Establishing Relations between Law and Other Forms of Thought and Language

The law does not, and could not, exist in an intellectual or linguistic vacuum. No one believes that the law is or should be impervious to other languages, other bodies of knowledge. In this sense the argument about the ‘autonomy’ of law is an empty one: law cannot be, should not be, perfectly autonomous, unconnected with any other system of thought and expression; yet it plainly has it own identity as a discourse, it own intellectual and linguistic habits, which it is our task as lawyers to understand and develop. It follows that an essential topic of legal thought is the proper relation between law and other forms of thought and expression – a topic that is important, difficult and full of interest

Effect of Fuel Type on Flame Ignition by Transient Plasma Discharges

Rise and delay times of mixtures of methane, propane, n-butane, iso-butane and iso-octane mixed with air ignited by transient plasma discharge were investigated and compared with spark discharge ignition. Multi-ignition site effect and high electron energy are suggested to contribute to shortening of rise and delay times

Supersymmetry and Localization in the Quantum Hall Effect

We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which employs both complex (bosonic) and Grassman (fermionic) fields, we map the problem of localization to the problem of diagonalizing a one-dimensional non-Hermitian Hamiltonian of interacting bosons and fermions. An exact solution is obtained in a restricted subspace of the Hilbert space which preserves boson-fermion supersymmetry. The physically relevant regime is investigated using the density matrix renormalization group (DMRG) method, and critical behavior is found at the plateau transition.Comment: 14 RevTex pages, 3 eps figures; This revised version contains an extended disussion of supersymmetry and improved numerical result

Very long optical path-length from a compact multi-pass cell

The multiple-pass optical cell is an important tool for laser absorption spectroscopy and its many applications. For most practical applications, such as trace-gas detection, a compact and robust design is essential. Here we report an investigation into a multi-pass cell design based on a pair of cylindrical mirrors, with a particular focus on achieving very long optical paths. We demonstrate a path-length of 50.31 m in a cell with 40 mm diameter mirrors spaced 88.9 mm apart - a 3-fold increase over the previously reported longest path-length obtained with this type of cell configuration. We characterize the mechanical stability of the cell and describe the practical conditions necessary to achieve very long path-lengths

Impurity Energy Level Within The Haldane Gap

An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When $J{'}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{'})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{'}>J$. The impurity level appears only when the deviation $dev=(J{'}-J)/J{'}$ is greater than $B_{c}$, which is near 0.3 in our calculation.Comment: Latex file,9 pages uuencoded compressed postscript including 4 figure

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models

We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.Comment: 5 pages, 5 figures; to appear in Physical Review

Staggered flux and stripes in doped antiferromagnets

We have numerically investigated whether or not a mean-field theory of spin textures generate fictitious flux in the doped two dimensional $t-J$-model. First we consider the properties of uniform systems and then we extend the investigation to include models of striped phases where a fictitious flux is generated in the domain wall providing a possible source for lowering the kinetic energy of the holes. We have compared the energetics of uniform systems with stripes directed along the (10)- and (11)-directions of the lattice, finding that phase-separation generically turns out to be energetically favorable. In addition to the numerical calculations, we present topological arguments relating flux and staggered flux to geometric properties of the spin texture. The calculation is based on a projection of the electron operators of the $t-J$ model into a spin texture with spinless fermions.Comment: RevTex, 19 pages including 20 figure

In vitro evaluation of electrospun blends of gelatin and PCL for application as a partial thickness corneal graft

The advent of innovative surgical procedures utilizing partial thickness corneal grafts has created a need for the development of synthetic implants to recreate corneal stromal tissue. This work evaluates electrospun gelatin and polycaprolactone (PCL) scaffolds as a potential biomaterial suitable for use in regeneration of corneal stromal tissue. Electrospun gelatin has been used for many years in tissue engineering, however, post‐production modification, such as crosslinking, is usually required to mechanically strengthen such scaffolds. This paper aims therefore to compare glutaraldehyde (GA) cross‐linked electrospun gelatin scaffolds with electrospun blends of gelatin and PCL at different ratios. Scaffolds were fabricated using electrospinning and characterized by scanning electron microscopy, Attenuated Total Reflectance‐Fourier Transform Infrared Spectroscopy (ATR‐FTIR), and tensile testing. To evaluate biocompatibility, primary human corneal stromal cells (hCSC) were seeded upon the scaffolds to assess adherence, proliferation and phenotype. Results demonstrated that scaffolds fabricated from mixtures of gelatin and PCL showed increased mechanical strength and plasticity compared to scaffolds fabricated from GA cross‐linked gelatin alone. In addition, scaffolds fabricated from PCL and gelatin showed comparable support of hCSC adhesion and proliferation. In conclusion, blended mixtures of gelatin and PCL can be considered as an option in the selection of corneal repair materials in the future