Heat flux measuring system Patent

Heat flux sensor adapted for mounting on aircraft or spacecraft to measure aerodynamic heat flux inflow to aircraft ski

A direct proof of Kim's identities

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like $1 - q^{\sqrt{n}}$ and $1 - q^{n^2}$, instead of $1 - q^n$. We show here that there is a fourth relation that naturally completes the set, in much the same way that there are four relations for the four elliptic theta functions. We derive all of them directly by proving and using a specialization of Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics

The Effects of Variable Capital Utilization on the Measurement and Properties of Sectoral Productivity: Some International Evidence

This paper explores how accounting for variations in factor utilization rates alters the empirical characteristics of productivity residuals in the United States and Canada. Using data on 19 manufacturing industries, we study the behavior of productivity using three proxies for capital services. We find that adjusting for cyclical movements in capital utilization alters many of the empirical characteristics of productivity, both within and across countries.

Bethe Equations "on the Wrong Side of Equator"

We analyse the famous Baxter's $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from its usual polynomial (trigonometric) solution, which provides the solution of Bethe-Ansatz equations, there exists also the second solution which should corresponds to Bethe-Ansatz beyond $N/2$. This second solution of Baxter's equation plays essential role and together with the first one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio

Spectral characteristics of earth-space paths at 2 and 30 FHz

Spectral characteristics of 2 and 30 GHz signals received from the Applications Technology Satellite-6 (ATS-6) are analyzed in detail at elevation angles ranging from 0 deg to 44 deg. The spectra of the received signals are characterized by slopes and break frequencies. Statistics of these parameters are presented as probability density functions. Dependence of the spectral characteristics on elevation angle is investigated. The 2 and 30 GHz spectral shapes are contrasted through the use of scatter diagrams. The results are compared with those predicted from turbulence theory. The average spectral slopes are in close agreement with theory, although the departure from the average value at any given elevation angle is quite large

Gas release and conductivity modification studies

The behavior of gas clouds produced by releases from orbital velocity in either a point release or venting mode is described by the modification of snowplow equations valid in an intermediate altitude regime. Quantitative estimates are produced for the time dependence of the radius of the cloud, the average internal energy, the translational velocity, and the distance traveled. The dependence of these quantities on the assumed density profile, the internal energy of the gas, and the ratio of specific heats is examined. The new feature is the inclusion of the effect of the large orbital velocity. The resulting gas cloud models are used to calculate the characteristics of the field line integrated Pedersen conductivity enhancements that would be produced by the release of barium thermite at orbital velocity in either the point release or venting modes as a function of release altitude and chemical payload weight

Tetromino tilings and the Tutte polynomial

We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte polynomial Z\_G(Q,v) (known also to physicists as the partition function of the Q-state Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure