An accelerated minimal gradient method with momentum for strictly convex quadratic optimization

BIT Numerical Mathematics - In this article we address the problem of minimizing a strictly convex quadratic function using a novel iterative method. The new algorithm is based on the well-known...     

Correspondence between de Saint-Venant and Boussinesq. 1: Birth of the Shallow–Water Equations

The Shallow–Water Equations (SWEs), also referred to as the de Saint-Venant equations, constitute the current governing mathematical tool for free-surface water flows. These include, e.g., flood flows in rivers and in urban zones, flows across hydraulic structures as dams or wastewater facilities, flows in the environmental fields, glaciology, or meteorology. Despite this attractiveness, the system of two partial differential equations has an exact mathematical solution only for a limited number of problems of practical relevance.This historical work on the SWEs is based on a correspondence between two 19th-century scientists, de Saint-Venant and Boussinesq. Their well-known papers are thus commented from the point of development of their theory; the input of both scientists is evidenced by their writings, and comments of both to each other that led to what is commonly known as the SWEs. Given the age difference of the two of 45 years, the experienced engineer de Saint-Venant, and the mathematician Boussinesq, two eminent researchers, met to discuss not only problems in hydraulics, but in physics generally. In addition, their correspondence embraced also questions in ethics, religion, history of sciences, and personal news.The results of the SWEs cease to hold if streamline curvature effects dominate; this includes breaking waves, solitary and cnoidal waves, or non-linear waves in general. In most other cases, however, the SWEs perfectly apply to typical flows in engineering practice; they are considered the fundamental system of equations describing open channel flows. This work thus provides a background to its birth, including lots of comments as to its improvement, physical meanings, methods of solution, and a discussion of the results. This paper also deals with the steady flow equations, gives a short account on the main persons mentioned in the Correspondence, and provides a summary of further developments of the SWEs until 1920.     

Crystal Chemistry of Ordered Rocksalt-Type SrCaNF

Journal of Chemical Crystallography - A new Group 2 bimetallic nitride fluoride phase of approximate composition SrCaNF has been prepared and characterized via high resolution single crystal X-ray...     

Glycopeptides by Linch-Pin C−H Activations for Peptide-Carbohydrate Conjugation by Manganese(I)-Catalysis

Late-stage C−H glycosylations of structurally complex amino acids and peptides were accomplished by means of racemization-free manganese(I)-catalyzed C−H activation. Thus, glycosylative modifications proved to be viable by a linch-pin approach, featuring chemo- and site-selective C−H transformations. The peptide–saccharide conjugation provided modular access to structurally complex glycopeptides, likewise enabling the assembly of fluorescent-labelled glycopeptides.     

Evaluation of Fe and Ru Pincer‐Type Complexes as Catalysts for the Racemization of Secondary Benzylic Alcohols

Fe and Ru pincer‐type catalysts are used for the racemization of benzylic alcohols. Racemization with the Fe catalyst was achieved within 30 minutes under mild reaction conditions, with a catalyst loading as low as 2 mol %. This reaction constitutes the first example of an iron‐catalyzed racemization of an alcohol. The efficiency for racemization of the Fe catalyst and its Ru analogue was evaluated for a wide range of sec‐benzylic alcohols. The commercially available Ru complex proved to be highly robust and even tolerated the presence of water in the reaction mixture.     

A Preorganized Hydrogen-Bonding Motif for the Molecular Recognition of Carbohydrates

The choice between adaptive and preorganized architectures, or of the most effective hydrogen bonding groups to be selected, are dilemmas that supramolecular chemists must address in designing synthetic receptors for such a challenging guest as carbohydrates. In this paper, structurally related architectures featuring two alternative hydrogen bonding motifs were compared to ascertain the structural and functional origin of their binding differences and the advantages that can be expected in monosaccharide recognition. A set of structurally related macrocyclic receptors were prepared, and their binding properties were measured by NMR and ITC techniques in chloroform vs a common saccharidic target, namely, the β-octyl glycoside of D-glucose. Results showed that the diaminocarbazolic motif, recently reported as the constituting unit of highly effective receptors for saccharides in water, is a superior hydrogen bonding motif compared to the previously described diaminopyrrolic motif, which was successfully employed in molecular recognition of carbohydrates in polar organic solvents, due to intrinsic structural and functional factors, rather than to hydrophobic contributions. In addition, the occurrence of a rare example of a thermodynamic template effect exerted by the beta-glucoside has been ascertained, enhancing the synthesis outcome of the otherwise low yielding preparation of the described macrocyclic receptors.     

Broadening the frequency bandwidth of a finite extensibility nonlinear vibration absorber by exploiting its internal resonances

Nonlinear Dynamics - In this paper, the dynamics response of a finite extensibility nonlinear elastic (FENE) absorber attached to a nonlinear primary system is investigated by writing the modal...     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.