The secondary structure of RNA under tension

We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second-order phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a macroscopic end-to-end distance at high forces. At low temperatures, the sequence inhomogeneities modify the critical behaviour. We provide numerical evidence for the universality of the critical exponents which, by extrapolation of the scaling laws to zero force, contain useful information on the ground-state (f = 0) properties. This provides a good method for quantitative studies of scaling exponents characterizing the collapsed globule. In order to get rid of the blurring effect of thermal fluctuations, we restrict ourselves to the ground state at fixed external force. We analyze the statistics of rearrangements, in particular below the critical force, and point out its implications for force-extension experiments on single molecules. Received 18 June 2002 and Received in final form 23 September 2002 RID="a" ID="a"e-mail: muller@ipno.in2p3.fr     

Core percolation in random graphs: a critical phenomena analysis

We study both numerically and analytically what happens to a random graph of average connectivity α when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced subgraph we call the core. In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs at α = e = 2.718 ... : below the transition, the core is small but above the transition, it occupies a finite fraction of the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random graphs. Received 31 January 2001 and Received in final form 26 June 2001     

Symmetry-breaking in local Lyapunov exponents

Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time Lyapunov exponents are nonzero, but owing to a symmetry, their global averages vanish. When the system becomes nonintegrable, this symmetry is broken. A parallel to this phenomenon occurs in mappings which derive from quasiperiodic Schr?dinger problems in 1-dimension. For values of the energy such that the eigenstate is extended, the Lyapunov exponent is zero, while if the eigenstate is localized, the Lyapunov exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local Lyapunov exponents, and corresponds to a breaking of a symmetry of the wavefunction in extended and critical states. Received 25 October 2001 / Received in final form 8 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: r.ramaswamy@mail.jnu.ac.in     

The timescale of spinodal dewetting at a polymer/polymer interface

We investigate the dynamics of spinodal dewetting in liquid-liquid polymer systems. Dewetting of poly(methyl-methacrylate) (PMMA) thin films on polystyrene (PS) “substrates” is followed in situ using neutron reflectivity. By following the development of roughness at the PS/PMMA interface and the PMMA surface we extract characteristic growth times for the dewetting process. These characteristic growth times are measured as a function of the molecular weight of the two polymers. By also carrying out experiments in the regime where the dynamics are independent of the PS molecular weight, we are able to use dewetting to probe the scaling of the PMMA thin film viscosity with temperature and molecular weight. We find that this scaling reflects bulk behaviour. However, absolute values are low compared to bulk viscosities, which we suggest may be due in part to slippage at the polymer/polymer interface. Received 25 June 2001 and Received in final form 5 December 2001     

Lyapunov exponent, generalized entropies and fractal dimensions of hot drops

We calculate the maximal Lyapunov exponent, the generalized entropies, the asymptotic distance between nearby trajectories and the fractal dimensions for a finite two-dimensional system at different initial excitation energies. We show that these quantities have a maximum at about the same excitation energy. The presence of this maximum indicates the transition from a chaotic regime to a more regular one. In the chaotic regime the system is composed mainly of a liquid drop while the regular one corresponds to almost freely flowing particles and small clusters. At the transitional excitation energy the fractal dimensions are similar to those estimated from the Fisher model for a liquid-gas phase transition at the critical point. Received: 16 March 2001 / Accepted: 12 July 2001     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite-size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin. Received 19 September 2001 and Received in final form 19 March 2002     

A shell-model approach to fractal-induced turbulence

We present a shell-model of fractal induced turbulence which predicts that structure function scaling exponents decrease in absolute value as the fractal dimension of the turbulence-inducing fractal object increases. This qualitative prediction is in agreement with laboratory measurements. Finer details of the fractal induced turbulence statistics and dynamics depend on the fractal force's phases, i.e. on the detailed construction of the fractal stirrer. In a case of deterministic forcing phases, a critical fractal dimension exists below which the average rate of inter-scale energy transfer <T _n> is a decreasing function of the wavenumber k_n and the structure function scaling exponents take close to Kolmogorov values. Above this critical fractal dimension, <T _n> is an increasing function of k_n and the structure function scaling exponents deviate significantly from Kolmogorov values. Received 25 June 2001 / Received in final form 5 April 2002 Published online 19 July 2002     

Complex dynamics in gelling systems

We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical-mechanics model. The model is based on percolation and bond fluctuation dynamics. The values for the critical exponents of the viscosity and elasticity agree with a part of the experimental observations and of the theoretical predictions. The obtained relaxation patterns well reproduce the behaviour observed in different gelling systems. Received 10 March 2002 and Received in final form 30 April 2002     

Phase transitions in a cluster molecular field approximation

Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of improving the molecular field approximation by inserting spin clusters of variable sizes into a homogeneously magnetised background. The density of states of these spin clusters is then computed exactly. We show that the true non-classical critical exponents can be extracted from spin clusters treated in such a manner. For this purpose a molecular field finite size scaling theory is discussed and effective critical exponents are analysed. Reliable values of critical quantities of various Ising and Potts models are extracted from very small system sizes. Received 30 September 2002 / Received in final form 25 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: pleim@theorie1.physik.uni-erlangen.de     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Ferromagnetic ordering in graphs with arbitrary degree distribution

We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical exponents as a function of the moments of the degree distribution. Two regimes of the degree distribution are of particular interest. In the case of a divergent second moment, the system is ferromagnetic at all temperatures. In the case of a finite second moment and a divergent fourth moment, there is a ferromagnetic transition characterized by non-trivial critical exponents. Finally, if the fourth moment is finite we recover the mean field exponents. These results are analyzed in detail for power-law distributed random graphs. Received 4 April 2002 Published online 19 July 2002     

Localization, Dirac fermions and Onsager universality

Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universality of the localized fermions where the fluctuations in localized wave functions are universal. We further show that the fluctuations about localized nonrelativistic fermions describe relativistic fermions. This provides a new approach to understand the absence of localization in disordered Dirac fermions. We investigate how disorder affects well known universality of the spin chains by examining the multifractal exponents. Finally, we examine the effects of correlations on the localization characteristics of relativistic fermions. Received 28 September 2001 / Received in final form 30 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: isatija@nickel.nist.gov     

GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of ²⁰⁸Pb. In this study, we rely on a coherent approach based on the Generator Coordinate Method (GCM) including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF + BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations. Received: 31 May 2001 / Accepted: 23 August 2001     

Failure time and critical behaviour of fracture precursors in heterogeneous materials

The acoustic emission of fracture precursors, and the failure time of samples of heterogeneous materials (wood, fiberglass) are studied as a function of the load features and geometry. It is shown that in these materials the failure time is predicted with a good accuracy by a model of microcrack nucleation proposed by Pomeau. We find that the time interval δt between events (precursors) and the energy ɛ are power law distributed and that the exponents of these power laws depend on the load history and on the material. In contrast, the cumulated acoustic energy E presents a critical divergency near the breaking time τ which is E∼ . The positive exponent γ is independent, within error bars, on all the experimental parameters. Received 31 July 2001 and Received in final form 17 December 2001     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Viscosity critical behaviour at the gel point in a 3d lattice model

Within a recently introduced model based on the bond-fluctuation dynamics, we study the viscoelastic behaviour of a polymer solution at the gelation threshold. We here present the results of the numerical simulation of the model on a cubic lattice: the percolation transition, the diffusion properties and the time autocorrelation functions have been studied. From both the diffusion coefficients and the relaxation times critical behaviour a critical exponent k for the viscosity coefficient has been extracted: the two results are comparable within the errors giving , in close agreement with the Rouse model prediction and with some experimental results. In the critical region below the transition threshold the time autocorrelation functions show a long-time tail which is well fitted by a stretched exponential decay. Received 20 December 1999 and Received in final form 18 February 2000     

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce. Received 7 February 2002 / Received in final form 10 April 2002 Published online 9 July 2002     

Renormalization group analysis of weakly charged polyelectrolytes

We present a field-theoretic Renormalization Group (RG) analysis of the statistical mechanics of long flexible, screened polyelectrolyte chains (Debye-Hückel chains) in polar solvents where the screening length is of the order of the chain size. A systematic analysis of the resulting field theory shows that the system is one with two length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. This means that care must be taken to understand the interplay of the length-scales. Using the RG we identify the relevant scaling variables and explicitly calculate the scaling behaviour of the end-to-end distance for single chains. In addition we consider the many-chain system and calculate the scaling behaviour of the osmotic pressure of a dilute solution of chains. Received 16 December 1999 and Received in final form 13 December 2000     

Polaronic behavior in single- and many-electron Holstein model: A new perturbation approach

A new perturbation approach is developed for single- and many-electron Holstein model in one-, two-, and three-dimension. The results show that this approach has a good agreement with the Migdal theory in the adiabatic regime when the coupling is moderate (λ < 1), but with the Lang-Firsov theory in the antiadiabatic regime ( ω/W≫ 1). In the intermediate region, our approach can describe the transition from a large-polaron Fermi-liquid to the small-polaron, and this transition may be discontinuous in adiabatic regime, which means a phase transition appears in many-electron system. In single-electron case, we eliminate the abrupt transition using the degenerate perturbation theory, and the calculated ground state energy and effective mass are successfully compared with those of previous authors. Besides, the method has the advantage of requiring little computational effort. Received 27 December 2001 / Received in final form 8 April 2002 Published online 31 July 2002