Priyanka Shukla

This book discusses the dynamical and rheological properties of high molecular weight entangled polymer melts, commonly known as viscoelastic subdiffusive fluids. Unlike dilute liquids, these materials exhibit molecular transport within a sublinear regime, meaning the timescale of diffusive transport is sublinear. The text emphasizes the potential of fractional calculus in modeling these fluids and introduces a novel fractional model to investigate regions of spatiotemporal instability in channel flows. At the microscale, the entanglement of polymer chains leads to localized, non-homogeneous regions with increased viscosity, which manifest as spatiotemporal macrostructures at the macroscale. To capture these macrostructures within the flow, direct numerical simulations are employed using a newly developed, physically realizable structure tensor, contributing to a deeper understanding of this complex class of fluids.

Modern grammar is basically a deliberate contrast with traditional grammar. It's related to, but different from, the difference between prescriptive and descriptive grammar. In the case of English, traditional grammar is ultimately Latin-based, because the first scholars understood Latin grammar and applied its principles to English. This worked fairly well, but only up to a point. Both are Indo-European but Latin is a romance language, while English is Germanic. Application of Latin rules also resulted in strange rules like "a preposition magically transforms into an adverb when it has no complement". They also just made mistakes generally.Modern grammar is scientific, so it is based on the corpus analysis. It's not in thrall to Latin grammar, and it's not afraid to throw traditional ideas away if there are simpler rules that can be used instead. In the case of our example about prepositions, we can permit one word prepositional phrases in English, and the awkward transformation into adverbs becomes unnecessary.