An Improved Upper Bound for the Ring Loading Problem

The Ring Loading Problem emerged in the 1990s to model an important special case of telecommunication networks (SONET rings) which gained attention from practitioners and theorists alike. Given an undirected cycle on $n$ nodes together with non-negative demands between any pair of nodes, the Ring Loading Problem asks for an unsplittable routing of the demands such that the maximum cumulated demand on any edge is minimized. Let $L$ be the value of such a solution. In the relaxed version of the problem, each demand can be split into two parts where the first part is routed clockwise while the second part is routed counter-clockwise. Denote with $L^*$ the maximum load of a minimum split routing solution. In a landmark paper, Schrijver, Seymour and Winkler [SSW98] showed that $L \leq L^* + 1.5D$, where $D$ is the maximum demand value. They also found (implicitly) an instance of the Ring Loading Problem with $L = L^* + 1.01D$. Recently, Skutella [Sku16] improved these bounds by showing that $L \leq L^* + \frac{19}{14}D$, and there exists an instance with $L = L^* + 1.1D$. We contribute to this line of research by showing that $L \leq L^* + 1.3D$. We also take a first step towards lower and upper bounds for small instances

Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses

Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm for the study of dynamic buckling with controlled loads. Experimentally, an elastic ring is placed within a soap film. When the film outside the ring is removed, surface tension pulls the ring inward, mimicking an external pressurization. Here we present a theoretical analysis of this process by performing a post-bifurcation analysis of an elastic ring under pressure. This analysis allows us to understand how inertia, material properties, and loading affect the observed shape. In particular, we combine direct numerical solutions with a post-bifurcation asymptotic analysis to show that inertia drives the system towards higher modes that cannot be selected in static buckling. Our theoretical results explain experimental observations that cannot be captured by a standard linear stability analysis.Comment: 18 pages, 10 figure

A ring trap for ultracold atoms

We propose a new kind of toroidal trap, designed for ultracold atoms. It relies on a combination of a magnetic trap for rf-dressed atoms, which creates a bubble-like trap, and a standing wave of light. This new trap is well suited for investigating questions of low dimensionality in a ring potential. We study the trap characteristics for a set of experimentally accessible parameters. A loading procedure from a conventional magnetic trap is also proposed. The flexible nature of this new ring trap, including an adjustable radius and adjustable transverse oscillation frequencies, will allow the study of superfluidity in variable geometries and dimensionalities.Comment: 4 figures, 10 pages ; the order of the sections has been changed ; to appear in Phys. Rev.

Beam Loading Compensation in the Main Linac of CLIC

Compensation of multi-bunch beam loading is of great importance in the main linac of the Compact Linear Collider (CLIC). The bunch-to-bunch energy variation has to stay below 1 part in 1000. In CLIC, the RF power is obtained by decelerating a drive beam which is formed by merging a number of short bunch trains. A promising scheme for tackling beam loading in the main linac is based on varying the lengths of the bunch trains in the drive beam. The scheme and its expected performance are presented.Comment: LINAC 2000, paper ID MOA0

A kinematically exact finite element formulation of planar elastic-plastic frames

A finite element formulation of finite deformation static analysis of plane elastic-plastic frames subjected to static loads is presented, in which the only function to be interpolated is the rotation of the centroid axis of the beam. One of the advantages of such a formulation is that the problem of the field-consistency does not arise. Exact non-linear kinematic relationships of the finite-strain beam theory are used, which assume the Bernoulli hypothesis of plane cross-sections. Finite displacements and rotations as well as finite extensional and bending strains are accounted for. The effects of shear strains and non-conservative loads are at present neglected, yet they can simply be incorporated in the formulation. Because the potential energy of internal forces does not exist with elastic-plastic material, the principle of virtual work is introduced as the basis of the finite element formulation. A generalized principle of virtual work is proposed in which the displacements, rotation, extensional and bending strains, and the Lagrangian multipliers are independent variables. By exploiting the special structure of the equations of the problem, the displacements, the strains and the multipliers are eliminated from the generalized principle of virtual work. A novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation. It is shown that (N-1)-point numerical integration must be employed in conjunction with N-node interpolation polynomials for the rotation, and the Lobatto rule is recommended. Regarding the integration over the cross-section, it is demonstrated by numerical examples that, due to discontinuous integrands, no integration order defined as `computationally efficient yet accurate enough' could be suggested. The theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

UK Rules For Unfired Pressure Vessels

The present code PD 5500, formerly BS 5500 [1] evolved partly from the well-known BS 1500 [2] in the 1950's and BS 1515 [3] first published in 1965; the latter permitted higher level allowable stresses and more advanced rules. In 1969, following a report from the Committee of Enquiry into the Pressure Vessel Industry, the British Standards Institution brought all the pressure vessel interests together under one general committee in order to rationalise the activity. This became PVE/ and presides over a large committee structure. There are a series of functional sub-committees who deal with specific aspects and a large number of technical committees as well as many additional sub committees and working groups. Most of these meet regularly. The technical committee PVE/1, Pressure Vessels, has overall responsibility for BS 5500. The functional committee PVE/1/15 Design Methods has an overall responsibility relating to 'Design' with particular reference to the design section of BS 5500 (Section 3). The first edition of BS 5500 was issued in 1976. The actual issue was delayed for some time because, in the early 1970's, there was an attempt in Europe to produce an international pressure vessel standard. A draft of the international standard appeared as ISO DIS 2694 [4] in 1973 but it was not generally accepted and the attempt was abandoned in the mid 70's. It was decided to use some of the material from 2694 within BS 5500 so that although the Standard was long delayed it benefited to some extent from the international efforts. Initially, committee PVE/l set out the concept of a "master" pressure vessel standard which could readily be applied to any vessel in either ferrous or non-ferrous materials and for highly specialised application with the minimum of supplementary requirements. The layout of BS 5500 is consistent with this concept and although the Standard has perhaps not fulfilled this high ideal, it has certainly been employed widely in many industries including non pressure vessel type applications. When issued it had a number of distinctive features compared with other pressure codes viz; weld joint factors were removed, the present three categories of construction were introduced, there was a new novel external pressure section, it has a loose leaf format and an annual updating was introduced. Further editions of BS 5500 have been issued every three years since 1982

A similarity law for stressing rapidly heated thin-walled cylinders

When a thin cylindrical shell of uniform thickness is very rapidly heated by hot high-pressure gas flowing inside the shell, the temperature of material decreases steeply from a high temperature at the inside surface to ambient temperatures at the outside surface. Young's modulus of material thus varies. The purpose of the present paper is to reduce the problem of stress analysis of such a cylinder to an equivalent problem in conventional cylindrical shell without temperature gradient in the wall. The equivalence concept is expressed as a series of relations between the quantities for the hot cylinder and the quantities for the cold cylinder. These relations give the similarity law whereby strains for the hot cylinder can be simply deduced from measured strains on the cold cylinder and thus greatly simplify the problem of experimental stress analysis

A kinematically exact finite element formulation of elastic-plastic curved beams

A finite element, large displacement formulation of static elastic-plastic analysis of slender arbitrarily curved planar beams is presented. Non-conservative and dynamic loads are sit present not included. The Bernoulli hypothesis of plane cross-sections is assumed and the effect of hear strains is neglected. Exact non-linear kinematic equations of curved beams, derived by Reissner are incorporated into;a generalized principle of virtual work through Lagrangian multipliers. The only function that has to be interpolated in the finite element implementation is the rotation of the centroid axis of a beam. This is an important advantage over other classical displacement approaches since the field consistency problem and related locking phenomena do not arise. Numerical examples, comprising elastic and elastic-plastic, curved and straight beams, at large displacements and rotations, show very nice computational and accuracy characteristics of the present family of finite elements. The comparisons with other published results very clearly show the superior performance of the present elements. (C) 1998 Elsevier Science Ltd. All rights reserved

A Low-Cost Robust Distributed Linearly Constrained Beamformer for Wireless Acoustic Sensor Networks with Arbitrary Topology

We propose a new robust distributed linearly constrained beamformer which utilizes a set of linear equality constraints to reduce the cross power spectral density matrix to a block-diagonal form. The proposed beamformer has a convenient objective function for use in arbitrary distributed network topologies while having identical performance to a centralized implementation. Moreover, the new optimization problem is robust to relative acoustic transfer function (RATF) estimation errors and to target activity detection (TAD) errors. Two variants of the proposed beamformer are presented and evaluated in the context of multi-microphone speech enhancement in a wireless acoustic sensor network, and are compared with other state-of-the-art distributed beamformers in terms of communication costs and robustness to RATF estimation errors and TAD errors