Geometric characterizations of centroids of simplices

We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.     

The thermal decomposition of peroxyacetic nitric anhydride (PAN) and peroxymethacrylic nitric anhydride (MPAN)

The rate coefficients of thermal decomposition of peroxyacetic nitric anhydride (PAN) and peroxymethacrylic nitric anhydride (MPAN) were measured over the temperature range 302–323 K. The resulting Arrhenius expressions were k = 10^17.4±0.4 exp(?28.5 ± 0.5/RT) for PAN, and k = 10^16.2±0.7 exp(?26.8 ± 1.0/RT) for MPAN, where the activation energy is in Kcal/mol. These results are in good agreement with previous studies of PAN and other PAN-type compounds, and imply that energies of RC(O)OO? NO₂ bonds are relatively independent of the nature of R.     

Time resolved measurements of the flow generated by suction feeding fish

The majority of aquatic vertebrates are suction feeders: by rapidly expanding the mouth cavity they generate a fluid flow outside of their head in order to draw prey into their mouth. In addition to the biological relevance, the generated flow field is interesting fluid mechanically as it incorporates high velocities, is localized in front of the mouth, and is unsteady, typically lasting between 10 and 50 ms. Using manometry and high-speed particle image velocimetry, this is the first study to quantify pressure within and outside the mouth of a feeding fish while simultaneously measuring the velocity field outside the mouth. Measurements with a high temporal (2 ms) and spatial (<1 mm) resolution were made for several feeding events of a single largemouth bass (Micropterus salmoides). General properties of the flow were evaluated, including the transient velocity field, its relationship to pressure within the mouth and pressure at the prey. We find that throughout the feeding event a relationship exists for the magnitude of fluid speed as a function of distance from the predator mouth that is based on scaling the velocity field according to the size of the mouth opening and the magnitude of fluid speed at the mouth. The velocity field is concentrated within an area extending approximately one mouth diameter from the fish and the generated pressure field is even more local to the mouth aperture. Although peak suction pressures measured inside the mouth were slightly larger than those that were predicted using the equations of motion, we find that these equations give a very accurate prediction of the timing of peak pressure, so long as the unsteady nature of the flow is included.     

Chaotic vibrations of a beam with non-linear boundary conditions

Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force. The beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value. The stiffness of the beam has the properties of a bi-linear spring. The results may be typical of a class of mechanical oscillators with play or amplitude constraining stops. Subharmonic oscillations are found to be characteristic of these types of motions. For certain values of forcing frequency and amplitude the periodic motion becomes unstable and nonperiodic bounded vibrations result. These chaotic motions have a narrow band spectrum of frequency components near the subharmonic frequencies. Digital simulation of a single mode mathematical model of the beam using a Runge-Kutta algorithm is shown to give results qualitatively similar to experimental observations.     

Selective Alkylation of C‐Rich Bulge Motifs in Nucleic Acids by Quinone Methide Derivatives

A quinone methide precursor featuring a bis‐cyclen anchoring moiety has been synthesized and its capacity to alkylate oligonucleotide targets quantified in the presence and absence of divalent metal ions (Zn²⁺, Ni²⁺ and Cd²⁺). The oligonucleotides were designed for testing the sequence and secondary structure specificity of the reaction. Gel electrophoretic analysis revealed predominant alkylation of C‐rich bulges, regardless of the presence of divalent metal ions or even the bis‐cyclen anchor. This C‐selectivity appears to be an intrinsic property of the quinone methide electrophile as reflected by its reaction with an equimolar mixture of the 2′‐deoxynucleosides. Only dA‐N1 and dC‐N3 alkylation products were detected initially and only the dC adduct persisted for detection under conditions of the gel electrophoretic analysis.