A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.     

A Plausible Simultaneous Synthesis of Amino Acids and Simple Peptides on the Primordial Earth

Following his seminal work in 1953, Stanley Miller conducted an experiment in 1958 to study the polymerization of amino acids under simulated early Earth conditions. In the experiment, Miller sparked a gas mixture of CH₄, NH₃, and H₂O, while intermittently adding the plausible prebiotic condensing reagent cyanamide. For unknown reasons, an analysis of the samples was not reported. We analyzed the archived samples for amino acids, dipeptides, and diketopiperazines by liquid chromatography, ion mobility spectrometry, and mass spectrometry. A dozen amino acids, 10 glycine‐containing dipeptides, and 3 glycine‐containing diketopiperazines were detected. Miller’s experiment was repeated and similar polymerization products were observed. Aqueous heating experiments indicate that Strecker synthesis intermediates play a key role in facilitating polymerization. These results highlight the potential importance of condensing reagents in generating diversity within the prebiotic chemical inventory.     

Maximal admissible faces and asymptotic bounds for the normal surface solution space

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system.To achieve these results we examine the layout of admissible points within these polytopes. We show that these points correspond to well-behaved substructures of the face lattice, and we study properties of the corresponding “admissible faces”. Key lemmata include upper bounds on the number of maximal admissible faces of each dimension, and a bijection between the maximal admissible faces in the two coordinate systems mentioned above.     

The Relationship Between Various Filter Notions on aGL-Monoid

The notion of a generalised filter is extended to the setting of aGL-monoid. It is shown that there exists a one-to-one correspondence between the collection of generalised filters on a setXand the collection of strongly stratifiedL-filters onX. Specialising to the case whereLis the closed unit interval [0, c] viewed as a Heyting algebra, we show that any strongly stratified [0, c]-filter onXcan be uniquely identified with a saturated filter onI^Xwith characteristic valuec. In this way, the notion of a generalised filter unifies various filter notions. In particular, necessity measures and finitely additive probability measures are specific examples of generalised filters.     

Fette, Wachse, Ceresin

Ohne Zusammenfassung     

A Convenient Preparation of Carboxylic Acid Anhydrides Using a “Supported” Phosphorus Pentoxide Reagent

Treatment of carboxylic acids with a “supported” phosphorus pentoxide reagent provides a convenient route to the corresponding anhydrides.