Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self-interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one-loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (Δ/b ^d)N ^{2 - νd}≥1, where Δ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non-ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength Δ _c ∼ N ^{- γ} where the exponent γ ≈ 0.25 and does not depend from the solvent quality. Received 17 December 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: vilgis@mpip-mainz.mpg.de     

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy F_N, depending on N(N - 1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 2⁴ < N < 2⁸ and for an open chain of length 50 < N < 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented. Received 7 June 2001 and Received in final form 17 October 2001     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar     

The structure of 99Ru from (α,3n) reaction

The results of in-beam investigations of excited states of ⁹⁹Ru using the ⁹⁸Mo(α,3n) reaction are presented. Angular distributions of γ–rays and γ–γ coincidences have been measured. Excited states have been identified up to an energy of E = 5603 keV and spin of I^π= 31/2⁻. Mean lifetimes τ have been determined using the DSA method for eleven levels. Aligned angular momenta are discussed and the probable (νh _11/2) origin of a backbending at frequency about 0.5 MeV was confirmed. The possible role of (νd _5/2) alignment at frequencies above 0.5 MeV was pointed out. Received: 13 January 1999 / Revised version: 26 March 1999     

Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

Side wall effects in Rayleigh Bénard experiments

In Rayleigh Bénard experiments, the side wall conductivity is traditionally taken into account by subtracting the empty cell heat conductivity from the measured one. We present a model showing that the correction to apply could be considerably larger. We compare to experiments and find good agreement. One of the consequences is that the Nusselt behavior for Ra < 10¹⁰ could be closer to Nu∝Ra ^1/3 than currently assumed. Also, the wall effect can appear as a continuous change in the γ exponent Nu∝Ra ^γ. Received 26 April and Received in final form 1st October 2001     

Steps and facets at the surface of soft crystals

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found. Received 25 June 2001     

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the (n) vector ϕ⁴ model, with long-range interaction decaying algebraically with the interparticle distance r like r ^{-d - σ}, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T _c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d _< = σ) and the upper ( d _> = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001     

Universal properties of shortest paths in isotropically correlated random potentials

We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2ν - ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations. Received 20 December 2002 / Received in final form 10 April 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: schorr@lusi.uni-sb.de     

Phase equilibria in random multiblock copolymers

A mean-field theory for domain structures in random multiblock copolymer melts is developed. We focus on the finite molecular weight effects resulting in a competition between macroscopic phase separation and microdomain formation in the system. We identify an essential parameter N ε controlling the phase behavior of the system, where N is the number of blocks per chain and ε is the composition asymmetry parameter (= the difference between the mean copolymer composition and its critical value). The phase diagram involving N ε and the reduced temperature as variables is obtained. The regions of coexistence of two or more phases are identified. We show that a superstructure formation on cooling is always pre-empted by a macroscopic phase separation of the macroscopically homogeneous (disordered) system yielding two homogeneous phases: H ₀↦H ₁ + H ₂. The third (lamellar) phase separates on further cooling. Then hexagonal and body-centred-cubic phases take over if N ε 1. As the Flory interaction parameter χ increases further, the standard transitions BCC↦HEX↦LAM take place. Received 13 July 2001     

Mixing and sorting of bidisperse two-dimensional bubbles

We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area λ ( λ≤1). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of λ, the minimal configuration for N → ∞. For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in “phase-separated” clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair (N,λ). As λ is varied, this alternates between a circular cluster of one of the mixed tilings, and “partial wetting” of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area λ. Received 1 August 2002 RID="a" ID="a"e-mail: paulo@ist.utl.pt     

Persistence of opinion in the Sznajd consensus model: computer simulation

The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/t ^θ. We find θ ≃ 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however, the exponent differs from the Ising θ. With simultaneous updating of sublattices instead of the usual random sequential updating, the number of persistent opinions decays roughly exponentially. Some of the simulations used multi-spin coding. Received 22 August 2002 / Received in final form 12 November 2002 Published online 31 December 2002     

Coherent and incoherent π0 photoproduction from the deuteron

Differential cross-sections for the reactions d (γ,π⁰)d and d (γ,π⁰)pn have been measured at MAMI with the TAPS detector setup in the energy range 140 MeV < E _γ < 306 MeV. By use of the Glasgow tagging spectrometer an 0.8 MeV energy resolution for photons incident on the target was achieved. The π⁰ missing energy resolution was sufficient for a reliable separation of coherent and incoherent channels. The data for the break-up channel exhibit very strong final state interaction effects, whereas the observed angular dependence of the inclusive process d (γ,π⁰)X is in quantitative agreement with predictions for a quasi-free process. The observed absolute d (γ,π⁰)X cross-sections, on the other hand, are significantly smaller than predicted by the quasi-free process for E _γ >∼ 250 MeV. Associating this failure with the π⁰ photoproduction on the neutron would suggest that its cross-section is up to 25% below the presently believed value. Received: 13 February 2001 / Accepted: 13 April 2001     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000     

The low-spin structure of <Superscript>115</Superscript>Xe

The low-spin band structure of neutron-deficient ¹¹⁵ ₅₄Xe has been studied following a low-energy (212.3 MeV) ⁶⁰Ni(⁵⁸Ni,2pnγ) reaction performed at IReS, Strasbourg, with the Garel⁺ spectrometer. The relative excitation energies of νh_11/2 (isomeric), νg_7/2, and νd_5/2 bandheads have been established. Received: 23 March 2000     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Maximally aligned states in 99Ag

Excited states of ⁹⁹Ag were populated via the ⁵⁰Cr + ⁵⁸Ni (261 MeV) reaction using the NORDBALL detector array equipped with charged-particle and neutron detector systems for reaction channel separation. On the basis of the measured γγ-coincidence relations and angular distribution ratios a significantly extended level scheme has been constructed up to E _x ∼ 7.8 MeV and I = 35/2. The experimental results were described within the framework of the shell model. Candidates for states fully aligned in the πg _9/2 ^-3ν(d _5/2, g _7/2)² valence configuration space were found at 4109 and 6265 keV. Received: 18 June 2002 / Accepted: 11 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: sohler@atomki.hu Communicated by J. ?yst?     

Shapes of the neutron-rich 88-94Kr nuclei

Neutron-rich, ^88-94Kr nuclei, populated in spontaneous fission of ²⁴⁸Cm, have been studied with EUROGAM 2, by measuring prompt γ-rays. Many new excited states in even-even Kr isotopes have been identified. For the first time spins and parities were determined experimentally in these nuclei. Our results indicate that the quadrupole deformation of Kr isotopes will appear only above N = 58, as observed in Sr and Zr nuclei. The newly found 3^- level at 1506.4 keV in ⁹⁰Kr suggests the exsistence of a new region of increased octupole correlations, probably associated with the ν(d _5/2 h _11/2) pair of Δl = Δj = 3 orbitals. Received: 18 September 2000 / Accepted: 18 October 2000     

Spectroscopy of 112Pd using heavy-ion-induced fission

High-spin states in ¹¹²Pd were studied using prompt γ-ray spectroscopy with Gammasphere following heavy-ion-induced fission in the reaction ¹⁸O + ²⁰⁸Pb at 91 MeV. A new 8⁺ level at 2638 keV was discovered with transitions connecting it to the yrast band and the quasi-gamma band. The three, now established, closely spaced 8⁺ states indicate a mixing between the ground-state band, s-band, and quasi-gamma band. Several high-spin structures with likely negative parity have been extended to higher spin and it is proposed that they are based on the νh _11/2(g _7/2 d _5/2) and νh _11/2(s _1/2 d _3/2) configurations. Received: 28 November 2000 / Accepted: 8 February 2001     

Yrast bands in N = 91 isotones

The in-beam spectroscopy on N = 91 isotones has been carried out using the ¹²C + ¹⁵⁰Nd reaction. The νi _13/2 and νh _11/2 bands of ¹⁵³Sm have been extended up to 33/2⁺ and 31/2^-, respectively. Two new γ-rays have been located on the top of the unfavored band with νi _13/2 configuration in ¹⁵⁷Dy. Two identical relationships have been established in the low-spin region of the yrast νi _13/2 configuration between ¹⁵³Sm and ¹⁵⁵Gd, and between unfavored bands of ¹⁵⁵Gd and ¹⁵⁷Dy. Here all these nuclei have the same neutron number N = 91. Received: 28 June 2000 / Accepted: 20 October 2000