Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

Loop-erased self-avoiding random walk in two and three dimensions

If(n) is the position of the self-avoiding random walk in ^d obtained by erasing loops from simple random walk, then it is proved that the mean square displacementE(¦(n)¦²) grows at least as fast as the Flory predictions for the usual SAW, i.e., at least as fast asn ^3/2 ford=2 andn ^6/5 ford=3. In particular, if the mean square displacement of the usual SAW grows liken ^1.18... ind=3, as expected, then the loop-erased process is in a different universality class.     

Ageing of random porous media following fluid deterministic displacement, freezing, thawing

This paper introduces and investigates a simple model of random porous media degradation via several fluid displacing, freezing, and thawing cycles. The fluid transport is based on the deterministic method. The result shows that the topology and the geometry of porous media have a strong effect on displacement processes. The cluster size of the viscous fingering (VF) pattern in the percolation cluster increases with the increase of iteration parameter n. When iteration parameter , the VF pattern does not change with n. When and , the peak value of the distribution increases as n increases; is the normalized distribution of throat sizes after different displacement-damage but before the freezing. The distribution of throat size N(r) after displacement but before freezing damage, shows that the major change, after successive cycles, happens at r>0.9. The peak value of the distribution reaches a maximum when and r=1, where is the normalized distribution of the size of invaded throats for different iterations. This result is different from invasion percolation. The distribution of velocities normal to the interface of VF in the percolation cluster is also studied. When , the scaling function distribution is very sharp. The sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L. And E has a minimum as L increases to the maximum size of the lattice. The VF pattern in the percolation cluster has one frozen zone and one active zone. Received 30 March 1999 and Received in final form 8 August 1999     

Conversion from n bands color space to HSI n color space

This paper presents the method to get the equations that transform a color space of n independent primary colors to the HIS _n color system (H: hue, S: saturation, I: intensity); n indicates the number of bands and the shape of the HIS _n space. For n = 3 the structure is a double triangular pyramid, for n 4 it is the structure of the double pyramid tetrangular, and so on.     

Unimolecular Decay of Metastable Cluster Anions: (O2)N−* → (O2) + O2

Unimolecular dissociation of metastable excited states of (O₂)_n^?* into (O₂) cluster anions has been detected and studied quantitatively for n in the range of 13 to 22. The apparent metastable (decay rates determined increase with cluster size in from ～ 5000 s^?1 (for n = 13) up to ～ 8500 s^?1 for n = 22).     

位移损伤剂量法评估空间GaAs/Ge太阳电池辐照损伤过程

本文针对GaAs/Ge太阳电池,利用位移损伤剂量法研究了其在轨服役条件下的性能退化行为.首先在地面模拟辐照环境中,试验获得了在不同能量的电子和质子辐照下的电池性能随辐照注量的退化行为.基于上述实验结果以及计算获得的带电粒子在电池中的非电离能量损失(NIEL)获得了不同能量电子辐照位移损伤的等效指数n为1.7,电子损伤剂量转化为质子损伤剂量等效系数为5.2,并进一步建立了电池性能随位移损伤剂量的退化方程.利用该方法对国产GaAs/Ge太阳电池在500,22000和36000 km轨道带电粒子辐 关键词： GaAs/Ge太阳电池 辐照损伤 带电粒子 位移损伤剂量     

Canonical Representations of Sp(1,n) Associated with Representations of Sp(1)

Canonical representations of Sp(1,n) associated with finite dimensional irreducible representations of Sp(1) are defined using vector-valued Berezin kernels. Their decomposition into irreducible representations is determined by decomposing the corresponding reproducing distributions in terms of positive definite trace spherical functions on Sp(1,n). The canonical representatons are also identified with the restriction to Sp(1,n) of certain maximal degenerate representations of SL(n+1,H). Received: 1 May 1998 / Accepted: 18 November 1998     

Radiation defect clusters in electron-irradiated silicon

Radiation defect formation in Czochralski-grown (pulled) and vacuum float-zone n-Si (ρ=15 to 150 ωcm) irradiated by electrons with energy E_e=2.5 to 1200 MeV has been studied. The results have been obtained from an analysis of the dose, energy and temperature dependences of the concentration n, Hall mobility μ _n , and charge-carrier lifetime τ. The experimentally observed peculiarities in the variation of n, μ _n , and τ irradiation by electrons with E10 MeV have been explained taking into account the formation of radiation defect clusters in the bulk of the crystal induced by such electrons. The correlation coefficients K_i have bsen obtained which take into consideration the “evolution” of primary displacement cascades in the location of which clusters are formed. The parameters of radiation defect clusters produced by electrons of different energies have been calculated using these coefficients.     

On Spherically Symmetric Solutions¶of the Compressible Isentropic Navier–Stokes Equations

We prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier–Stokes equations in ℝ ⁿ (n= 2, 3) when the Cauchy data are spherically symmetric. The proof is based on the exploitation of the one-dimensional feature of symmetric solutions and use of a new (multidimensional) property induced by the viscous flux. The present paper extends Lions' existence theorem [15] to the case 1< γ <γ _n for spherically symmetric initial data, where γ is the specific heat ratio in the pressure, γ _n = 3/2 for n= 2 and γ _n = 9/5 for n= 3. Dedicated to Professor Rolf Leis on the occasion of his 70th birthday Received: 17 January 2000 / Accepted: 3 July 2000     

Geometrical derivation of a new ground state formula for the n-electron Friedel resonance model

The n-electron ground state of the Friedel resonance model can be written as a single Slater determinant of n s-electrons plus d-electron-s-hole companion. This new formula is derived geometrically in the Hilbert space. The derivation uses the fact that a n-electron Slater determinant, built from N band states, corresponds to a n-dimensional subspace in the N-dimensional Hilbert space. Received: 4 November 1997 / Accepted: 19 November 1997     

Two Peculiar Classes of Solvable Systems Featuring 2 Dependent Variables Evolving in Discrete-Time via 2 Nonlinearly-Coupled First-Order Recursion Relations

In this paper we identify certain peculiar systems of 2 discrete-time evolution equations,

which are algebraically solvable. Here l is the “discrete-time” independent variable taking integer values (l = 0, 1, 2, . . .), x_n ≡ x_n(l) are 2 dependent variables, and are the corresponding 2 updated variables. In a previous paper the 2 functions F⁽ⁿ⁾(x₁, x₂), n = 1, 2, were defined as follows: F⁽ⁿ⁾(x₁, x₂) = P₂ (x_n, x_n+1), n = 1, 2 mod[2], with P₂(x₁, x₂) a specific second-degree homogeneous polynomial in the 2 (indistinguishable!) dependent variables x₁(l) and x₂(l). In the present paper we further clarify some aspects of that model and we present its extension to the case when a specific homogeneous function of arbitrary (integer) degree k (hence a polynomial of degree k when k > 0) in the 2 dependent variables x₁(l) and x₂(l).     

On some natural and model 2D bimodal random cellular structures

The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated. The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i=1,2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally compared with the predictions of various literature models. Received: 24 December 1997 / Revised: 7 April 1998 / Accepted: 20 April 1998     

Magnetic resonance imaging on CO(2) miscible and immiscible displacement in oil-saturated glass beads pack

In this study, the displacement processes were observed as gaseous or supercritical CO₂ was injected into n-decane-saturated glass beads packs using a 400-MHz magnetic resonance imaging (MRI) system. Two-dimensional images of oil distribution in the vertical median section were obtained using a spin-echo pulse sequence. Gas channeling and viscous fingering appeared obviously in immiscible gaseous CO₂ displacement. A piston-like displacement front was detected in miscible supercritical CO₂ displacement that provided high sweep efficiency. MRI images were processed with image intensity analysis methods to obtain the saturation profiles. Final oil residual saturations and displacement coefficients were also estimated using this imaging intensity analysis. It was proved that miscible displacement can enhance the efficiency of CO₂ displacement notably. Finally, a special coreflood analysis method was applied to estimate the effects of capillary, viscosity and buoyancy based on the obtained saturation data.     

Wavelength and temperature dependence properties of human blood-serum

For biological importance and general scientific interest, the present paper studies the physical properties dependent on wavelength and temperature, for six different samples of human blood-serum, at two different laser wavelengths (514.5 and 632.8 nm). The properties are described in terms of scalar quantities, viz. refractive index or optical permittivity, optical and dielectric dispersion. A modified and high accurate laser Mach–Zehnder interferometric technique is used for measurement of the refractive index (n) and its gradient with temperature (dn/dT). The values of n and dn/dT are applied to calculate the optical permittivity () and its gradient with temperature d/dT. The refractive properties such as the variation of n, , −dn/dT and, −d/dT as a functions of wavelengths are determined. On the other hand, the optical properties such as reflectance, transmittance and absorptance as a function of light incident angle, temperature and wavelength are studied. Additionally the following dielectric parameters are calculated: specific refractivity, specific dispersivity, polarizability per unit volume, wave impedance, volume expansion coefficient and the electric susceptibility.