With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various...With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.展开更多
Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and ...Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and that a stable limitt cycle existsaround the singularity (1/2, 2) when K∈(9-δ, 9).展开更多
To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and ho...To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and how light propagates in bio-tissue is analyzed in virtue of mathematics and physics equations. The relations,in which light intensity of Class 1 and Class 2 light with different wavelengths changes with their permeation depth,and in which Class 1 light intensity (signal light intensity) changes with the probing depth, and in which angularly resolved diffuse reflectance and diffuse transmittance change with the exiting angle, are studied. The results show that Monte Carlo simulation results are consistent with the theory data.展开更多
Hot Dry Rock(HDR)is the most potential renewable geothermal energy in the future.Enhanced Geothermal System(EGS)is the most effective method for the development and utilization of HDR resources,and fractures are the m...Hot Dry Rock(HDR)is the most potential renewable geothermal energy in the future.Enhanced Geothermal System(EGS)is the most effective method for the development and utilization of HDR resources,and fractures are the main flow channels and one of the most important conditions for studying heat transfer process of EGS.Therefore,the heat transfer process and the heat transfer mechanism in fractures of EGS have been the hot spots of research.Due to the particularity of the mathematical models of heat transfer,research in this field has been at an exploratory stage,and its methods are mainly experimental tests and numerical simulations.This paper introduces the progress on heat transfer in fractures of Hot Dry Rock EGS in detail,provides a comparative analysis of the research results and prospects for future research directions:It is suggested that relevant scholars should further study the mathematical equations which are applicable to engineering construction of seepage heat transfer in irregular fractures of the rock mass,the unsteady heat transfer process between multiple fractures of the rock mass and the heat transfer mechanism of the complex three-dimensional models of EGS.展开更多
A mathematical model for the thermoregulation in the dermal layers of the human body is proposed. The skin is composed mainly of three layers - epidermis, dermis and subcutaneous tissues. The relative constancy of the...A mathematical model for the thermoregulation in the dermal layers of the human body is proposed. The skin is composed mainly of three layers - epidermis, dermis and subcutaneous tissues. The relative constancy of the body temperature is remarkable because there is a continuous exchange of heat with the external environment as well as within the different compartments of the body. A model describes the distribution of dermal tempera- ture as a function of internal and external parameters, such as temperature of the incoming arterial blood, blood flow, ambient temperature, and heat exchange with the environment. It is shown that substantial changes in human dermal temperature can be accomplished only through changes in the temperature of the incoming arterial blood or substantial suppression of blood flow. Other parameters can lead only to temperature changes near the skin surface.展开更多
Microdamage is produced in bone tissue under the long-termeffects of physiological loading,as well as age,disease and other factors.Bone remodeling can repair microdamage,otherwise this damage will undermine bone qual...Microdamage is produced in bone tissue under the long-termeffects of physiological loading,as well as age,disease and other factors.Bone remodeling can repair microdamage,otherwise this damage will undermine bone quality and even lead to fractures.In this paper,the damage variable was introduced into the remodeling algorithm.The new remodeling algorithm contains a quadratic term that can simulate reduction in bone density after large numbers of loading cycles.The model was applied in conjunction with the 3Dfinite elementmethod(FEM)to the remodeling of the proximal femur.The results showed that the initial accumulation of fatigue damage led to an increase in density but when the damage reached a certain level,the bone density decreased rapidly until the femur failed.With the accumulation of damage,bone remodeling was coupled with fatigue damage to maintain the function of bone.When the accumulation of damage reached a certain level,bone remodeling failed to repair the accumulated fatigue damage in time,and continued cyclic loading significantly weakened the loadbearing capacity of the bone.The new mathematical model not only predicts fatigue life,but also helps to further understand the compromise between damage repair and damage accumulation,which is of great significance for the prevention and treatment of clinical bone diseases.展开更多
Papaya (<em>Carica papaya</em> L.) is a typical plant with a tropical climate, but also grown in subtropical regions. Using mathematical models well-adjusted allows with good precision to estimate characte...Papaya (<em>Carica papaya</em> L.) is a typical plant with a tropical climate, but also grown in subtropical regions. Using mathematical models well-adjusted allows with good precision to estimate characteristics of interest. The objective was to adjust an equation tha<em></em>t estimates the fruit mass for each cultivar of papaya, Alian<span style="white-space:nowrap;">ç</span>a and THB, using only one measure, length or width. The experiment was conducted in the municipality of Linhares in the state of Espírito Santo, Brazil. Seedlings were planted on the same day, spaced 3.6 × 1.5 m and in rows side by side. Initially, the equations were modeled, they were linearized and then the covariance analysis was performed in order to verify the possibility of an equation that would serve both cultivars. As the covariance was significant, it was necessary to develop equations for each cultivar. To obtain the growth equations, 350 fruits of cultivar Alian<span style="white-space:nowrap;">ç</span>a and 550 of THB were used. The validation was performed with 50 fruits of each. The characteristics evaluated were the largest width (W in mm), the longest fruit length (L, in mm) and the observed mass (OM in g). The equations that best fit were those of the power model that use width (W) as an independent variable.展开更多
Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be...Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.展开更多
This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of...This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor R<sub>Co</sub> is a control that aims to prevent sudden variations in the intensity of the electric current i<sub>1</sub>(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance R<sub>A</sub> of the ammeter used in the calculation of the intensity of the electric current i<sub>1</sub>(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kU<sub>C</sub>(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kU<sub>C</sub>(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.展开更多
By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final r...By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final results were represented in hyperbolic function, trigonometric function and rational function with arbitrary parameters.展开更多
In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the neces...In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered.展开更多
文摘With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.
文摘Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and that a stable limitt cycle existsaround the singularity (1/2, 2) when K∈(9-δ, 9).
文摘To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and how light propagates in bio-tissue is analyzed in virtue of mathematics and physics equations. The relations,in which light intensity of Class 1 and Class 2 light with different wavelengths changes with their permeation depth,and in which Class 1 light intensity (signal light intensity) changes with the probing depth, and in which angularly resolved diffuse reflectance and diffuse transmittance change with the exiting angle, are studied. The results show that Monte Carlo simulation results are consistent with the theory data.
基金provided by the Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Project No.SJCX20_0984).
文摘Hot Dry Rock(HDR)is the most potential renewable geothermal energy in the future.Enhanced Geothermal System(EGS)is the most effective method for the development and utilization of HDR resources,and fractures are the main flow channels and one of the most important conditions for studying heat transfer process of EGS.Therefore,the heat transfer process and the heat transfer mechanism in fractures of EGS have been the hot spots of research.Due to the particularity of the mathematical models of heat transfer,research in this field has been at an exploratory stage,and its methods are mainly experimental tests and numerical simulations.This paper introduces the progress on heat transfer in fractures of Hot Dry Rock EGS in detail,provides a comparative analysis of the research results and prospects for future research directions:It is suggested that relevant scholars should further study the mathematical equations which are applicable to engineering construction of seepage heat transfer in irregular fractures of the rock mass,the unsteady heat transfer process between multiple fractures of the rock mass and the heat transfer mechanism of the complex three-dimensional models of EGS.
文摘A mathematical model for the thermoregulation in the dermal layers of the human body is proposed. The skin is composed mainly of three layers - epidermis, dermis and subcutaneous tissues. The relative constancy of the body temperature is remarkable because there is a continuous exchange of heat with the external environment as well as within the different compartments of the body. A model describes the distribution of dermal tempera- ture as a function of internal and external parameters, such as temperature of the incoming arterial blood, blood flow, ambient temperature, and heat exchange with the environment. It is shown that substantial changes in human dermal temperature can be accomplished only through changes in the temperature of the incoming arterial blood or substantial suppression of blood flow. Other parameters can lead only to temperature changes near the skin surface.
基金This research was funded by National Natural Science Foundation of China(Grant No.11972247).
文摘Microdamage is produced in bone tissue under the long-termeffects of physiological loading,as well as age,disease and other factors.Bone remodeling can repair microdamage,otherwise this damage will undermine bone quality and even lead to fractures.In this paper,the damage variable was introduced into the remodeling algorithm.The new remodeling algorithm contains a quadratic term that can simulate reduction in bone density after large numbers of loading cycles.The model was applied in conjunction with the 3Dfinite elementmethod(FEM)to the remodeling of the proximal femur.The results showed that the initial accumulation of fatigue damage led to an increase in density but when the damage reached a certain level,the bone density decreased rapidly until the femur failed.With the accumulation of damage,bone remodeling was coupled with fatigue damage to maintain the function of bone.When the accumulation of damage reached a certain level,bone remodeling failed to repair the accumulated fatigue damage in time,and continued cyclic loading significantly weakened the loadbearing capacity of the bone.The new mathematical model not only predicts fatigue life,but also helps to further understand the compromise between damage repair and damage accumulation,which is of great significance for the prevention and treatment of clinical bone diseases.
文摘Papaya (<em>Carica papaya</em> L.) is a typical plant with a tropical climate, but also grown in subtropical regions. Using mathematical models well-adjusted allows with good precision to estimate characteristics of interest. The objective was to adjust an equation tha<em></em>t estimates the fruit mass for each cultivar of papaya, Alian<span style="white-space:nowrap;">ç</span>a and THB, using only one measure, length or width. The experiment was conducted in the municipality of Linhares in the state of Espírito Santo, Brazil. Seedlings were planted on the same day, spaced 3.6 × 1.5 m and in rows side by side. Initially, the equations were modeled, they were linearized and then the covariance analysis was performed in order to verify the possibility of an equation that would serve both cultivars. As the covariance was significant, it was necessary to develop equations for each cultivar. To obtain the growth equations, 350 fruits of cultivar Alian<span style="white-space:nowrap;">ç</span>a and 550 of THB were used. The validation was performed with 50 fruits of each. The characteristics evaluated were the largest width (W in mm), the longest fruit length (L, in mm) and the observed mass (OM in g). The equations that best fit were those of the power model that use width (W) as an independent variable.
文摘Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.
文摘This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor R<sub>Co</sub> is a control that aims to prevent sudden variations in the intensity of the electric current i<sub>1</sub>(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance R<sub>A</sub> of the ammeter used in the calculation of the intensity of the electric current i<sub>1</sub>(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kU<sub>C</sub>(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kU<sub>C</sub>(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.
文摘By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final results were represented in hyperbolic function, trigonometric function and rational function with arbitrary parameters.
文摘In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered.
