Damage spreading in a single-component irreversible reaction process: Dependence of the system's immunity on the Euclidean dimension

The spreading of a globally distributed damage, created in the stationary regime, is studied in a single-component irreversible reaction process, i.e., the BK model [Browne and Kleban,Phys. Rev. A 40, 1615 (1989)]. The BK model describes one variant of the A+AA₂ reaction process on a lattice in contact with a reservoir of A species. The BK model has a single parameter, namely the rate of arrival of A species to the lattice (Y). The model, exhibits an irreversible phase transition between a stationary reactive state with production of A₂ species and a poisoned state with the lattice fully covered by A species. The transition takes place at critical points (Y _C ) which solely depend on the Euclidean dimensiond. It is found that the system is immune ford=1 andd=2, in the sense that even 100% of initial damage is healed within a finite healing period (T _H ). Within the reactive regime,T _H diverges when approachingY _C according toT _H (Y _C –Y)^–, with 1.62 and 1.08 ford=1 andd=2, respectively. Ford=3 a frozen-chaotic transition is found close toY _s 0.4125, i.e., well inside the reactive regime 0YY _C 0.4985. Just atY _S the damageD(t) heals according toD(t) t ^–, with 0.71. For the frozen-chaotic transition atd=3 the order parameter critical exponent 0.997 is determined.     

Collective structures of the <Superscript>131</Superscript>Cs nucleus

The collective structures of ¹³¹Cs have been investigated by in-beam -ray spectroscopic techniques following the ¹²⁴Sn (^11B , 4n) reaction at a beam energy E_lab = 57MeV. The previously established rotational bands, built on g_7/2, d_5/2 and the unique-parity h_11/2 orbitals, have been extended and evolve into new bands involving rotationally aligned (h_11/2)² and (h_11/2)² quasiparticles. In addition, a new multiquasiparticle band based on the g_7/2 g_7/2 h_11/2 configuration has also been observed. Theoretical interpretations for the assigned configurations are discussed in the framework of Total Routhian Surface (TRS) and Tilted Axis Cranking (TAC) model calculations. TAC model calculations predict a decrease in the B(M1) values with increasing rotational frequency for the g_7/2/d_5/2 (h_11/2)² and h_11/2 (h_11/2)² bands, thus indicating a magnetic rotation character for these bands.     

Brownian dynamics of colloidal hard spheres. 3. Extended investigations at the phase transition regime

The phase behavior of hard-sphere colloidal systems in the volume fraction regime 0.46<<0.64 has been studied in detail using a new and efficient algorithm to treat the nonanalytic interaction pair potential. In particular the influence of various initial configurations such as purely random and facecentered cubic (FCC) has been investigated, and former simulations have been extended toward much longer time scales. Thus, in the case of randomly initiated systems, crystallization could be suppressed for a comparably long time (500 _R , where _R is the structural relaxation time) where the system remained in a metastable glassy state. The concentration dependence of the long-time self-diffusion coefficients of these systems has been analyzed according to free volume theory (Doolittle equation). Numerical data fit excellently to the theoretical predictions, and the volume fraction of zero particle mobility was found close to the expected value of random close packing. In case of the FCC initiated systems, samples remained crystalline within the simulated evolution time of 500 _R if their volume fraction was above the predicted freezing transition _F = 0.494, whereas at lower concentrations rapid melting into a fluidlike disordered state is observed. It should be noted that this algorithm, which neglects higher-order correlations, considering only direct pair interactions, nevertheless yields the correct hard-sphere crystallization phase behavior as predicted in the literature.     

The GHS inequality for a large external field

We consider general even ferromagnetic systems with pair interactions in a nonnegative external magnetic fieldh. Classes of single-site measures are found such that the GHS inequality is valid for allh h, whereh 0 is a number depending on but independent of the size of the system. These measures include both absolutely continuous and discrete measures. For =a ₀+{(1–a)/2} · ( ₁ + _–1), somea [0, 1),h is determined exactly.Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation grant No. MCS 80-02149.Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation grant No. MCS 77-20683 and by the U.S.-Israel Binational Science Foundation.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

Repeller structure in a hierarchical model. II. Metric properties

We study the renormalization dynamics deriving from a hierarchical tight-binding Schrödinger equation. In the Part I of this work we analyzed the topological structure of the recurrent set-a chaotic repeller- and its relation with the spectral problem. In this part we turn our attention to the metric properties of the repeller. We first study periodic orbits and their bifurcation unfolding, and we organize them on a binary tree. We then apply a thermodynamic formalism which provides a complete characterization of the scaling properties of the energy spectrum. The distributionf() of local dimensions is determined by computing both a generalized -function through the periodic orbits and the bandwidths of periodic approximants of the Schrödinger operator. When the growth rateR of the potential is smaller than 1, we find evidence of a phase transition, implying that two different classes of states coexist in the spectrum. The asymptotic behavior of the Lebesgue measure of the spectrum is also studied. A linear scaling of to 0 is observed forR 1_–, while forR > 1, the measure of the periodic approximants goes to 0 as R^–h with the hierarchical orderh. Finally, we show that the localized state, present for R<1, is characterized by a superexponential scaling of the bandwidth.     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

Ergodicité et limite semi-classique

Consider a self adjoint quantic hamiltonian:P(h)=p(x, hD _x) whereh>0 is the Planck's constant andp some smooth classical observable on the phase space R²ⁿ . When the classical flow on a compact energy shell {p=} is ergodic we prove that in the limith 0 almost all the eigenfunctions ofP(h) whose energy is near of are distributed according to the Liouville measure on {p=}.In the high energy case ( +) this sort of problem was considered by A. Schnirelman, S. Zelditch, and Y. Colin de Verdière.     

On the Effect of Increasing the Radiative-Transition Rate Near a Nanosize Point

A short review of theoretical and experimental studies concerning the photoexcited florescence and Raman scattering of light for a substance in a space containing small material bodies is presented. Calculations of the radiativetransition probability for atoms (molecules) in the vicinity of bodies with a size much smaller than the light wavelength are performed. The probabilities of the singlephoton and doublephoton transitions are shown to increase by factors of 9 and 81 in the vicinity of a nanosize sphere with dielectric constant ||\ 1. The probability of a radiative transition in the vicinity of the vertex of a conic needle bearing up against a plane (both with || 1) increases by factors of (/R _in)² and (/R _in)⁴ for singlephoton and doublephoton transitions, respectively (R _in is the curvature radius for the needle vertex). This theoretical result is suggested as an explanation of the effect of increasing the radiation process intensity in the experiments carried out in the studies cited below.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

On the interface stiffness of the random field ising model

Recent results of Grinstein, Ma, Villain and Binder on interface roughening incontinuum andlattice random field Ising models are related by introducing an effective interface stiffness function {ei247-1}. Ford3 dimensions the continuum theory is shown to be valid for non-zero random field strengthh for all temperatures and on a length scaleL>l _d (h,T) _d (h,T). Ford=2 and smallT a smeared spin-glass transition occurs at ₂(h,T)h. It is argued, that for 3<d<5 interface roughening occurs only forh larger than a critical field strengthh _R (T).     

The asymmetric contact process on a finite set

The contact process onZ has one phase transition; let _c be the critical value at which the transition occurs. Let _N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants ₁() and ₂() such that if < _c , lim _{N N} /logN = 1/₁(); if > _c , lim _N log _N /N = ₂(); if = _c , lim _{N N} /N= and lim _{N N} /N ⁴=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values _c1< _c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < _c1 and > _c2. We show that for [ _c1< _c2), lim _{N N} /N=-1/, (where _i is an edge speed) and for = _c2, lim _N log _N /logN=2 in probability.     

High-spin states and band structures in the doubly odd <Superscript>136</Superscript>La nucleus

High-spin states of ¹³⁶La have been investigated with the reaction ¹³⁰Te( ¹¹B, 5n) at a beam energy of 60 MeV. The level scheme with three collective bands has been updated with spin up to 20 . The observed h_11/2 h_11/2 band shows -instability with increasing spin according to the TRS calculations. The band crossing and the signature splitting and inversion have been discussed. Other two collective bands based on 12^-and 16⁺ levels were proposed as oblate deformation with -60^°. They most probably originate from four- and six-quasiparticle configurations, that is, h_11/2 g_7/2h_11/2² and g_7/2 g_7/2²d_5/2h_11/2² respectively.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

On Percolation with Fibers or Layers

We consider site percolation on Z ^d, directed edges going from any sZ ^d to s+A ₁,..., s+A _n, where A ₁,..., A _n are the same for all sites and at least two of them are noncollinear. A site is closed if it belongs to p+Block, where p is a point in a Poisson distribution in R ^dZ ^d with a density and Block={sL: |s|M}+{sR ^d: |s|}, where L is a linear subspace of R ^d, |·| is the Euclidean norm, =max(|A ₁|,..., |A _n|) and M is a parameter. We study the behavior of *, the critical value, and P _closed*, corresponding critical percentage of closed sites, when M. Denote R ^d/L the factor space. Call two nonzero vectors U, V codirected if U=kV, where k>0. Theorem. If there are A _i and A _j whose projections to R ^d/L are not codirected, then *1/M ^dim(L) and P _closed* remains separated both from 0 and 1 when M. If projections of all A ₁,..., A _n to R ^d/L are codirected, then *1/M ^dim(L)+1 and P _closed*1/M when M.     

AnL p -theory for then-dimensional,stationary, compressible Navier-Stokes equations,and the incompressible limit for compressible fluids. The equilibrium solutions

In this paper we study the system (1.1), (1.3), which describes the stationary motion of a given amount of a compressible heat conducting, viscous fluid in a bounded domain ofR ⁿ, n2. Hereu(x) is the velocity field, (x) is the density of the fluid, (x) is the absolute temperature,f(x) andh(x) are the assigned external force field and heat sources per unit mass, andp(, ) is the pressure. In the physically significant case one hasg=0. We prove that for small data (f, g, h) there exists a unique solution (u, , ) of problem (1.1), (1.3)₁, in a neighborhood of (0,m, ₀); for arbitrarily large data the stationary solution does not exist in general (see Sect. 5). Moreover, we prove that (for barotropic flows) the stationary solution of the Navier-Stokes equations (1.8) is the incompressible limit of the stationary solutions of the compressible Navier-Stokes equations (1.7), as the Mach number becomes small. Finally, in Sect. 5 we will study the equilibrium solutions for system (4.1). For a more detailed explanation see the introduction.     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel

Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version wherec _t =c ₁ (t) is the concentration ofl-particle clusters at timet. We prove that for initial data satisfyingc ₁(0)>0 and the condition 0 c _l (0) <A (1+)^-l (A >0), the solutions behave asymptotically likec ₁ (t)t ^–2c(lt^–1) ast withlt ^–1 kept fixed. The scaling function c() is (1/gr), where , a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation wherec(v, t) is the oncentration of clusters of sizev.