Wind tunnel model surface gauge for measuring roughness

The optical inspection of surface roughness research has proceeded along two different lines. First, research into a quantitative understanding of light scattering from metal surfaces and into the appropriate models to describe the surfaces themselves. Second, the development of a practical instrument for the measurement of rms roughness of high performance wind tunnel models with smooth finishes. The research is summarized, with emphasis on the second avenue of research

Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first eleven terms with the large-$q$ series for $W(hc,q)$. Second, we investigate the heteropolygonal Archimedean $4 \cdot 8^2$ lattice, derive a rigorous lower bound, on $W(4 \cdot 8^2,q)$, and calculate the large-$q$ series for this function to $O(y^{12})$ where $y=1/(q-1)$. Remarkably, these agree exactly to all thirteen terms calculated. We also report Monte Carlo measurements, and find that these are very close to our lower bound and series. Third, we study the effect of non-nearest-neighbor couplings, focusing on the square lattice with next-nearest-neighbor bonds.Comment: 13 pages, Latex, to appear in Phys. Rev.

Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals

We prove a general rigorous lower bound for $W(\Lambda,q)=\exp(S_0(\Lambda,q)/k_B)$, the exponent of the ground state entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean lattice $\Lambda$. We calculate large-$q$ series expansions for the exact $W_r(\Lambda,q)=q^{-1}W(\Lambda,q)$ and compare these with our lower bounds on this function on the various Archimedean lattices. It is shown that the lower bounds coincide with a number of terms in the large-$q$ expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions $W_r(\Lambda,q)$ for large $q$ on the various lattices $\Lambda$. Plots of $W_r(\Lambda,q)$ are given, and the general dependence on lattice coordination number is noted. Lower bounds and series are also presented for the duals of Archimedean lattices. As part of the study, the chromatic number is determined for all Archimedean lattices and their duals. Finally, we report calculations of chromatic zeros for several lattices; these provide further support for our earlier conjecture that a sufficient condition for $W_r(\Lambda,q)$ to be analytic at $1/q=0$ is that $\Lambda$ is a regular lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in Phys. Rev.

Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers

Great prominence is put on the design of aeronautical gas turbines due to increasingly stringent regulations and the need to tackle rising fuel prices. This drive towards innovation has resulted sometimes in new concepts being prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. Since one of the most limiting factors in performing Large Eddy Simulation (LES) of real combustors is estimating the adequate grid, the effects of mesh resolution are investigated by computing full annular LES of a realistic helicopter combustion chamber on three grids, respectively made of 38, 93 and 336 million elements. Results are compared in terms of mean and fluctuating fields. LES captures self-established azimuthal modes. The presence and structure of the modes is discussed. This study therefore highlights the potential of LES for studying combustion instabilities in annular gas turbine combustors

Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets

We study the asymptotic limiting function $W({G},q) = \lim_{n \to \infty}P(G,q)^{1/n}$, where $P(G,q)$ is the chromatic polynomial for a graph $G$ with $n$ vertices. We first discuss a subtlety in the definition of $W({G},q)$ resulting from the fact that at certain special points $q_s$, the following limits do not commute: $\lim_{n \to \infty} \lim_{q \to q_s} P(G,q)^{1/n} \ne \lim_{q \to q_s} \lim_{n \to \infty} P(G,q)^{1/n}$. We then present exact calculations of $W({G},q)$ and determine the corresponding analytic structure in the complex $q$ plane for a number of families of graphs ${G}$, including circuits, wheels, biwheels, bipyramids, and (cyclic and twisted) ladders. We study the zeros of the corresponding chromatic polynomials and prove a theorem that for certain families of graphs, all but a finite number of the zeros lie exactly on a unit circle, whose position depends on the family. Using the connection of $P(G,q)$ with the zero-temperature Potts antiferromagnet, we derive a theorem concerning the maximal finite real point of non-analyticity in $W({G},q)$, denoted $q_c$ and apply this theorem to deduce that $q_c(sq)=3$ and $q_c(hc) = (3+\sqrt{5})/2$ for the square and honeycomb lattices. Finally, numerical calculations of $W(hc,q)$ and $W(sq,q)$ are presented and compared with series expansions and bounds.Comment: 33 pages, Latex, 5 postscript figures, published version; includes further comments on large-q serie

Topology by Design in Magnetic nano-Materials: Artificial Spin Ice

Artificial Spin Ices are two dimensional arrays of magnetic, interacting nano-structures whose geometry can be chosen at will, and whose elementary degrees of freedom can be characterized directly. They were introduced at first to study frustration in a controllable setting, to mimic the behavior of spin ice rare earth pyrochlores, but at more useful temperature and field ranges and with direct characterization, and to provide practical implementation to celebrated, exactly solvable models of statistical mechanics previously devised to gain an understanding of degenerate ensembles with residual entropy. With the evolution of nano--fabrication and of experimental protocols it is now possible to characterize the material in real-time, real-space, and to realize virtually any geometry, for direct control over the collective dynamics. This has recently opened a path toward the deliberate design of novel, exotic states, not found in natural materials, and often characterized by topological properties. Without any pretense of exhaustiveness, we will provide an introduction to the material, the early works, and then, by reporting on more recent results, we will proceed to describe the new direction, which includes the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte

X-ray microscopy using collimated and focussed synchrotron radiation

X-ray microscopy is a field that has developed rapidly in recent years. Two different approaches have been used. Zone plates have been employed to produce focused beams with sizes as low as 0.07 ..mu..m for x-ray energies below 1 keV. Images of biological materials and elemental maps for major and minor low Z have been produced using above and below absorption edge differences. At higher energies collimators and focusing mirrors have been used to make small diameter beams for excitation of characteristic K- or L-x rays of all elements in the periodic table. The practicality of a single instrument combining all the features of these two approaches is unclear. The use of high-energy x rays for x-ray microscopy has intrinsic value for characterization of thick samples and determination of trace amounts of most elements. A summary of work done on the X-26 beam line at the National Synchrotron Light Source (NSLS) with collimated and focused x rays with energies above 4 keV is given here. 6 refs., 5 figs., 1 tab

Overview of the Characteristic Features of the Magnetic Phase Transition with Regards to the Magnetocaloric Effect: the Hidden Relationship Between Hysteresis and Latent Heat

This article was published in the journal, Metallurgical and Materials Transactions E [Springer / © The Minerals, Metals & Materials Society and ASM International]. The final publication is available at Springer via http://dx.doi.org/10.1007/s40553-014-0015-8The magnetocaloric effect has seen a resurgence in interest over the last 20 years as a means towards an alternative energy efficient cooling method. This has resulted in a concerted effort to develop the so-called “giant” magnetocaloric materials with large entropy changes that often come at the expense of hysteretic behavior. But do the gains offset the disadvantages? In this paper, we review the relationship between the latent heat of several giant magnetocaloric systems and the associated magnetic field hysteresis. We quantify this relationship by the parameter Δμ 0 H/ΔS L, which describes the linear relationship between field hysteresis, Δμ 0 H, and entropy change due to latent heat, ΔS L. The general trends observed in these systems suggest that itinerant magnets appear to consistently show large ΔS L accompanied by small Δμ 0 H (Δμ 0 H/ΔS L = 0.02 ± 0.01 T/(J K−1 kg−1)), compared to local moment systems, which show significantly larger Δμ 0 H as ΔS L increases (Δμ 0 H/ΔS L = 0.14 ± 0.06 T/(J K−1 kg−1))