A multigrid perspective on the parallel full approximation scheme in space and time

For the numerical solution of time‐dependent partial differential equations, time‐parallel methods have recently been shown to provide a promising way to extend prevailing strong‐scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and benchmarks. However, a solid and reliable mathematical foundation is still missing. We show that, under certain assumptions, the PFASST algorithm can be conveniently and rigorously described as a multigrid‐in‐time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using blockwise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type.     

Soliton experiments in stimulated Raman scattering

Experimental observations of solitons in stimulated Raman scattering are reported. Soliton formation resulted from the introduction of a phase shift in the incident Stokes beam as predicted by theory. Pulse sharpening and retardation on propagation in the Raman medium have been observed along with amplitude diminution. The first two features were predicted and the third was not. Spontaneous soliton formation has been observed in the absense of any amplitude modulation or apparent phase shift in the optical fields, indicating that additional sets of initial conditions may result in soliton formation.Work performed under the auspices of the U.S. Department of Energy.     

On the gap problem for the sequence ∥mβ∥

We discuss the gap problem for the sequence m used in our previous Letter (D. H. Mayer, Lett. Math. Phys. 16, 139–143 (1988)).     

Synthesis and NMR Analysis in Solution of Oligo(3‐hydroxyalkanoic acid) Derivatives with the Side Chains of Alanine,Valine, and Leucine (β‐Depsides): Coming Full Circle from PHB to β‐Peptides to PHB

Oligomers of 3‐hydroxyalkanoic acids that contain two, three, and six residues with and without O‐terminal (tBu)Ph₂Si and C‐terminal PhCH₂ protection have been synthesized in such a way that the side chains on the oligoester backbone were those of the proteinogenic amino acids Ala (Me), Val (CHMe₂), and Leu (CH₂CHMe₂). The enantiomerically pure 3‐hydroxyalkanoates were obtained by Noyori hydrogenation of the corresponding 3‐oxo‐alkanoates with [Ru((R)‐binap)Cl₂](binap=2,2′bis(diphenylphosphanyl)‐1,1′‐binaphthalene)/H₂ (Scheme 1), and the coupling was achieved under the conditions (pyridine/(COCl)₂, CH₂Cl₂, −78°) previously employed for the synthesis of various oligo(3‐hydroxybutanoic acids) (Schemes 2 and 3). The Cotton effects in the CD spectra of the new oligoesters provided no hints about chiral conformation (cf. a helix) in MeOH, MeCN, octan‐1‐ol, or CF₃CH₂OH solutions (Figs. 1 and 2). Detailed NMR investigations in CDCl₃ solution (Figs. 3–6, and Tables 1–5) of the hexa(3‐hydroxyalkanoic acid) with the side chains of Val (HC), Ala (HB), Leu (HH), Val, Ala, Leu (from O‐ to C‐terminus; 3 ) gave, on the NMR time‐scale, no evidence for the presence of any significant amount of a 2₁‐ or a 3₁‐helical conformation, comparable to those identified in stretched fibers of poly[(R)‐3‐hydroxybutanoic acid], or in lamellar crystallites and in single crystals of linear and cyclic oligo[(R)‐3‐hydroxybutanoic acids], or in the corresponding β‐peptide(s) (the oligo(3‐aminoalkanoic acid) analogs; 1 – 3 ). Thus, the extremely high flexibility (averaged or ‘random‐coil' conformation) of the polyester chain (CO−O rotational barrier ca. 13 kcal/mol; no hydrogen bonding), as compared to polyamide chains (CO−NH barrier ca. 18 kcal/mol; hydrogen bonding) has been demonstrated once again. The possible importance of this structural flexibility, which goes along with amphiphilic properties, for the role of PHB in biology, in evolution, and in prebiotic chemistry is discussed. Structural similarities of natural potassium‐channeling proteins and complexes of oligo(3‐hydroxybutanoates) with Na⁺, K⁺, or Ba²⁺ are alluded to (Figs. 7–9).     

Mechanical Properties of Bacterially Synthesized Nanocellulose Hydrogels

The mechanical characteristics of bacterially synthesized nano-cellulose (BNC) were studied with uniaxial compression and tensile tests. Compressive loads result in a release of water and the deformation of the water-saturated network corresponds approximately to the volume of released water. The BNC hydrogel exhibits a mainly viscous response under compression. The strain response under tensile loads has an elastic and a viscous component. This can be described with a Maxwell model, where the viscosity is strain rate-dependent. When the aqueous phase of the BNC hydrogel is stabilized with an additional alginate hydrogel matrix, the system exhibits an elastic response under compressive loads. The analysis of the ‘alginated’ BNC network with the Maxwell model shows that the alginate matrix increases the viscosity of the composite system. The results of the mechanical tests show that the water absorbed in the BNC hydrogel strongly influences its mechanical behavior.