In this paper, we analytically discuss the scaling properties of the average square end-to-end distance < R-2 > for anisotropic random walk in D-dimensional space (D >= 2), and the returning probability P-n(r...In this paper, we analytically discuss the scaling properties of the average square end-to-end distance < R-2 > for anisotropic random walk in D-dimensional space (D >= 2), and the returning probability P-n(r(0)) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for < R-2 > and P-n(r(0)), but also point out that if there is a symmetric axis for the distribution of the probability density of a single step displacement, we always obtain < R-perpendicular to n(2) > similar to n, where perpendicular to refers to the projections of the displacement perpendicular to each symmetric axes of the walk; in D-dimensional space with D symmetric axes perpendicular to each other, we always have < R-n(2)> similar to n and the random walk will be like a purely random motion; if the number of inter-perpendicular symmetric axis is smaller than < R-n(2)> similar to n(2) the dimensions of the space, we must have n for very large n and the walk will be like a ballistic motion. It is worth while to point out that unlike the isotropic random walk in one and two dimensions, which is certain to return into the neighborhood of the origin, generally there is only a nonzero probability for the anisotropic random walker in two dimensions to return to the neighborhood.展开更多
Methyl or ethyl esters of vegetable oils are the reliable alternative fuels for the petroleum diesel, because their properties are very nearer to the petroleum diesel. But the flash point and auto-ignition temperature...Methyl or ethyl esters of vegetable oils are the reliable alternative fuels for the petroleum diesel, because their properties are very nearer to the petroleum diesel. But the flash point and auto-ignition temperatures are very high for these esters. CR （compression ratio） is one of the parameter which influences the atomization and vaporization of fuel. It is also caused for improvement in the turbulence which leads to better combustion. In this work the single cylinder diesel engine was tested at different compression ratios i.e. 16.5：1, 17.5：1, 18.5：1, 19：1 with palm kernel methyl ester without modifications. On increasing compression ratio closeness of molecules of air increases and fuel is injected into that air caused for better combustion. The inbuilt oxygen of methyl or ethyl ester will participate in the combustion and causes for reduction of HC and CO. Better compression ratio for an engine with particular fuel provides satisfactory thermal efficiency and less environmental pollution. In the investigations, for palm kernel methyl ester, 18.5：1 compression ratio is preferable on single cylinder Dl-diesel engine.展开更多
文摘In this paper, we analytically discuss the scaling properties of the average square end-to-end distance < R-2 > for anisotropic random walk in D-dimensional space (D >= 2), and the returning probability P-n(r(0)) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for < R-2 > and P-n(r(0)), but also point out that if there is a symmetric axis for the distribution of the probability density of a single step displacement, we always obtain < R-perpendicular to n(2) > similar to n, where perpendicular to refers to the projections of the displacement perpendicular to each symmetric axes of the walk; in D-dimensional space with D symmetric axes perpendicular to each other, we always have < R-n(2)> similar to n and the random walk will be like a purely random motion; if the number of inter-perpendicular symmetric axis is smaller than < R-n(2)> similar to n(2) the dimensions of the space, we must have n for very large n and the walk will be like a ballistic motion. It is worth while to point out that unlike the isotropic random walk in one and two dimensions, which is certain to return into the neighborhood of the origin, generally there is only a nonzero probability for the anisotropic random walker in two dimensions to return to the neighborhood.
文摘Methyl or ethyl esters of vegetable oils are the reliable alternative fuels for the petroleum diesel, because their properties are very nearer to the petroleum diesel. But the flash point and auto-ignition temperatures are very high for these esters. CR （compression ratio） is one of the parameter which influences the atomization and vaporization of fuel. It is also caused for improvement in the turbulence which leads to better combustion. In this work the single cylinder diesel engine was tested at different compression ratios i.e. 16.5：1, 17.5：1, 18.5：1, 19：1 with palm kernel methyl ester without modifications. On increasing compression ratio closeness of molecules of air increases and fuel is injected into that air caused for better combustion. The inbuilt oxygen of methyl or ethyl ester will participate in the combustion and causes for reduction of HC and CO. Better compression ratio for an engine with particular fuel provides satisfactory thermal efficiency and less environmental pollution. In the investigations, for palm kernel methyl ester, 18.5：1 compression ratio is preferable on single cylinder Dl-diesel engine.
