Optimal repair-cost limit for a consumer following expiry of a warranty

This paper develops a methodology for obtaining the optimalrepair-cost limit for the repair-replace decision that a consumerfaces on the expiry of a product warranty, where the producthas been minimally repaired on failure during the warranty.Three cases are considered; (i) an exponentially distributedtime to failure with an arbitrary repair-cost distribution,(ii) an exponentially distributed time to failure with a uniformrepair-cost distribution, and (iii) a Weibull-distributed timeto failure with a beta-distributed repair cost. Numerical optimizationsare performed for the third case, and conclusions drawn as tothe sensitivity of the optimal repair-cost limit on the parametervalues of the distributions involved.     

MODEL FOR THE RATIONALIZATION OF MAGNETIC FIELD EFFECTS IN VIVO. APPLICATION OF THE RADICAL-PAIR MECHANISM TO BIOLOGICAL SYSTEMS

Abstract: A model for magnetic field effects in biological systems is proposed. This model employs the basic concepts of the radical pair mechanism, and predicts that magnetic fields will increase the average radical concentration, lengthen their lifetime and enhance the probability of radical reactions with cellular components. The relevance of these effects in relation to cancer initiation, promotion and progression is discussed.     

Availability measures for components maintained by repair-replacement policies

A renewal-reward process model is given for a component maintainedby a general repair-replacement policy. The point availabilityof the component at time t and its expected operating time overthe interval (0, t) are defined in terms of a pair of relatedintegral equations. These two equations are then solved numericallyto obtain values of the two measures for the policy of repairplus replacement at age .     

A collapsing bubble in a fluid: a statistical mechanical approach

The first non-equilibrium statistical mechanical theory is presented for the mechanical and thermal behaviour of the collapse of a microsropically small bubble in a liquid. First the number density and temperature space-time profiles for the special case of weakly interacting particles, the perfect gas model, are obtained. This is then generalized to a model in which the motion of the molecules is characterized by a single finite diffusion constant. The results for the collapse of a small bubble in a typical fluid are compared with those recently obtained through computer simulation. The agreement with the simulation is remarkably good for the perfect gas model; very high temperatures, sufficient for sonoluminescence, appear in a simple and natural way. An unexpected conclusion is that the perfect gas model agrees better with computer simulation than the model characterized by a single bulk diffusion constant. This may be because the collapse of the bubble is controlled by the leading shell of the fluid where the fluid density is low.     

Best Chebyshev approximation from families of ordinary differential equations

Within the framework of the Meinardus and Schwedt theory ofnonlinear Chebyshev approximation we consider the approximationof functions and data by approximants generated from the solutionof parameter dependent initial value problems in ordinary differentialequations. New results are obtained for the uniqueness and characterizationof best approximations in terms of properties of the differentialequation. Some examples of new approximating families are givenalong with computed best approximations.     

Synthesis, Structure and Alkali Metal Ion Binding Properties of a Podand Polyether Derived from Calix[4]arene, 5,11,17,23-tetra-tert-butyl-25,27-di(phenylmethoxy)-26,28-di(2‘-methoxyethoxy)-calix[4]arene

The ligand 5,11,17,23-tetra-t-butyl-25,27-di(phenylmethoxy)-26,28-di(2-methoxy-ethoxy)calix[4]arene,designed as an analogue of some calixcrown speciesin order to evaluate possible origins of their selectivity in alkali metal ion binding, has been synthesised and structurally characterised by X-ray crystallography. The crystals are monoclinic, P21/n, a = 15.940(6), b = 19.388(5), c = 20.020(5) Å, = 109.10(2) deg., Z = 4, conventional R on |F| being 0.073 for 3454 independent, observed (I > 3(I)) reflections. 1H-NMR studies in 1:1 CD3CN/CDCl3solvent have shown that the ligand exerts a strong preference for the lighteralkali metal ions (Li+ and Na+) contrary to the binding behaviour of knowncalixcrowns. This may reflect interactions restricted to the lower rim donor atoms without concomitant interaction with the calixarene -electrons, perhaps because the latter interactions are substituted by those with the benzyl group -electrons.     

Costing minimal-repair replacement policies over finite time horizons

An integral-equation technique is used to evaluate the expectedcost of maintaining a system functioning over the period (O,t] using two minimal-repair replacement policies. These costfunctions provide appropriate criteria to determine T^*, theoptimal scheduled replacement period over this finite time horizon.For both policies, it is shown that significant cost savingscan be achieved by using the T^* values predicted by the newmodels with a finite time horizon rather than those obtainedfrom the established asymptotic formulations. An adaptive finiteminimal-repair replacement policy is also formulated using dynamicprogramming, and the expected cost of this policy is shown tobe only slightly less than that of the best stationary policy.     

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C_v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ? (r) = ?(σ/r)ⁿ. The C_v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C_v(t) to order O(t⁴) for n large are derived for this fluid. We propose novel expressions for C_v (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, T_E.     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.