In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using ...In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.展开更多
The rationality of using strain energy storage index(Wet)for evaluating rockburst proneness was theoretically verified based on linear energy storage(LES)law in this study.The LES law is defined as the linear relation...The rationality of using strain energy storage index(Wet)for evaluating rockburst proneness was theoretically verified based on linear energy storage(LES)law in this study.The LES law is defined as the linear relationship between the elastic strain energy stored inside the solid material and the input strain energy during loading.It is used to determine the elastic strain energy and dissipated strain energy of rock specimens at various loading/unloading stress levels.The results showed that the Wetvalue obtained from experiments was close to the corresponding theoretical one from the LES law.Furthermore,with an increase in the loading/unloading stress level,the ratio of elastic strain energy to dissipated strain energy converged to the peak-strength strain energy storage index(Wp et).This index is stable and can better reflect the relative magnitudes of the stored energy and the dissipated energy of rocks at the whole pre-peak stage than the strain energy storage index.The peak-strength strain energy storage index can replace the conventional strain energy storage index as a new index for evaluating rockburst proneness.展开更多
The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defin...The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy;2) the formal axiomatic epistemology-and-axiology theory Sigma has been defined precisely and applied to proper-physics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion “formal-axiological law of algebra of metaphysics” is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.展开更多
In this work,we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo’s form.The L1 implicit scheme is shown to preserve a variational energy dissipation law o...In this work,we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo’s form.The L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform time meshes by using the recent discrete analysis tools,i.e.,the discrete orthogonal convolution kernels and discrete complementary convolution kernels.Then the discrete embedding techniques and the fractional Gronwall inequality are applied to establish an L^(2)norm error estimate on nonuniform time meshes.An adaptive time-stepping strategy according to the dynamical feature of the system is presented to capture the multi-scale behaviors and to improve the computational performance.展开更多
Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system...Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.展开更多
To evaluate the coal burst proneness more precisely,a new energy criterion namely the residual elastic energy index was proposed.This study begins by performing the single-cyclic loading-unloading uniaxial compression...To evaluate the coal burst proneness more precisely,a new energy criterion namely the residual elastic energy index was proposed.This study begins by performing the single-cyclic loading-unloading uniaxial compression tests with five pre-peak unloading stress levels to explore the energy storage characteristics of coal.Five types of coals from different mines were tested,and the instantaneous destruction process of the coal specimens under compression loading was recorded using a high speed camera.The results showed a linear relationship between the elastic strain energy density and input energy density,which confirms the linear energy storage law of coal.Based on this linear energy storage law,the peak elastic strain energy density of each coal specimen was obtained precisely.Subsequently,a new energy criterion of coal burst proneness was established,which was called the residual elastic energy index(defined as the difference between the peak elastic strain energy density and post peak failure energy density).Considering the destruction process and actual failure characteristics of coal specimens,the accuracy of evaluating coal burst proneness based on the residual elastic energy index was examined.The results indicated that the residual elastic energy index enables reliable and precise evaluations of the coal burst proneness.展开更多
Many underground engineering projects show that rockburst can occur in rocks at great depth and high temperature, and temperature is a critical factor affecting the intensity of rockburst. In general, temperature can ...Many underground engineering projects show that rockburst can occur in rocks at great depth and high temperature, and temperature is a critical factor affecting the intensity of rockburst. In general, temperature can affect the energy storage, dissipation, and surplus in rock. To explore the influence of temperature on the energy storage and dissipation characteristics and rockburst proneness, the present study has carried out a range of the uniaxial compression(UC) and single-cyclic loading-unloading uniaxial compression(SCLUC) tests on pre-heated granite specimens at 20℃-700℃. The results demonstrate that the rockburst proneness of pre-heated granite initially increases and subsequently decreases with the increase of temperature. The temperature of 300℃ has been found to be the threshold for rockburst proneness. Meanwhile, it is found that the elastic strain energy density increases linearly with the total input strain energy density for the pre-heated granites, confirming that the linear energy property of granite has not been altered by temperature. According to this inherent property, the peak elastic strain energy of pre-heated granites can be calculated accurately. On this basis, utilising the residual elastic energy index, the rockburst proneness of pre-heated granite can be determined quantitatively. The obtained results from high to low are: 317.9 k J/m^(3)(300℃), 264.1 k J/m^(3)(100℃), 260.6 k J/m^(3)(20℃), 235.5 k J/m^(3)(500℃), 158.9 k J/m^(3)(700℃), which are consistent with the intensity of actual rockburst for specimens. In addition, the relationship between temperature and energy storage capacity(ESC) of granite was discussed, revealing that high temperature impairs ESC of rocks, which is essential for reducing the rockburst proneness. This study provides some new insights into the rockburst proneness evaluation in high-temperature rock engineering.展开更多
The cleavage force F(z) needed to separate parallel atomic planes by a distance z is first discussed for simple s-p metals using density functional theory.For the s-p nearly free-electron metals the linearized Thomas-...The cleavage force F(z) needed to separate parallel atomic planes by a distance z is first discussed for simple s-p metals using density functional theory.For the s-p nearly free-electron metals the linearized Thomas-Fermi equation is solved self-consistently in the cases of (a) semi-infinite planes of jellium (i.e. smeared uniform positive ions) and (b) a semi-infinite cylinder of finite radius, cleaved by a plane perpendicular to its axis. In (a), the elastic region has the form F(z)=Az ∝ Zrs-11/2, where rs is the mean interelectronic distance in the jellium model. Size effects are then considered, with possible relevance to atomic force microscopy.Defect energies are treated, using both electron theory and pair force laws.展开更多
The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special r...The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.展开更多
The strain energy storage index WET was widely used to evaluate coal burst liability,but the scientific evidence for selecting the unloading stress level interval(around 80%of peak strength)remains lacking,and WET can...The strain energy storage index WET was widely used to evaluate coal burst liability,but the scientific evidence for selecting the unloading stress level interval(around 80%of peak strength)remains lacking,and WET can not reflect the energy storage and dissipation ratio(ESD ratio)of the whole pre-peak stage for coal materials.In this study,these two key problems in WET calculation and application were solved based on the linear energy storage(LES)law.The LES law was defined as the linear relationship between the elastic strain energy and input strain energy for solid material during loading.Using the LES law,the elastic strain energy and dissipated strain energy of at 10 types of coals were calculated precisely,and ideal ESD ratio and general ESD ratio at any stress level will be obtained subsequently.The results also show that WET is extremely close to the ideal and general ESD ratio,which proves that the selecting stress level of WET calculation is scientific and reasonable.Furthermore,the general ESD ratio converges to the peak ESD ratio(namely peak strain energy storage index WET P)as stress level increases.Compared with WET,Wp ET not only reflects the ESD ratio of coal materials over the whole pre-peak loading stage,but also exhibits excellent stability.Consequently,Wp ET is suggested as a new evaluation index of coal burst liability.展开更多
There is an obvious gap in sprint level at home and abroad,and there are different opinions on the reasons.According to the analysis,physical energy and its distribution in each segment are the main factors restrictin...There is an obvious gap in sprint level at home and abroad,and there are different opinions on the reasons.According to the analysis,physical energy and its distribution in each segment are the main factors restricting the sprint performance in China.Different from middle and long-distance running,we must rely on accurate sectional timing technology to master the law of speed-physical energy change in the process of sprint.Each stage is an integral part of the whole dash process,and each part restricts each other.Each stage has a relative best achievement.Simply pursuing the optimal state of segment is not only not helpful to the final result,but also counterproductive.展开更多
Unidentified Infrared emission bands (UIBs) are infrared discrete emissions from circumstellar regions, interstellar media (ISM), star-forming regions, and extragalactic objects for which the identity of the emitting ...Unidentified Infrared emission bands (UIBs) are infrared discrete emissions from circumstellar regions, interstellar media (ISM), star-forming regions, and extragalactic objects for which the identity of the emitting materials is unknown. The main infrared features occur around peaks at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 μm with the photon’s rest energy at the peaks 0.376, 0.200, 0.161, 0.144, 0.111, and 0.098 eV, respectively. The UIB emission phenomenon has been studied for about forty five years. The prevailing hypothesis is that the materials responsible for UIB are polycyclic aromatic hydrocarbon (PAH) molecules. PAHs are thought to be one of the main forms in which carbon exists in space. And yet, not a single member of this group of compounds had been identified in space definitively until now [1]. In frames of Hypersphere World-Universe Model (WUM), we introduced Dark Matter (DM) particles, named DIONs, with the rest energy 0.199 eV and an energy density of 68.8% of the total energy density of the World. DIONs compose Outer shells of DM Supercluster’s Cores—the main objects of the World [2]. In this paper, we give an explanation of UIB emission based on the self-annihilation of DM particles DIONs and biDIONs (DIONs pairs) with a rest energy about 0.38 eV that depends on the binding energy. To the best of our knowledge, WUM is the only cosmological model in existence that is consistent with UIB emission phenomenon.展开更多
As a promising strategy to adjust the order in the variable-order BDF algorithm,a time filtered backward Euler scheme is investigated for the molecular beam epitaxial equation with slope selection.The temporal second-...As a promising strategy to adjust the order in the variable-order BDF algorithm,a time filtered backward Euler scheme is investigated for the molecular beam epitaxial equation with slope selection.The temporal second-order convergence in the L^(2)norm is established under a convergence-solvability-stability(CSS)-consistent time-step constraint.The CSS-consistent condition means that the maximum stepsize limit required for convergence is of the same order to that for solvability and stability(in certain norms)as the small interface parameterε→0^(+).Similar to the backward Euler scheme,the time filtered backward Euler scheme preserves some physical properties of the original problem at the discrete levels,including the volume conservation,the energy dissipation law and L^(2)norm boundedness.Numerical tests are included to support the theoretical results.展开更多
Dark energy has been introduced in order to explain the observed acceleration of the expansion of our Universe. It seems to be distributed almost uniformly and it has an essential influence on the present value of the...Dark energy has been introduced in order to explain the observed acceleration of the expansion of our Universe. It seems to be distributed almost uniformly and it has an essential influence on the present value of the Hubble constant which characterizes the rate of this expansion. The Newtonian theory of gravitation is formulated so that the laws of conservation of energy and momentum hold. However, the Universe is designed so that the total amount of energy is slowly, but continually increasing, since its expansion is accelerating. Our examples show that even the Solar System and also our Galaxy imperceptibly expand thanks to dark energy whose origins are tiny antigravity forces. We claim that these forces appear due to the finite speed of gravitational interaction, which causes gravitational aberration effects. We show that effects of dark energy are observable;they are not only globally, but also in local systems. These effects can be measured and are comparable with the present value of the Hubble constant.展开更多
The empirically reported values of the critical current density (<i>j<sub>c</sub></i>) of Bi-2212 as 2.4 × 10<sup>5</sup> (<i>j<sub>c</sub></i><sub&g...The empirically reported values of the critical current density (<i>j<sub>c</sub></i>) of Bi-2212 as 2.4 × 10<sup>5</sup> (<i>j<sub>c</sub></i><sub>1</sub>;Sample 1) and 1.0 × 10<sup>6</sup> A/cm<sup>2</sup> (<i>j<sub>c</sub></i><sub>2</sub>;Sample 2) are intriguing because both of them correspond to the <i>same</i> values of the temperature <i>T</i> = 4.2 K and the applied magnetic field <i>H</i> = 12 × 10<sup>4</sup> G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential <i>μ</i> subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of <i>μ</i> of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (<i>e-e</i>) and the hole-hole (<i>h-h</i>) pairs to <i>j<sub>c</sub></i>—a feature to which no heed was paid earlier. The essence of our findings is that the <i>j<sub>c</sub></i>s of the two samples differ because they are characterized by different values of the <i>primary</i> variables <i>μ<sub>i</sub></i><sub> </sub>and <img src="Edit_e1b831e9-dc51-4c3b-bd84-fa905e3e62b5.png" alt="" />, where <img src="Edit_1f775a80-30ab-447d-861f-afb4ba8fba6a.png" alt="" /> is the effective mass of a charge-carrier and <i>m<sub>e</sub></i><sub> </sub>is the free-electron mass and <i>i</i> = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being <i>predominantly h-h</i> pairs, the values of these parameters are estimated to be: <i>μ</i><sub>1</sub> ≈ 12.3 meV, <i>η</i><sub>1</sub> ≈ 0.58;<i>μ</i><sub>2</sub> ≈ 22.7 meV, <i>η</i><sub>2</sub> ≈ 0.94. Following from these and similar estimates when the charge-carriers are <i>e-e</i> pairs, given below for each sample are the detailed results for the values of the <i>secondary</i> variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.展开更多
In the relativistic mechanics, we calculate a minimal distance between the time scale of a one-dimensional motion having a larger velocity and the time scale of a similar motion with a lower velocity. Concerning the q...In the relativistic mechanics, we calculate a minimal distance between the time scale of a one-dimensional motion having a larger velocity and the time scale of a similar motion with a lower velocity. Concerning the quantum theory, we demonstrate that mechanical parameters entering the electron motion in the Bohr hydrogen atom can provide us with a correct size of the time interval entering the Joule-Lenz law for the emission energy between two neighbouring quantum levels of the atom.展开更多
Current status and the progress of PV in China are introduced with detailed data,covering PV manufacturing,market development,cost reduction and technology innovation.Fast growing of PV industry in China is due to ser...Current status and the progress of PV in China are introduced with detailed data,covering PV manufacturing,market development,cost reduction and technology innovation.Fast growing of PV industry in China is due to series of incentive policies provided by the Chinese government,which are provided in this paper as well.To slow down the speed of PV development,the 5.31 new policy is issued on May 31,2018 by the Chinese government as a milestone.The affections of the new policy and future PV market are analyzed.The target of energy transition of China and the role of PV are provided.PV will have more broad space in development when it comes to grid parity in the future.展开更多
This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in“1+2”dimension case.We consider the planar pressure driven flow where the direction of the molecules is constraine...This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in“1+2”dimension case.We consider the planar pressure driven flow where the direction of the molecules is constrained in the shear plane.The modified Crank-Nicolson finite difference scheme satisfying a discrete energy law will be developed.By using this scheme,it is observed numerically that the direction of the molecules will tumble from the boundary layer and later on the inner layer with a much longer time period.This is consistent with the theoretical prediction.Moreover,we find some complex phenomena,where the tumbling rises from boundary layer and is then embedded into the interior area more clearly when the viscosity coefficientµof the macro flow has a larger value.The norm of the molecular director d will endure greater change as well.This implies that the viscosity of flow plays the role of an accelerator in the whole complex fluids.Comparing these results with the theoretical analysis,we can find that the gradient of the velocity has direct impact on the tumbling phenomena.These results show that the proposed scheme is capable of exploring some physical phenomena embedded in the macro-micro model.展开更多
In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation la...In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost surely.Numerical experiments confirm well the theoretical analysis results.Furthermore,we present a detailed numerical investigation of the optical phenomena based on the compact scheme.By numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time.In particular,if the noise is relatively strong,the soliton will be totally destroyed.Meanwhile,we observe that the phase shift is sensibly modified by the noise.Moreover,the numerical results present inelastic interaction which is different from the deterministic case.展开更多
基金Yanhai Lin was supported by the National Natural Science Foundation of China(Grant No.11702101)the Fundamental Research Funds for the Central Universities and the Promo-tion Program for Young and Middle aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-PY502)+1 种基金the Natural Science Foundation of Fujian Province(Grant No.2019105093)Quanzhou High-Level Talents Support Plan.
文摘In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.
基金supported by the National Natural Science Foundation of China(Grant Nos.42077244 and 41877272)the Fundamental Research Funds for the Central Universities(Grant No.2242022k30054)。
文摘The rationality of using strain energy storage index(Wet)for evaluating rockburst proneness was theoretically verified based on linear energy storage(LES)law in this study.The LES law is defined as the linear relationship between the elastic strain energy stored inside the solid material and the input strain energy during loading.It is used to determine the elastic strain energy and dissipated strain energy of rock specimens at various loading/unloading stress levels.The results showed that the Wetvalue obtained from experiments was close to the corresponding theoretical one from the LES law.Furthermore,with an increase in the loading/unloading stress level,the ratio of elastic strain energy to dissipated strain energy converged to the peak-strength strain energy storage index(Wp et).This index is stable and can better reflect the relative magnitudes of the stored energy and the dissipated energy of rocks at the whole pre-peak stage than the strain energy storage index.The peak-strength strain energy storage index can replace the conventional strain energy storage index as a new index for evaluating rockburst proneness.
文摘The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy;2) the formal axiomatic epistemology-and-axiology theory Sigma has been defined precisely and applied to proper-physics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion “formal-axiological law of algebra of metaphysics” is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.
基金The authors would like to thank Dr.Bingquan Ji for his help on numerical computations.H.-L.Liao is supported by the National Natural Science Foundation of China(Grant 12071216)J.Wang is supported by the Hunan Provincial Innovation Foundation for Postgraduate(Grant XDCX2020B078).
文摘In this work,we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo’s form.The L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform time meshes by using the recent discrete analysis tools,i.e.,the discrete orthogonal convolution kernels and discrete complementary convolution kernels.Then the discrete embedding techniques and the fractional Gronwall inequality are applied to establish an L^(2)norm error estimate on nonuniform time meshes.An adaptive time-stepping strategy according to the dynamical feature of the system is presented to capture the multi-scale behaviors and to improve the computational performance.
基金supported by the Chinese Scholarship Council(CSC)(No.201806340074)Shenzhen Clean Energy Research Institute and National Natural Science Foundation of China(No.12005141)+3 种基金supported by the US Department of Energy(No.DE-AC02-09CH11466)supported by the National MC Energy R&D Program(No.2018YFE0304100)National Key Research and Development Program(Nos.2016YFA0400600,2016YFA0400601 and 2016YFA0400602)the National Natural Science Foundation of China(Nos.11905220 and 11805273)。
文摘Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.
基金This work was supported by the National Natural Science Foundation of China(No.41877272)the Fundamental Research Funds for the Central Universities of Southeast University(No.2242021R10080).
文摘To evaluate the coal burst proneness more precisely,a new energy criterion namely the residual elastic energy index was proposed.This study begins by performing the single-cyclic loading-unloading uniaxial compression tests with five pre-peak unloading stress levels to explore the energy storage characteristics of coal.Five types of coals from different mines were tested,and the instantaneous destruction process of the coal specimens under compression loading was recorded using a high speed camera.The results showed a linear relationship between the elastic strain energy density and input energy density,which confirms the linear energy storage law of coal.Based on this linear energy storage law,the peak elastic strain energy density of each coal specimen was obtained precisely.Subsequently,a new energy criterion of coal burst proneness was established,which was called the residual elastic energy index(defined as the difference between the peak elastic strain energy density and post peak failure energy density).Considering the destruction process and actual failure characteristics of coal specimens,the accuracy of evaluating coal burst proneness based on the residual elastic energy index was examined.The results indicated that the residual elastic energy index enables reliable and precise evaluations of the coal burst proneness.
基金supported by the National Natural Science Foundation of China (Grant No. 41877272)the Fundamental Research Funds for the Central Universities (Grant No.2242022k30054)the Fundamental Research Funds for the Central Universities of Central South University (Grant No.2021zzts0861)。
文摘Many underground engineering projects show that rockburst can occur in rocks at great depth and high temperature, and temperature is a critical factor affecting the intensity of rockburst. In general, temperature can affect the energy storage, dissipation, and surplus in rock. To explore the influence of temperature on the energy storage and dissipation characteristics and rockburst proneness, the present study has carried out a range of the uniaxial compression(UC) and single-cyclic loading-unloading uniaxial compression(SCLUC) tests on pre-heated granite specimens at 20℃-700℃. The results demonstrate that the rockburst proneness of pre-heated granite initially increases and subsequently decreases with the increase of temperature. The temperature of 300℃ has been found to be the threshold for rockburst proneness. Meanwhile, it is found that the elastic strain energy density increases linearly with the total input strain energy density for the pre-heated granites, confirming that the linear energy property of granite has not been altered by temperature. According to this inherent property, the peak elastic strain energy of pre-heated granites can be calculated accurately. On this basis, utilising the residual elastic energy index, the rockburst proneness of pre-heated granite can be determined quantitatively. The obtained results from high to low are: 317.9 k J/m^(3)(300℃), 264.1 k J/m^(3)(100℃), 260.6 k J/m^(3)(20℃), 235.5 k J/m^(3)(500℃), 158.9 k J/m^(3)(700℃), which are consistent with the intensity of actual rockburst for specimens. In addition, the relationship between temperature and energy storage capacity(ESC) of granite was discussed, revealing that high temperature impairs ESC of rocks, which is essential for reducing the rockburst proneness. This study provides some new insights into the rockburst proneness evaluation in high-temperature rock engineering.
文摘The cleavage force F(z) needed to separate parallel atomic planes by a distance z is first discussed for simple s-p metals using density functional theory.For the s-p nearly free-electron metals the linearized Thomas-Fermi equation is solved self-consistently in the cases of (a) semi-infinite planes of jellium (i.e. smeared uniform positive ions) and (b) a semi-infinite cylinder of finite radius, cleaved by a plane perpendicular to its axis. In (a), the elastic region has the form F(z)=Az ∝ Zrs-11/2, where rs is the mean interelectronic distance in the jellium model. Size effects are then considered, with possible relevance to atomic force microscopy.Defect energies are treated, using both electron theory and pair force laws.
文摘The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.
基金supported by the National Natural Science Foundation of China (Grant No.41877272,42077244).
文摘The strain energy storage index WET was widely used to evaluate coal burst liability,but the scientific evidence for selecting the unloading stress level interval(around 80%of peak strength)remains lacking,and WET can not reflect the energy storage and dissipation ratio(ESD ratio)of the whole pre-peak stage for coal materials.In this study,these two key problems in WET calculation and application were solved based on the linear energy storage(LES)law.The LES law was defined as the linear relationship between the elastic strain energy and input strain energy for solid material during loading.Using the LES law,the elastic strain energy and dissipated strain energy of at 10 types of coals were calculated precisely,and ideal ESD ratio and general ESD ratio at any stress level will be obtained subsequently.The results also show that WET is extremely close to the ideal and general ESD ratio,which proves that the selecting stress level of WET calculation is scientific and reasonable.Furthermore,the general ESD ratio converges to the peak ESD ratio(namely peak strain energy storage index WET P)as stress level increases.Compared with WET,Wp ET not only reflects the ESD ratio of coal materials over the whole pre-peak loading stage,but also exhibits excellent stability.Consequently,Wp ET is suggested as a new evaluation index of coal burst liability.
文摘There is an obvious gap in sprint level at home and abroad,and there are different opinions on the reasons.According to the analysis,physical energy and its distribution in each segment are the main factors restricting the sprint performance in China.Different from middle and long-distance running,we must rely on accurate sectional timing technology to master the law of speed-physical energy change in the process of sprint.Each stage is an integral part of the whole dash process,and each part restricts each other.Each stage has a relative best achievement.Simply pursuing the optimal state of segment is not only not helpful to the final result,but also counterproductive.
文摘Unidentified Infrared emission bands (UIBs) are infrared discrete emissions from circumstellar regions, interstellar media (ISM), star-forming regions, and extragalactic objects for which the identity of the emitting materials is unknown. The main infrared features occur around peaks at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 μm with the photon’s rest energy at the peaks 0.376, 0.200, 0.161, 0.144, 0.111, and 0.098 eV, respectively. The UIB emission phenomenon has been studied for about forty five years. The prevailing hypothesis is that the materials responsible for UIB are polycyclic aromatic hydrocarbon (PAH) molecules. PAHs are thought to be one of the main forms in which carbon exists in space. And yet, not a single member of this group of compounds had been identified in space definitively until now [1]. In frames of Hypersphere World-Universe Model (WUM), we introduced Dark Matter (DM) particles, named DIONs, with the rest energy 0.199 eV and an energy density of 68.8% of the total energy density of the World. DIONs compose Outer shells of DM Supercluster’s Cores—the main objects of the World [2]. In this paper, we give an explanation of UIB emission based on the self-annihilation of DM particles DIONs and biDIONs (DIONs pairs) with a rest energy about 0.38 eV that depends on the binding energy. To the best of our knowledge, WUM is the only cosmological model in existence that is consistent with UIB emission phenomenon.
基金The work of H.-L.Liao is supported by NSF of China(Grant No.12071216)。
文摘As a promising strategy to adjust the order in the variable-order BDF algorithm,a time filtered backward Euler scheme is investigated for the molecular beam epitaxial equation with slope selection.The temporal second-order convergence in the L^(2)norm is established under a convergence-solvability-stability(CSS)-consistent time-step constraint.The CSS-consistent condition means that the maximum stepsize limit required for convergence is of the same order to that for solvability and stability(in certain norms)as the small interface parameterε→0^(+).Similar to the backward Euler scheme,the time filtered backward Euler scheme preserves some physical properties of the original problem at the discrete levels,including the volume conservation,the energy dissipation law and L^(2)norm boundedness.Numerical tests are included to support the theoretical results.
文摘Dark energy has been introduced in order to explain the observed acceleration of the expansion of our Universe. It seems to be distributed almost uniformly and it has an essential influence on the present value of the Hubble constant which characterizes the rate of this expansion. The Newtonian theory of gravitation is formulated so that the laws of conservation of energy and momentum hold. However, the Universe is designed so that the total amount of energy is slowly, but continually increasing, since its expansion is accelerating. Our examples show that even the Solar System and also our Galaxy imperceptibly expand thanks to dark energy whose origins are tiny antigravity forces. We claim that these forces appear due to the finite speed of gravitational interaction, which causes gravitational aberration effects. We show that effects of dark energy are observable;they are not only globally, but also in local systems. These effects can be measured and are comparable with the present value of the Hubble constant.
文摘The empirically reported values of the critical current density (<i>j<sub>c</sub></i>) of Bi-2212 as 2.4 × 10<sup>5</sup> (<i>j<sub>c</sub></i><sub>1</sub>;Sample 1) and 1.0 × 10<sup>6</sup> A/cm<sup>2</sup> (<i>j<sub>c</sub></i><sub>2</sub>;Sample 2) are intriguing because both of them correspond to the <i>same</i> values of the temperature <i>T</i> = 4.2 K and the applied magnetic field <i>H</i> = 12 × 10<sup>4</sup> G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential <i>μ</i> subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of <i>μ</i> of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (<i>e-e</i>) and the hole-hole (<i>h-h</i>) pairs to <i>j<sub>c</sub></i>—a feature to which no heed was paid earlier. The essence of our findings is that the <i>j<sub>c</sub></i>s of the two samples differ because they are characterized by different values of the <i>primary</i> variables <i>μ<sub>i</sub></i><sub> </sub>and <img src="Edit_e1b831e9-dc51-4c3b-bd84-fa905e3e62b5.png" alt="" />, where <img src="Edit_1f775a80-30ab-447d-861f-afb4ba8fba6a.png" alt="" /> is the effective mass of a charge-carrier and <i>m<sub>e</sub></i><sub> </sub>is the free-electron mass and <i>i</i> = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being <i>predominantly h-h</i> pairs, the values of these parameters are estimated to be: <i>μ</i><sub>1</sub> ≈ 12.3 meV, <i>η</i><sub>1</sub> ≈ 0.58;<i>μ</i><sub>2</sub> ≈ 22.7 meV, <i>η</i><sub>2</sub> ≈ 0.94. Following from these and similar estimates when the charge-carriers are <i>e-e</i> pairs, given below for each sample are the detailed results for the values of the <i>secondary</i> variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.
文摘In the relativistic mechanics, we calculate a minimal distance between the time scale of a one-dimensional motion having a larger velocity and the time scale of a similar motion with a lower velocity. Concerning the quantum theory, we demonstrate that mechanical parameters entering the electron motion in the Bohr hydrogen atom can provide us with a correct size of the time interval entering the Joule-Lenz law for the emission energy between two neighbouring quantum levels of the atom.
文摘Current status and the progress of PV in China are introduced with detailed data,covering PV manufacturing,market development,cost reduction and technology innovation.Fast growing of PV industry in China is due to series of incentive policies provided by the Chinese government,which are provided in this paper as well.To slow down the speed of PV development,the 5.31 new policy is issued on May 31,2018 by the Chinese government as a milestone.The affections of the new policy and future PV market are analyzed.The target of energy transition of China and the role of PV are provided.PV will have more broad space in development when it comes to grid parity in the future.
基金Hui Zhang’s research is partially supported by the Key Basic Research Project of the Ministry of Education of China under Grant No.107016the State Key Basic Research Project of China under Grant No.2005CB321704.
文摘This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in“1+2”dimension case.We consider the planar pressure driven flow where the direction of the molecules is constrained in the shear plane.The modified Crank-Nicolson finite difference scheme satisfying a discrete energy law will be developed.By using this scheme,it is observed numerically that the direction of the molecules will tumble from the boundary layer and later on the inner layer with a much longer time period.This is consistent with the theoretical prediction.Moreover,we find some complex phenomena,where the tumbling rises from boundary layer and is then embedded into the interior area more clearly when the viscosity coefficientµof the macro flow has a larger value.The norm of the molecular director d will endure greater change as well.This implies that the viscosity of flow plays the role of an accelerator in the whole complex fluids.Comparing these results with the theoretical analysis,we can find that the gradient of the velocity has direct impact on the tumbling phenomena.These results show that the proposed scheme is capable of exploring some physical phenomena embedded in the macro-micro model.
基金This work was supported by the National Natural Science Foundation of China(Nos.91530118,91130003,11021101,11290142,11471310,11601032,11301234,11271171)the Provincial Natural Science Foundation of Jiangxi(Nos.20142BCB23009,20161ACB20006,20151BAB201012).
文摘In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost surely.Numerical experiments confirm well the theoretical analysis results.Furthermore,we present a detailed numerical investigation of the optical phenomena based on the compact scheme.By numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time.In particular,if the noise is relatively strong,the soliton will be totally destroyed.Meanwhile,we observe that the phase shift is sensibly modified by the noise.Moreover,the numerical results present inelastic interaction which is different from the deterministic case.
