An analytical expression for the electron tunneling time has been derived for symmetrical rectangular double-barrier structures. It gives values of the tunneling time equal to those calculated by the dwell time method for the resonant tunneling state. The obtained tunneling time is given by the sum of the time connected with the barrier layer width and the time connected with the well layer width. Moreover, the derived equation may lead to an approximate tunneling time for an off-resonance state.
From dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS) measurements, the aspect ratio f of twotypesofTEMPO-oxidizednanocellulose(TOCN)withdifferentfiberlengthswasquantitativelycalculated.Asaresult, the aspect ratios fofthenormallengthN-typeandtheshortfiberlengthS-typewere243and77,respectively.Rheologicalanalysiswascarriedoutinthedilutedtosemi-diluteconcentrationregionsoftwotypesofTOCNaqueoussuspensions.TheviscosityofsuspensionsincreasedlinearlywithTOCNconcentrationinthediluteregion,butin-creasedexponentiallyabovethecriticalconcentrationC * .BothC * andintrinsicviscosity[η]canbedescribedasafunction of f, which is in agreement with those of Tanaka et al. Furthermore, storage modulus G′ in the semi-dilute region showed anelasticgelwithaquasi-flatelasticmodulusG p ′independentoffrequency.SinceG p ′isproportionaltotheTOCNcon-centrationraisedtothepowerof1.9-2.3,wespeculatethatthedevelopmentofelasticityisduetotheentanglementbetweennanofibers.However,S-typeG p ′increasedsharplywithTOCNconcentrationexceeded1.5wt%,deviatingfromthe powerlaw.Thisseemstosuggestthatthereisanewelasticmechanismotherthanentanglement.
This paper reports strain and frequency dependencies of dynamic viscoelasticity of commercial plain yoghurts and trial foods for swallowing disorders. We prepared four test samples adjusting hardness to a level similar to that of commercial plain yoghurts. Guar gum and modified starch were used as ingredients for preparation of two samples, respectively. Commercial plain yoghurts and modified starch samples exhibited viscoelastic behaviors strongly dependent on shear, while they behaved as nearly elastic material in the linear viscoelastic region. These properties are shown to be consistent to the swallowing mechanism to which well organized cooperative motions of several organs are related. Viscoelastic properties of guar gum samples were found to be quite different from those of commercial plain yoghurts, which suggests that modified starch is a better ingredient than guar gum for preparation of test samples and for detailed research on swallowing disorders.
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