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

Grain boundary partitioning of Ar and He

An experimental procedure has been developed that permits measurement of the partitioning of Ar and He between crystal interiors and the intergranular medium (ITM) that surrounds them in synthetic melt-free polycrystalline diopside aggregates. ^(37)Ar and ^(4)He are introduced into the samples via neutron irradiation. As samples are crystallized under sub-solidus conditions from a pure diopside glass in a piston cylinder apparatus, noble gases diffusively equilibrate between the evolving crystal and intergranular reservoirs. After equilibration, ITM Ar and He is distinguished from that incorporated within the crystals by means of step heating analysis. An apparent equilibrium state (i.e., constant partitioning) is reached after about 20 h in the 1450 °C experiments. Data for longer durations show a systematic trend of decreasing ITM Ar (and He) with decreasing grain boundary (GB) interfacial area as would be predicted for partitioning controlled by the network of planar grain boundaries (as opposed to ITM gases distributed in discrete micro-bubbles or melt). These data yield values of GB-area-normalized partitioning, K¯^(Ar)_(ITM), with units of (Ar/m^3 of solid)/(Ar/m^2 of GB) of 6.8 x 10^3 – 2.4 x 104 m^(-1). Combined petrographic microscope, SEM, and limited TEM observation showed no evidence that a residual glass phase or grain boundary micro-bubbles dominated the ITM, though they may represent minor components. If a nominal GB thickness (δ) is assumed, and if the density of crystals and the grain boundaries are assumed equal, then a true grain boundary partition coefficient (K^(Ar)_(GB) = X^(Ar)_(crystals)/X^(Ar)_(GB) may be determined. For reasonable values of δ, K^(Ar)_(GB) is at least an order of magnitude lower than the Ar partition coefficient between diopside and melt. Helium partitioning data provide a less robust constraint with K¯^(He)_(ITM) between 4 x 10^3 and 4 x 10^4 cm^(-1), similar to the Ar partitioning data. These data suggest that an ITM consisting of nominally melt free, bubble free, tight grain boundaries can constitute a significant but not infinite reservoir, and therefore bulk transport pathway, for noble gases in fine grained portions of the crust and mantle where aqueous or melt fluids are non-wetting and of very low abundance (i.e., <0.1% fluid). Heterogeneities in grain size within dry equilibrated systems will correspond to significant differences in bulk rock noble gas content

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

General scalar products in the arbitrary six-vertex model

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the Yang-Baxter equation. We have derived a recurrence relation for the scalar product. The solution of this relation was written in terms of the domain wall partition functions. By its turn, these partition functions were also obtained for generic Boltzmann weights, which provided us with an explicit expression for the general scalar product.Comment: 24 page

Buoyant Venus station feasibility study. Volume IV - Communications and power Final report

Telecommunication and power supply requirements for inflatable buoyant Venus statio

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

A new class o^N{\hat o}_N of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable SS-matrix

Statistical models corresponding to a new class of braid matrices ($\hat{o}_N; N\geq 3$) presented in a previous paper are studied. Indices labeling states spanning the $N^r$ dimensional base space of $T^{(r)}(\theta)$, the $r$-th order transfer matrix are so chosen that the operators $W$ (the sum of the state labels) and (CP) (the circular permutation of state labels) commute with $T^{(r)}(\theta)$. This drastically simplifies the construction of eigenstates, reducing it to solutions of relatively small number of simultaneous linear equations. Roots of unity play a crucial role. Thus for diagonalizing the 81 dimensional space for N=3, $r=4$, one has to solve a maximal set of 5 linear equations. A supplementary symmetry relates invariant subspaces pairwise ($W=(r,Nr)$ and so on) so that only one of each pair needs study. The case N=3 is studied fully for $r=(1,2,3,4)$. Basic aspects for all $(N,r)$ are discussed. Full exploitation of such symmetries lead to a formalism quite different from, possibly generalized, algebraic Bethe ansatz. Chain Hamiltonians are studied. The specific types of spin flips they induce and propagate are pointed out. The inverse Cayley transform of the YB matrix giving the potential leading to factorizable $S$-matrix is constructed explicitly for N=3 as also the full set of $\hat{R}tt$ relations. Perspectives are discussed in a final section.Comment: 27 page

Exact clesed form of the return probability on the Bethe lattice

An exact closed form solution for the return probability of a random walk on the Bethe lattice is given. The long-time asymptotic form confirms a previously known expression. It is however shown that this exact result reduces to the proper expression when the Bethe lattice degenerates on a line, unlike the asymptotic result which is singular. This is shown to be an artefact of the asymptotic expansion. The density of states is also calculated.Comment: 7 pages, RevTex 3.0, 2 figures available upon request from [email protected], to be published in J.Phys.A Let

A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models

In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator representations used previously. We derive generalized T-Q relations in which 3 of these parameters shift. After a suitable restriction of parameters, we give an explicit expression for the Q-operator of the 6-vertex model and show the connection with Baxter's expression for the central block of his corresponding operator.Comment: 22 pages, Latex2e. This replacement is a revised version that includes a simple explicit expression for the Q matrix for the 6-vertex mode

Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices

We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse matrices, each of dimension ~ 3^m, where m is the number of lattice spacings across the strip. As a specific application, we obtain the large-q series of the bulk, surface and corner free energies of the chromatic polynomial. This extends the existing series for the square lattice by 32 terms, to order q^{-79}. On the triangular lattice, we verify Baxter's analytical expression for the bulk free energy (to order q^{-40}), and we are able to conjecture exact product formulae for the surface and corner free energies.Comment: 17 pages. Version 2: added 4 further term to the serie