The scholarship assignment problem

There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is that the best student should get the most prestigious scholarship, the second-best student should get the second most prestigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor wants one particular student to get the most prestigious scholarship and wants the remaining scholarships to be assigned according to the socially optimal outcome. We consider the problem of finding a mechanism such that in equilibrium, all scholarships are assigned according to the socially optimal outcome.Publicad

Liquid-gas coexistence and critical point shifts in size-disperse fluids

Specialized Monte Carlo simulations and the moment free energy (MFE) method are employed to study liquid-gas phase equilibria in size-disperse fluids. The investigation is made subject to the constraint of fixed polydispersity, i.e. the form of the `parent' density distribution $\rho^0(\sigma)$ of the particle diameters $\sigma$, is prescribed. This is the experimentally realistic scenario for e.g. colloidal dispersions. The simulations are used to obtain the cloud and shadow curve properties of a Lennard-Jones fluid having diameters distributed according to a Schulz form with a large (40%) degree of polydispersity. Good qualitative accord is found with the results from a MFE method study of a corresponding van der Waals model that incorporates size-dispersity both in the hard core reference and the attractive parts of the free energy. The results show that polydispersity engenders considerable broadening of the coexistence region between the cloud curves. The principal effect of fractionation in this region is a common overall scaling of the particle sizes and typical inter-particle distances, and we discuss why this effect is rather specific to systems with Schulz diameter distributions. Next, by studying a family of such systems with distributions of various widths, we estimate the dependence of the critical point parameters on $\delta$. In contrast to a previous theoretical prediction, size-dispersity is found to raise the critical temperature above its monodisperse value. Unusually for a polydisperse system, the critical point is found to lie at or very close to the extremum of the coexistence region in all cases. We outline an argument showing that such behaviour will occur whenever size polydispersity affects only the range, rather than the strength of the inter-particle interactions.Comment: 14 pages, 12 figure

Phase behaviour and particle-size cutoff effects in polydisperse fluids

We report a joint simulation and theoretical study of the liquid-vapor phase behaviour of a fluid in which polydispersity in the particle size couples to the strength of the interparticle interactions. Attention is focussed on the case in which the particles diameters are distributed according to a fixed Schulz form with degree of polydispersity $\delta=14$. The coexistence properties of this model are studied using grand canonical ensemble Monte Carlo simulations and moment free energy calculations. We obtain the cloud and shadow curves as well as the daughter phase density distributions and fractional volumes along selected isothermal dilution lines. In contrast to the case of size-{\em independent} interaction strengths (N.B. Wilding, M. Fasolo and P. Sollich, J. Chem. Phys. {\bf 121}, 6887 (2004)), the cloud and shadow curves are found to be well separated, with the critical point lying significantly below the cloud curve maximum. For densities below the critical value, we observe that the phase behaviour is highly sensitive to the choice of upper cutoff on the particle size distribution. We elucidate the origins of this effect in terms of extremely pronounced fractionation effects and discuss the likely appearance of new phases in the limit of very large values of the cutoff.Comment: 12 pages, 15 figure

High magnification crack-tip field characterisation under biaxial conditions

This work presents a novel methodology for characterising fatigue cracks under biaxial conditions.The methodology uses high magnification Digital Image Correlation (DIC) technique for measuringdisplacement and strain crack-tip fields. By applying micro-speckle pattern on the metal surface it is possible toachieve high magnification for DIC technique. The speckles were created by electro-spray technique. Thevalidity of this novel technique is demonstrated by direct comparison with standard extensometermeasurements, under tension-compression and torsion conditions. In order to image the correct region, thenotch effect on the fatigue life was also evaluated

Characterizing the Risk Profiles of Intensive Care Units

OBJECTIVE: To develop a new method to evaluate the performance of individual ICUs through the calculation and visualisation of risk profiles. METHODS: The study included 102,561 patients consecutively admitted to 77 ICUs in Austria. We customized the function which predicts hospital mortality (using SAPS II) for each ICU. We then compared the risks of hospital mortality resulting from this function with the risks which would be obtained using the original function. The derived risk ratio was then plotted together with point-wise confidence intervals in order to visualise the individual risk profile of each ICU over the whole spectrum of expected hospital mortality. MAIN MEASUREMENTS AND RESULTS: We calculated risk profiles for all ICUs in the ASDI data set according to the proposed method. We show examples how the clinical performance of ICUs may depend on the severity of illness of their patients. Both the distribution of the Hosmer-Lemeshow goodness-of-fit test statistics and the histogram of the corresponding P values demonstrated a good fit of the individual risk models. CONCLUSIONS: Our risk profile model makes it possible to evaluate ICUs on the basis of the specific risk for patients to die compared to a reference sample over the whole spectrum of hospital mortality. Thus, ICUs at different levels of severity of illness can be directly compared, giving a clear advantage over the use of the conventional single point estimate of the overall observed-to-expected mortality ratio

Structure of the Vacuum in Deformed Supersymmetric Chiral Models

We analyze the vacuum structure of N=1/2 chiral supersymmetric theories in deformed superspace. In particular we study O'Raifeartaigh models with C-deformed superpotentials and canonical and non-canonical deformed Kahler potentials. We find conditions under which the vacuum configurations are affected by the deformations.Comment: 15 pages, minor corrections. Version to appear in JHE

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation effects. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or re-entrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus only be defined for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find in addition that coexistence of several solids with a fluid phase is also possible

Magnetic Properties of the Metamagnet Ising Model in a three-dimensional Lattice in a Random and Uniform Field

By employing the Monte Carlo technique we study the behavior of Metamagnet Ising Model in a random field. The phase diagram is obtained by using the algorithm of Glaubr in a cubic lattice of linear size $L$ with values ranging from 16 to 42 and with periodic boundary conditions.Comment: 4 pages, 6 figure