A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid

A novel accurate numerical model for shallow water equations on sphere have been developed by implementing the high order multi-moment constrained finite volume (MCV) method on the icosahedral geodesic grid. High order reconstructions are conducted cell-wisely by making use of the point values as the unknowns distributed within each triangular cell element. The time evolution equations to update the unknowns are derived from a set of constrained conditions for two types of moments, i.e. the point values on the cell boundary edges and the cell-integrated average. The numerical conservation is rigorously guaranteed. in the present model, all unknowns or computational variables are point values and no numerical quadrature is involved, which particularly benefits the computational accuracy and efficiency in handling the spherical geometry, such as coordinate transformation and curved surface. Numerical formulations of third and fourth order accuracy are presented in detail. The proposed numerical model has been validated by widely used benchmark tests and competitive results are obtained. The present numerical framework provides a promising and practical base for further development of atmospheric and oceanic general circulation models. (C) 2009 Elsevier Inc. All rights reserved.

Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

Phylogenetic relationships of Danio within the order cypriniformes: A framework for comparative and evolutionary studies of a model species

The evolutionary relationships of species of Danio and the monophyly and phylogenetic placement of the genus within the family Cyprinidae and subfamily Rasborinae provide fundamentally important phyloinformatics necessary for direct evaluations of an array of pertinent questions in modern comparative biology. Although the genus Danio is not one of the most diverse within the family, Danio rerio is one of the most important model species in biology. Many investigations have used this species or presumed close relatives to address specific questions that have lasting impact on the hypothesis and theory of development in vertebrates. Largely lacking from this approach has been a holistic picture of the exact phylogenetic or evolutionary relationships of this species and its close relatives. One thing that has been learned over the previous century is that many organismal attributes (e.g., developmental pathways, ecologies, behaviors, speciation) are historically constrained and their origins and functions are best explained via a phylogenetic approach. Herein, we provide a molecular evaluation of the phylogenetic placement of the model species Danio rerio within the genus Danio and among hypothesized closely related species and genera. Our analysis is derived from data using two nuclear genes (RAG1, rhodopsin) and five mitochondrial genes (ND4, ND4L, ND5, COI, cyt b) evaluated using parsimony, maximum likelihood, and Bayesian analyses. The family Cyprinidae is resolved as monophyletic but the subfamily Rasborinae (priority over Danioinae) is an unnatural assemblage. Danio is identified as a monophyletic group sister to a clade inclusive of the genera Chela, Microrasbora, Devario, and Inlecypris, not Devario nor Esomus as hypothesized in previous studies. Danio rerio is sister to D. kyathit among the species of Danio evaluated in this analysis. Microrasbora and Rasbora are non-monophyletic assemblages; however, Boraras is monophyletic.

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.