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The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of…
We present a Monte Carlo study of the fractal geometry of clusters formed by discrete-time simple random walks (sRW) of $L^2$ steps on a periodic square $L\times L$ lattice. We verify with high precision that the asymptotic behavior of the…
We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed system are used to estimate the properties of a system perturbed by an external harmonic…
The statistics of equally weighted random paths (ideal polymer) is studied in $2$ and $3$ dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of $N$ step walks follows a…
We consider the model of self-avoiding walks on the $d$-dimensional hypercubic lattice interacting with a $d^*$-dimensional defect, where $1\leq d^*<d$. Such an interaction can be attractive or repulsive, and is controlled by a Boltzmann…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
Recent studies of scattering amplitudes in planar N=4 SYM theory revealed the existence of a hidden dual superconformal symmetry. Together with the conventional superconformal symmetry it gives rise to powerful restrictions on the planar…
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…
We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for $N$-step walks is compatible with…
Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique…
We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of $2+1$-dimensional discrete-height…
A growing self-avoiding walk (GSAW) is a stochastic process that starts from the origin on a lattice and grows by occupying an unoccupied adjacent lattice site at random. A sufficiently long GSAW will reach a state in which all adjacent…
We show that the scaling limit exists and is invariant to dilations and rotations. We give some tools that might be useful to show universality.
On a M\"obius surface, as defined by D. Calderbank, we study a variant of the Einstein-Weyl (EW) equation which we call scalar-flat M\"obius EW (sf-MEW). This is a conformally invariant, finite type, overdetermined system of semi-linear…
We develop a superspace formulation for ${\cal N}=3$ conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group $\mathsf{SU}(2,2|3)$. Upon imposing certain covariant constraints, the algebra of…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm,…
We investigate, by series methods, the behaviour of interacting self-avoiding walks (ISAWs) on the honeycomb lattice and on the square lattice. This is the first such investigation of ISAWs on the honeycomb lattice. We have generated data…
We present a quantitative comparison between extensive Monte Carlo simulations and self-consistent field calculations on the phase diagram and wetting behavior of a symmetric, binary (AB) polymer blend confined into a film. The flat walls…
We introduce and numerically study the branching annihilating random walks with long-range attraction (BAWL). The long-range attraction makes hopping biased in such a manner that particle's hopping along the direction to the nearest…