Reptation and interdiffusion in polystyrene networks

We have used helium-3 nuclear reaction analysis to measure the interdiffusion of linear polystyrene into a film of crosslinked polystyrene and the intradiffusion of polystyrene in polystyrene networks. The interdiffusion is compared with that predicted from the Kramer-Sillescu theory, and is found to be considerably faster. This is attributed to the relaxation of inhomogeneities in the network. The molecular weight and crosslinking dependence of the intradiffusion coefficients of free polystyrene chains trapped inside networks is discussed in terms of the simple tube model and provides reasonably good agreement with that predicted from reptation theory. Received 2 August 2000 and Received in final form 6 November 2000     

Structure of nuclei far from the stability in relativistic approach

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, axially deformed relativistic Hartree-Bogoliubov approach in Woods-Saxon basis aiming at halo nucleus, time-odd triaxial RMF approach, the adiabatic and configuration-fixed constrained triaxial RMF approaches, a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ,ω,ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.     

Film thickness effects on the distribution of high-molecular-weight heterotelechelic polymers

High-molecular-weight heterotelechelic deuteriopolystyrene, NDPSF, possessing an amine functional group at one end of the chain and a fluorocarbon group at the other was tethered to a silicon substrate by its amine functional group. These layers were coated with an unfunctionalised polystyrene matrix, HPS, such that the total film thickness covered a range from 2.2 to 9 times the radius of gyration of NDPSF. The detailed distribution of the polymers after annealing for times much greater than the reptation period of either of the components, was obtained using neutron reflectometry. No evidence for bridging of the two interfaces was found for the thicker films, but the finite concentration of the NDPSF polymer observed for the thinnest films may be due to bridging since the energy gain of the fluorocarbon end is just greater than the loss due to configurational entropy losses. A linear increase in the ellipsometric thickness of the excess of NDPSF at the substrate was discovered and we attribute this to the NDPSF slowly being leached out of the layer initially at the substrate followed by diffusion into the bulk of the film. The concentration profiles obtained are consistent with hindered relaxation of the large NDPSF molecules, when they are tethered at the substrate or at the vacuum surface. Received 21 August 2001 and Received in final form 7 January 2002     

Economic small-world behavior in weighted networks

The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation is valid only for topological networks. In this paper we propose a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are “cheap” to build, and nevertheless efficient in propagating information, both at global and local scale. In this way we provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are studied, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems. Received 6 November 2002 / Received in final form 24 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: latora@ct.infn.it     

Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings

We demonstrate the usefulness of two-dimensional hyperbolic geometry as a tool to generate three-dimensional Euclidean (E³) networks. The technique involves projection of edges of tilings of the hyperbolic plane (H²) onto three-periodic minimal surfaces, embedded in E³. Given the extraordinary wealth of symmetries commensurate with H², we can generate networks in E³ that are difficult to construct otherwise. In particular, we form four-, five- and seven-connected (E³) nets containing three- and five-rings, viz. (3, 7), (5, 4) and (5, 5) tilings in H². Received 14 January 2002 / Received in final form 12 August 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: stephen.hyde@anu.edu.au     

Epidemic outbreaks in complex heterogeneous networks

We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures. Received 20 September 2001 and Received in final form 4 February 2002     

Interactions between isolated nucleosome core particles: A tail-bridging effect?

Interactions between isolated nucleosome core particles are studied as a function of the monovalent salt concentration by osmometry and by electrophoretic mobility measurements. The data are compared to the measurements performed on the protein-free DNA fragments and also analysed using the conventional theoretical approach. At low salt, an electrostatic screening effect accounts for the variation of the second virial coefficient whereas the simple hard-core contribution becomes predominant at high salt. In the intermediate range, an attraction occurs. In the light of previous results (Mangenot et al. Biophys. J. 82, 345 (2002)), we show that the flexible basic proteic tails are responsible for this attraction. A tail-bridging effect is discussed. Received 4 October 2001     

Band termination in the Z = N odd-odd nuclei <Superscript>46</Superscript>V and <Superscript>50</Superscript>Mn

The configuration-dependent cranked Nilsson-Strutinsky approach has been employed to study the properties and band structures at high spin in the Z = N odd-odd nuclei ⁴⁶V and ⁵⁰Mn. The observed bands are explained and terminating states are confirmed by the calculations. The calculated and observed bands are in good agreement without normalization, especially for terminating states. Possible bands with rotation around the intermediate axis and the effect of γ-deformation on the total energy of several interesting configurations are discussed. Received: 2 April 2002 / Accepted: 27 January 2003 / Published online: 15 April 2003     

Properties of a growing random directed network

We study a number of properties of a simple random growing directed network which can be used to model real directed networks such as the world-wide web and call graphs. We confirm numerically that the distributions of in- and out-degree are consistent with a power law, in agreement with previous analytical results and with empirical measurements from real graphs. We study the distribution and mean of the minimum path length, the high degree nodes, the appearance and size of the giant component and the topology of the nodes outside the giant component. These properties are compared with empirical studies of the world-wide web. Received 15 June 2001 and Received in final form 12 July 2001     

Melting and unzipping of DNA

Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule consist of an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In the present study we take into account in an approximate way the excluded-volume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a first-order melting transition in d = 2 dimensions and above, consistent with the experimental results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach. Received 21 August 2001 and Received in final form 26 January 2002     

Valuation and dynamic replication of contingent claims in the framework of the beliefs-preferences gauge symmetry

Although symmetries play a major role in physics, their use in finance is relatively new and, to the best of our knowledge, can be traced to 1995 when Kholodnyi introduced the beliefs-preferences gauge symmetry. One of the main outcomes of the beliefs-preferences gauge symmetry is that it allows for the valuation and dynamic replication of contingent claims in a general market environment, that is, in the case of a general, not necessarily diffusion Markov process for the prices of underlying securities. This valuation and dynamic replication is based on the novel ideas of symmetry in contrast to the standard approach which uses stochastic analysis. The practical applications of the beliefs-preferences gauge symmetry range from the detection of a new type of true arbitrage to the beliefs-preferences-independent valuation and dynamic replication of contingent claims in a general market environment. Received 31 December 2001     

Formation of adhesive contacts: Spreading versus dewetting

A soft bead (radius R _b) is pressed with a force F against a hydrophobic glass plate through a water drop (“wet” JKR set-up). We observe with a fast camera the growth of the contact zone bridging the rubber bead to the glass. Depending on the approach velocity V, two regimes are observed : i) at large V a liquid film is squeezed at the interface and dewets by nucleation and growth of a dry contact; ii) at low velocities, the bead remains nearly spherical. As it comes into contact, the rubber bead spreads on the glass with a characteristic time (in the range of one millisecond) τ ≈ ηR _b ²/F, where η is the liquid viscosity. The laws of spreading are interpreted by a balance of global mechanical and viscous forces. Received: 22 December 2002 / Accepted: 24 March 2003 / Published online: 29 April 2003 RID="a" ID="a"e-mail: brochard@curie.fr     

Isovector deformation and its link to the neutron shell closure

DWBA analysis of the inelastic ^30-40S(p,p') and ^18-22O(p,p') scattering data measured in the inverse kinematics has been performed to determine the isoscalar (δ₀) and isovector (δ₁) deformation lengths of the 2⁺₁ excitations in the Sulfur and Oxygen isotopes using a compact folding approach. A systematic N-dependence of δ₀ and δ₁ has been established which shows a link between δ₁ and the neutron-shell closure. Strong isovector deformations were found in several cases, e.g., the 2⁺₁ state in ²⁰O where δ₁ is nearly three times larger than δ₀. These results confirm the relation δ₁>δ₀ anticipated from the core polarization by the valence neutrons in the open-shell (neutron rich) nuclei. The effect of neutron shell closure at N=14 or 16 has been discussed based on the folding model analysis of the inelastic ²²O+p scattering data at 46.6 MeV/u measured recently at GANIL.     

Excitation of hydrogen atom by positron using hylleraas time-dependent approach

The time-dependent treatment of positron-hydrogen scattering for a zero total angular momentum has been presented. The initial wavefunction of the positron-hydrogen scattering system has been expanded in terms of three dimensional dynamical wave functions to include all higher angular momenta by solving a set of three coupled differential equations. This wavefunction is then time evolved using Taylor series expansion of the evolution operator. The excitation probabilities are monitored as the wavefunction propagates until there is no more change in the probabilities. The positron impact excitation cross-sections extracted from the final wavefunction are compared with the available results of converged close coupling approach. Received 23 July 2001 and Received in final form 25 November 2001     

Vector potential gauge for superconducting regular polygons

An approach to the Ginzburg-Landau problem of superconducting polygons is developed, based on the exact fulfillment of superconducting boundary conditions along the boundary of the sample. To this end an analytical gauge transformation for the vector potential A is found which gives A _n = 0 for the normal component along the boundary line of an arbitrary regular polygon. The use of the new gauge reduces the Ginzburg-Landau problem of superconducting polygons in external magnetic fields to an eigenvalue problem in a basis set of functions obeying Neumann boundary conditions. The advantages of this approach, especially for low magnetic fields, are illustrated and novel vortex patterns are obtained which can be probed experimentally. Received 28 February 2002 and Received in final form 12 April 2002 Published online 6 June 2002     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Self-similar approach to market analysis

A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the Law of Self-Similar Evolution, according to which any complex system develops self-similarly. There always exist some internal laws governing the evolution of a system, say of a market, so that each of such systems possesses its own character regulating its behaviour. The problem is how to discover these hidden internal laws defining the system character. This problem can be solved by employing the self-similar approximation theory, which supplies the mathematical foundation for the law of self-similar evolution. In this report, the theoretical basis of the new approach to analyzing time series is formulated, with an accurate explanation of its principal points. Received 15 August 2000     

Parity and ruin in a stochastic game

We study an elementary two-player card game where in each round players compare cards and the holder of the card with the smaller value wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn randomly. We obtain an exact solution for arbitrary initial conditions. In general, the game approaches a steady state where the card value densities of the two players are proportional to each other. The leading small value behavior of the initial densities determines the corresponding proportionality constant, while the next correction governs the asymptotic time dependence. The relaxation toward the steady state exhibits a rich behavior, e.g., it may be algebraically slow or exponentially fast. Moreover, in ruin situations where one player eventually wins all cards, the game may even end in a finite time. Received 24 August 2001 and Received in final form 12 November 2001     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

Dynamical properties of the slithering-snake algorithm: A numerical test of the activated-reptation hypothesis

Correlations in the motion of reptating polymers in a melt are investigated by means of Monte Carlo simulations of the three-dimensional slithering-snake version of the bond-fluctuation model. Surprisingly, the slithering-snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (created either by chain length N or by the volume fraction φ of occupied lattice sites), where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound (N) is set by the density of chain ends φ/N. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of “snakes” at t ≪ is identical to that of a benchmark system where all chains but one are frozen. We demonstrate that the subdiffusive dynamical regime is caused by the slow creeping of a chain out of its correlation hole. Our results are in good qualitative agreement with the activated-reptation scheme proposed recently by Semenov and Rubinstein (Eur. Phys. J. B, 1 (1998) 87). Additionally, we briefly comment on the relevance of local relaxation pathways within a slithering-snake scheme. Our preliminary results suggest that a judicious choice of the ratio of local to slithering-snake moves is crucial to equilibrate a melt of long chains efficiently. Received: 18 December 2002 / Accepted: 3 April 2003 / Published online: 12 May 2003 RID="a" ID="a"e-mail: jwittmer@dpm.univ-lyon1.fr RID="b" ID="b"Current address: University of Illinois at Urbana-Champaign.