131 citations · 962 across the 53 of their papers we have counts for
47 papers · 1 filter
New duality relation for the Discrete Gaussian SOS model on a torus
F. Cornu, H. J. Hilhorst, M. Bauer
We construct a new duality for two-dimensional Discrete Gaussian models. It is based on a known one-dimensional duality and on a mapping, implied by the Chinese remainder theorem,…
Iterated star-triangle transformation on inhomogeneous 2D Ising lattices
H. J. Hilhorst
We consider infinite or periodic 2D triangular Ising lattices with arbitrary positive or negative nearest-neighbor couplings , where and indicate the bo…
On the oddness of percolation
C. Appert-Rolland, H. J. Hilhorst
Recently Mertens and Moore [arXiv:1909.01484v1] showed that site percolation "is odd." By this they mean that on an square lattice the number of distinct site configura…
Density decay and growth of correlations in the Game of Life
F. Cornu, H. J. Hilhorst
We study the Game of Life as a statistical system on an square lattice with periodic boundary conditions. Starting from a random initial configuration of density $ρ_{\r…
Glauber's Ising chain between two thermostats
F. Cornu, H. J. Hilhorst
We consider a one-dimensional Ising model each of whose spins is in contact with two thermostats of distinct temperatures and . Under Glauber dynamics the stationary…
Imaginary noise and parity conservation in the reaction A+A <--> 0
O. Deloubrière, L. Frachebourg, H. J. Hilhorst +1
The master equation for the reversible reaction A+A <--> 0 is considered in Poisson representation, where it is equivalent to a Langevin equation with imaginary noise for a complex…
Exact asymptotic statistics of the n-edged face in a 3D Poisson-Voronoi tessellation
H. J. Hilhorst
We consider the 3D Poisson-Voronoi tessellation. We investigate the joint probability distribution pi_n(L) for an arbitrarily selected cell face to be n-edged and for the distance…
A parity breaking Ising chain Hamiltonian as a Brownian motor
F. Cornu, H. J. Hilhorst
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian \begin{equation} {\cal H} = -U_2\sum_{k} s_{k}s_{k+1} - U_3\sum_{k} s_{k…
Stripe formation instability in crossing traffic flows
J. Cividini, H. J. Hilhorst
At the intersection of two unidirectional traffic flows a stripe formation instability is known to occur. In this paper we consider coupled time evolution equations for the densiti…
Many-faced cells and many-edged faces in 3D Poisson-Voronoi tessellations
H. J. Hilhorst, E. A. Lazar
Motivated by recent new Monte Carlo data we investigate a heuristic asymptotic theory that applies to n-faced 3D Poisson-Voronoi cells in the limit of large n. We show how this the…
Exact domain wall theory for deterministic TASEP with parallel update
J. Cividini, H. J. Hilhorst, C. Appert-Rolland
Domain wall theory (DWT) has proved to be a powerful tool for the analysis of one-dimensional transport processes. A simple version of it was found very accurate for the Totally As…
Crossing pedestrian traffic flows,diagonal stripe pattern, and chevron effect
J. Cividini, H. J. Hilhorst, C. Appert-Rolland
We study two perpendicular intersecting flows of pedestrians. The latter are represented either by moving hard core particles of two types, eastbound ($\symbp$) and northbound ($\s…
Continuous and first-order jamming transition in crossing pedestrian traffic flows
H. J. Hilhorst, J. Cividini, C. Appert-Rolland
After reviewing the main results obtained within a model for the intersection of two perpendicular flows of pedestrians, we present a new finding: the changeover of the jamming tra…
Diagonal patterns and chevron effect in intersecting traffic flows
Julien Cividini, Cecile Appert-Rolland, Hendrik-Jan Hilhorst
We study a lattice model of two perpendicular intersecting flows of pedestrians represented by hard core particles of two types, eastbound (`$\pE$') and northbound (`$\pN$'). Each…
A multi-lane TASEP model for crossing pedestrian traffic flows
H. J. Hilhorst, C. Appert-Rolland
A one-way {\em street} of width M is modeled as a set of M parallel one-dimensional TASEPs. The intersection of two perpendicular streets is a square lattice of size M times M. We…
Intersection of two TASEP traffic lanes with frozen shuffle update
C. Appert-Rolland, J. Cividini, H. J. Hilhorst
Motivated by interest in pedestrian traffic we study two lanes (one-dimensional lattices) of length that intersect at a single site. Each lane is modeled by a TASEP (Totally As…
Frozen shuffle update for an asymmetric exclusion process with open boundary conditions
C. Appert-Rolland, J. Cividini, H. J. Hilhorst
We introduce a new update algorithm for exclusion processes, more suitable for the modeling of pedestrian traffic. Pedestrians are modeled as hard-core particles hopping on a discr…
Frozen shuffle update for an asymmetric exclusion process on a ring
C. Appert-Rolland, J. Cividini, H. J. Hilhorst
We introduce a new rule of motion for a totally asymmetric exclusion process (TASEP) representing pedestrian traffic on a lattice. Its characteristic feature is that the positions…
Two interacting Ising chains in relative motion
H. J. Hilhorst
We consider two parallel cyclic Ising chains counter-rotating at a relative velocity v, the motion actually being a succession of discrete steps. There is an in-chain interaction b…
Note on a q-modified central limit theorem
H. J. Hilhorst
A q-modified version of the central limit theorem due to Umarov et al. affirms that q-Gaussians are attractors under addition and rescaling of certain classes of strongly correlate…
Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic
C. Appert-Rolland, H. J. Hilhorst, G. Schehr
First we consider a unidirectional flux ω_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as…
Heuristic theory for many-faced d-dimensional Poisson-Voronoi cells
H. J. Hilhorst
We consider the d-dimensional Poisson-Voronoi tessellation and investigate the applicability of heuristic methods developed recently for two dimensions. Let p_n(d) be the probabili…
Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics
H. J. Hilhorst
We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort…
Central limit theorems for correlated variables: some critical remarks
H. J. Hilhorst
In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated rand…