Is Human Development Multidimensional?

Stiglitz's Commission on the Measurement of Economic Performance and Social Progress (CMEPSP) argued that well-being is multidimensional and identified eight distinct dimensions. Conventional linear techniques confirm that a large number of dimensions are needed to describe development. In contrast, a new non-linear technique that we introduce from chaos theory shows that a smaller number of dimensions are needed to span the development space. From the analysis, variables representing the Health, Education, Inequality and Individual Rights areas of life quality would provide a broad picture of development, whereas income per capita adds little extra information.

A biogeography-based optimization algorithm with mutation strategies for model parameter estimation of solar and fuel cells

Mathematical models are useful tools for simulation, evaluation, optimal operation and control of solar cells and proton exchange membrane fuel cells (PEMFCs). To identify the model parameters of these two type of cells efficiently, a biogeography-based optimization algorithm with mutation strategies (BBO-M) is proposed. The BBO-M uses the structure of biogeography-based optimization algorithm (BBO), and both the mutation motivated from the differential evolution (DE) algorithm and the chaos theory are incorporated into the BBO structure for improving the global searching capability of the algorithm. Numerical experiments have been conducted on ten benchmark functions with 50 dimensions, and the results show that BBO-M can produce solutions of high quality and has fast convergence rate. Then, the proposed BBO-M is applied to the model parameter estimation of the two type of cells. The experimental results clearly demonstrate the power of the proposed BBO-M in estimating model parameters of both solar and fuel cells.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Is the number of species on earth increasing or decreasing? Time, chaos and the origin of species

Darwin's On the Origin of Species has led to a theory of evolution with a mass of empirical detail on population genetics below species level, together with heated debate on the details of macroevolutionary patterns above species level. Most of the main principles are clear and generally accepted, notably that life originated once and has evolved over time by descent with modification. Here, I review the fossil and molecular phylogenetic records of the response of life on Earth to Quaternary climatic changes. I suggest that the record can be best understood in terms of the nonlinear dynamics of the relationship between genotype and phenotype, and between climate and environments. 'The origin of species' is essentially unpredictable, but is nevertheless an inevitable consequence of the way that organisms reproduce through time. The process is 'chaotic', but not 'random'. I suggest that biodiversity is best considered as continuously branching systems of lineages, where 'species' are the branch tips. The Earth's biodiversity should thus (1) be in a state of continuous increase and (2) show continuous discrepancies between genetic and morphological data in time and space. © The Palaeontological Association.

Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF (J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.