Related papers: Polymers with Randomness: Phases and Phase Transit…
A phase diagram for a surface interacting long flexible partially directed polymer chain in a two-dimensional poor solvent where the possibility of collapse in the bulk exists is determined using exact enumeration method. We used a model of…
The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…
The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one…
We consider the patterns of collective motion emerging when many aligning, self-propelling units move in two dimensions while interacting through a repulsive potential and are also subject to delays and random perturbations. In this…
We present a unifying picture of the compact, dense and dilute phases of two-dimensional polymers. The lattice dependence of the scaling exponents for compact polymers is reconciled with their universality in the dense and dilute case. In…
In this article we study from a non-perturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac $\delta-$function potential. An exact formula of the so-called second moment of…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
We study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1…
An analysis of the random lattice gas in the annealed limit is presented. The statistical mechanics of disordered lattice systems is briefly reviewed. For the case of the lattice gas with an arbitrary uniform interaction potential and…
We study the direct incoherent energy transfer from an immobile excited donor molecule to acceptor molecules, which are all attached to polymer chains, randomly arranged in a viscous solvent. The decay forms are found explicitly, in terms…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
These notes focus on the description of the phases of matter in two dimensions. Firstly, we present a brief discussion of the phase diagrams of bidimensional interacting passive systems, and their numerical and experimental measurements.…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
The phase diagram of a system constituted of neutrons and $\Lambda$-hyperons in thermal equilibrium is evaluated in the mean-field approximation. It is shown that this simple system exhibits a complex phase diagram with first and second…
We consider directed semiflexible polymers embedded in a fluctuating surface which is governed by either surface tension or bending rigidity. The attractive interactions induced by the fluctuations of the surface reduce the rigidity of the…
Sequence heterogeneity broadens the binding transition of a polymer onto a linear or planar substrate. This effect is analyzed in a real-space renormalization group scheme designed to capture the statistics of rare events. In the strongly…
A theory for surface transitions in the presence of a disordered pinning potential is presented. Arbitrary disorder correlations are treated in the framework of a dynamical functional renormalization group. The roughening transition, where…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…