A Lie theoretic categorification of the coloured Jones polynomial

We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labelled by an arbitrary finite-dimensional representation. As a special case, we obtain a categorification of the coloured Jones polynomial of links.     

On the potentiality of a cluster-beam source to produce free-standing one-dimensional and two-dimensional FeAg nanostructures: mechanisms underlying their shape genesis

Controlling the morphology and composition of one-dimensional (1D) and two-dimensional (2D) assemblies of matter is essential to design and create nanostructures with exceptional material properties, for applications ranging from nanoelectronics to nanomedicine. Within this latter, a great interest is placed on assembling magnetoplasmonic nanostructures to enable multimodal biosensing and bioimaging for early diagnosis and prognosis of diseases. To date, the synthesis of such complex nanostructures is mostly relying on wet chemistry and templates. Herein, we employed a templateless physical method to generate FeAg-based anisotropic nanostructures, using a modified cluster source. Under tuned experimental conditions, we demonstrated the successful magnetic-assisted assembly of Fe nanoclusters (Fe NCs), to form stable and permanent branched Fe nanorods (Fe NRs), core@shell Fe@Ag-NRs, Fe nanosheets (Fe NSs), and Fe/Ag-NSs. This assembly is driven by the need to reduce their magnetic interaction energy on one hand and their overall surface energy on the other hand. When NCs and NRs are magnetically brought into intimate contact, they undergo a coalescence process, through the interfacial diffusion of the surface atoms, resulting in the formation of 1D and 2D nanostructures. For Fe@Ag NRs, the advantage conferred by the Ag shell is to protect Fe NRs from oxidation and prevent them from aggregation at the same time. The observed contrast reversal in Scanning Electron Microscopy (SEM) images of Fe NRs and Fe NSs is discussed.     

A Method for Determining Model‐Structure Errors and for Locating Damage in Vibrating Systems

A method is proposed for the determination of natural frequencies and mode shapes of a system which is constrained so that unknown stiffnesses are replaced by rigid connections. The constraint is not imposed physically but only in mathematics so that the behaviour of the constrained system is inferred from the unconstrained measurements. Since stiffnesses which are made rigid cannot experience any elastic strain they can have no effect on the inferred measurements. A procedure for comparing the inferred measurements with similarly constrained finite element predictions can be used to determine modelstructure errors. Damage, such as a crack in a beam, can be located by comparing the inferred measurements from the structure in its undamaged and current states. It is demonstrated how unmeasured rotations may be constrained by using rigidbody modes and a reduction/expansion transformation from a finite element model.Sommario. Viene proposto un metodo per la determinazione delle frequenze proprie e dei modi di vibrazione di un sistema vincolato in modo tale che alcuni elementi elastici siano sostituiti da collegamenti rigidi. Il vincolo non viene imposto fisicamente, ma solo matematicamente, e pertanto il comportamento del sistema vincolato viene dedotto dalle misure sul sistema non vincolato. Poiché gli elementi che sono resi rigidi non possono subire alcuna deformazione elastica, essi non hanno certamente alcun effetto sulle misure dedotte per il sistema vincolato. Una procedura che mette a confronto le misure dedotte per il sistema vincolato con le previsioni fornite da un modello ad elementi finiti con analoghi vincoli, può essere utilizzata per determinare errori nella struttura del modello. Danni del tipo di una cricca su una trave possono essere localizzati confrontando le misure dedotte – per sistemi analogamente vincolati – da quelle effettuate sulla struttura non danneggiata e sulla struttura danneggiata. Si dimostra come si possono imporre vincoli sulle rotazioni (non misurate) utilizzando i modi di corpo rigido dell'elemento e una tecnica di riduzione/espansione dei gradi di libertà di un modello ad elementi finiti.     

Basic formulation of static and dynamic behaviours of soil and other porous media

This paper treats the soil and rock or concrete as a two-phase medium composed of a solid skeleton and an interstitial fluid. Under the unsaturated condition of interstitial fluid, the third phase is taken into consideration. In this paper, we consider the constitutive relation, dynamic and kinematic relations, and also various approximations with their limits of validity, including those of most practical engineering situations such as the consolidation problem and the undrained behaviour. The finite element discretization and the time dependent solution of various classes of soil problem are also discussed.     

Effects of sound on flow separation from blunt flat plates

The effect of sound on the flow around plates with semicircular or square leading edges and square trailing edges located in a low turbulence open jet has been studied. In all circumstances the length of the leading edge separation bubbles associated with square leading edge plates was found to oscillate. When sound was applied to the flow around these plates, the leading edge shear layers reattached closer to the leading edge and the oscillations in bubble length occurred at the applied sound frequency, generating patches of concentrated vorticity in the boundary layers. These vorticity patches moved downstream near the plate surface and then beyond the trailing edge to form vortex cores in a street with a Strouhal number equal to the applied sound value. Sometimes these vortex streets are unstable and break down into streets with Strouhal numbers approaching those observed without sound. These effects of sound were not observed in the flow around plates with semicircular leading edges. Without sound, square leading edge plates of intermediate length did not shed regular vortex streets.     

Flocculation and rheology of kaolinite/quartz suspensions

Rheological properties of suspensions of Na-kaolinite and colloidal quartz (Min-U-Sil) at constant overall volume concentration of 2% are determined with a Weissenberg Rheogoniometer using a combined Couette and cone-and-plate geometry. The results are interpreted in terms of the flocculation behaviour of the constituent particles in the presence of high salt concentrations (0.1–0.75m NaCl) at pH 6, 7 and 8. In these chemical environments these suspensions are pseudoplastic for much of the range of mixture compositions becoming Newtonian for suspensions containing only quartz. These properties reflect the dominant influence of interactions between kaolinite particles on the flocculation behaviour of the mixture.Nomenclature a ₁, a₂ radii of spheres - A Hamaker constant - b radius of cylinder - C volumetric solids concentration - e ₀ electronic charge - H ₀ shortest distance between surfaces - I ionic strength - J collision frequency per unit volume - k Boltzmann constant - l length of cylinder - m number in eq. (2) - N particle number concentration - S (H ₀ + b)/b in eq. (4) - T absolute temperature - U electrophoretic mobility - V _A van der Waals attractive energy - V _R coulombic energy - V _T total energy of interaction - X H ₀/2a₁ in eq. (5) - Y a ₂/a₁ in eq. (5) - thickness of plate - shear rate - permittivity - zeta potential - k Debye-Hückel parameter - µ dynamic viscosity - µ _pl plastic viscosity - v valency of counter ion - shear stress - _B Bingham stress - ₁, ₂ dimensionless potentials - ₁, ₂ surface potentials     

Time studies of ionization processes

Summary Measurements of the temporal growth of ionization between parallel plane electrodes in hydrogen have been made. The results show that for low values ( 40 V/cm mm Hg) of the ratio of electric fieldE to gas pressurep the growth times can be short ( 1s for over-voltages V 1 %) while at values ofE/p 300 V/cm mm Hg the times are of the order of milli seconds withV 5%. Comparison of the experimental data with Davidson's mathematical analysis of current growth based upon the action of primary and secondary ionization processes shows that the relative significance of the possible secondary processes changes asE/p is altered. For the low values ofE/p, the predominant secondary process contributing to the growth was found to be photoelectric emission from the cathode, but with increasing values ofE/p the role of positive ion interaction with the cathode becomes increasingly important. No single secondary process was exclusively operating in any of the conditions examined.     

Low-level flow-induced acoustic resonances in ducts

Acoustic resonances are generated by air moving past a plate with a semi-circular leading edge located in a duct. The sound stimulates the small separation bubble near the leading edge to shed vortices into the boundary layer at the sound frequency. The acoustic energy required to sustain the resonances is generated as these vortices pass the trailing edge of the plate.