In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) ...In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented.展开更多
Spatio-temporal variation in the Martian surface temperature(MST)is an indicator of ground level thermal processes and hence a building block for climate models.However,the distribution of MST exhibits different level...Spatio-temporal variation in the Martian surface temperature(MST)is an indicator of ground level thermal processes and hence a building block for climate models.However,the distribution of MST exhibits different levels of spatial aggregation or heterogeneity,and varies in space and time.Furthermore,the effect of regional differences in meteorological or environmental factors on the MST is not well understood.Thus,we investigated the degree of spatial autocorrelation of MST across the surface of Mars globally by Moran’s I,and identified the hot spots by GetisOrd G;*.We also estimated the regional differences in the influence of seasonally dominant factors including thermal inertia(TI),albedo,surface pressure,latitude,dust and slope on MST by a geographically weighted regression model.The results indicate(1)that MST is spatially aggregated and hot and cold spots varied over time and space.(2)Hemispheric differences in topography,surface TI and albedo were primarily responsible for the hemispheric asymmetry of hot spots.(3)The dominant factors varied by geographical locations and seasons.For example,the seasonal Hadley circulation dominates at the low-latitudes and CO;circulation at the high-latitudes.(4)Regions with extreme variations in topography and low TI were sensitive to meteorological and environmental factors such as dust and CO_(2)ice.We conclude that the spatial autocorrelation of MST and the spatial and seasonal heterogeneity of influencing factors must be considered when simulating Martian climate models.This work provides a reference for further exploration of Martian climatic processes.展开更多
Fitting C2-continuous or superior surfaces to a set S of points sampled on a 2-manifold is central to reverse engineering, computer aided geometric modeling, entertaining, modeling of art heritage, etc. This article a...Fitting C2-continuous or superior surfaces to a set S of points sampled on a 2-manifold is central to reverse engineering, computer aided geometric modeling, entertaining, modeling of art heritage, etc. This article addresses the fitting of analytic (ellipsoid, cones, cylinders) surfaces in general position in . Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimating the geometric distance between a point of S and the analytic surface F. These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set. In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids. A conjecture for the calculation of the distance point-ellipsoid is also proposed. Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm. Ongoing work addresses the fitting of free-form parametric surfaces to S.展开更多
基金mostly financed by the FP7 Project ASTARTE "Assessment,Strategy and Risk Reduction for 740 Tsunamis in Europe"(FP7-ENV2013 6.4-3,Grant603839)the Italian National Project RITMARE that,among others,treat landslide models with tsunamigenic potential
文摘In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented.
基金supported by the pre-research Project on Civil Aerospace Technologies(No.D020103)supported by the National Natural Science Foundation of China(Grant No.42030110)。
文摘Spatio-temporal variation in the Martian surface temperature(MST)is an indicator of ground level thermal processes and hence a building block for climate models.However,the distribution of MST exhibits different levels of spatial aggregation or heterogeneity,and varies in space and time.Furthermore,the effect of regional differences in meteorological or environmental factors on the MST is not well understood.Thus,we investigated the degree of spatial autocorrelation of MST across the surface of Mars globally by Moran’s I,and identified the hot spots by GetisOrd G;*.We also estimated the regional differences in the influence of seasonally dominant factors including thermal inertia(TI),albedo,surface pressure,latitude,dust and slope on MST by a geographically weighted regression model.The results indicate(1)that MST is spatially aggregated and hot and cold spots varied over time and space.(2)Hemispheric differences in topography,surface TI and albedo were primarily responsible for the hemispheric asymmetry of hot spots.(3)The dominant factors varied by geographical locations and seasons.For example,the seasonal Hadley circulation dominates at the low-latitudes and CO;circulation at the high-latitudes.(4)Regions with extreme variations in topography and low TI were sensitive to meteorological and environmental factors such as dust and CO_(2)ice.We conclude that the spatial autocorrelation of MST and the spatial and seasonal heterogeneity of influencing factors must be considered when simulating Martian climate models.This work provides a reference for further exploration of Martian climatic processes.
文摘Fitting C2-continuous or superior surfaces to a set S of points sampled on a 2-manifold is central to reverse engineering, computer aided geometric modeling, entertaining, modeling of art heritage, etc. This article addresses the fitting of analytic (ellipsoid, cones, cylinders) surfaces in general position in . Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimating the geometric distance between a point of S and the analytic surface F. These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set. In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids. A conjecture for the calculation of the distance point-ellipsoid is also proposed. Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm. Ongoing work addresses the fitting of free-form parametric surfaces to S.
