Quantum Euler Relation for Local Measurements

In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.

Tesla Bladed Pump (Disc Bladed Pump) Preliminary Experimental Performance Analysis

A preliminary experimental work on a centrifugal pump model specifically designed to transport slurry and multiphase flows is presented. The impeller design corresponds to the so-called “Tesla Bladed Pump” adapted from an existing DiscflowTM pump design for the petroleum deep-sea application. The overall performance results of such a specific pump design are presented for different rotational speeds and discussed in relation to affinity laws coefficients. The results show that the performance of the tested disc pump strongly differs from the conventional centrifugal bladed pump. A one-dimensional approach using complete Euler relation is used to explain the differences in the present case. Moreover, it has been found that available results in open literatures do not correspond to the real optimum conditions, more detailed research work must be performed to get a better understanding on this kind of bladed disc pump.

Cell Complexes, Valuations, and the Euler Relation

1. Recently a number of functions have been shown to satisfy relations on polytopes similar to the classic Euler relation. Much of this work has been done by Shephard, and an excellent summary of results of this type may be found in [11]. For such functions, only continuity (with respect to the Hausdorff metric) is required to assure that it is a valuation, and the relationship between these two concepts was explored in [8]. It is our aim in this paper to extend the results obtained there to illustrate the relationship between valuations and the Euler relation on cell complexes.To fix our notions, we will suppose that everything takes place in a given finite-dimensional Euclidean space X.A polytope is the convex hull of a finite set of points and will be referred to as a d-polytope if it has dimension d. Polytopes have faces of all dimensions from 0 to d – 1 and each of these is in turn a polytope. A k-dimensional face will be termed simply a k-face.

Polytopes, Valuations, and the Euler Relation

By a d-polytope we shall mean a d-dimensional convex polytope. We shall denote a j-dimensional face (or j-face) of a polytope by Fj. Every d-polytope P has proper j-faces for 0 ≦j ≦d — 1 and we shall also say that P is a d-face of itself. Observe that every face of a polytope is again a polytope. The collection of all convex polytopes shall be denoted by .