Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.Comment: Key words: Bootstrap percolation, anisotropy, finite-size effect

High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions

We study the two and four dimensional Nishimori multicritical point via high temperature expansions for the $\pm J$ distribution, random-bond, Ising model. In $2d$ we estimate the the critical exponents along the Nishimori line to be $\gamma=2.37\pm 0.05$, $\nu=1.32\pm 0.08$. These, and earlier $3d$ estimates $\gamma =1.80\pm 0.15$, $\nu=0.85\pm 0.08$ are remarkably close to the critical exponents for percolation, which are known to be $\gamma=43/18$, $\nu=4/3$ in $d=2$ and $\gamma=1.805\pm0.02$ and $\nu=0.875\pm 0.008$ in $d=3$. However, the estimated $4d$ Nishimori exponents $\gamma=1.80\pm 0.15$, $\nu=1.0\pm 0.1$, are quite distinct from the $4d$ percolation results $\gamma=1.435\pm 0.015$, $\nu=0.678\pm 0.05$.Comment: 5 pages, RevTex, 3 postscript files; To appear in Physical Review

Wetting and particle adsorption in nanoflows

Molecular dynamics simulations are used to study the behavior of closely-fitting spherical and ellipsoidal particles moving through a fluid-filled cylinder at nanometer scales. The particle, the cylinder wall and the fluid solvent are all treated as atomic systems, and special attention is given to the effects of varying the wetting properties of the fluid. Although the modification of the solid-fluid interaction leads to significant changes in the microstructure of the fluid, its transport properties are found to be the same as in bulk. Independently of the shape and relative size of the particle, we find two distinct regimes as a function of the degree of wetting, with a sharp transition between them. In the case of a highly-wetting suspending fluid, the particle moves through the cylinder with an average axial velocity in agreement with that obtained from the solution of the continuum Stokes equations. In contrast, in the case of less-wetting fluids, only the early-time motion of the particle is consistent with continuum dynamics. At later times, the particle is eventually adsorbed onto the wall and subsequently executes an intermittent stick-slip motion.We show that van der Walls forces are the dominant contribution to the particle adsorption phenomenon and that depletion forces are weak enough to allow, in the highly-wetting situation, an initially adsorbed particle to spontaneously desorb

Dilemmas in doing insider research in professional education

This article explores the dilemmas I encountered when researching social work education in England as an insider researcher who was simultaneously employed as an educator in the host institution. This was an ethnographic project deploying multiple methods and generating rich case study material which informed the student textbook Becoming a Social Worker the four-year period of the project. First, ethical dilemmas emerged around informed consent and confidentiality when conducting surveys of students and reading their portfolios. Second, professional dilemmas stemmed from the ways in which my roles as a researcher, academic tutor, social worker and former practice educator converged and collided. Third, political dilemmas pertained to the potential for the project to crystallize and convey conflicts among stakeholders in the university and community. Since the majority of research in social work education is conducted by insiders, we have a vital interest in making sense of such complexity

Spectra of random Hermitian matrices with a small-rank external source: supercritical and subcritical regimes

Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$ external source matrix has two distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity $n-r$. The source is small in the sense that $r$ is finite or $r=\mathcal O(n^\gamma)$, for $0< \gamma<1$. For a Gaussian potential, P\'ech\'e \cite{Peche:2006} showed that for $|a|$ sufficiently small (the subcritical regime) the external source has no leading-order effect on the eigenvalues, while for $|a|$ sufficiently large (the supercritical regime) $r$ eigenvalues exit the bulk of the spectrum and behave as the eigenvalues of $r\times r$ Gaussian unitary ensemble (GUE). We establish the universality of these results for a general class of analytic potentials in the supercritical and subcritical regimes.Comment: 41 pages, 4 figure

Between overt and covert research: concealment and disclosure in an ethnographic study of commercial hospitality

This article examines the ways in which problems of concealment emerged in an ethnographic study of a suburban bar and considers how disclosure of the research aims, the recruitment of informants, and elicitation of information was negotiated throughout the fieldwork. The case study demonstrates how the social context and the relationships with specific informants determined overtness or covertness in the research. It is argued that the existing literature on covert research and covert methods provides an inappropriate frame of reference with which to understand concealment in fieldwork. The article illustrates why concealment is sometimes necessary, and often unavoidable, and concludes that the criticisms leveled against covert methods should not stop the fieldworker from engaging in research that involves covertness

From Current to Constituent Quarks: a Renormalization Group Improved Hamiltonian-based Description of Hadrons

A model which combines the perturbative behavior of QCD with low energy phenomenology in a unified framework is developed. This is achieved by applying a similarity transformation to the QCD Hamiltonian which removes interactions between the ultraviolet cutoff and an arbitrary lower scale. Iteration then yields a renormalization group improved effective Hamiltonian at the hadronic energy scale. The procedure preserves the standard ultraviolet behavior of QCD. Furthermore, the Hamiltonian evolves smoothly to a phenomenological low energy behavior below the hadronic scale. This method has the benefit of allowing radiative corrections to be directly incorporated into nonperturbative many-body techniques. It is applied to Coulomb gauge QCD supplemented with a low energy linear confinement interaction. A nontrivial vacuum is included in the analysis via a Bogoliubov-Valatin transformation. Finally, the formalism is applied to the vacuum gap equation, the quark condensate, and the dynamical quark mass.Comment: 36 pages, RevTeX, 5 ps figures include

Hypercomplex quantum mechanics

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module.Comment: Plain Tex, 11 page

Nuclear Modification Factor for Charged Pions and Protons at Forward Rapidity in Central Au+Au Collisions at 200 GeV

We present spectra of charged pions and protons in 0-10% central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV at mid-rapidity ($y=0$) and forward pseudorapidity ($\eta=2.2$) measured with the BRAHMS experiment at RHIC. The spectra are compared to spectra from p+p collisions at the same energy scaled by the number of binary collisions. The resulting nuclear modification factors for central Au+Au collisions at both $y=0$ and $\eta=2.2$ exhibit suppression for charged pions but not for (anti-)protons at intermediate $p_T$. The $\bar{p}/\pi^-$ ratios have been measured up to $p_T\sim 3$ GeV/$c$ at the two rapidities and the results indicate that a significant fraction of the charged hadrons produced at intermediate $p_T$ range are (anti-)protons at both mid-rapidity and $\eta = 2.2$

Strange particle production at RHIC in a single-freeze-out model

Strange particle ratios and pT-spectra are calculated in a thermal model with single freeze-out, previously used successfully to describe non-strange particle production at RHIC. The model and the recently released data for phi, Lambda, anti-Lambda, and K*(892) are in very satisfactory agreement, showing that the thermal approach can be used to describe the strangeness production at RHIC.Comment: We have added the comparison of the model predictions to the newly released Lambda and K*(892) pT-spectra from STA