In this paper we deduce the analytic solutions of the first- and second-order vertical derivative zero points for gravity anomalies in simple regular models with single, double, and multiple edges and analyze their sp...In this paper we deduce the analytic solutions of the first- and second-order vertical derivative zero points for gravity anomalies in simple regular models with single, double, and multiple edges and analyze their spatial variation. For another simple regular models where it is difficult to obtain the analytic expression of the zero point, we try to use the profile zero points to analyze the spatial variation. The test results show that the spatial variation laws of both first- and second-order vertical derivative zero points are almost the same but the second-order derivative zero point position is closer to the top surface edge of the geological bodies than the first-order vertical derivative and has a relatively high resolution. Moreover, with an increase in buried depth, for a single boundary model, the vertical derivative zero point location tends to move from the top surface edge to the outside of the buried body but finally converges to a fixed value. For a double boundary model, the vertical derivative zero point location tends to migrate from the top surface edge to the outside of the buried body. For multiple boundary models, the vertical derivative zero point location converges from the top surface edge to the outside of the buried body where some zero points coincide and finally vanish. Finally, the effectiveness and reliability of the proposed method is verified using real field data.展开更多
This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), whe...This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.展开更多
Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or...Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.展开更多
In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetr...In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.展开更多
The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, lea...The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.展开更多
I. INTRODUCTION Derivative action was introduced into the Chinese Company Law for the very first time during the revision process in 2005. Some scholars have argued that derivative action was actually permitted under ...I. INTRODUCTION Derivative action was introduced into the Chinese Company Law for the very first time during the revision process in 2005. Some scholars have argued that derivative action was actually permitted under the Chinese Company Law of 1993 because article 111 of the Chinese Company Law of 1993 provided that shareholders have the right to raise a suit when directors violate the law.1 However, main stream scholars object to this view and assert that this article was only intended for shareholders1 personal actions in joint stock companies.展开更多
基金jointly supported by the National Major Science and Technology Program (No. 2008ZX05025)the National 973 Program (Grant No. 2009CB219400)
文摘In this paper we deduce the analytic solutions of the first- and second-order vertical derivative zero points for gravity anomalies in simple regular models with single, double, and multiple edges and analyze their spatial variation. For another simple regular models where it is difficult to obtain the analytic expression of the zero point, we try to use the profile zero points to analyze the spatial variation. The test results show that the spatial variation laws of both first- and second-order vertical derivative zero points are almost the same but the second-order derivative zero point position is closer to the top surface edge of the geological bodies than the first-order vertical derivative and has a relatively high resolution. Moreover, with an increase in buried depth, for a single boundary model, the vertical derivative zero point location tends to move from the top surface edge to the outside of the buried body but finally converges to a fixed value. For a double boundary model, the vertical derivative zero point location tends to migrate from the top surface edge to the outside of the buried body. For multiple boundary models, the vertical derivative zero point location converges from the top surface edge to the outside of the buried body where some zero points coincide and finally vanish. Finally, the effectiveness and reliability of the proposed method is verified using real field data.
文摘This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.
基金This work was supported by the Natural Science Foundation of China(Grant Nos.61673169,11701176,11626101,11601485).
文摘Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.
基金Supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates under Grant No.201410290039the Fundamental Research Funds for the Central Universities under Grant Nos.2015QNA53 and 2015XKQY14+2 种基金the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Minesthe General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2015M570498Natural Sciences Foundation of China under Grant No.11301527
文摘In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.
文摘The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.
基金funded by National Social Science Funding Project(17CFX072)Southwest University of Political Science and Law 2018 Key Projects and the 19th Special Project(2017)
文摘I. INTRODUCTION Derivative action was introduced into the Chinese Company Law for the very first time during the revision process in 2005. Some scholars have argued that derivative action was actually permitted under the Chinese Company Law of 1993 because article 111 of the Chinese Company Law of 1993 provided that shareholders have the right to raise a suit when directors violate the law.1 However, main stream scholars object to this view and assert that this article was only intended for shareholders1 personal actions in joint stock companies.
