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We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no…

Computational Complexity · Computer Science 2015-03-13 Matthew Cook , Yunhui Fu , Robert T. Schweller

The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain…

Probability · Mathematics 2025-03-27 Makoto Nakashima

We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…

Probability · Mathematics 2020-12-09 Nicola Kistler , Adrien Schertzer

Long linear polymers in dilute solutions are known to undergo a collapse transition from a random coil (expand itself) to a compact ball (fold itself up) when the temperature is lowered, or the solvent quality deteriorates. A natural model…

Probability · Mathematics 2015-06-12 Gia Bao Nguyen , Nicolas Petrelis

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with…

Statistical Mechanics · Physics 2007-05-23 Michael Praehofer , Herbert Spohn

Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of…

Statistical Mechanics · Physics 2015-12-04 Pablo Serna , Guy Bunin , Adam Nahum

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length $L$, the high temperature phase is characterized by a diffusive behavior for the end-point displacement…

Disordered Systems and Neural Networks · Physics 2007-05-23 Cecile Monthus , Thomas Garel

We investigate the high-temperature behavior of the directed polymer model in dimension $1+2$. More precisely we study the difference $\Delta \mathtt{F}(\beta)$ between the quenched and annealed free energies for small values of the inverse…

Mathematical Physics · Physics 2015-07-01 Quentin Berger , Hubert Lacoin

We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…

Probability · Mathematics 2011-08-25 Dmitry Ioffe , Yvan Velenik

We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitely the set of disorder configurations that give rise to localization of the polymer. We study both relevant cases of…

Probability · Mathematics 2016-08-16 Élise Janvresse , Thierry De La Rue , Yvan Velenik

We have generalized the Edwards' method of collective description of dense polymer systems in terms of effective potentials to polymer blends in the presence of a surface. With this method we have studied conformationally asymmetric…

Soft Condensed Matter · Physics 2009-11-11 Semjon Stepanow , Andrei A. Fedorenko

We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…

Statistical Mechanics · Physics 2010-05-14 Geza Odor , Bartosz Liedke , Karl-Heinz Heinig

A simple application of classical density functional theory is derived and applied to a system of polymers grafted to a plane. The system is assumed to have symmetry in directions parallel to the grafting plane hence it being a…

Soft Condensed Matter · Physics 2016-12-02 Luke Kristopher Davis

The morphological scaling properties of linear polymer films grown by vapor deposition polymerization (VDP) are studied by 1+1D Monte Carlo simulations. The model implements the basic processes of random angle ballistic deposition ($F$),…

Computational Physics · Physics 2010-10-25 Sairam Tangirala , David P. Landau , Y. -P. Zhao

We study the KPZ equation (in D = 2, 3 and 4 spatial dimensions) by using a RSOS discretization of the surface. We measure the critical exponents very precisely, and we show that the rational guess is not appropriate, and that 4D is not the…

Statistical Mechanics · Physics 2009-10-31 E. Marinari , A. Pagnani , G. Parisi

We uncover a nontrivial signature of the hierarchical structure of quasi-degenerate random directed polymers (RDPs) at zero temperature in 1+1 dimensional lattices. Using a cylindrical geometry with circumference $8 \leq W \leq 512$, we…

Statistical Mechanics · Physics 2009-10-31 Per Jögi , Didier Sornette

We explain how the claims of the KPZ scaling theory are confirmed by a recent proof of Borodin and Corwin on the asymptotics of the semi-discrete directed polymer.

Statistical Mechanics · Physics 2012-01-04 Herbert Spohn

We study the question of how the competition between $\textit{bulk disorder}$ and a $\textit{localized microscopic defect}$ affects the macroscopic behavior of a system in the directed polymer context at the free energy level. We consider…

Probability · Mathematics 2018-04-04 Neal Madras , Gökhan Yıldırım

We consider a model for a polymer interacting with an attractive wall through a random sequence of charges. We focus on the so-called diluted limit, when the charges are very rare but have strong intensity. In this regime, we determine the…

Probability · Mathematics 2008-07-26 Erwin Bolthausen , Francesco Caravenna , Béatrice de Tilière

Behavior of a dilute polymer solution in a random three-dimensional flow with an average shear is studied experimentally. Polymer contribution to the shear stress is found to be more than two orders of magnitude higher than in a laminar…

Chaotic Dynamics · Physics 2009-10-31 Alexander Groisman , Victor Steinberg