This paper presents a technique for the adaptive refinement of tetrahedral meshes. What makes it unique is that no neighbor information is required for the refined mesh to be compatible everywhere. Refinement consists of inserting new vertices at edge midpoints until some tolerance (geometric or otherwise) is met. For a tetrahedron, the six edges present 2 = 64 possible subdivision combinations...

We consider the effects of local impurities in highly frustrated diamond-lattice antiferromagnets, which exhibit large but nonextensive ground-state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an ordered magnetic ground state and provide a mechanism of degeneracy breaking. The states that are selec...

The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e., finding out how many different lengths exist for periodic orbits with a given period and the average number of periodic orbits with the same length) is necessary for the...

The genetic code structure into distinct multiplet-classes as well as the numeric degeneracies of the latter are revealed by a two-step process. First, an empirical inventory of the degeneracies (of the shuffled multiplets) in two specific equal moieties of the experimental genetic code table is made and transcribed in the form of a sequence of integers. Second, a Gödel Encoding procedure is ap...

Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems is linked to degeneracies in the system zero dynamics. Accordingly, the obvious remedy is to change the system input-output structure, but there are other possibilities as well. In this paper we summarize the main results connecting bifurcation beha...

We present several pieces of evidence for strong-weak coupling duality symmetry in the heterotic string theory, compactified on a six dimensional torus. These include symmetry of the 1) low energy effective action, 2) allowed spectrum of electric and magnetic charges in the theory, 3) allowed mass spectrum of particles saturating the Bogomol’nyi bound, and 4) Yukawa couplings between massless n...

We present ab initio and k·p calculations of the spin texture on the Fermi surface of tensile-strained HgTe, which is obtained by stretching the zinc-blende lattice along the (111) axis. Tensile-strained HgTe is a semimetal with pointlike accidental degeneracies between a mirror symmetry protected twofold degenerate band and two nondegenerate bands near the Fermi level. The Fermi surface consis...

For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P , the positive integer I ≡ gcd(Q ∧ P ) is an invariant of the U-duality group. We propose the microscopic theory for computing the spectrum of all dyons for all values of I, generalizing earlier results that exist only for the simplest case of I = 1. Our derivation uses a...

Controlled Perturbation is a framework for perturbing geometric sets to make the processes that use them more robust for fixed-precision manipulation. We present a Controlled Perturbation scheme for sets of line segments in IR (CPLS, for short). CPLS iteratively perturbs the endpoints of the line segments to eliminate potential degeneracies that may cause round-off errors when using fixed-preci...

We adapt the Jain–Taylor (2003) shear-ratio geometric lensing method to measure the dark energy equation of state, w = pv/ρv and its time derivative from dark matter haloes in cosmologies with arbitrary spatial curvature. The full shear-ratio covariance matrix is calculated for lensed sources, including the intervening large-scale structure and photometric redshift errors as additional sources ...