Completing bases in four dimensions

Criteria for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given. This, in particular, has consequences for the task of ``completing'' one or more bases or contexts of a (hyper)graph: find a complete faithful orthogonal representation (aka coordinatization) of a hypergraph when only a coordinatization of the intertwining observables is known. In general indecomposability and thus physical entanglement and the encoding of relational properties by quantum states ``prevails'' and occurs more often than separability associated with well defined individual, separable states.

Vortex fluidics mediated non-covalent physical entanglement of tannic acid and gelatin for entrapment of nutrients

We have developed a simple process for the entrapment of nutrients in shear stress induced non-covalent physically entangled tannic acid-gelatin gel in a thin film vortex fluidic device (VFD) operating under continuous flow.

Hydrogel-Based Technologies for the Diagnosis of Skin Pathology

Hydrogels, swellable hydrophilic polymer networks fabricated through chemical cross-linking or physical entanglement are increasingly utilized in various biomedical applications over the past few decades. Hydrogel-based microparticles, dressings and microneedle patches have been explored to achieve safe, sustained and on-demand therapeutic purposes toward numerous skin pathologies, through incorporation of stimuli-responsive moieties and therapeutic agents. More recently, these platforms are expanded to fulfill the diagnostic and monitoring role. Herein, the development of hydrogel technology to achieve diagnosis and monitoring of pathological skin conditions are highlighted, with proteins, nucleic acids, metabolites, and reactive species employed as target biomarkers, among others. The scope of this review includes the characteristics of hydrogel materials, its fabrication procedures, examples of diagnostic studies, as well as discussion pertaining clinical translation of hydrogel systems.

ENTANGLED NETWORK INFLUENCED BY CARBON BLACK IN SOLUTION SBR VULCANIZATES REVEALED BY THEORY AND EXPERIMENT

ABSTRACT The contribution of carbon black (CB) on changes in cross-link density and physical entanglement has been quantified by swelling and uniaxial stress–strain measurements considering Mooney–Rivlin parameters. Solution SBR (SSBR) vulcanizates with varying content of high abrasion furnace (HAF) CB were studied. Rubber–filler networks increase the cross-link density values, which were determined by using Flory–Rehner and modified Guth–Gold equations by equilibrium swelling study. The Mooney–Rivlin parameter C1 was quantified using cross-link density, whereas parameter C2, representing physical entanglement, was determined for filled rubber by correlating with tensile results. The parameter C2 is monitored to be decreased with increasing CB (HAF) loading. A simple parabolic trend for physical entanglement parameter with increasing CB loading is proposed, and it shows a correlation coefficient of 0.99595. Atomic force microscopy study confirms the generation of filler networking in the rubber matrix. The current findings elucidate a way for quantifying physical network changes due to fillers in an unfilled rubber system.

Physical entanglement hydrogels: ultrahigh water content but good toughness and stretchability

Physical entanglement of polymer chains is an interaction that is believed to be too weak to build polymer networks for hydrogelation.

Cultivating Romance

This chapter demonstrates the nuances of plant metaphors in wedding and love poetry. Plant metaphors in love poetry praise beautiful youths by equating them with flowers threatened by the passage of time. Such threats are meant to be warnings to recalcitrant lovers. In the wedding discourse, flowers risk being violently destroyed and symbolize peaceful independence for female speakers. While floral metaphors do not permit safe interaction beyond aesthetic appreciation, vine metaphors emphasize physical entanglement and fruitful productivity. Accounts of nuptial productivity use imagery and terminology connected with fruit, not grain crops, which further distinguishes the discourse of the wedding ritual from the agricultural language of the marriage. Plant imagery at times alludes to specific literary predecessors, but may also refer to generally recognizable commonplaces that are part of a larger cultural matrix of natural symbols.

Absence of knots in known RNA structures

The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also, abound in viral DNA packaged inside bacteriophages. RNA molecules, however, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the several thousand RNA structures present in the Protein Data Bank (PDB). The search identified no more than three deeply knotted RNA molecules. These entries are rRNAs of about 3,000 nt solved by cryo-EM. Their genuine knotted state is, however, doubtful based on the detailed structural comparison with homologs of higher resolution, which are all unknotted. Compared with the case of proteins and viral DNA, the observed incidence of knots in available RNA structures is, therefore, practically negligible. This fact suggests that either evolutionary selection or thermodynamic and kinetic folding mechanisms act toward minimizing the entanglement of RNA to an extent that is unparalleled by other types of biomolecules. A possible general strategy for designing synthetic RNA sequences capable of self-tying in a twist-knot fold is finally proposed.

Sub-micron sized saccharide fibres via electrospinning

In this work, the production of continuous submicron diameter saccharide fibres is shown to be possible using the electrospinning process. The mechanism for the formation of electrospun polymer fibres is usually attributed to the physical entanglement of long molecular chains. The ability to electrospin continuous fibre from a low molecular weight saccharides was an unexpected phenomenon. The formation of sub-micron diameter “sugar syrup” fibres was observed in situ using highspeed video. The trajectory of the electrospun saccharide fibre was observed to follow that typical of electrospun polymers. Based on initial food grade glucose syrup tests, various solutions based on combinations of syrup components, i.e. mono-, di- and tri-saccharides, were investigated to map out materials and electrospinning conditions thatwould lead to the formation of fibre. Thiswork demonstrated that sucrose exhibits the highest propensity for fibre formation during electrospinning amongst the various types of saccharide solutions studied. The possibility of electrospinning low molecular weight saccharides into sub-micron fibres has implications for the electrospinability of supramolecular polymers and other biomaterials.