Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The ...Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.展开更多
The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical h...The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.展开更多
In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously pe...In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.展开更多
The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the k...The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.展开更多
Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the eff...Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.展开更多
文摘Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.
文摘The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.
基金supported by National Natural Science Foundation of China(Grant No.61761011)Natural Science Foundation of Guangxi(Grant No.2020GXNSFBA297078).
文摘In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.
文摘The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.
文摘Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.
