1,750 research outputs found

    Extremal Segments in Random Sequences

    Full text link
    We investigate the probability for the largest segment in with total displacement QQ in an NN-step random walk to have length LL. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large NN limit. In particular, the size of the longest loop has a distribution with a square-root singularity at L/N=1\ell\equiv L/N=1, an essential singularity at =0\ell=0, and a discontinuous derivative at =1/2\ell=1/2.Comment: 3 pages, REVTEX 3.0, with multicol.sty, epsf.sty and EPS figures appended via uufiles. (Email in case of trouble.) CHANGES: Missing figure added to figures.uu MIT-CMT-KE-94-

    Statistics of Largest Loops in a Random Walk

    Full text link
    We report further findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor, Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional random walks (RWs), this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which exhibits an essential singularity. We establish analytical upper and lower bounds on the probability distribution, and numerically probe the distribution down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15}) using a recursive Monte Carlo algorithm. We also investigate the possibility of singularities at \ell=1/k for integer k.Comment: 5 pages and 4 eps figures, requires RevTeX, epsf and multicol. Postscript file also available at http://cmtw.harvard.edu/~deniz/publications.htm

    Randomly Charged Polymers, Random Walks, and Their Extremal Properties

    Full text link
    Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW to have length L. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large N limit. In particular, the size of the longest neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe

    A Model Ground State of Polyampholytes

    Full text link
    The ground state of randomly charged polyampholytes is conjectured to have a structure similar to a necklace, made of weakly charged parts of the chain, compacting into globules, connected by highly charged stretched `strings'. We suggest a specific structure, within the necklace model, where all the neutral parts of the chain compact into globules: The longest neutral segment compacts into a globule; in the remaining part of the chain, the longest neutral segment (the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so on. We investigate the size distributions of the longest neutral segments in random charge sequences, using analytical and Monte Carlo methods. We show that the length of the n-th longest neutral segment in a sequence of N monomers is proportional to N/(n^2), while the mean number of neutral segments increases as sqrt(N). The polyampholyte in the ground state within our model is found to have an average linear size proportional to sqrt(N), and an average surface area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.

    Collapse of Randomly Self-Interacting Polymers

    Full text link
    We use complete enumeration and Monte Carlo techniques to study self--avoiding walks with random nearest--neighbor interactions described by v0qiqjv_0q_iq_j, where qi=±1q_i=\pm1 is a quenched sequence of ``charges'' on the chain. For equal numbers of positive and negative charges (N+=NN_+=N_-), the polymer with v0>0v_0>0 undergoes a transition from self--avoiding behavior to a compact state at a temperature θ1.2v0\theta\approx1.2v_0. The collapse temperature θ(x)\theta(x) decreases with the asymmetry x=N+N/(N++N)x=|N_+-N_-|/(N_++N_-)Comment: 8 pages, TeX, 4 uuencoded postscript figures, MIT-CMT-

    Theta-point universality of polyampholytes with screened interactions

    Full text link
    By an efficient algorithm we evaluate exactly the disorder-averaged statistics of globally neutral self-avoiding chains with quenched random charge qi=±1q_i=\pm 1 in monomer i and nearest neighbor interactions qiqj\propto q_i q_j on square (22 monomers) and cubic (16 monomers) lattices. At the theta transition in 2D, radius of gyration, entropic and crossover exponents are well compatible with the universality class of the corresponding transition of homopolymers. Further strong indication of such class comes from direct comparison with the corresponding annealed problem. In 3D classical exponents are recovered. The percentage of charge sequences leading to folding in a unique ground state approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl

    Ground States of Two-Dimensional Polyampholytes

    Full text link
    We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers ±q0\pm q_0, restricted to a 2-dimensional square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We study the ground state properties of the polymers as a function of their excess charge QQ for all possible charge sequences up to a polymer length N=18. We find that the ground state of the neutral ensemble is compact and its energy extensive and self-averaging. The addition of small excess charge causes an expansion of the ground state with the monomer density depending only on QQ. In an annealed ensemble the ground state is fully stretched for any excess charge Q>0Q>0.Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.

    La mise en oeuvre de la Liste unique des garanties.

    Get PDF
    L’élaboration, depuis le 1er janvier 2007, de la Liste unique des garanties éligibles aux opérations de refinancement de l’Eurosystème entraîne des adaptations dans les méthodes d’évaluation de la qualité des actifs remis en garantie.Eurosystème, Liste unique, garanties, collatéral, refinancement, qualité de signature, créances privées, actifs négociables.

    Folding transition of the triangular lattice in a discrete three--dimensional space

    Get PDF
    A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter (cond-mat/9502063) describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method. The model describes the behaviour of a polymerized membrane in a discrete three--dimensional space. We have introduced a curvature energy and a symmetry breaking field and studied the phase diagram of the resulting model. By varying the curvature energy parameter, a first-order transition has been found between a flat and a folded phase for any value of the symmetry breaking field.Comment: 11 pages, latex file, 2 postscript figure

    Folding of the Triangular Lattice with Quenched Random Bending Rigidity

    Full text link
    We study the problem of folding of the regular triangular lattice in the presence of a quenched random bending rigidity + or - K and a magnetic field h (conjugate to the local normal vectors to the triangles). The randomness in the bending energy can be understood as arising from a prior marking of the lattice with quenched creases on which folds are favored. We consider three types of quenched randomness: (1) a ``physical'' randomness where the creases arise from some prior random folding; (2) a Mattis-like randomness where creases are domain walls of some quenched spin system; (3) an Edwards-Anderson-like randomness where the bending energy is + or - K at random independently on each bond. The corresponding (K,h) phase diagrams are determined in the hexagon approximation of the cluster variation method. Depending on the type of randomness, the system shows essentially different behaviors.Comment: uses harvmac (l), epsf, 17 figs included, uuencoded, tar compresse
    corecore