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 $L = 10$, 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.

El estilo de "Los cachorros".

Sin resume

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 $\langle \bar{\psi} \psi \rangle$ 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 $[a,b]$. Second, if a site topples - which happens if the amount at that site is larger than a threshold value $E_c$ (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 $a$ and $b$. 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 $a \geq E_c/2$, indeed tends to that of the ASM (up to a scaling factor), in agreement with Zhang's conjecture. For the case $a=0$, $b=1$ we provide strong evidence that the stationary expectation tends to $\sqrt{1/2}$.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 (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ 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 $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ 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