1,059 research outputs found
Corrections to scaling for percolative conduction: anomalous behavior at small L
Recently Grassberger has shown that the correction to scaling for the
conductance of a bond percolation network on a square lattice is a nonmonotonic
function of the linear lattice dimension with a minimum at , while this
anomalous behavior is not present in the site percolation networks. We perform
a high precision numerical study of the bond percolation random resistor
networks on the square, triangular and honeycomb lattices to further examine
this result. We use the arithmetic, geometric and harmonic means to obtain the
conductance and find that the qualitative behavior does not change: it is not
related to the shape of the conductance distribution for small system sizes. We
show that the anomaly at small L is absent on the triangular and honeycomb
networks. We suggest that the nonmonotonic behavior is an artifact of
approximating the continuous system for which the theory is formulated by a
discrete one which can be simulated on a computer. We show that by slightly
changing the definition of the linear lattice size we can eliminate the minimum
at small L without significantly affecting the large L limit.Comment: 3 pages, 4 figures;slightly expanded, 2 figures added. Accepted for
publishing in Phys. Rev.
Modal fields calculation using the finite difference beam propagation method
A method is described to construct modal fields for an arbitrary one- or two-dimensional refractive index structure. An arbitrary starting field is propagated along a complex axis using the slowly varying envelope approximation (SVEA). By choosing suitable values for the step-size, one mode is maximally increased in amplitude on propagating, until convergence has been obtained. For the calculation of the next mode, the mode just found is filtered out, and the procedure starts again. The method is tested for one-dimensional refractive index structures, both for nonabsorbing and for absorbing structures, and is shown to give fast convergenc
The antiferromagnetic phi4 Model, II. The one-loop renormalization
It is shown that the four dimensional antiferromagnetic lattice phi4 model
has the usual non-asymptotically free scaling law in the UV regime around the
chiral symmetrical critical point. The theory describes a scalar and a
pseudoscalar particle. A continuum effective theory is derived for low
energies. A possibility of constructing a model with a single chiral boson is
mentioned.Comment: To appear in Phys. Rev.
Abelian Dominance in Chiral Symmetry Breaking
Calculations of the chiral condensate on
the lattice using staggered fermions and the Lanczos algorithm are presented.
Three gauge fields are considered: the quenched non-Abelian field, the Abelian
field projected in the maximal Abelian gauge, and the monopole field further
decomposed from the Abelian field. The results show that the Abelian monopoles
largely reproduce the chiral condensate values of the full non-Abelian theory,
both in SU(2) and in SU(3).Comment: 4 pages in Latex with 4 embedded Postscript figures, uses
espcrc2.sty, psfig.sty. All are uuencoded, gzipped in a self-extracting file.
Contribution to Lattice'95, Melbourne, Australi
A probabilistic approach to Zhang's sandpile model
The current literature on sandpile models mainly deals with the abelian
sandpile model (ASM) and its variants. We treat a less known - but equally
interesting - model, namely Zhang's sandpile. This model differs in two aspects
from the ASM. First, additions are not discrete, but random amounts with a
uniform distribution on an interval . Second, if a site topples - which
happens if the amount at that site is larger than a threshold value
(which is a model parameter), then it divides its entire content in equal
amounts among its neighbors. Zhang conjectured that in the infinite volume
limit, this model tends to behave like the ASM in the sense that the stationary
measure for the system in large volumes tends to be peaked narrowly around a
finite set. This belief is supported by simulations, but so far not by
analytical investigations.
We study the stationary distribution of this model in one dimension, for
several values of and . When there is only one site, exact computations
are possible. Our main result concerns the limit as the number of sites tends
to infinity, in the one-dimensional case. We find that the stationary
distribution, in the case , indeed tends to that of the ASM (up
to a scaling factor), in agreement with Zhang's conjecture. For the case ,
we provide strong evidence that the stationary expectation tends to
.Comment: 47 pages, 3 figure
Higgs sector and R-parity breaking couplings in models with broken U(1)_B-L gauge symmetry
Four different supersymmetric models based on SU(2)_L X U(1)_R X U(1)_B-L and
SU(2)_L X SU(2)_R X U(1)_B-L gauge symmetry groups are studied. U(1)_B-L
symmetry is broken spontaneously by a vacuum expectation value (VEV) of a
sneutrino field. The right-handed gauge bosons may obtain their mass solely by
sneutrino VEV. The physical charged lepton and neutrino are mixtures of
gauginos, higgsinos and lepton interaction eigenstates. Explicit formulae for
masses and mixings in the physical lepton fields are found. The spontaneous
symmetry breaking mechanism fixes the trilinear R-parity breaking couplings.
Only some special R-parity breaking trilinear couplings are allowed. There is a
potentially large trilinear lepton number breaking coupling - which is unique
to left-right models - that is proportional to the SU(2)_R gauge coupling g_R.
The couplings are parametrized by few mixing angles, making the spontaneous
R-parity breaking a natural ``unification framework'' for R-parity breaking
couplings in SUSYLR models.Comment: 19 pages, no figures, uses REVTeX. To be published in PR
Uniqueness and Nondegeneracy of Ground States for in
We prove uniqueness of ground state solutions for the
nonlinear equation in , where
and for and for . Here denotes the fractional Laplacian
in one dimension. In particular, we generalize (by completely different
techniques) the specific uniqueness result obtained by Amick and Toland for
and in [Acta Math., \textbf{167} (1991), 107--126]. As a
technical key result in this paper, we show that the associated linearized
operator is nondegenerate;
i.\,e., its kernel satisfies .
This result about proves a spectral assumption, which plays a central
role for the stability of solitary waves and blowup analysis for nonlinear
dispersive PDEs with fractional Laplacians, such as the generalized
Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page
Price-based control of ancillary services for power balancing
A reliable and an efficient power system is a necessity for any industrialized society. Governments have to enforce regulations to guarantee that such a power system, in spite of many competing stakeholders, participants, companies, and regulating agencies can be operational. This paper analyzes the present arrangements and the future requirements to be posed on incentives and regulation for ancillary services (AS) for power balancing. The paper proposes companies to assess their own needs for AS. A two-sided market for AS is being described to replace the existing arrangements for secondary control. The proposed solution guarantees a reliable and efficient operation of power systems in a market environment with responsive, reliable, and accountable but also competing prosumers, a large penetration of less-predictable renewables and continent-spanning transmission networks
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