Free Vibration Analysis of Rotating Nonlinearly Elastic Structures with Symmetry: An Efficient Group-Equivariance Approach

A study is made of the dynamics of oscillating systems with a slowly varying parameter. A slowly varying forcing periodically crosses a critical value corresponding to a pitchfork bifurcation. The instantaneous phase portrait exhibits a centre when the forcing does not exceed the critical value, and a saddle and two centres with an associated double homoclinic loop separatrix beyond this value. The aim of this study is to construct a Poincaré map in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. For that purpose averaging methods and asymptotic matching techniques connecting local solutions are applied. Given the initial state and the values of the parameters the properties of the Poincaré map can be studied. Both sensitive dependence on initial conditions and (quasi) periodicity are observed. Moreover, Lyapunov exponents are computed. The asymptotic expressions for the Poincaré map are compared with numerical solutions of the full system that includes small damping.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

The Quantum Double Model with Boundary: Condensations and Symmetries

Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to the boundary. We then consider two phases of the quantum double model corresponding to two groups with a domain wall between them, and study the tunneling of anyons from one phase to the other. Using this framework we discuss the necessary and sufficient conditions when two different groups give the same anyon types. As an application we show that in the quantum double model for S ₃ (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. This group is indeed a special case of groups of the form of the semidirect product of the additive and multiplicative groups of a finite field, for all of which we prove a similar symmetry.     

On H-Linked Graphs

For a fixed multigraph H, possibly containing loops, with V(H)={h₁, . . . , h_k}, we say a graph G is H-linked if for every choice of k vertices v₁, . . . , v_k in G, there exists a subdivision of H in G such that v_i represents h_i (for all i). This notion clearly generalizes the concept of k-linked graphs (as well as other properties). In this paper we determine, for a connected multigraph H and for any sufficiently large graph G, a sharp lower bound on δ(G) (depending upon H) such that G is H-linked.     

Subdivision Extendibility

Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V(G) (the ground set) the image of V(H) under the isomorphism. We consider connectivity and minimum degree or degree sum conditions sufficient to imply there is a spanning subgraph of G isomorphic to a subdivision of H on the same ground set S. These results generalize a number of theorems in the literature.     

Die thermodynamischen Eizenschaften von Wasser, das an Quarz adsorbiert ist

Ohne Zusammenfassung     

Fast-neutron total and scattering cross sections of58Ni

Neutron total cross sections of⁵⁸Ni were measured at 25 keV intervals from 0.9 to 4.5 MeV with 50–100 keV resolutions. Attention was given to self-shielding corrections to the observed total cross sections. Differential elastic- and inelastic-scattering cross sections were measured at 50 keV intervals from 1.35 to 4.0 MeV with 50–100 keV resolutions. Inelastic excitation of levels at 1.458±0.009, 2.462+-0.010, 2.791±0.015, 2.927+-0.012 and 3.059+-0.025 MeV was observed. The experimental results were interpreted in terms of optical-statistical and coupled-channels models.     

Hydrogen bonding incis-2,3-epoxycyclooctanol

Hydrogen bonding and the electron-withdrawing or electron-donating characteristics of substituent groups that are neighboring to epoxide groups can affect the reactivity of the epoxide ring. The crystal structure ofcis-2,3-epoxycyclooctanol has been determined as a saturated eight-membered ring compound in which a hydroxyl group is attached to the C(1) atom that is adjacent to a 2,3-fused epoxy ring. The findings are that the longer epoxide C-O bond (and hence the one expected to be more readily broken) is the one farther from the hydroxyl group [1.462(1) å versus 1.447(1) å] and that the optimal hydrogen bonding is to an adjacent molecule radier than within the molecule. The shortest C-C bond is that of the epoxide group; the bond adjacent to it (on the side farther from the hydroxyl group) is the next shortest.     

Controlled ventilation during NMR spectroscopic studies: hemodynamic and biochemical consequences

The effects of different ventilation methods on cardiac output measured by the indicator-dilution method, liver blood flow measured by a deuterium washout technique using 2H nuclear magnetic resonance (NMR) and liver concentrations of ATP and intracellular pH determined with 31P NMR were compared in anesthetized rats. No differences in mean arterial blood pressure were demonstrable with the different modes of ventilation. However, significant drops in cardiac output were observed between freely breathing and animals ventilated with positive pressure but not the high frequency oscillatory method (407 +/- 46 and 520 +/- 88 vs. 633 +/- 86 ml/min/kg, p less than 0.05 and p = NS, respectively). Moreover, liver blood flow was significantly reduced during positive pressure but not high frequency oscillatory ventilation compared with free breathing rats (32 +/- 4 and 43 +/- 10 vs. 46 +/- 8 ml/100 g, p less than 0.05 and p = NS, respectively). 31P NMR spectroscopy revealed no effects of either ventilation method on tissue ATP or intracellular pH as estimated by the chemical shift of inorganic phosphate. These data suggest that controlled ventilation in normal rats accomplished with standard positive pressure methods is associated with major decreases in cardiac output and liver blood flow despite maintenance of normal blood pressure. High frequency oscillatory ventilation appears to effect less compromise of cardiac output and hepatic perfusion than positive pressure ventilation and may, therefore, be preferable for some biological studies.     

Molecular mechanisms of visual excitation: A concatenation of nonlinear cellular processes

The mechanism of transduction in the photoreceptor remains the least understood link in the chain of molecular and cellular processes that are responsible for vision. This paper reviews the molecular species and processes involved in the absorption of light and subsequent biochemical responses of the photoreceptor cell. The cells' electrical response and the probable ionic basis of the response are described. We develop the outlines of a mechanistic model that attempts to link biochemical and electrophysiological responses of photoreceptors of the vertebrate retina.