Maximal proper acceleration and the structure of spacetime

A limiting proper acceleration in nature follows deductively from known physics and compels the union of spacetime and four-velocity space into a maximal-acceleration invariant phase space having an intrinsic Kaluza-Klein-type fiber-bundle structure with manifest gauge properties. The Riemann curvature scalar of the bundle manifold is determined, and a possible action principle is considered to serve as a basis for the generation of field equations.1. This is an expanded version of an invited paper presented at the Fifth Marcel Grossmann Meeting at the University of Western Australia, 8–12 August 1988.     

Free Energy as a Geometric Invariant

The free energy plays a fundamental role in statistical and condensed matter physics. A related notion of free energy plays an important role in the study of hyperbolic dynamical systems. In this paper we introduce and study a natural notion of free energy for surfaces with variable negative curvature. This geometric free energy encodes a new type of marked length spectrum of closed geodesics, which lies between the well-known marked length spectrum (marked by the corresponding element of the fundamental group) and the unmarked length spectrum. We prove that the free energy parametrizes the boundary of the domain of convergence of a Poincaré series which also encodes this spectrum. We also show that this new length spectrum, or equivalently the geometric free energy, is not an isometry invariant. In the final section we use tools from multifractal analysis to effect a fine asymptotic comparison of word length and geodesic length of closed geodesics. We hope that our geometric understanding of free energy will provide new insight into this fundamental physical and dynamical quantity. The work of the second author was partially supported by a National Science Foundation grant DMS-0355180. This work was completed during a visit by the first author to Penn State as a Shapiro Fellow.     

Crystallization in organo-mineral micro-domains in the crossed-lamellar layer of Nerita undata (Gastropoda, Neritopsina)

Crossed-lamellar shell microstructure consists of a sophisticated arrangement of interspersed lamellae, which is very commonly found in Gastropoda or Bivalvia shell layers. Its smallest constitutive microstructural units are usually described as sub-micrometric fibers, or rods, and form very ordered and regular patterns. Atomic force microscopy (AFM) and transmission electron microscopy (TEM) imaging confirms the presence of even smaller building units in the form of organo-mineral granules, and we further investigate their internal structure within aragonite crossed-lamellar internal layer of Nerita undata (Gastropoda, Neritopsina) shell. Their coalescence may have controlled anisotropically the propagation of the crystallographic coherence through this complex microstructure, as suggested by the propagation of the microtwinning pattern between neighboring granules.     

An LX-10 kinetic model calibrated using simulations of multiple small-scale thermal safety tests

A new chemical kinetic model for the beta-delta transition and decomposition of LX-10 (95% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, 5% Viton A binder) is presented here. This model implements aspects of previous kinetic models but calibrates the model parameters to data sets of three experiments: differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and one-dimensional time to explosion (ODTX). The calibration procedure contains three stages: one stage uses open-pan DSC and TGA to develop a base reaction for formation of heavy gases, a second stage features closed-pan DSC to ascertain the autocatalytic behavior of reactant gases attacking the solid explosive, and a final stage adjusts the rate for the breakdown of heavy reactant gases using ODTX experimental data. The resultant model presents a large improvement in the agreement between simulated DSC and TGA results and their respective experiments while maintaining the same level of agreement with ODTX, scaled thermal explosion, and laser heating explosion times when compared to previous models.     

Confocal microscopy study of uptake kinetics of α‐lactalbumin and β‐lactoglobulin onto the cation‐exchanger SP Sepharose FF

Confocal laser scanning microscopy (CLSM) was used to study single‐ and two‐component protein uptake for α‐lactalbumin (ALA) and β‐lactoglobulin (BLG), as models for whey proteins, to SP Sepharose FF at pH 3.7 during batch experiments in a finite bath. By coupling a fluorescent dye with the protein molecule, the penetration into individual adsorbent particles at different times during batch uptake was visualised. In a single‐component system, BLG penetrated fast into the adsorbent beads and gradually filled them in a shell‐wise fashion, while adsorption of ALA was mostly confined to the outer shells of the adsorbent. For the two‐component studies, the results showed that ALA was able to displace BLG despite its lower affinity to the adsorbent under the employed conditions. CLSM results were then compared both qualitatively and quantitatively to their counterparts obtained in traditional experiments by indirect measurements of the protein concentration in the fluid phase. A novel quantitative approach was undertaken by modifying the simple kinetic rate model traditionally used to determine the kinetic rate constant, k₁, for batch uptake experiments, in order to describe batch uptake kinetics based on CLSM data. Although BLG results were in good agreement, there was a discrepancy in ALA results.     

Organic chemistry of dinitrogen and related ligands. Part 2. Non-radical acylation of ligating dinitrogen

Summary Ligating dinitrogen, in the complexes,trans-M(N₂)₂(Ph₂PCH₂CH₂PPh₂)₂ (where M=Mo or W) may be acylated by trifluoroacetic anhydride, to give trifluoroacetyldiazenido complexes in high yield. Unlike corresponding reactions with acyl halides, trifluoroacetylation proceeds under nonradical conditions, and a mechanism analogous to that of protonation is suggested.Dinitrogen-derived ligands may also be acylated by (CF₃CO)₂O, so that the methyldiazenido ligand is converted into a methyl (trifluoroacetyl) hydrazido (2-) ligand, and the acetyldiazenido ligand undergoes transacylation to give a trifluoroacetyl diazenido derivative.New complexes were characterised by i.r.,¹⁹F and¹H n.m.r. spectra, and by elemental analysis.Part 1 is ref. 10     

Efficient method for the synthesis of chiral pyrrolidine derivatives via ring-closing enyne metathesis reaction

[reaction: see text] A series of new pyrrolidine derivatives were prepared directly in very good yields, from the substrates containing a basic or nucleophilic N atom via ring-closing enyne metathesis reaction under mild reaction conditions. Moreover, the reaction occurs smoothly without the presence of ethylene gas.