Regular Torus Research Articles

Geometric Phases for Classical and Quantum Dynamics: Hannay Angle and Berry Phase for Loops on a Torus

In this paper we have considered closed trajectories of a particle on a two-torus where the loops are noncontractible (poloidal and toroidal loops and knots embedded on a regular torus). We have calculated Hannay angle and Berry phase for particle traversing such loops and knots when the torus itself is adiabatically revolving. Since noncontractible loops do not enclose any area Stokes theorem has to be applied with caution. In our computational scheme we have worked with line integrals directly thus avoiding Stokes theorem.

Towards cost-effective and low latency data center network architecture

This paper presents the design, analysis, and implementation of a novel data center network architecture, named NovaCube. Based on regular Torus topology, NovaCube is constructed by adding a number of most beneficial jump-over links, which offers many distinct advantages and practical benefits. Moreover, in order to enable NovaCube to achieve its maximum theoretical performance, a probabilistic oblivious routing algorithm PORA is carefully designed. PORA is a both deadlock and livelock free routing algorithm, which achieves near-optimal performance in terms of average routing path length with better load balancing thus leading to higher throughput. Theoretical derivation and mathematical analysis together with extensive simulations further prove the good performance of NovaCube and PORA.

SUBGROUPS OF SIMPLE ALGEBRAIC GROUPS CONTAINING REGULAR TORI, AND IRREDUCIBLE REPRESENTATIONS WITH MULTIPLICITY 1 NON-ZERO WEIGHTS

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple linear algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of independent interest. In particular, we determine the irreducible representations of simple algebraic groups whose non-zero weights occur with multiplicity 1.

Design and fabrication of double-circular-arc torus milling cutter

Focusing on the feed rate limitation and high cutting force of regular torus milling cutter in machining dies, a double-circular-arc torus milling cutter is designed and fabricated in this work. The geometric characteristics, cutting force, and milling process of the milling cutter are analyzed and presented. The mathematical models of the cutting edge and radius of the main-circular-arc cutting edge are built. To ensure the cutting performance of the milling cutter, a grinding method combining theory, simulation, fabrication, and test is proposed for the fabrication of the milling cutter. The grinding model is built through coordinate transformation. The evaluation of grinding accuracy is proposed. The milling cutter is shaped on a five-axis NC grinding machine, and its accuracy is tested by a tool test center. The test results show the feasibility of the grinding process and the grinding accuracy is ensured. To verify the cutting performance of the proposed double-circular-arc torus milling cutter, milling experiments are conducted. The cutting force and surface roughness of ball-end milling cutter, regular torus milling cutter, and two double-circular-arc torus milling cutters are measured and compared. It is shown that the double-circular-arc torus milling cutters can generate low cutting force and low surface roughness.

The effect of thermo-oxidation on plasma performance and in-vessel components in DIII-D

In April 2010, two thermo-oxidation experiments (‘O-bakes’) were performed in the DIII-D tokamak. Internal surfaces of the tokamak, as well as a number of specimens inserted into the torus, were exposed to a mixture of 20% O2/80% He at a nominal pressure of 9.5 Torr (1.27 kPa) at a temperature of 350–360 °C for a duration of 2 h. Three primary conclusions have been drawn from these experiments: (1) laboratory measurements on the release of deuterium from tokamak codeposits by oxidation have been duplicated in a tokamak environment, (2) no internal tokamak components or systems were adversely affected by the oxidation and (3) the recovery of plasma performance following oxidation was similar to that following regular torus openings.

Quantum revivals in two degrees of freedom integrable systems: The torus case

The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomomenon of wave packet revivals is demonstrated in this article. The framework of this paper is semi-classical analysis (limit :). For the proofs we use standard tools of real analysis, Fourier analysis and basic analytic number theory.

Crystal structure of α-cyclodextrin-acetonitrile-hexahydrate

Crystals of the ternary α-cyclodextrin-acetonitrile hexahydrate inclusion complex belong to the orthorhombic space group P2 12 12 1 with unit cell dimensions a=9.479(2), b=14.323(4), c=37.397(9) Å. Refinement against 4202 X-ray diffraction data converged at R=0.059. The α-cyclodextrin macrocycle forms a regular torus which is stabilized by intramolecular O-3–O-2 hydrogen bonds between neighboring glucose units. Within the cavity, one acetonitrile and one water molecule are located with occupancy factors of 0.8 and 0.7, respectively. They are hydrogen bonded to disordered O65B, and acetonitrile is stabilized in position by C-5–H⋯N interactions. The remaining five water molecules link symmetry related cyclodextrin molecules.

Zur Lösung räumlicher Probleme der Elastizitätstheorie für torusberandete Gebiete mit Potentialen vom Typ der einfachen Schicht

The problem of the elastic homogeneous and isotropic whole space, with a simple connected inclusion of other material in clastotatics and for stationary elastic vibrations is considered. On the contact surface L the jumps of displacements and tractions are given. L is assumed to be homeomorphic to the boundary surface of a regular torus, and to belong to the class C^{1,\beta} . Using the elastic single layer potential, a system of integral equations is obtained, which is transformed to a twodimensional singular integral equation system by the aid of a Beltrami differential operator \Omega . The singular system is normal solvable and has the index 0. Studying the kernel and the range of the operator \Omega , the existence of solutions of the original problems can be proved. Some generalisations of the approach on other problems are discussed.

Cobordism of regular torus actions

Cobordism of regular torus actions