Herglotz) analytic
averaged Green functions is obtained. We use the limit of high spatial
dimensions to demonstrate how nonlocal corrections to the (CPA)
solution emerge. The general parquet construction is applied to the calculation
of vertex corrections to the electrical conductivity. With the aid of the
high-dimensional asymptotics of the nonlocal irreducible vertex in the
electron-hole scattering channel we derive a mean-field approximation for the
conductivity with vertex corrections. The impact of vertex corrections onto the
electronic transport is assessed quantitatively within the proposed mean-field
description on a binary alloy.Comment: REVTeX 19 pages, 9 EPS diagrams, 6 PS figure
Static chaos and scaling behaviour in the spin-glass phase
We discuss the problem of static chaos in spin glasses. In the case of
magnetic field perturbations, we propose a scaling theory for the spin-glass
phase. Using the mean-field approach we argue that some pure states are
suppressed by the magnetic field and their free energy cost is determined by
the finite-temperature fixed point exponents. In this framework, numerical
results suggest that mean-field chaos exponents are probably exact in finite
dimensions. If we use the droplet approach, numerical results suggest that the
zero-temperature fixed point exponent is very close to
. In both approaches is the lower critical dimension in
agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil
Equilibrium and off-equilibrium simulations of the 4d Gaussian spin glass
In this paper we study the on and off-equilibrium properties of the four
dimensional Gaussian spin glass. In the static case we determine with more
precision that in previous simulations both the critical temperature as well as
the critical exponents. In the off-equilibrium case we settle the general form
of the autocorrelation function, and show that is possible to obtain
dynamically, for the first time, a value for the order parameter.Comment: 16 pages and 13 figures, uses epsfig.sty and rotate.sty. Some minor
grammatical changes. Also available at
http://chimera.roma1.infn.it/index_papers_complex.htm
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