Hard competition: stabilizing the elusive biaxial nematic phase in suspensions of colloidal particles with extreme lengths

We use computer simulations to study the existence and stability of a biaxial nematic $N_b$ phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long ($L$), medium ($M$), and short ($S$) particle axis. For all three shape families, we find stable $N_b$ states provided the shape is not only close to the so-called dual shape with $M = \sqrt{LS}$ but also sufficiently anisotropic with $L/S>9,11,14, 23$ for rhombi, prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-$N_b$ transition does not occur in these systems due to a destabilization of $N_b$ by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small $L/S$, or by an intervening uniaxial nematic phase at large $L/S$. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.Comment: minor changes to the introduction, numbering of bibliography correcte

Martingales, endomorphisms, and covariant systems of operators in Hilbert space

We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant system in a Hilbert space of L^2-martingales. Our martingale construction depends on a prescribed set of transition probabilities, given by a non-negative function. Our main theorem describes the induced martingale systems completely. The applications of our theorem include wavelets, the dynamics defined by iterations of rational functions, and sub-shifts in symbolic dynamics. In the theory of wavelets, in the study of subshifts, in the analysis of Julia sets of rational maps of a complex variable, and, more generally, in the study of dynamical systems, we are faced with the problem of building a unitary operator from a mapping r in a compact metric space X. The space X may be a torus, or the state space of subshift dynamical systems, or a Julia set. While our motivation derives from some wavelet problems, we have in mind other applications as well; and the issues involving covariant operator systems may be of independent interest.Comment: 44 pages, LaTeX2e ("jotart" document class); v2: A few opening paragraphs were added to the paper; an addition where a bit of the history is explained, and where some more relevant papers are cited. Corrected a typographical error in Proposition 8.1. v3: A few minor additions: More motivation and explanations in the Intro; Remark 3.3 is new; and eleven relevant references/citations are added; v4: corrected and updated bibliography; v5: more bibliography updates and change of LaTeX document clas

Compatible systems of Galois representations associated to the exceptional group E6

We construct, over any CM field, compatible systems of l-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all l) algebraic monodromy groups equal to the exceptional group of type E6.Comment: bibliography fixed in new version. comments welcom

Problems of organizational structure in C3 systems

"March, 1982."Bibliography: p. 54.With: On modeling teams of interacting decisionmakers with bounded rationality / Alexander H. Levis, Kevin L. Boettcher. Cambridge, Mass. : Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, [1982]NASA Grant No. NAG1-2by Alexander H. Levis

Intramolecular Diels-Alder reactions of conformationally restricted systems

Bibliography: leaves 184-191.In the first phase of this investigation, the synthesis of triene systems, linked via a diester tether was investigated with the aim of studying the respective thermal Intramolecular Diels-Alder (IMDA) properties. It was envisaged that the diene and dienophile would be linked via a conformationally restricted spacer, trans-cyc1ohexane-l,2-dicarboxylic acid anhydride

Aspects of phosphorus nutrition in endomycorrhizal fungi of the Ericaceae

Bibliography: pages 133-144.An investigation was undertaken on the phosphorus nutrition of the ericoid endophytes isolated from the root systems of Vaccinium macrocarpon, Aiton, Rhododendron ponticum L., Calluna vulgaris (L.) Hull, Erica hispidula L., and E. mauritanica L

Applications Of The Rational Canonical Form Of Matrices To Systems Of First Order Linear Differential Equations With Constant Coefficients

The theory of matrices plays an integral role in applied and pur® mathematics. In recent years, matrices have become very essential in many different fields of study. They are used in applications in engineering, physics, economics, and many other fields. It is the purpose of this paper to use matrix theory to study systems of first-order linear differential equations with constant coefficients with respect to (l) existence of solution; (2) uniqueness of solution; and. (3) form of solutions. This study will have the following form: Chapter I will include some basic definitions and notations used in differential equations and matrix theory. Chapter II contains the basic theorems used. Chapter III will show the existence, uniqueness, and form of solutions. Chapter IV Includes applications of systems of first-order linear differential equations with constant coefficients and Chapter V gives the aumbry. The bibliography follows Chapter V

On the origin of the galaxy luminosity function

Evidence is summarized that suggests that when a protogalaxy collapses, a fraction $f$ of its gas fails to heat to the virial temperature, where $f$ is large for haloes less massive than the value $M^*$ associated with $L^*$ galaxies. Stars and galaxies form only from the cool gas fraction. Hot gas is ejected from low-mass systems as in conventional semi-analytic models of galaxy formation. In high-mass systems it is retained but does not cool and form stars. Instead it builds up as a largely inert atmosphere, in which cooling is inhibited by an episodically active galactic nucleus. Cold gas frequently falls into galactic haloes. In the absence of a dense atmosphere of virial-temperature gas it builds up on nearly circular orbits and forms stars. When there is a sufficiently dense hot atmosphere, cold infalling gas tends to be ablated and absorbed by the hot atmosphere before it can form stars. The picture nicely explains away the surfeit of high-luminosity galaxies that has recently plagued semi-analytic models of galaxy formation, replacing them by systems of moderate luminosity from old stars and large X-ray luminosities from hot gas.Comment: 5 pages. Version to appear in MNRAS Minor changes & corrected bibliography since first versio