Teaching topics in numerical linear algebra using spreadsheets

The argument is advanced that spreadsheet programs operating on microcomputers have a significant role to play in the teaching of numerical analysis. They offer a simple and direct means of programming numerical computations which is more powerful than a pocket calculator but quicker and more flexible than conventional high level language programming. In addition the spreadsheet concepts offers significant pedagogical advantages in the exploration of numerical methods. The argument is illustrated using some examples drawn from the field of numerical linear algebra.     

A theoretical investigation of the binding of TiCln to MgCl2

The structure of the (0 0 0 1) surface of the -MgCl₂ crystal has been investigated using DFT-GGA periodic calculations. The calculated surface relaxation is in agreement with LEED measurements. Motivated for the use of MgCl₂ as support for the Ziegler–Natta reaction, we have studied the adsorption of the catalyst (titanium chlorides as monomers or dimers) on the (1 0 0) and (1 1 0) MgCl₂ surfaces. The structures of adsorbed species are close to those previously found on cluster models: bridging chlorine atoms connect the Ti to the Mg atoms and the systems remain in high spin states. The (0 0 0 1) surface is the most stable face of the -MgCl₂ crystal; however it is Cl-terminated and henceforth poorly reactive; it had been suggested to deposit metallic Mg in order to improve its reactivity. Our modelling explains the failure of this tentative; the interaction between the deposited metal and the surface is repulsive and uncharged Mg atom does not bind.     

Adiabatic calorimetry of the metallomesogen purple cobalt stearate Co(O2CC17H35)2

The heat capacity of the metallomesogen purple cobalt stearate Co(O₂CC₁₇H₃₅)₂ has been measured by adiabatic calorimetry at temperatures between 16 and 420?K. This compound exhibits two crystalline phases (low temperature Cr2 and high temperature Cr1 phases), mesophase (M phase), and isotropic liquid (I phase). A third crystalline phase Cr3, which is entirely metastable with respect to all the others, is suggested by DSC studies. The Cr2-to-Cr1, Cr1-to-M, and M-to-I phase transitions occurred at 362.1, 380.9, and 400.4?K, respectively. The enthalpy and entropy gains at these phase transitions were determined. The mesophase is either smectic A or nematic.     

Cation-deficient lanthanum manganite oxides: Experimental and theoretical studies

Cation-deficient lanthanum manganite oxides with 0.8 ≤ La/Mn ≤ 1.25 were synthesized using a multi-step decomposition of gel precursors and investigated from experimental and theoretical point of view. The XRD (X-Ray Diffraction) analysis of the mixed LaMnO₃ oxide crystal concludes to a hexagonal structure, space group R-3c, excluding the presence of pure oxides such as La₂O₃, Mn₂O₃, or MnO₂ whatever the ratio La/Mn is. Oxides with nominal formulae La_1?xMnO_3+y and LaMn_1?x′O_3+y contain more than one defect structure involving valence defect (holes h), anionic vacancies as well as cationic vacancies in A and B sublattices of the perovskite structure. With the increase of La or Mn non-stoichiometry, the oxygen content y decreases more with La-deficient compositions than with Mn-deficient ones. The La/Mn ratio influences strongly the relationship between [h], [V_O], [V_La^?] and [V_Mn^?].The DFT-GGA (Density functional Theory, Generalized-Gradient Approximation) simulation of these compounds using VASP (Vienna Ab-initio Simulation Package) concludes that the electronic structure for the optimized stoichiometric La₆Mn₆O₁₈ is not optimal, relative to that expected considering Mn(III) ions with four alpha electrons each. The non-stoichiometry is the easiest way of reducing the Jahn–Teller instability by depopulating the half-filled e_g orbitals. A partial oxidation is then stabilizing. Creation of defects, either an O insertion or a cationic vacancy, allows finding an ideal count. In the case of pure cationic defects (missing a La(III) or a Mn(III) cation), the amount of vacancies is one missing cation upon twelve. The compact nature of lanthanum manganite oxide does not allow oxygen insertion within the bulk structure and oxidation can only be achieved at the surface without O penetration. The formation of antisites is endothermic. The creation of mixed vicinal vacancies, one oxygen and one cationic vacancy (La or Mn), is exothermic for a concentration of defects of one defect per twelve cations.     

Increasing the detection speed of an all-electronic real-time biosensor

Biosensor response time, which depends sensitively on the transport of biomolecules to the sensor surface, is a critical concern for future biosensor applications. We have fabricated carbon nanotube field-effect transistor biosensors and quantified protein binding rates onto these nanoelectronic sensors. Using this experimental platform we test the effectiveness of a protein repellent coating designed to enhance protein flux to the all-electronic real-time biosensor. We observe a 2.5-fold increase in the initial protein flux to the sensor when upstream binding sites are blocked. Mass transport modelling is used to calculate the maximal flux enhancement that is possible with this strategy. Our results demonstrate a new methodology for characterizing nanoelectronic biosensor performance, and demonstrate a mass transport optimization strategy that is applicable to a wide range of microfluidic based biosensors.