Related papers: Full-path localization of directed polymers
Quantitative tracking of features from video images is a basic technique employed in many areas of science. Here, we present a method for the tracking of features that partially overlap, in order to be able to track so-called colloidal…
In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two-thirds power of the interpolating distance. This…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
Anderson localization is derived directly from the path integral representation of quantum mechanics in the presence of a random potential energy function. The probability distribution of the potential energy is taken to be a Gaussian in…
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes…
We have obtained the universal conductance distribution of two-dimensional disordered systems in the strongly localized limit. This distribution is directly related to the Tracy-Widom distribution, which has recently appeared in many…
We have developed a theory of polymer entanglement using an extended Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive term, operating over mesoscales, which is interpreted as giving rise to entanglement, and the…
We consider a directed polymer of length $N$ interacting with a linear interface. The monomers carry i.i.d. random charges $(\omega_i)_{i=1}^N$ taking values in $\mathbb{R}$ with mean zero and variance one. Each monomer $i$ contributes an…
In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these…
The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the…
We perform a Monte Carlo study of $N$-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions ($d=2$), or the tip of an impenetrable cone in $d=3$, of sizes ranging up to $N=10^6$ steps. We find that the…
Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions. We show…
The tumbling dynamics of individual polymers in semidilute solution is studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We find that the tumbling time is equal to the non-equilibrium relaxation time of the polymer…
By a new type of finite size scaling analysis on the square lattice, and by renormalization group calculations on hierarchical lattices we investigate the effects of dilution on optimal undirected self-avoiding paths in a random…
We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic…
The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is…