Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating Solutions

New explicit, zero dissipative, hybrid Numerov type methods are presented in this paper. We derive these methods using an alternative which avoids the use of costly high accuracy interpolatory nodes. We only need the Taylor expansion at some internal points then. The method is of sixth algebraic order at a cost of seven stages per step while their phase lag order is fourteen. The zero dissipation condition is satisfied, so the methods possess an non empty interval of periodicity. Numerical results over some well known problems in physics and mechanics indicate the superiority of the new method.     

Towards molecular-scale electronics and biomolecular self-assembly

This paper provides an overview of recent research developments in the field of nanoelectronics with organic materials such as carbon nanotubes and DNA-templated nanowires. Carbon nanotubes and gold electrodes are chemically functionalized in order to contact carbon nanotubes by self-assembly. The transport properties of these nanotubes are dominated by charging effects and display clear Coulomb blockade behaviour. A different approach towards nanoscale electronics is based on the molecular recognition properties of biomolecules such as DNA. As an example, DNA is stretched between electrodes using a molecular combing technique. A two-step metallization procedure leads to the formation of highly conductive gold nanowires.     

Electronic transport properties of bismuth nanobridges through silicon-nitride membranes

The electronic transport through nanostructured bismuth nanobridges has been investigated at low temperatures (T<2 K) and in magnetic fields B up to 8.5 T. The samples show reproducible resistance fluctuations as a function of B, superimposed on a large magnetoresistance of up to 50%. In addition, time-dependent resistance fluctuations in zero magnetic field demonstrate the presence of bistable scatterers in the constriction region of our samples, which are described by two-level systems. Their dynamics are shown to be sensitive to subtle modifications of the static scatterer configuration in their vicinity, which cannot be detected in the sample magnetofingerprint.     

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.     

Local Feasible QP-Free Algorithms for the Constrained Minimization of SC1 Functions

We consider the problem of minimizing an SC¹ function subject to inequality constraints. We propose a local algorithm whose distinguishing features are that: (a) a fast convergence rate is achieved under reasonable assumptions that do not include strict complementarity at the solution; (b) the solution of only linear systems is required at each iteration; (c) all the points generated are feasible. After analyzing a basic Newton algorithm, we propose some variants aimed at reducing the computational costs and, in particular, we consider a quasi-Newton version of the algorithm.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

The Heat Equation with Initial Data Corrupted by Measurement Error and Missing Data

In this work the Cauchy problem for the one-dimensional heat equation is considered. In contrast to existing literature it is assumed that the initial state f is unknown and that information regarding f is obtained by some process of measurement. To enhance realism, both measurement errors and missing data are allowed for. Under assumptions on f in the Fourier-domain first an approximation to f is derived from the data by means of a novel uncertainty principle. Then, it is studied how this perturbation in the initial state propagates with time.