Melting transition of a network model in two dimensions

The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths. Received 4 June 1999 and Revised in final form 1 September 1999     

Unbinding of three strings in the Born-Oppenheimer approximation

The unbinding transition of three strings, fluctuating without overhangs in two dimensions, is considered in the Born-Oppenheimer approximation. The calculation, which is extremely simple, gives some insight into the physical considerations that determine the universality class. In the case of short-range pair interactions the unbinding transition is predicted to be universal, with the same critical exponents as in the unbinding of two strings. For strings bound by short-range three-body interactions the unbinding transition is nonuniversal. Both of these predictions are in agreement with recent exact studies.Dedicated to H. Wagner     

Quantum gravity,random geometry and critical phenomena

We discuss the theory of non-critical strings with extrinsic curvature embedded in a target space dimensiond greater than one. We emphasize the analogy between 2d gravity coupled to matter and non self-avoiding liquid-like membranes with bending rigidity. We first outline the exact solution for strings in dimensionsd<1 via the double scaling limit of matrix models and then discuss the difficulties of an extension tod>1. Evidence from recent and ongoing numerical simulations of dynamically triangulated random surfaces indicate that there is a non-trivial crossover from a crumpled to an extended surface as the bending rigidity is increased. If the cross-over is a true second order phase transition corresponding to a critical point there is the exciting possibility of obtaining a well defined continuum string theory ford>1. This essay received the third award from the Gravity Research Foundation, 1992-Ed.     

Topological crossovers in the forced folding of self-avoiding matter

We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of three-dimensional plates to the folding of two-dimensional sheets, and further to the packing of one-dimensional strings, are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry, we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.     

Scaling behaviour and correlations in the string fusion model for heavy ion collisions

The KNO scaling, the scaling of multiplicities, the behaviour of fluctuations in the transverse momentum as a function of the multiplicity and the long range correlations in nucleus-nucleus collisions are studied by a Monte Carlo code based on the string fusion model. It is shown that the fusion of strings produces a strong reduction of the long range correlations at high multiplicities, which could be detected experimentally. On the contrary the KNO scaling, the scaling of multiplicities and the behaviour of fluctuations in the transverse momentum are not modified when string fusion is included.On leave of absence from the Department of High Energy Physics, University of St. Petersburg, 198904 St. Petersburg, Russia     

From bunches of membranes to bundles of strings

Bunches of membranes and bundles of strings exhibit unbinding transitions from a bound state at low temperatures to an unbound state at high temperatures.N freely suspended manifolds unbind continuously at the unique unbinding temperatureT _u ^f which is independent ofN. The amplitudes of the critical singularities have a strongN-dependence, however, which implies that the critical region for the continuous transition becomes very small and the transition becomes very abrupt in the limit of largeN. IfN membranes or strings are bound to a rigid surface, they undergo a sequence of either two or ofN successive transitions. In general, the rigid surface affects the contact probabilities of the fluctuating manifolds. For effectively repulsive interactions, the contact exponent ₂ which governs the probability for local pair contacts satisfies the scaling relation ₂=d + whered and denote the dimensionality and the roughness exponent of these manifolds.Dedicated to Herbert Wagner on the occasion of his 60th birthday     

Deconfinement in the two-dimensional XY model

The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system supports two phase transitions, one in which closed strings proliferate, and a second in which vortices unbind. The transitions are shown to be dual to one another, and are remarkably continuous. Possible consequences for a variety of systems are discussed.     

A rational method for probing macromolecules dissociation: the antibody-hapten system

The unbinding process of a protein-ligand complex of major biological interest was investigated by means of a computational approach at atomistic classical mechanical level. An energy minimisation-based technique was used to determine the dissociation paths of the system by probing only a relevant set of generalized coordinates. The complex problem was reduced to a low-dimensional scanning along a selected distance between the protein and the ligand. Orientational coordinates of the escaping fragment (the ligand) were also assessed in order to further characterise the unbinding. Solvent effects were accounted for by means of the Poisson–Boltzmann continuum model. The corresponding dissociation time was derived from the calculated barrier height, in compliance with the experimentally reported Arrhenius-like behaviour. The computed results are in good agreement with the available experimental data.     

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     

Vortex deconfinement in the XY model with a magnetic field

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.     

Poisson brackets,strings and membranes

We construct Poisson brackets at the boundaries of open strings and membranes with constant background fields which are compatible with their boundary conditions. The boundary conditions are treated as primary constraints which give infinitely many secondary constraints. We show explicitly that we need only two (the primary one and one of the secondary ones) constraints to determine the Poisson brackets of strings. We apply this to membranes by using canonical transformations. Received: 2 May 2002 / Revised version: 29 May 2002 / Published online: 16 August 2002 RID="a" ID="a" e-mail: tezuka@physics.s.chiba-u.ac.jp     

Can one ADM quantize relativistic bosonicstrings and membranes?

The standard methods for quantizing relativistic strings diverge significantly from the Dirac-Wheeler-DeWitt program for quantization of generally covariant systems and one wonders whether the latter could be successfully implemented as an alternative to the former. As a first step in this direction, we consider the possibility of quantizing strings (and also relativistic membranes) via a partially gauge-fixed ADM (Arnowitt, Deser and Misner) formulation of the reduced field equations for these systems. By exploiting some (Euclidean signature) Hamilton-Jacobi techniques that Mike Ryan and I had developed previously for the quantization of Bianchi IX cosmological models, I show how to construct Diff(S ¹)-invariant (or Diff(Σ)-invariant in the case of membranes) ground state wave functionals for the cases of co-dimension one strings and membranes embedded in Minkowski spacetime. I also show that the reduced Hamiltonian density operators for these systems weakly commute when applied to physical (i.e. Diff(S ¹) or Diff(Σ)-invariant) states. While many open questions remain, these preliminary results seem to encourage further research along the same lines.     

Adhesion of membranes with active stickers

We consider a theoretical model for membranes with adhesive receptors, or stickers, that are actively switched between two conformational states. In their "on" state, the stickers bind to ligands in an apposing membrane, whereas they do not interact with the ligands in their "off" state. We show that the adhesiveness of the membranes depends sensitively on the rates of the conformational switching process. This dependence is reflected in a resonance at intermediate switching rates, which can lead to large membrane separations and unbinding. Our results may provide insights into novel mechanisms for the controlled adhesion of biological or biomimetic membranes.     

Statistical mechanics of bilayer membranes in troubled aqueous media

We consider a bilayer membrane surrounded by small impurities, assumed to be attractive or repulsive. The purpose is a quantitative study of the effects of these impurities on the statistical properties of the supported membrane. Using the replica trick combined with a variational method, we compute the membrane mean-roughness and the height correlation function for almost-flat membranes, as functions of the primitive elastic constants of the membrane and some parameter that is proportional to the volume fraction of impurities and their interaction strength. As results, the attractive impurities increase the shape fluctuations due to the membrane undulations, while repulsive ones suppress these fluctuations. Second, we compute the equilibrium diameter of (spherical) vesicles surrounded by small random particles starting from the curvature equation. Third, the study is extended to a lamellar phase composed of two parallel fluid membranes, which are separated by a finite distance. This lamellar phase undergoes an unbinding transition. We demonstrate that the attractive impurities increase the unbinding critical temperature, while repulsive ones decrease this temperature. Finally, we say that the presence of small impurities in an aqueous medium may be a mechanism to suppress or to produce an unbinding transition, even the temperature and polarizability of the aqueous medium are fixed, in lamellar phases formed by parallel lipid bilayers.     

Scaling Behaviour and Memory in Heart Rate of Healthy Human

We investigate a set of complex heart rate time series from healthy human in different behaviour states with the detrended fluctuation analysis and diffusion entropy （DE） method. It is proposed that the scaling properties are influenced by behaviour states. The memory detected by DE exhibits an approximately same pattern after a detrending procedure. Both of them demonstrate the long-range strong correlations in heart rate. These findings may be helpful to understand the underlying dynamical evolution process in the heart rate control system, as well as to model the cardiac dynamic process.     

Enhancement of steric repulsion with temperature in oriented lipid multilayers

We have studied the temperature dependence of the stacking periodicity, d, of oriented phospholipid multilayers using grazing angle neutron scattering techniques. d is found to increase substantially at higher temperatures, just before the bilayers peel off from the substrate. Although we do not observe thermal unbinding, our results are consistent with the notion that the unbinding transition is driven by steric repulsion arising from thermal fluctuations of the membranes, in contrast to those of a recent study by Vogel et al. [Phys. Rev. Lett. 84, 390 (2000)].     

Brownian rotation of classical spins: dynamical equations for non-bilinear spin-environment couplings

Given two strings X and Y of N and M characters respectively, the Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between X and Y. Using extensive Monte-Carlo simulations for this problem, we find a finite size scaling law of the form for the average LCS length of two random strings of size N over S letters. We provide precise estimates of for .We consider also a related Bernoulli Matching model where the different entries of an array are occupied with a match independently with probability 1/S. On the basis of a cavity-like analysis we find that the length of a longest sequence of matches in that case behaves as where r=M/N and . This formula agrees very well with our numerical computations. It provides a very good approximation for the Random String model, the approximation getting more accurate as S increases. The question of the “universality class” of the LCS problem is also considered. Our results for the Bernoulli Matching model show very good agreement with the scaling predictions of [#!HwaLassig96_PRL!#] for Needleman-Wunsch sequence alignment. We find however that the variance of the LCS length has a scaling different from Var in the Random String model, suggesting that long-ranged correlations among the matches are relevant in this model. We finally study the “ground state” properties of this problem. We find that the number of solutions typically grows exponentially with N. In other words, this system does not satisfy “Nernst's principle”. This is also reflected at the level of the overlap between two LCSs chosen at random, which is found to be self averaging and to approach a definite value q _S <1 as . Received: 23 April 1998 / Revised: 30 July 1998 / Accepted: 14 August 1998     

The link overlap and finite size effects for the 3D Ising spin glass

We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte-Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature. Received 25 May 1999     

A Solvable Symbiosis-Driven Growth Model

We introduce a two-species symbiosis-driven growth model, in which two species can mutually benefit for their monomer birth and the self-death of each species simultaneously occurs. By means of the generalized rate equation, we investigate the dynamic evolution of the system under the monodisperse initial condition. It is found that the kinetic behaviour of the system depends crucially on the details of the rate kernels as well as the initial concentration distributions. The cluster size distribution of either species cannot be scaled in most cases; while in some special cases, they both consistently take the universal scaling form. Moreover, in some cases the system may undergo a gelation transition and the pre-gelation behaviour of the cluster size distributions satisfies the scaling form in the vicinity of the gelation point. On the other hand, the two species always live and die together.