Related papers: Self-avoiding trails with nearest neighbour intera…
We study magnetic polymers, defined as self-avoiding walks where each monomer $i$ carries a "spin'' $s_i$ and interacts with its first neighbor monomers, let us say $j$, via a coupling constant $J(s_i,s_j)$. Ising-like [$s_i = \pm 1$, with…
Our first main result is that correlations between monomers in the dimer model in $\mathbb{Z}^d$ do not decay to zero when $d > 2$. This is the first rigorous result about correlations in the dimer model in dimensions greater than two and…
The myopic (or `true') self-avoiding walk model (MSAW) was introduced in the physics literature by Amit, Parisi and Peliti (1983). It is a random motion in Z^d pushed towards domains less visited in the past by a kind of negative gradient…
We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] \times [0, L]$ on the square lattice ${\mathbb Z}^2$. The number of distinct walks…
The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact…
Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was…
Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of…
Some time ago Salmhofer demonstrated the equivalence of the strong coupling lattice Schwinger model with Wilson fermions to a certain 8-vertex model which can be understood as a self-avoiding loop model on the square lattice with bending…
We study the interlayer scattering mediated by long-range Coulomb interaction between electrons (density n) and holes (p) in a double-layer system. The gated device is made of InAs (e) and InGaSb (h) quantum wells separated by a AlSb middle…
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices,…
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically…
We consider a class of systems where, due to the large mismatch of dielectric constants, the Coulomb interaction is approximately one-dimensional. Examples include ion channels in lipid membranes and water filled nanopores in silicon or…
We propose a new coarse-grained model for the description of liquid-vapor phase separation of colloid-polymer mixtures. The hard-sphere repulsion between colloids and between colloids and polymers, which is used in the well-known…
We find the exact solution of three interacting friendly directed walks on the square lattice in the bulk, modelling a system of homopolymers that can undergo gelation by introducing two distinct interaction parameters that differentiate…
This paper introduces a method to enhance Interactive Imitation Learning (IIL) by extracting touch interaction points and tracking object movement from video demonstrations. The approach extends current IIL systems by providing robots with…
We consider a system of two-dimensional electrons strongly localized by disorder. Interactions create a gap in the average tunneling density of states $\nu(E)$ at energies, E, close to the Fermi level. We derive a system of self-consistent…
We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in…
We develop an approach for performing scaling analysis of $N$-step Random Walks (RWs). The mean square end-to-end distance, $\langle\vec{R}_{N}^{2}\rangle$, is written in terms of inner persistence lengths (IPLs), which we define by the…
Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time $t$ with the territory already visited at earlier times $t'<t$. This class of non-Markovian random walks has…
We investigate the effect of polydispersity on fluctuation-induced interactions between colloids trapped at a fluid interface. Using the scattering-matrix formalism, we calculate the interaction energy in two- and three-body systems under…