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We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid based AMR-code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if…
We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set…
When the symmetries of homogenous isotropic turbulent flows are broken, different sets of modes with different physical roles emerge. In particular, choosing a forcing which puts more weight on one or the other of these sets may result in…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
Using a standard definition of fractional powers on the universal cover $\exp:S\to \mathbb{C}^*$ seen as an infinite helicoid embedded in $\mathbb{R}^3$, we study the statistics of pairs from the countable family $\{n^\alpha \, : \, n \in…
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of…
We study algebraic structures of certain submonoids of the monoid of homology cylinders over a surface and the homology cobordism groups, using Reidemeister torsion with non-commutative coefficients. The submonoids consist of ones whose…
Monte Carlo computer simulations are used to study the segregation behaviour of two polymers under cylindrical confinement. Using a multiple-histogram method, the conformational free energy, F, of the polymers was measured as a function of…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is…
The enumeration of Hamiltonian cycles on 2n*2n grids of nodes is a longstanding problem in combinatorics. Previous work has concentrated on counting all cycles. The current work enumerates nonisomorphic cycles -- that is, the number of…
We compute the exact partition function of the isotropic 6-vertex model on a cylinder geometry with free boundary conditions, for lattices of intermediate size, using Bethe ansatz and algebraic geometry. We perform the computations in both…
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to…
Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of…
The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was proposed in a…
The convex hull of n+1 affinely independent vertices of the unit n-cube Cn is called a 0/1-simplex. It is nonobtuse if none its dihedral angles is obtuse, and acute if additionally none of them is right. In terms of linear algebra, acute…
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp…
We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background…
Quandles are self-distributive algebraic structures known as sources of strong knots invariants, but also appearing in other contexts. From any quandle, one can construct two invariants: the structure group and the second quandle homology…
The Hardy space H^2(R) for the upper half plane together with a unimodular function group representation u(\lambda) = \exp(i(\lambda_1\psi_1 + ... + \lambda_n\psi_n)) for \lambda in R^n, gives rise to a manifold M of orthogonal projections…