We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γlimit is also stable under volume constraint and various type of boundary conditions.

Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral

We perform a scaling analysis of the terms composing Ffowcs-Williams and Hawkings (FWH) equation, which rules propagation noise generated by rigid body in motion. Our extends seminal work Lighthill ( Proc. R. Soc. Lond. A, vol. 211, 1952, pp. 564–587) dimensional classical sources (monopole, dipole quadrupole) considering all FWH integral terms. Scaling properties are analysed light perfect/imp...

Introduction The following is an excerpt from the first draft of volume 2 of the Kosmos trilogy, tentatively titled Kosmic Karma (volume 1 of that trilogy was Sex, Ecology, Spirituality). This excerpt suggests a coherent and comprehensive theory of the many approaches to subtle energies, their origin, nature, and development. This particular excerpt comes toward the end of the volume, which mea...

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge M − N coincides with the Itzyskon-Zuber type integral for M × N rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.

The path integral for higher-derivative quantum gravity with torsion is considered. Applying the methods of two-dimensional quantum gravity, this path integral is analyzed in the limit of conformally self-dual metrics. A scaling law for fixed-volume geometry is obtained.

The aim of this study was to investigate the potential of jaw tracking with the volumetric-modulated arc therapy (VMAT) to reduce the normal tissue dose. Plans of nasopharynx, lung, and prostate cancers (10 plans for each) were used to perform VMAT with and without jaw tracking. The dose reduction was evaluated in terms of organ doses and integral doses. Organ-dose reduction with jaw tracking w...

We present a new continuous adjoint method for Aerodynamic Shape Optimization (ASO) using the Euler equations, which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral. The savings are particularly significant for three-dimensional ASO problems on general unstructured and overset meshes. In order to validate...