OPTIMAL CONTROL APPLIED TO RIFT VALLEY FEVER

Abstract Rift Valley Fever (RVF) virus is a mosquito‐born pathogen that infects livestock but it also has the capability to infect humans through direct or indirect contact with blood or organs of infected animals and by bites from infected mosquitos. The economic and social cost of the disease to rural populations can lead to a cascade of negative effects on the sustainability of animal and human populations. Vaccines exist to protect against this disease. Through a compartment model depicting the interactions leading to the spread of RVF in Aedes and Culex mosquitos and a livestock population, an optimal control problem is developed to minimize the number of vaccinated livestock at the final time while minimizing the negative effects of the infected Aedes and Culex mosquitos and the cost of the vaccination process. The unique optimal vaccination strategy is produced for given high transmission parameters and numerical results portray that vaccination depends on the level of effectiveness of the protocol.     

Low-Loss Many-to-One Fiber Couplers with Few or Single-Moded Inputs and a Multi-Mode Output

The coupling of light from a number of few or single-moded fibers into a single multi-mode fiber is analyzed using geometric optics, and simple results demonstrating mode conservation are derived. Coupling from multiple single-mode fibers into a multi-mode fiber is investigated in detail using the overlap integral to determine coupling into each mode of the output fiber as a function of the light phase in the inputs. As well as results with practical relevance to fiber tapped delay-line filters and optical CDMA, the analysis provides pedagogic insight into light propagation and the light-gathering properties of fiber.     

A simulation study of the effects of adsorbent energy on the diffusion of molecules in slit pores: 1 commensurate slit widths

Equilibrium molecular dynamics simulation has been used to study the self-diffusion coefficients (from correlation of the molecular velocity) and the collective, or centre of mass diffusion coefficients (from correlation of the streaming velocity) of a Lennard-Jones fluid in model slit pores. The slit widths were chosen to be integer multiples of the Lennard-Jones adsorbate diameter, and therefore are close to being commensurate with layered adsorbate structures. Slits of reduced width H* = 3 and 5 were examined at a reduced temperature of T* = 1.0. The adsorbate densities ranged from 0.3 to 0.9 in reduced units. The adsorbent adsorbate interaction was modelled as a simple potential with inverse 4th power attraction plus hard wall repulsion, and systems with reduced parameter u₀* ranging from ?5 to +5 were studied. Molecule-wall scattering was represented by a diffuse reflection algorithm. The density distributions show strong layering in the attractive system, but this is absent in the most repulsive slits, except at very high densities. Self-diffusion is only weakly dependent on u₀* and slit width at high densities, but a strong dependence on u₀* appears at low densities. The collective diffusion coefficient is less easy to calculate with high accuracy; nevertheless, it is clear that there is a strong dependence of this property on u₀* Trajectory plots show zones in which the particles are more or less strongly localized, but undergo irregular oscillatory motion corresponding to regions of high density in the single-particle distributions.     

Interatomic interactions and the Cotton—Mouton effect for helium

We report calculations of the interaction-induced polarizability (δα^anis), magnetizability (δξ^anis;) and hypermagnetizability (δη^anis) anisotropies for the helium gas as a function of the interatomic separation. From these data we determine the virial coefficients for the Cotton—Mouton effect and the hypermagnetizability anisotropy of helium. We also find the mean polarizability and magnetizability as a function of the interatomic separation and the virial coefficients for these properties. The results for the Cotton—Mouton effect indicate that pressure affects the Cotton—Mouton constant to the same extent as it does the second hyperpolarizability (γ) and the virial coefficient b^CME(ω, T) lies in the range of ?1.6 to ?1.8 cm³ mol^?1. This means that pressure effects for the Cotton-Mouton constant could be detected with modern experimental techniques. All calculations were carried out using the full configuration interaction technique and large basis sets of London atomic orbitals. The polarizability calculations were performed both for relevant optical frequencies as well as the static case.     

An analytical theory for diffusion of fluids in crystalline nanoporous materials

An analytical theory for diffusion of fluids in zeolites and other nanoporous materials has been developed. The theory incorporates molecular level information about the nanoporous material, which is obtainable from an energy minimization and does not require molecular dynamics computer simulations. The theory is statistical mechanical in nature and assumes a lattice composed of adsorption sites. The theory yields a self-diffusion coefficient, which is a function of (i) temperature, (ii) adsorbate density, (iii) adsorbate size, (iv) adsorbate-adsorbate energetic interaction and (v) adsorbate-pore energetic interaction. The theory is generalized and is applicable to nanoporous materials with three-dimensional porous networks (e.g. faujusite) and one-dimensional porous networks (e.g. A1P0₄-5).

The theory is self-contained and incorporates no fitting parameters. The theory does not require computational effort beyond a few seconds on a standard personal computer.     

High Sensitivity Negative Ion GC-MS Method for Detection of Estrogens in Urine

A sensitive negative chemical ionization (NCI) gas-chromatography/mass spectrometry (GC/MS) method for the detection of estrogens is described. After hydrosis and clean-up by C₁₈ ODS solid phase extraction (SPE) cartridge, the extracts obtained were derivatized with heptafluorobutyric anhydride and analyzed in the negative ion mode by GC/MS. Stability of derivatives was good. Selected ion monitoring (SIM) mode was applied to increase the sensitivity and, when possible, the higher m/z ions were selected to improve identification. The detection limit of the HFB esters in NCI using SIM was below 10 femtograms.     

FINITE ELEMENT ANALYSIS OF ANISOTROPIC FLUID SUSPENSIONS

The orientation tensor L is introduced to construct a modified Leslie–Ericksen model for the viscous, incompressible flow of anisotropic suspensions (including electric field effects). This is then utilized to develop a weak variational formulation and finite element scheme for computing the flow and orientation fields. Numerical results are presented for exploratory test problems.     

COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.     

A Signalling Problem for Near-Equilibrium Flows in the Fickett-Majda Model of Combustion

The signalling problem for chemico-acoustic interactions ina simplified model of combustion and detonation is considered.The problem is examined in different limits, depending uponthe sensitivity of the reaction rate with the degree of reactioncoordinate and with the thermodynamic state. In one limit, theproblem is singular, and singular perturbation techniques areused to obtain an approximate solution. In the general case,a combination Riemann function-Laplace transform method is usedto obtain exact solutions with arbitrary boundary data. Thiscombined method allows the Riemann method to be applied to certainwave problems with discontinuous data.