Wear Tests of a Potential Biolubricant for Orthopedic Biopolymers

Most wear testing of orthopedic implant materials is undertaken with dilute bovine serum used as the lubricant. However, dilute bovine serum is different to the synovial fluid in which natural and artificial joints must operate. As part of a search for a lubricant which more closely resembles synovial fluid, a lubricant based on a mixture of sodium alginate and gellan gum, and which aimed to match the rheology of synovial fluid, was produced. It was employed in a wear test of ultra high molecular weight polyethylene pins rubbing against a metallic counterface. The test rig applied multidirectional motion to the test pins and had previously been shown to reproduce clinically relevant wear factors for ultra high molecular weight polyethylene. After 2.4 million cycles (125 km) of sliding in the presence of the new lubricant, a mean wear factor of 0.099 × 10−6 mm3/Nm was measured for the ultra high molecular weight polyethylene pins. This was over an order of magnitude less than when bovine serum was used as a lubricant. In addition, there was evidence of a transfer film on the test plates. Such transfer films are not seen clinically. The search for a lubricant more closely matching synovial fluid continues

Chamber Structure and Wallcrossing in the ADHM Theory of Curves II

This is the second part of a project concerning variation of stability and chamber structure for ADHM invariants of curves. Wallcrossing formulas for such invariants are derived using the theory of stack function Ringel-Hall algebras constructed by Joyce and the theory of generalized Donaldson-Thomas invariants of Joyce and Song. Some applications are presented, including strong rationality for local stable pair invariants of higher genus curves and comparison with wallcrossing formulas of Kontsevich and Soibelman, and the halo formula of Denef and Moore.Comment: 32 pages, AMS LaTex; v.2: Thm 1.2 improved; v3: many proofs simplified based on a remark of Dominic Joyce, results unchanged; v3: 18 pages, shorter version to appear in J Geom Phy

Ultrasonic reflection from mixed liquid-solid contacts and the determination of interface stiffness

In thin film or boundary lubricated contacts there is a possibility of potentially damaging asperity contact occurring. Whilst there are many models of this contact mechanism, experimental verification of the proportion of solid contact is difficult to achieve. Electrical methods will only indicate that contact has occurred. Whereas, optical methods can be used to determine the proportion of contact, but only when one surface is transparent. In this work the use of ultrasonic reflection is investigated as a means to analyse these types of mixed solid-liquid contacts. A pulse of ultrasound is partially reflected at the contact between two rough surfaces. The proportion of the wave reflected can be readily used to determine the stiffness of the interface. Experimental data has been obtained from grit-blasted surfaces pressed together, both with and without liquid at the interface. The interface stiffness can be modelled by two springs in series, one of them representing the solid contact stiffness, Ksolid and the other the stiffness of the liquid fluid, Kliquid. The variation of these stiffness values with contact pressure has been investigated. At this stage it is not possible to directly determine the proportion of liquid or solid contact from the stiffness. The results however, give qualitative comparisons and information about the approach of the surfaces and hence the mean thickness of the liquid layer at the interface

Evaluation of an ultrasonic method for measurement of oil film thickness in a hydraulic motor piston ring

The efficiency of a hydraulic motor depends on the lubrication performance of the piston ring. If the film is too thin then wear occurs quickly, if it is too thick then oil is lost into the cylinder and efficiency is reduced. In this paper a technique for oil film measurement based on ultrasonic reflection is investigated. This has the potential to be used non-invasively on real components. An ultrasonic pulse will reflect from a thin film interposed between two solids. The proportion of the pulse that is reflected depends on the stiffness of the intermediate layer. If the acoustic properties of the film material are known, then the stiffness can readily be used to determine the film thickness. This principle has been employed for the piston ring lubrication case. A piston/cylinder test bench has been used to evaluate the ultrasonic method. A focusing piezo-electric transducer is mounted outside the cylinder and ultrasonic pulses reflected back from the inner bore. The variation of these pulses as the piston ring passes underneath is investigated and used to determine oil film thickness. Films in the range 0.7 to 1.3 μm were measured; the thickness did not depend strongly on either ring speed or sealed pressure. Several practical aspects were investigated such as, attenuation in the cylinder material, response time, and transducer resolution. Whilst this study demonstrated that film thickness measurement is feasible, there are a number of practical considerations that require further work, principally the focusing and coupling of the ultrasonic transducer and the response time

D-Branes and Spin^c Structures

It was recently pointed out by E. Witten that for a D-brane to consistently wrap a submanifold of some manifold, the normal bundle must admit a Spin^c structure. We examine this constraint in the case of type II string compactifications with vanishing cosmological constant, and argue that in all such cases, the normal bundle to a supersymmetric cycle is automatically Spin^c.Comment: 9 pages, LaTe

Complex solutions of Monge-Amp\`ere equations

We describe a method to reduce partial differential equations of Monge-Amp\`ere type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the special lagrangian equation, the real Monge-Amp\`ere equations and the Plebanski equations.Comment: 16 pages, 5 tables To appear in Journal of Geometry and Physic

Constant Scalar Curvature Metrics on Connected Sums

The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension $n \geq 3$, which minimizes the total scalar curvature of this conformal class. Let $(M',g')$ and $(M'',g'')$ be compact Riemannian $n$-manifolds. We form their connected sum $M'\#M''$ by removing small balls of radius $\epsilon$ from $M'$, $M''$ and gluing together the $S^{n-1}$ boundaries, and make a metric $g$ on $M'\#M''$ by joining together $g'$,$g''$ with a partition of unity. In this paper we use analysis to study metrics with constant scalar curvature on $M'\#M''$ in the conformal class of $g$. By the Yamabe problem, we may rescale $g'$ and $g''$ to have constant scalar curvature 1, 0 or -1. Thus there are 9 cases, which we handle separately. We show that the constant scalar curvature metrics either develop small `necks' separating $M'$ and $M''$, or one of $M'$, $M''$ is crushed small by the conformal factor. When both sides have positive scalar curvature we find three metrics with scalar curvature 1 in the same conformal class

A theory of quaternionic algebra, with applications to hypercomplex geometry

In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic geometry" of noncompact hypercomplex manifolds. The basic building blocks of the theory are AH modules, which should be thought of "vector spaces" over the quaternions. An AH-module is a left module over the quaternions H, together with a real vector subspace. There are natural concepts of linear map and tensor product of AH-modules, which have many of the properties of linear maps and tensor products of vector spaces. However, the definition of tensor product of AH-modules is strange and has some unexpected properties. Let M be a hypercomplex manifold. Then there is a natural class of H-valued "q-holomorphic functions" on M, satisfying a quaternionic analogue of the Cauchy-Riemann equations, which are analogues of holomorphic functions on complex manifolds. The vector space of q-holomorphic functions A on M is an AH-module. Now some pairs of q-holomorphic functions can be multiplied together to get another q-holomorphic function, but other pairs cannot. So A has a kind of partial algebra structure. It turns out that this structure can be very neatly described using the quaternionic tensor product and AH-morphisms, and that A has the structure of an "H-algebra", a quaternionic analogue of commutative algebra.Comment: 66 pages, LaTeX, uses packages amstex and amssym