We evaluate the pion mass in finite volume to two loops within Chiral Perturbation Theory. The results are compared with a recently proposed extension of the asymptotic formula of Lüscher. We find that contributions, which were neglected in the latter, are numerically very small at the two-loop level. The pion mass in finite volume to two loops Christoph Haefeli

A finite volume method for solving the degenerate chemotaxis model is presented, along with numerical examples. This model consists of a degenerate parabolic convection– diffusion PDE for the density of the cell-population coupled to a parabolic PDE for the chemoattractant concentration. It is shown that discrete solutions exist, and the scheme converges.

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in [32, 7, 6]. Recently, it has been observed in [3] that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in [7], based on the high order finite volume WENO scheme with subcell resolution and utilizing...

Let M be a complete simply connected Riemannian manifold, with sectional curvature K ≤ −1. Under some assumptions on the geometry of ∂M , which are satisfied for instance if M is a symmetric space, or has dimension 2, we prove that given any family of horoballs in M , and any point x0 outside these horoballs, it is possible to shrink uniformly, by a finite amount depending only on M , these hor...

Cooper and Long generalised Epstein and Penner’s Euclidean cell decomposition of cusped hyperbolic n–manifolds of finite volume to non-compact strictly convex projective n–manifolds of finite volume. We show that Weeks’ algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces.

In this paper we define a new invariant of the incomplete hyperbolic structures on a 1-cusped finite volume hyperbolic 3-manifold M , called the ortholength invariant. We show that away from a (possibly empty) subvariety of excluded values this invariant both locally parameterises equivalence classes of hyperbolic structures and is a complete invariant of the Dehn fillings of M which admit a hy...

What happens to the uncertainity relations along the process of gravitational collapses ? What is the position-space wave function of two finite volume massive bosons if we take contact interaction into account? What is the microscopic explanation in terms of particle exchanges of the force in the Casimir effect?

We will mainly consider the Sinh-Gordon model in finite spacial volume which corresponds to imposing the periodic boundary conditions φ(x + R) = φ(x). A lot is known about the Sinh-Gordon model in infinite volume R → ∞, see e.g. [1, 2, 3, 4, 5]. The spectrum contains a single particle with mass m which is related to the parameter μ in (1.1) in a definite way [6], see eqn. (5.32) below. The S-ma...

We prove the Coleman’s conjecture on the equivalence between the massless Sine-Gordon model with finite volume interaction and the Thirring model with a finite volume mass term.

In this paper, we describe a one-dimensional adaptive moving mesh method and apply it to two traffic flow models introduced in 2009 by Kurganov and Polizzi. These models can be written as a scalar conservation law with a global flux. The proposed schemes are extension of the moving non-oscillatory central schemes, which belong to a class of moving finite volume methods. We also modify the model...