The Fundamental Plane of Galaxy Clusters

Velocity dispersion $\sigma$, radius $R$ and luminosity $L$ of elliptical galaxies are known to be related, leaving only two degrees of freedom and defining the so-called ``fundamental plane". In this {\em Letter} we present observational evidence that rich galaxy clusters exhibit a similar behaviour. Assuming a relation $L \propto R^{\alpha}\sigma^{2 \beta}$, the best-fit values of $\alpha$ and $\beta$ are very close to those defined by galaxies. The dispersion of this relation is lower than 10 percent, i.e. significantly smaller than the dispersion observed in the $L-\sigma$ and $L-R$ relations. We briefly suggest some possible implications on the spread of formation times of objects and on peculiar velocities of galaxy clusters.Comment: 11pp., 4 figures (available on request), LaTeX, BAP-04-1993-015-OA

Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.Comment: 18 pages, 12 figures. Minor corrections to one figur

Evaluation of the thermal and hydraulic performances of a very thin sintered copper flat heat pipe for 3D microsystem packages

The reported research work presents numerical studies validated by experimental results of a flat micro heat pipe with sintered copper wick structure. The objectives of this project are to produce and demonstrate the efficiency of the passive cooling technology (heat pipe) integrated in a very thin electronic substrate that is a part of a multifunctional 3-D electronic package. The enhanced technology is dedicated to the thermal management of high dissipative microsystems having heat densities of more than 10W/cm2. Future applications are envisaged in the avionics sector. In this research 2D numerical hydraulic model has been developed to investigate the performance of a very thin flat micro heat pipe with sintered copper wick structure, using water as a refrigerant. Finite difference method has been used to develop the model. The model has been used to determine the mass transfer and fluid flow in order to evaluate the limits of heat transport capacity as functions of the dimensions of the wick and the vapour space and for various copper spheres radii. The results are presented in terms of liquid and vapour pressures within the heat pipe. The simulated results are validated by experiments and proved that the method can be further used to predict thermal performance of the heat pipe and to optimise its design.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

Human Like Adaptation of Force and Impedance in Stable and Unstable Tasks

Abstract—This paper presents a novel human-like learning con-troller to interact with unknown environments. Strictly derived from the minimization of instability, motion error, and effort, the controller compensates for the disturbance in the environment in interaction tasks by adapting feedforward force and impedance. In contrast with conventional learning controllers, the new controller can deal with unstable situations that are typical of tool use and gradually acquire a desired stability margin. Simulations show that this controller is a good model of human motor adaptation. Robotic implementations further demonstrate its capabilities to optimally adapt interaction with dynamic environments and humans in joint torque controlled robots and variable impedance actuators, with-out requiring interaction force sensing. Index Terms—Feedforward force, human motor control, impedance, robotic control. I

Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation

We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems which describe large particle ensembles interacting by either electromagnetic fields or a relativistic scalar gravity model. For both systems we derive a radiation formula analogous to the Einstein quadrupole formula in general relativity.Comment: 21 page

Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Investigation of peak shapes in the MIBETA experiment calibrations

In calorimetric neutrino mass experiments, where the shape of a beta decay spectrum has to be precisely measured, the understanding of the detector response function is a fundamental issue. In the MIBETA neutrino mass experiment, the X-ray lines measured with external sources did not have Gaussian shapes, but exhibited a pronounced shoulder towards lower energies. If this shoulder were a general feature of the detector response function, it would distort the beta decay spectrum and thus mimic a non-zero neutrino mass. An investigation was performed to understand the origin of the shoulder and its potential influence on the beta spectrum. First, the peaks were fitted with an analytic function in order to determine quantitatively the amount of events contributing to the shoulder, also depending on the energy of the calibration X-rays. In a second step, Montecarlo simulations were performed to reproduce the experimental spectrum and to understand the origin of its shape. We conclude that at least part of the observed shoulder can be attributed to a surface effect

Interactions between trivalent rare earth oxides and mixed [Hbet][Tf2N]:H2O systems in the development of a one-step process for the separation of light from heavy rare earth elements

The factors, including ionic liquid:water ratios, temperature, solvent:solute contact times, and the effect of dissolved rare earth metal ions on the [Hbet][Tf2N]:H2O thermometric phase change are determined to develop a process for separating the light from the heavy rare earth metal oxides in [Hbet][Tf2N]:H2O mixtures. The relative solubility data for three light (La2O3, Nd2O3, and Eu2O3), two heavy (Y2O3 and Yb2O3) rare earth metal oxides (REOs), and Gd2O3 at different temperatures and different solute:solvent contact times are reported for 1:1 [Hbet][Tf2N]:H2O. The light REOs dissolve easily at 57 °C with the La and Eu reaching maximum solubility within minutes while the heavy REOs have very low solubilities at this temperature with negligible amounts being dissolved for contact times less than 80 min. Gd2O3 dissolves more slowly than the La, Eu, and Nd oxides at 57 °C reaching maximum solubility only after 160 min. Changing the [Hbet][Tf2N]:H2O ratio from 1:1 to 16:1 increases the time required to dissolve the REOs. The times taken to reach maximum solubility decrease for all of the REOs up to 95 °C, resulting in the separations between the light and heavy rare earth elements, and Gd becoming less distinct. The presence of rare earth metal ions in [Hbet][Tf2N]:H2O results in a reduction in the upper critical solution temperature (UCST) of the solvent from 55.6 °C to as low as 31.8 °C with Gd3+. The best separation of light from heavy REOs is achieved at 57 °C but better separation of Gd from the light REOs is achieved at 40 °C, below the solvent UCST. The best conditions for a one-step separation of light from heavy REOs in [Hbet][Tf2N]:H2O mixtures is achieved with 1:1 [Hbet][Tf2N]:H2O at 57 °C using short contact oxide:solvent times (maximum 5 min). Separations of light from heavy REOs, in waste phosphor samples, containing La2O3, CeO2, Eu2O3, Gd2O3, Tb3O4 and Y2O3, are also achieved even in the presence of high concentrations of heavy REOs using short contact times. The use of [Hbet][Tf2N]:H2O as a means of separating light and heavy REOs is aided by the ease of recycling the solvent which can be recycled and reused at least five times with little loss of solvent quality or efficiency

Policy-based management for body-sensor networks

Accepted versio