Semi-infinite Potts model and percolation at surfaces

The effects of surfaces on percolation are investigated near the bulk percolation threshold ind=6– dimensions. Using field-theoretic methods, this is done within the framework of a semi-infinite continuousq-state Potts model withq1. Renormalization-group equations are obtained which imply that the usual scaling laws for surface and bulk exponents are valid to all orders in , and the surface exponents at the ordinary and special transition are computed to order . Our result for ₁ ^ord is in conformity with the one by Carton.     

On the structure of Σ-hypernuclei

We investigate the-nucleus potential in the framework of a relativistic mean field approximation. As input for the elementaryN interaction we supplement the-repulsion by the exchange of an effective, complex-meson to account for theN N conversion. As the main result we find that the strength of ths absorptive central potential is smaller than the corresponding real part, whereas in the spin-orbit interaction, which is expected to be much weaker than for a nucleon, the imaginary component dominates.This work was partially supported by CNPq, FINEP (Brazil) and by the Bilateral Cooperation W. Germany — Brazil (KFA — CNPq).     

Directed paths on percolation clusters

We consider a variant of the problem of directed polymers on a disordered lattice, in which the disorder is geometrical in nature. In particular, we allow a finite probability for each bond to be absent from the lattice. We show, through the use of numerical and scaling arguments on both Euclidean and hierarchical lattices, that the model has two distinct scaling behaviors, depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold. We are particularly interested in the exponents and, defined by ft and xt , describing the free-energy and transverse fluctuations, respectively. Above the percolation threshold, the scaling behavior is governed by the standard random energy exponents (=1/3 and =2/3 in 1+1 dimensions). At the percolation threshold, we predict (and verify numerically in 1+1 dimensions) the exponents=1/2 and =v/v, where v and v are the directed percolation exponents. In addition, we predict the absence of a free phase in any dimension at the percolation threshold.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Deposition kinetics of the γ′ phase in N36T2YU2 steel

Electron microscopy is reported for the deposition in this steel; quantitative results are given on the particle size of the phase deposited during a continuous and uninterrupted decomposition. The deposition of the phase occurs in one stage, while the two stages in the variation in the mechanical properties arise from features of the interaction of dislocations with the phase particles. There appears to be only a small energy barrier to the generation of phase particles. Spherulites are formed in regions of interrupted decomposition. The effects of quenching temperature on the deposition mechanism are discussed.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 41–45, March, 1973.     

Magnetic moments of proton drip-line nuclei13O and9C

The magnetic moments of the proton drip-line nuclei¹³O(I = 3/2^–,T _1/2 = 8.6 ms) and 9C(I = 3/2^–,T _1/2 = 126 ms) have been determined for the first time through the combined techniques of polarized radioactive nuclear beams and-NMR detection. The observed magnetic moments are ¦(¹³O)¦ = 1.3891 ±0.0003 _N and ¦(⁹C)¦ = 1.3914 ±0.0005 _N. Spin expectation values are deduced to be 0.76 and 1.44 for¹³O and⁹C, respectively. While the of¹³O is consistent with the systematics from isospinT= 1/2 mirror pairs, the of⁹C is unusually large, even far larger than the single particle value, = 1.     

Mean field theory of self-organized critical phenomena

A mean field theory is presented for the recently discovered self-organized critical phenomena. The critical exponents are calculated and found to be the same as the mean field values for percolation. The power spectrum has 1/f behavior with exponentg4=1.     

True self-avoiding walk on critical percolation clusters and lattice animal

The statistics of true-self-avoiding walk model on two dimensional critical percolation clusters and lattice animals are studied using real-space renormalization group method. The correlation length exponents 's are found to be _TSAW ^pc 0.576 and _TSAW ^LA 0.623 respectively for the critical percolation clusters and lattice animals.     

Cluster Structure of Collapsing Polymers

In order to better understand the geometry of the polymer collapse transition, we study the distribution of geometric clusters made up of the nearest neighbor interactions of an interacting self-avoiding walk. We argue for this new correlated percolation problem that in two dimensions, and possibly also in three dimensions, a percolation transition takes place at a temperature lower than the collapse transition. Hence this novel transition should be governed by exponents unrelated to the -point exponents. This also implies that there is a temperature range in which the polymer has collapsed, but has no long-range cluster structure. We use Monte Carlo to study the distribution of clusters on the simple cubic and Manhattan lattices. On the Manhattan lattice, where the data are most convincing, we find that the percolation transition occurs at _p =1.461(3), while the collapse transition is known to occur exactly at =1.414.... We propose a finite-size scaling form for the cluster distribution and estimate several of the critical exponents. Regardless of the value of _p , this percolation problem sheds new light on polymer collapse.     

Monte Carlo study of the surface area of liquid droplets

Computer simulation of droplets containingl molecules (l 1000) in a lattice gas shows that the average surface area is proportional tol ; 0.6 in two and = 0.825 in three dimensions for small droplets. These exponents agree approximately with those in Kadanoff's modification of Fisher's droplet model near critical points [= (1 + )/; ourT/T _c is 0.4, 0.7, and 0.9]. For larger droplets, these exponents change to 1/2 (d = 2) and 2/3 (d = 3), the transition occurring for droplet diameters larger than the coherence length and smaller than the critical diameter in the nucleation of supersaturated vapors. This latter result rises some doubts on a recent nucleation theory of Eggingtonet al.     

The C1 Σ +-B1-Σ + amplified spontaneous emission in CO

The first observation of the amplified spontaneous emission (ASE) from the RydbergC ^{1 +}( = 0) state of CO is reported. When theC ^{1 +}( = 0) state was populated through the two-photon excitation, infrared radiation near 2.0 m was ejected in forward as well as backward directions along the laser propagation. The assignment as theC ^{1 +}( = 0) B ^{1 +}( = 0) transition was confirmed. Several characteristics of ASE from theC ^{1 +}( = 0) state are presented.This work was supported by the Morino Foundation, a Grant-in-Aid (No. 07640697) and that on Priority-Area-Research Photoreaction Dynamics (No. 07228268) from the Ministry of Education, Science, Sports and Culture, Japan.     

Theta-point exponent for polymer chain in random media

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that the-point size exponent _p ⁰ of polymer chains remains unchanged for small disorder concentration (p>p _c ). At the percolation thresholdp=p _c , using a Flory-type approximation, we conjecture that _pc ⁰ =5/(d _B +7), whered _B is the percolation backbone dimension. It shows that the upper critical dimensionality for the-point transition atp=p _c shifts to a dimensiond _c >3. We also propose that the-point varies practically linearly withp for 1>pp _c .     

Scaling Limit and Critical Exponents for Two-Dimensional Bootstrap Percolation

Consider a cellular automaton with state space {0,1} ² where the initial configuration _0 is chosen according to a Bernoulli product measure, 1s are stable, and 0s become 1s if they are surrounded by at least three neighboring 1s. In this paper we show that the configuration _n at time n converges exponentially fast to a final configuration , and that the limiting measure corresponding to is in the universality class of Bernoulli (independent) percolation. More precisely, assuming the existence of the critical exponents , , and , and of the continuum scaling limit of crossing probabilities for independent site percolation on the close-packed version of ² (i.e. for independent *-percolation on ), we prove that the bootstrapped percolation model has the same scaling limit and critical exponents.This type of bootstrap percolation can be seen as a paradigm for a class of cellular automata whose evolution is given, at each time step, by a monotonic and nonessential enhancement [Aizenman and Grimmett, J. Stat. Phys. 63: 817--835 (1991); Grimmett, Percolation, 2nd Ed. (Springer, Berlin, 1999)     

The phase transition in a general class of Ising-type models is sharp

For a family of translation-invariant, ferromagnetic, one-component spin systems—which includes Ising and ⁴ models—we prove that (i) the phase transition is sharp in the sense that at zero magnetic field the high- and low-temperature phases extend up to a common critical point, and (ii) the critical exponent obeys the mean field bound 1/2. The present derivation of these nonperturbative statements is not restricted to regular systems, and is based on a new differential inequality whose Ising model version isMh+M ³+ M ²M/. The significance of the inequality was recognized in a recent work on related problems for percolation models, while the inequality itself is related to previous results, by a number of authors, on ferromagnetic and percolation models.     

Possible generalization of Boltzmann-Gibbs statistics

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS _q k [1 – _i=1 ^W p _i ^q ]/(q-1), whereq characterizes the generalization andp _i are the probabilities associated withW (microscopic) configurations (W). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq1 limit.     

Critical behavior of the site percolation model on the square lattice in aL×M geometry

Relevant aspects of the critical behavior of the site percolation model in aL×M geometry (LM) are studied. It is shown that this geometry favors the growth of percolating clusters in theL-direction with respect to those growing in theM-direction, causing pronounced finite-size effects on the percolation probabilities. Scaling functions have an additional parameter, namelyM, which introduces a dependence of these functions on the aspect ratioL/M. At criticality, the probability of a site belonging to the percolation clusters (P _L,M ) behaves likeP _L,M L ^/v (L/M) with =5/36 andv=4/3, where is a suitable scaling function. Using scaling arguments it is conjectured and then tested by means of Monte Carlo simulations, the following asymptotic behavior (L/M)(L/M), (L,M, =1), for the leading term. Systematic deviations of the Monte Carlo data from the conjectured behavior are due to second order corrections to the leading term which can also be under-stood on the basis of scaling ideas. Finite-size dependent critical probabilities are also functions ofL/M as it follows from scaling arguments which are corroborated by the simulations.Financially supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) de la República Argentina     

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.