Modeling of chemical tracer transport in the atmospheric environment and its impact on the global climate

Continental regions are experiencing rapid environmental changes due to expansion of industrial activities and land uses in different types of agricultural productions, burning of fossil fuels, etc., which lead to the emanation of huge amount of smog aerosol particulates and chemicals in the atmosphere. Information about these chemical tracers has been found from Indian Ocean Experiment (INDOEX), Intergovernmental Panel for Climate Change (IPCC) assessment reports as well as from other sources. The results of these computations may be interpreted by the chemical tracer transport model. In this paper, we have used a global atmospheric model in which the optical properties and the concentrations of the chemical tracers and aerosols have been incorporated. The aerosols and chemicals are transported in the atmospheric environment by the model cumulus convection and through the model semi-Lagrangian advection process . Thus, they are globally distributed along with the wind flow. The model has been used in studying the impact of the tropospheric chemical perturbations on the global environment.     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

Public debates driven by incomplete scientific data: The cases of evolution theory, global warming and H1N1 pandemic influenza

Public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to the current state of scientific knowledge, are studied. The cases of evolution theory, global warming and H1N1 pandemic influenza are investigated. The first two are of controversial impact while the third is more neutral and resolved. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with incorrect claims which cannot be scientifically refuted appears to be necessary but not sufficient to eventually win a public debate. The underlying key mechanisms of these puzzling and unfortunate conclusions are identified using the Galam sequential probabilistic model of opinion dynamics (Galam, 2002 [4], Galam, 2005 [18], Galam and Jacobs, 2007 [19]). It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data in public debates. Acting on one’s own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant initial supports. On the contrary focusing on open-minded agents may be useless given some topologies. When the evidence is not as strong as claimed, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate.     

Unconstrained and constrained global optimization of polynomial functions in one variable

In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated.     

Ab initio Tertiary Structure Prediction of Proteins

A daunting challenge in the area of computational biology has been to develop a method to theoretically predict the correct three-dimensional structure of a protein given its linear amino acid sequence. The ability to surmount this challenge, which is known as the protein folding problem, has tremendous implications. We introduce a novel ab initio approach for the protein folding problem. The accurate prediction of the three-dimensional structure of a protein relies on both the mathematical model used to mimic the protein system and the technique used to identify the correct structure. The models employed are based solely on first principles, as opposed to the myriad of techniques relying on information from statistical databases. The framework integrates our recently proposed methods for the prediction of secondary structural features including helices and strands, as well as -sheet and disulfide bridge formation. The final stage of the approach, which culminates in the tertiary structure prediction of a protein, utilizes search techniques grounded on the foundations of deterministic global optimization, powerful methods which can potentially guarantee the correct identification of a protein's structure. The performance of the approach is illustrated with bovine pancreatic trypsin inhibitor protein and the immunoglobulin binding domain of protein G.     

Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point

We investigate the six-dimensional Schrödinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of the distance between two particles and in the sought functions of the other three-body coordinates. Constructing such functions in angular bases composed of spherical and bispherical harmonics or symmetrized Wigner D-functions is reduced to solving simple recursive algebraic equations. For projections of physical solutions on the angular bases functions, we derive boundary conditions at the pair impact point.     

Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane

We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line.     

On 2x2 conservation laws with large data

We deal with a strictly hyperbolic system of two conservation laws in one spatial dimension. One of the eigenvalues of the system is of Temple type (rarefaction and shock curves coincide), the other eigenvalue is only required to be genuinely nonlinear.We consider the initial value problem for data of the following kind: the total variation of the Temple component is bounded, possibly large, while the total variation of the other component is small. For such data we prove global existence, uniqueness and L⊃-Lipschitz continuous dependence of solutions.AMS Subject Classification: Primary 35L65; Secondary 35D05, 35L45.     

A quadratic assignment formulation of the molecular conformation problem

The molecular conformation problem is discussed, and a concave quadratic global minimization approach for solving it is described. This approach is based on a quadratic assignment formulation of a discrete approximation to the original problem.     

Accelerations for global optimization covering methods using second derivatives

Two improvements for the algorithm of Breiman and Cutler are presented. Better envelopes can be built up using positive quadratic forms. Better utilization of first and second derivative information is attained by combining both global aspects of curvature and local aspects near the global optimum. The basis of the results is the geometric viewpoint developed by the first author and can be applied to a number of covering type methods. Improvements in convergence rates are demonstrated empirically on standard test functions.Partially supported by an University of Canterbury Erskine grant.