Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.

The Rocky Road of Social Sustainability : The Impact of Integrated Biodiversity Conservation and Development on the Local Realities in Ranomafana National Park, Madagascar

The objective of this study is to examine the social impacts of the integrated conservation and development project (ICDP) aimed at biodiversity conservation and local socio-economic development in the Ranomafana National Park (RNP), Madagascar. Furthermore, the study explores social sustainability and justice of the ICDP in Ranomafana. This ethnographically informed impact study uses of various field methods. The research material used consists of observation, interviews (key-person and focus group), school children's writings, official statistics and project documents. Fieldwork was conducted in three phases in 2001, 2002 and 2004 in twelve villages around the park, as well as in neighbouring areas of Ranomafana. However, four of those twelve villages were chosen for closer study. This study consists of five independent articles and a concluding chapter. Social impacts were studied through reproductive health indicators as well as a life security approach. Equity and distribution of benefits and drawbacks of ICDP were analysed and the actors related to the conservation in Ranomafana were identified. The children and adolescents' environmental views were also examined. The reproductive health indicators studied showed a poor state of reproductive health in the park area. Moreover, the existing social capital in the villages seemed to be fragmented due to economic difficulties that were partly caused by the conservation regulations. The ICDP in Ranomafana did not pay attention to the heterogeneity of the affected communities even though the local beneficiaries of the ICDP varied according to their ethnicity, living place, wealth, social position and gender. In addition, various conservation actors (local people in various groups, local authorities, tourist business owners, conservation NGOs and scientists) contest their interests over the forest, conservation and its related activities. This study corroborates the same type of evidence and conclusions discussed in other similar cases elsewhere: so called social conservation programmes still cannot meet the needs of the people living near the protected areas; on the contrary, they even have a reverse impact on the people's lives. A fundamental misunderstood assumption in the conservation process in Ranomafana was to consider the local people as a problem for biodiversity conservation. Major reasons for the failure of the ICDP in Ranomafana include a lack of local institutions that would have been able to communicate as equals with the conservation NGOs as well as to transfer the tradition of the authoritarian governance in conservation management together with the over-appreciation of scientific biodiversity, and lack of will to understand the local people's rights to use the forest for their livelihoods.

Evolutionary and conservation biology of the Finnish house sparrow

Recently it has been recognized that evolutionary aspects play a major role in conservation issues of a species. In this thesis I have combined evolutionary research with conservation studies to provide new insight into these fields. The study object of this thesis is the house sparrow, a species that has features that makes it interesting for this type of study. The house sparrow has been ubiquitous almost all over the world. Even though being still abundant, several countries have reported major declines. These declines have taken place in a relatively short time covering both urban and rural habitats. In Finland this species has declined by more than two thirds in just over two decades. In addition, as the house sparrow lives only in human inhabited areas it can also raise public awareness to conservation issues. I used both an extensive museum collection of house sparrows collected in 1980s from all over Finland as well as samples collected in 2009 from 12 of the previously collected localities. I used molecular techniques to study neutral genetic variation within and genetic differentiation between the study populations. This knowledge I then combined with data gathered on morphometric measurements. In addition I analyzed eight heavy metals from the livers of house sparrows that lived in either rural or urban areas in the 1980s and evaluated the role of heavy metal pollution as a possible cause of the declines. Even though dispersal of house sparrows is limited I found that just as the declines started in 1980s the house sparrows formed a genetically panmictic population on the scale of the whole Finland. When compared to Norway, where neutral genetic divergence has been found even with small geographic distances, I concluded that this difference would be due to contrasting landscapes. In Finland the landscape is rather homogeneous facilitating the movements of these birds and maintaining gene flow even with the low dispersal. To see whether the declines have had an effect on the neutral genetic variation of the populations I did a comparison between the historical and contemporary genetic data. I showed that even though genetic diversity has not decreased due to the drastic declines the populations have indeed become more differentiated from each other. This shows that even in a still quite abundant species the declines can have an effect on the genetic variation. It is shown that genetic diversity and differentiation may approach their new equilibriums at different rates. This emphasizes the importance of studying both of them and if the latter has increased it should be taken as a warning sign of a possible loss of genetic diversity in the future. One of the factors suggested to be responsible for the house sparrow declines is heavy metal pollution. When studying the livers of house sparrows from 1980s I discovered higher levels of heavy metal concentrations in urban than rural habitats, but the levels of the metals were comparatively low and based on that heavy metal pollution does not seem to be a direct cause for the declines in Finland. However, heavy metals are known to decrease the amount of insects in urban areas and thus in the cities heavy metals may have an indirect effect on house sparrows. Although neutral genetic variation is an important tool for conservation genetics it does not tell the whole story. Since neutral genetic variation is not affected by selection, information can be one-sided. It is possible that even neutral genetic differentiation is low, there can be substantial variation in additive genetic traits indicating local adaptation. Therefore I performed a comparison between neutral genetic differentiation and phenotypic differentiation. I discovered that two traits out of seven are likely to be under directional selection, whereas the others could be affected by random genetic drift. Bergmann s rule may be behind the observed directional selection in wing length and body mass. These results highlight the importance of estimating both neutral and adaptive genetic variation.

Evolution, Homology Conservation, and Identification of Unique Sequence Signatures in GH19 Family Chitinases

The discovery of GH (Glycoside Hydrolase) 19 chitinases in Streptomyces sp. raises the possibility of the presence of these proteins in other bacterial species, since they were initially thought to be confined to higher plants. The present study mainly concentrates on the phylogenetic distribution and homology conservation in GH19 family chitinases. Extensive database searches are performed to identify the presence of GH19 family chitinases in the three major super kingdoms of life. Multiple sequence alignment of all the identified GH19 chitinase family members resulted in the identification of globally conserved residues. We further identified conserved sequence motifs across the major sub groups within the family. Estimation of evolutionary distance between the various bacterial and plant chitinases are carried out to better understand the pattern of evolution. Our study also supports the horizontal gene transfer theory, which states that GH19 chitinase genes are transferred from higher plants to bacteria. Further, the present study sheds light on the phylogenetic distribution and identifies unique sequence signatures that define GH19 chitinase family of proteins. The identified motifs could be used as markers to delineate uncharacterized GH19 family chitinases. The estimation of evolutionary distance between chitinase identified in plants and bacteria shows that the flowering plants are more related to chitinase in actinobacteria than that of identified in purple bacteria. We propose a model to elucidate the natural history of GH19 family chitinases.

A one point shock capturing kinetic scheme for hyperbolic conservation laws

We have presented a new low dissipative kinetic scheme based on a modified Courant Splitting of the molecular velocity through a parameter φ. Conditions for the split fluxes derived based on equilibrium determine φ for a one point shock. It turns out that φ is a function of the Left and Right states to the shock and that these states should satisfy the Rankine-Hugoniot Jump condition. Hence φ is utilized in regions where the gradients are sufficiently high, and is switched to unity in smooth regions. Numerical results confirm a discrete shock structure with a single interior point when the shock is aligned with the grid.

Probing Fluorine Interactions in a Polyhydroxylated Environment: Conservation of a C-F center dot center dot center dot H-C Recognition Motif in Presence of O-H center dot center dot center dot O Hydrogen Bonds

Three conformationally locked fluorinated polycyclitols have been specially crafted on a rigid trans-decalin backbone, employing a surprisingly facile pyridine-poly(hydrogen fluoride)-mediated stereospecific epoxide ring opening as the key reaction. Molecula design of the three fluorinated probes under study focused on providing an efficient platform for (a) evaluating the ability of covalently bonded fluorine, vis-a-vis the isosteric hydroxy group, to act as a H-bond acceptor and (b) examining the possibility for an organic fluorine moiety, placed suitably in a spatially invariant position, to engage an 1,3-diaxial OH functionality in a purported intramolecular O-H center dot center dot center dot F hydrogen bond. The present endeavour reveals that C(sp(3))-F center dot center dot center dot H-C(sp(3)) hydrogen bonds, though weak and lesser investigated, can indeed be observed and supramolecular recognition motifs, involving such interactions, can be conserved even in crystal structures laden with stronger O-H center dot center dot center dot O hydrogen bonds.

Performance evaluation of an integrated solar water heater as an option for building energy conservation

Since a majority of residential and industrial building hot water needs are around 50 degrees C, an integrated solar water heater could provide a bulk source that blends collection and storage into one unit. This paper describes the design, construction and performance test results of one such water-heating device. The test unit has an absorber area of 1.3 m(2) and can hold 1701 of water, of which extractable volume per day is 1001. Its performance was evaluated under various typical operating conditions. Every morning at about 7:00 a.m., 1001 of hot water were drawn from the sump and replaced with cold water from the mains. Although, during most of the days, the peak temperatures of water obtained are between 50 and 60 degrees C, the next morning temperatures were lower at 45-50 degrees C. Daytime collection efficiencies of about 60% and overall efficiencies of about 40% were obtained. Tests were conducted with and without stratification. Night radiation losses were reduced by use of a screen insulation.

An Application of 3-D Kinematical Conservation Laws: Propagation of a 3-D Wavefront

Three-dimensional (3-D) kinematical conservation laws (KCL) are equations of evolution of a propagating surface Omega(t) in three space dimensions. We start with a brief review of the 3-D KCL system and mention some of its properties relevant to this paper. The 3-D KCL, a system of six conservation laws, is an underdetermined system to which we add an energy transport equation for a small amplitude 3-D nonlinear wavefront propagating in a polytropic gas in a uniform state and at rest. We call the enlarged system of 3-D KCL with the energy transport equation equations of weakly nonlinear ray theory (WNLRT). We highlight some interesting properties of the eigenstructure of the equations of WNLRT, but the main aim of this paper is to test the numerical efficacy of this system of seven conservation laws. We take several initial shapes for a nonlinear wavefront with a suitable amplitude distribution on it and let it evolve according to the 3-D WNLRT. The 3-D WNLRT is a weakly hyperbolic 7 x 7 system that is highly nonlinear. Here we use the staggered Lax-Friedrichs and Nessyahu-Tadmor central schemes and have obtained some very interesting shapes of the wavefronts. We find the 3-D KCL to be suitable for solving many complex problems for which there presently seems to be no other method capable of giving such physically realistic features.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

The changing role of legislation related to forest conservation and forest resources development.

XVIII IUFRO World Congress, Ljubljana 1986.