This is the fifth paper in a series on Time Dilation Cosmology, TDC. TDC is an eternal holographic model of the universe based on time dilation that ties astrophysics to quantum physics and resolves all the conundrums...This is the fifth paper in a series on Time Dilation Cosmology, TDC. TDC is an eternal holographic model of the universe based on time dilation that ties astrophysics to quantum physics and resolves all the conundrums in astrophysics and serves as a model for the unified field. In the author’s previous four TDC papers, it was demonstrated that all gravitationally induced velocities are compensation for the apparent difference in the rates of time, “dRt”, due to mass/energy densities, and, vice-versa, in all force-induced velocities the dRt is compensation for the velocity, so the uniform evolution of the continuum at c is maintained at the invariant 1 s/s rate of time of the universe as a whole. These compensations make it impossible for an event to lag behind or get ahead of the evolving continuum. When the author did the first velocity formula derivations in “General Relativity: Effects in Time as Causation” [1], the author felt the explanations for the appearance of the 2spatial and the 3temporal acceleration factors in the formulas were correct, but poorly explained and incomplete. This paper is a proof of the temporal and spatial acceleration factors used in the time dilation-based velocity formula derivations in the Time Dilation Cosmology model.展开更多
Based on the commonly-used definition of the semi-permeable material(SPM),in which the solvent(such as water)can pass through but the solute cannot move freely,a novel constitutive equation is presented,in this paper,...Based on the commonly-used definition of the semi-permeable material(SPM),in which the solvent(such as water)can pass through but the solute cannot move freely,a novel constitutive equation is presented,in this paper,to theoretically express the intrinsic constitutive relationship between the porosity variation rate with time and the solute concentration variation rate with time.From this theoretical finding,a mathematical model is established to describe the solute concentrationgradient driven water flow and solute concentration variation problem in solution-saturated semi-permeable materials(SSSPMs).In particular,the solute concentration variation in the considered problem can be mathematically described as a linear homogeneous second-order partial differential equation with a variable coefficient in the front of the time term.A special mathematical transform is presented and used to solve this equation,so that the analytical solution for the solute concentration variation in the considered problem has been derived in a purely mathematical manner.The derived analytical solution is then used to provide some theoretical understanding of solute concentration variations in the SSSPM layer.展开更多
文摘This is the fifth paper in a series on Time Dilation Cosmology, TDC. TDC is an eternal holographic model of the universe based on time dilation that ties astrophysics to quantum physics and resolves all the conundrums in astrophysics and serves as a model for the unified field. In the author’s previous four TDC papers, it was demonstrated that all gravitationally induced velocities are compensation for the apparent difference in the rates of time, “dRt”, due to mass/energy densities, and, vice-versa, in all force-induced velocities the dRt is compensation for the velocity, so the uniform evolution of the continuum at c is maintained at the invariant 1 s/s rate of time of the universe as a whole. These compensations make it impossible for an event to lag behind or get ahead of the evolving continuum. When the author did the first velocity formula derivations in “General Relativity: Effects in Time as Causation” [1], the author felt the explanations for the appearance of the 2spatial and the 3temporal acceleration factors in the formulas were correct, but poorly explained and incomplete. This paper is a proof of the temporal and spatial acceleration factors used in the time dilation-based velocity formula derivations in the Time Dilation Cosmology model.
基金supported by the National Natural Science Foundation of China(Grant No.42162028).
文摘Based on the commonly-used definition of the semi-permeable material(SPM),in which the solvent(such as water)can pass through but the solute cannot move freely,a novel constitutive equation is presented,in this paper,to theoretically express the intrinsic constitutive relationship between the porosity variation rate with time and the solute concentration variation rate with time.From this theoretical finding,a mathematical model is established to describe the solute concentrationgradient driven water flow and solute concentration variation problem in solution-saturated semi-permeable materials(SSSPMs).In particular,the solute concentration variation in the considered problem can be mathematically described as a linear homogeneous second-order partial differential equation with a variable coefficient in the front of the time term.A special mathematical transform is presented and used to solve this equation,so that the analytical solution for the solute concentration variation in the considered problem has been derived in a purely mathematical manner.The derived analytical solution is then used to provide some theoretical understanding of solute concentration variations in the SSSPM layer.
