Kirkwood–Buff integrals of finite systems: shape effects

Finite Yang-Mills Integrals

We use Monte Carlo methods to directly evaluate D-dimensional SU(N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for D = 3, N ≥ 4 and D = 4, N ≥ 3 and, lastly, D ≥ 5, N ≥ 2. We conclude that the D = 3 and D = 4 integrals exist in the large N limit, and therefore lead to a wel...

Shape Optimization of an Arterial Bypass in Cardiovascular Systems

A high performance numerical technique in the study of aorto-coronaric bypass anastomoses configurations using steady Stokes equations is presented. The problem is first expressed as an optimal control problem. Then, by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by ...

Batalin–Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV ) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangi...

Finite Part Integrals and Hypersingular Kernels

Singular integral equation method is one of the most effective numerical methods solving a plane crack problem in fracture mechanics. Depending on the choice of the density function, very often a higher order of sigularity appears in the equation, and we need to give a proper meaning of the integration. In this article we address the Hadamard finite part integral and how it is used to solve the...

The Connection of Shape Distributions and Haar Integrals