899 resultados para Arbitrary dimension


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Following the execution of Saudi Shiite cleric Nimr Baqer al-Nimr, the deep rooted rivalry between Iran and Saudi Arabia entered a new phase in January 2016. While the main objective for both countries still is regional hegemony, the Iranian-Saudi competition takes many different forms and shapes, and also extends into the field of energy. In this Policy Brief, David Ramin Jalilvand gives a detailed analysis of the energy-related aspects of the Iran-Saudi Arabia rivalry and its possible consequences for Europe’s energy market; both countries hold giant hydrocarbon reserves, so European energy will probably be affected by their competition in several regards; increased oil supplies will be available for the European market, while the cycle of low oil prices will be prolonged. According to Jalilvand, this is a mixed blessing; Europe’s energy import bill will be reduced, but its indigenous production will suffer, while Russia’s role in European natural gas will only continue to grow.

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Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

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In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

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"January 1996."

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Mode of access: Internet.

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"Contract No. AF33(616)-3220 Project No. 6(7-4600) Task 40572 Wright Air Development Center"

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Mode of access: Internet.

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Mode of access: Internet.

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Mode of access: Internet.

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"Paper written under Contract Nonr. 58304."

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"Aus den Sitzungsberichten der Kaiserl. Akademie der Wissenschaften in Wien. Mathem.-naturw. Classe. Bd. CI, Abt. 2 a. Feb. 1892."

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Includes also his The Book-keeper's diploma; or a full and lucid treatise on the equation of payments, N.Y., 1937. Also Preston's estimates of boxes, and casks ...