Design problem solved by optimal control theory

In this paper we present an application to airfoil design of an optimum design method based on optimal control theory. The method used here transforms the design problem by way of a change of variable into an optimal control problem for a distributed system with Neumann boundary control. This results in a set of variational inequalities which is solved by adding a penalty term to the differential equation. This is in turn solved by a finite element method.     

Motion by mean curvature by scaling a nonlocal equation: Convergence at all times in the two-dimensional case

The convergence to a motion by mean curvature by diffusively scaling a nonlocal evolution equation, describing the macroscopic behavior of a ferromagnetic spin system with Kac interaction and Glauber dynamics has recently been proved. The convergence is proven up to the times when the motion by curvature is regular. Here we show the convergence at all times in the two-dimensional case. Since, in this case, the only singularity is the shrinking to a point of a closed curve, we verify that the curve actually disappears past the singularity.     

Mössbauer study of elemental substitution in Nd18Fe76B6 alloy

Fe-rich Nd-Fe-B permanent magnetic materials are of great technological interest because of their superior magnetic properties such as coercivity and large energy products. These properties can be further enhanced by the substitution of Nd or Fe. We are presenting the results of atomic replacement of iron by Ga, Dy, Nb and Si, in the base material N₁₈Fe_{7 6}B₆, obtained by Mössbauer spectroscopy. It is observed that the net magnetization decreases for all compositions with the substitution of these elements.     

Cation distribution in Ni-substituted Mn-ferrites by Mössbauer technique

The neutron spectra of one outer (#10) and two inner (#2 and #3) sites of the Dalhousie University SLOWPOKE-2 reactor (DUSR) have been calibrated for the k ₀-based neutron activation analysis (k ₀-NAA). The parameters determined include the cadmium ratio (R _Cd), epithermal neutron flux shape factor (), subcadmium-to-epithermal neutron flux ratio (f), thermal-to-fast neutron flux ratio (f _F), modified spectral index r()(T_n/T₀)^1/2, Westcott g _Lu(T _n)-factor, and absolute neutron temperature (T _n). The a-values of -0.0098±0.0045 and -0.0425±0.0047 and -0.0422±0.0053 and f-values of 57.1±2.2 and 18.8±0.4 and 18.9±0.4 were obtained for the sites #10, #2 and #3, respectively. The modified spectral index (MSI), g _Lu(T _n)-factor, and T _n have been determined for the handling of non 1/v (n,) reactions. The accuracy of the method was evaluated by analyzing reference materials.     

Photoluminescence emission behavior on the reduced band gap of Fe doping in CeO2-SiO2 nanocomposite and photophysical properties

Fe/CeO₂-SiO₂ nanocomposite was synthesized via hydrothermal method. Bond length of nanocomposite was determined through FTIR analysis, while Raman analysis showed lattice relaxation of CeO₂ phase in Fe/CeO₂-SiO₂. TEM, XRD and DLS-PSA revealed an increase in size of Fe/CeO₂-SiO₂ as compared to CeO₂-SiO₂ which was attributed to have more oxygen vacancies in CeO₂ after doping of iron. Lattice contraction was also observed in some phases of CeO₂ in Fe/CeO₂-SiO₂ nanocomposite as compared to CeO₂-SiO₂ nanocomposite. This contraction was used for determination of Fe content incorporated in CeO₂ [1 1 1] phase. The band gap values of Fe/CeO₂-SiO₂ nanocomposite were found reduced after doping of Fe by factors of 0.62 and 0.55 eV, respectively. Photoluminescence study of the materials was carried out to study the different type of transitions occurring after absorption of electromagnetic radiation. Photoluminescence intensity at 2.12 eV was found enhanced after doping of Fe due to increased oxygen vacancy. Photocatalytic activity of the nanocomposites was studied with the degradation of chlorpyrifos pesticide.     

Speedy Motions of a Body Immersed in an Infinitely Extended Medium

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Ψ. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound (runaway effect). Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Ψ(r) diverges at short distances like gr ^−α , g,α>0, by showing that the runaway effect still occurs if α<2.     

On the stability problem of stationary solutions for the euler equation on a 2-dimensional torus

We study the linear stability problem of the stationary solution ψ* = −cos y for the Euler equation on a 2-dimensional flat torus of sides 2πL and 2π. We show that ψ* is stable if L ∈ (0, 1) and that exponentially unstable modes occur in a right neighborhood of L = n for any integer n. As a corollary, we gain exponentially instability for any L large enough and an unbounded growth of the number of unstable modes as L diverges.     

Gamma radiolytic degradation of the endrin insecticide in methanol and monitoring of radiolytic degradation products by HPLC

The objective of this investigation was to verify the degradation of endrin by gamma irradiation. ⁶⁰Co was used as radiation source for irradiation of 50 mg L^?1 endrin with a varied dose of 1–6 kGy. High performance liquid chromatography (HPLC) coupled with diode array detector was used as an analytical technique to monitor the degradation rate along with numbers of degradation products formed. At dose rate of 6 kGy ≥99% of endrin was degraded. It is proposed that utilization of ionization radiations can be an effective and efficient tool for the removal of halogenated pesticides.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.