Pair Connectedness and Shortest Path Scaling in Critical Percolation

We present high statistics data on the distribution of shortest path lengths between two near-by points on the same cluster at the percolation threshold. Our data are based on a new and very efficient algorithm. For $d=2$ they clearly disprove a recent conjecture by M. Porto et al., Phys. Rev. {\bf E 58}, R5205 (1998). Our data also provide upper bounds on the probability that two near-by points are on different infinite clusters.Comment: 7 pages, including 4 postscript figure

A lattice of double wells for manipulating pairs of cold atoms

We describe the design and implementation of a 2D optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms in an optical lattice. Atoms in the square lattice can be placed in a double well with any of their four nearest neighbors. The properties of the double well (the barrier height and relative energy offset of the paired sites) can be dynamically controlled. The topology of the lattice is phase stable against phase noise imparted by vibrational noise on mirrors. We demonstrate the dynamic control of the lattice by showing the coherent splitting of atoms from single wells into double wells and observing the resulting double-slit atom diffraction pattern. This lattice can be used to test controlled neutral atom motion among lattice sites and should allow for testing controlled two-qubit gates.Comment: 9 pages, 11 figures Accepted for publication in Physical Review

Dirac-like approach for consistent discretizations of classical constrained theories

We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the constraint surface and the Poisson or Dirac bracket structure. The conditions for the preservation of the constraints are more stringent than in the continuous case and as a consequence some of the continuum constraints become second class upon discretization and need to be solved by fixing their associated Lagrange multipliers. The gauge invariance of the discrete theory is encoded in a set of arbitrary functions that appear in the generating function of the evolution equations. The resulting scheme is general enough to accommodate the treatment of field theories on the lattice. This paper attempts to clarify and put on sounder footing a discretization technique that has already been used to treat a variety of systems, including Yang--Mills theories, BF-theory and general relativity on the lattice.Comment: 11 pages, RevTe

Influence of Laboratory Generated Turbulence on Phase Fluctuations of a Laser Beam

An experiment is performed the aim of which is to investigate the phase fluctuations of a laser beam artificially generated thermal turbulence. This is achieved by observing the displacements of a fringe pattern obtained by means of a Mach-Zehnder interferometer. The temporal decay of the mean square refractive index fluctuation is studied. An interpretation of the results is given on the basis of the theory of an isotropic turbulent scalar field

Preparing and probing atomic number states with an atom interferometer

We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state

Continuous decolourization of a sugar refinery wastewater in a modified rotating biological contactor with Phanerochaete chrysosporium immobilized on polyurethane foam disks

Phanerochaete chrysosporium immobilized on different support materials, such as polyurethane foam (PUF) and scouring web (SW), in shake cultures, was able to decolourize efficiently the sugar refinery effluent in a long-term repeated-batch operation. The decolourization medium composition was optimized using PUF-immobilized fungus. Addition of glucose was obligatory and the minimum glucose concentration was found to be 5 g/l. A rotating biological contactor (RBC) containing P. chrysosporium immobilized on PUF disks was operated with optimized decolourization medium, in continuous mode with a retention time of 3 days. By simply reversing the feed inlet of the reactor, after 17 days of operation, it was possible to double the active fungal lifetime. During the course of operation the colour, total phenols and chemical oxygen demand were reduced by 55, 63 and 48%, respectively.PEDIP Program - Project EUREKA EUROAGRI 1974 RESINAS

Influence of Thermal Turbulence in a Convective Ascending Stream on Phase Fluctuations of a Laser Beam

The effects of thermal turbulence on the phase fluctuations of a laser beam are investigated in laboratory. The turbulent region created by means of a horizontal heated Nichrome grid is made to shift upwards owing to the convective motion. A Mach-Zehnder interference experiment is performed in which two beams from a laser source are superimposed after crossing the turbulent region. The displacements of the fringe pattern allow one to study the temporal decay of the mean square refractive index fluctuation. An interpretation of the results is given on the basis of the theory of an isotropic turbulent scalar field

On the universality of distribution of ranked cluster masses at critical percolation

The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r shows a universal behaviour for different lattice sizes L (D is the fractal dimension). For different ranks however, there is a universal distribution function only in the large rank limit, i.e., $P(M/L^D,r)r^{-y\zeta } \sim g(Mr^y/L^D)$ (y and $\zeta$ are defined in the text), where the universal scaling function g is found to be Gaussian in nature.Comment: 4 pages, to appear in J. Phys.

Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton

We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and Phi(S)(r|l), giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance r. Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine the scaling behavior of the distribution functions in the limit x=r/l^(nu) much less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l) proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for g1, g1B, and g1S are in very good agreement with our numerical results.Comment: 10 pages, 3 figure

Planejamento fatorial para extra\ue7\ue3o de enzima fibrinolitica de Mucor subtilissimus UCP1262 mediante sistema de duas fases aquosas (PEG/fosfato)

A factorial design was used to select the best conditions of fibrinolytic protease from Mucor subtilissimus by aqueous two-phase system (PEG/phosphate)