The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the...The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.展开更多
In present note,we apply the Leibniz formula with the nabla operator in discrete fractional calculus(DFC)due to obtain the discrete fractional solutions of a class of associated Bessel equations(ABEs)and a class of as...In present note,we apply the Leibniz formula with the nabla operator in discrete fractional calculus(DFC)due to obtain the discrete fractional solutions of a class of associated Bessel equations(ABEs)and a class of associated Legendre equations(ALEs),respectively.Thus,we exhibit a new solution method for such second order linear ordinary differential equations with singular points.展开更多
We investigate the perturbation to discrete conformal invariance and the adiabatic invariants of Lagrangian systems. A variational algorithm is proposed for a system subjected to the perturbation quantities. The discr...We investigate the perturbation to discrete conformal invariance and the adiabatic invariants of Lagrangian systems. A variational algorithm is proposed for a system subjected to the perturbation quantities. The discrete determining equations of the perturbations to conformal invariance are established. For perturbed Lagrangian systems, the condition of the existence of adiabatic invariant is derived from the discrete perturbation to conformal invariance. The numerical simulations demonstrate that the variational algorithm has the higher precision and the longer time stability than the standard numerical method.展开更多
The formation of clay suspensions involves complex interactions among clay particles subjected to the geochemical environment during the sedimentation process. The structural characteristics have a major influence on ...The formation of clay suspensions involves complex interactions among clay particles subjected to the geochemical environment during the sedimentation process. The structural characteristics have a major influence on the physical and mechanical behavior of the suspension. A modeling framework involving a Discrete Element Method (DEM) model with customized particle mechanical interactions is proposed in this paper for the holistic prediction of the physical structure of clay suspensions. The particle interaction force model is based on the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory that accounts for electrostatic repulsion, van der Waals attraction, contact repulsion, etc. Kaolinite is used as the model clay to demonstrate the model performance. The surface charge density of kaolinite is obtained through Atomic Force Microscope (AFM) force measurement and is implemented in the particle interaction force model in the subsequent simulations. Influencing factors, such as centrifugal acceleration, ionic concentration, platy structure of particles, and particle size, on the formation of kaolinite suspensions are studied with the numerical model and compare favorably well with the experimental data. This work lays down a unique framework consisting of computational modeling and microscale characterization of clay particles to holistically predict the characteristics of clay suspensions, which paves the basis to model and predict their bulk physical and mechanical behavior.展开更多
To better understand the roles natural fractures play in porous media, an embedded discrete fracture model and streamline modeling method were combined to model natural fractures and compute the flow trajectory and ti...To better understand the roles natural fractures play in porous media, an embedded discrete fracture model and streamline modeling method were combined to model natural fractures and compute the flow trajectory and time of fluid in matrix and fractures systems. The effects of fracture conductivity, number of fractures and fracture locations on fluid flow trajectory and time were examined through analyzing the differences in water breakthrough time and sweeping volume of reservoirs with different fracture networks. When other conditions are the same, compared with homogeneous reservoir without fractures, the fractured reservoir has water breakthrough time 30% sooner and swept volume 10% smaller. Although increase of single fracture can lead to faster water breakthrough and smaller swept volume, adding more fractures wouldn’t necessarily reach the same effect. The effect of water flooding is also related to the strike and position of fractures. Fractures in different strikes and positions can result in 20% discrepancy in water breakthrough time and 9% gap in swept volume. The shorter the fracture, the less its effect on fluid flow trajectory and time will be. The position of fracture has a strong influence on sweeping efficiency, and the change of one fracture position could bring about 1% variation in swept volume.展开更多
This paper describes an analytical investigation into synchrophasing,a vibration control strategy on a machinery installation in which two rotational machines are attached to a beam-like raft by discrete resilient iso...This paper describes an analytical investigation into synchrophasing,a vibration control strategy on a machinery installation in which two rotational machines are attached to a beam-like raft by discrete resilient isolators.Forces and moments introduced by sources are considered,which effectively represent a practical engineering system.Adjusting the relative phase angle between the machines has been theoretically demonstrated to greatly reduce the cost function,which is defined as the sum of velocity squares of attaching points on the raft at each frequency of interest.The effect of the position of the machine is also investigated.Results show that altering the position of the secondary source may cause a slight change to the mode shape of the composite system and therefore change the optimum phase between the two machines.Although the analysis is based on a one-dimensional Euler– Bernoulli beam and each machine is considered as a rigid-body,a key principle can be derived from the results.However,the factors that can influence the synchrophasing control performance would become coupled and highly complicated.This condition has to be considered in practice.展开更多
The diagnosability of discrete event systems has been a topic of interest to many researchers. The diagnosability conditions for various systems have evolved based on a regularity condition that is imposed on faulty t...The diagnosability of discrete event systems has been a topic of interest to many researchers. The diagnosability conditions for various systems have evolved based on a regularity condition that is imposed on faulty traces with respect to their observable continuations. Improving upon this weak but necessary condition, a new model of diagnosability that is based on sensor outputs, which are called observatio ns, upon a command in put is proposed in this paper. Necessary and sufficient con ditions are derived for the proposed diagnosability model. The search performance of the proposed diagnosability condition is of linear complexity in terms of the power set of the system events and observations, compared to the exponential complexity of the search with the existing diag nosability regularity condition. Moreover, a system that is not diag no sable according to the existi ng diag nosability condition may be diagnosable in the proposed diagnosability model, which includes observations.展开更多
In this paper,we present stochastic intermittent stabilization based on the feedback of the discrete time or the delay time.By using the stochastic comparison principle,the Ito formula,and the BorelCantelli lemma,we o...In this paper,we present stochastic intermittent stabilization based on the feedback of the discrete time or the delay time.By using the stochastic comparison principle,the Ito formula,and the BorelCantelli lemma,we obtain two sufficient criteria for stochastic intermittent stabilization.The established criteria show that an unstable system can be stabilized by means of a stochastic intermittent noise via a discrete time feedback if the duration timeτis bounded byτ*.Similarly,stabilization via delay time feedback is equally possible if the lag timeτis bounded byτ**.The upper boundτ*andτ**can be computed numerically by solving corresponding equation.展开更多
The amount of digital data is increasing every day.At every step of our daily lives,we deal with technologies in which our data are stored (e.g.,mobile phones and laptops),and this is one of the main reasons for the d...The amount of digital data is increasing every day.At every step of our daily lives,we deal with technologies in which our data are stored (e.g.,mobile phones and laptops),and this is one of the main reasons for the design of various types of encryption and user identity verification algorithms.These algorithms are meant not only to fulfill the desire of protecting data but also to address the possibility of granting access of specific digital data to selected individuals.This process brings with it the problem of identity verification.This paper discusses the problem of voice verification and presents a voice verification method based on artificial intelligence methods. Numerous tests are performed herein to demonstrate the effectiveness of the presented solution.The research results are shown and discussed in terms of the advantages and disadvantages of the solution.展开更多
Design of waste rock barriers forming safety berms for haul trucks requires knowledge of complex interactions which cannot readily be tested by physical means.An advanced numerical model based on non-smooth multi-doma...Design of waste rock barriers forming safety berms for haul trucks requires knowledge of complex interactions which cannot readily be tested by physical means.An advanced numerical model based on non-smooth multi-domain mechanics is presented together with model calibration using limited fullscale experimental data.Waste rock is represented by spherical particles with rolling resistance,and an ultra-class haul truck is represented by a rigid multibody system interconnected with mechanical joints.The model components are first calibrated and then the calibrated model is used for simulating various collision scenarios with different approach conditions and safety berm geometries.Numerical predictions indicate that the width of the berm is most critical for efficiently stopping a runaway truck.The model can also predict if a certain berm geometry is capable of stopping a runaway truck.Results are summarised in a series of diagrams intended for use as design guidelines by practitioners and engineers.展开更多
In this paper we propose a discrete logistic system with pure delays. By giving the detail analysis of the right-hand side functional of the system, we consider its permanence property which is one of the most importa...In this paper we propose a discrete logistic system with pure delays. By giving the detail analysis of the right-hand side functional of the system, we consider its permanence property which is one of the most important topic in the study of population dynamics. The results obtained in this paper are good extensions of the existing results to the discrete case. Also we give an example to show the feasibility of our main results.展开更多
The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of K...The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability(KHI). It is found that, the relaxation time always strengthens the global nonequilibrium(GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are:(i) Initially,binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate.(ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI.(iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy(light) medium reduces(increases), because the heavy(light) medium has a relatively small(large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.展开更多
Recently, various toppling slopes have emerged with the development of hydropower projects in the western mountainous regions of China. The slope on the right bank of the Laxiwa Hydropower Station, located on the main...Recently, various toppling slopes have emerged with the development of hydropower projects in the western mountainous regions of China. The slope on the right bank of the Laxiwa Hydropower Station, located on the mainstream of the Yellow River in the Qinghai Province of Northwest China, is a typical hard rock slope. Further, its deformation characteristics are different from those of common natural hard rock toppling. Because this slope is located close to the dam of the hydropower station, its deformation mechanism has a practical significance. Based on detailed geological engineering surveys, four stages of deformation have been identified using discrete element numerical software and geological engineering analysis methods, including toppling creep, initial toppling deformation, intensified toppling deformation, and current slope formation. The spatial and time-related deformation of this site also exhibited four stages, including initial toppling, toppling development, intensification of toppling, and disintegration and collapse. Subsequently, the mechanism of toppling and deformation of the bank slope were studied. The results of this study exhibit important reference value for developing the prevention–control design of toppling and for ensuring operational safety in the hydropower reservoir area.展开更多
In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove ...In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.展开更多
We demonstrate that the new hierarchy of integrable lattice equations in Chin. Phys. B 21 090202(2012) can be changed into the integrable lattice hierarchy in Chin. Phys. B 13 1009(2004) by using a very simple transfo...We demonstrate that the new hierarchy of integrable lattice equations in Chin. Phys. B 21 090202(2012) can be changed into the integrable lattice hierarchy in Chin. Phys. B 13 1009(2004) by using a very simple transformation.展开更多
In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also...In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.展开更多
文摘The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.
文摘In present note,we apply the Leibniz formula with the nabla operator in discrete fractional calculus(DFC)due to obtain the discrete fractional solutions of a class of associated Bessel equations(ABEs)and a class of associated Legendre equations(ALEs),respectively.Thus,we exhibit a new solution method for such second order linear ordinary differential equations with singular points.
基金supported by the National Natural Science Foundation of China(Grant No.11502071)the Special Research Project of Beijing Information Science and Technology University,China.
文摘We investigate the perturbation to discrete conformal invariance and the adiabatic invariants of Lagrangian systems. A variational algorithm is proposed for a system subjected to the perturbation quantities. The discrete determining equations of the perturbations to conformal invariance are established. For perturbed Lagrangian systems, the condition of the existence of adiabatic invariant is derived from the discrete perturbation to conformal invariance. The numerical simulations demonstrate that the variational algorithm has the higher precision and the longer time stability than the standard numerical method.
基金the U.S. National Science Foundation via Grant no. 0900401.
文摘The formation of clay suspensions involves complex interactions among clay particles subjected to the geochemical environment during the sedimentation process. The structural characteristics have a major influence on the physical and mechanical behavior of the suspension. A modeling framework involving a Discrete Element Method (DEM) model with customized particle mechanical interactions is proposed in this paper for the holistic prediction of the physical structure of clay suspensions. The particle interaction force model is based on the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory that accounts for electrostatic repulsion, van der Waals attraction, contact repulsion, etc. Kaolinite is used as the model clay to demonstrate the model performance. The surface charge density of kaolinite is obtained through Atomic Force Microscope (AFM) force measurement and is implemented in the particle interaction force model in the subsequent simulations. Influencing factors, such as centrifugal acceleration, ionic concentration, platy structure of particles, and particle size, on the formation of kaolinite suspensions are studied with the numerical model and compare favorably well with the experimental data. This work lays down a unique framework consisting of computational modeling and microscale characterization of clay particles to holistically predict the characteristics of clay suspensions, which paves the basis to model and predict their bulk physical and mechanical behavior.
文摘To better understand the roles natural fractures play in porous media, an embedded discrete fracture model and streamline modeling method were combined to model natural fractures and compute the flow trajectory and time of fluid in matrix and fractures systems. The effects of fracture conductivity, number of fractures and fracture locations on fluid flow trajectory and time were examined through analyzing the differences in water breakthrough time and sweeping volume of reservoirs with different fracture networks. When other conditions are the same, compared with homogeneous reservoir without fractures, the fractured reservoir has water breakthrough time 30% sooner and swept volume 10% smaller. Although increase of single fracture can lead to faster water breakthrough and smaller swept volume, adding more fractures wouldn’t necessarily reach the same effect. The effect of water flooding is also related to the strike and position of fractures. Fractures in different strikes and positions can result in 20% discrepancy in water breakthrough time and 9% gap in swept volume. The shorter the fracture, the less its effect on fluid flow trajectory and time will be. The position of fracture has a strong influence on sweeping efficiency, and the change of one fracture position could bring about 1% variation in swept volume.
文摘This paper describes an analytical investigation into synchrophasing,a vibration control strategy on a machinery installation in which two rotational machines are attached to a beam-like raft by discrete resilient isolators.Forces and moments introduced by sources are considered,which effectively represent a practical engineering system.Adjusting the relative phase angle between the machines has been theoretically demonstrated to greatly reduce the cost function,which is defined as the sum of velocity squares of attaching points on the raft at each frequency of interest.The effect of the position of the machine is also investigated.Results show that altering the position of the secondary source may cause a slight change to the mode shape of the composite system and therefore change the optimum phase between the two machines.Although the analysis is based on a one-dimensional Euler– Bernoulli beam and each machine is considered as a rigid-body,a key principle can be derived from the results.However,the factors that can influence the synchrophasing control performance would become coupled and highly complicated.This condition has to be considered in practice.
文摘The diagnosability of discrete event systems has been a topic of interest to many researchers. The diagnosability conditions for various systems have evolved based on a regularity condition that is imposed on faulty traces with respect to their observable continuations. Improving upon this weak but necessary condition, a new model of diagnosability that is based on sensor outputs, which are called observatio ns, upon a command in put is proposed in this paper. Necessary and sufficient con ditions are derived for the proposed diagnosability model. The search performance of the proposed diagnosability condition is of linear complexity in terms of the power set of the system events and observations, compared to the exponential complexity of the search with the existing diag nosability regularity condition. Moreover, a system that is not diag no sable according to the existi ng diag nosability condition may be diagnosable in the proposed diagnosability model, which includes observations.
基金National Natural Science Foundation of China(Grant Nos.61304070,61773152)the Chinese Postdoctoral Science Foundation(Grant Nos.2016M601698,2017T100318)+1 种基金the Jiangsu Province Postdoctoral Science Foundation(Grant No.1701078B)the Project Funded by the Qing Lan Project of Jiangsu Province,China.
文摘In this paper,we present stochastic intermittent stabilization based on the feedback of the discrete time or the delay time.By using the stochastic comparison principle,the Ito formula,and the BorelCantelli lemma,we obtain two sufficient criteria for stochastic intermittent stabilization.The established criteria show that an unstable system can be stabilized by means of a stochastic intermittent noise via a discrete time feedback if the duration timeτis bounded byτ*.Similarly,stabilization via delay time feedback is equally possible if the lag timeτis bounded byτ**.The upper boundτ*andτ**can be computed numerically by solving corresponding equation.
基金the Diamond Grant 2016 (No.0080/DIA/2016/45) funded by the Polish Ministry of Science and Higher Education.
文摘The amount of digital data is increasing every day.At every step of our daily lives,we deal with technologies in which our data are stored (e.g.,mobile phones and laptops),and this is one of the main reasons for the design of various types of encryption and user identity verification algorithms.These algorithms are meant not only to fulfill the desire of protecting data but also to address the possibility of granting access of specific digital data to selected individuals.This process brings with it the problem of identity verification.This paper discusses the problem of voice verification and presents a voice verification method based on artificial intelligence methods. Numerous tests are performed herein to demonstrate the effectiveness of the presented solution.The research results are shown and discussed in terms of the advantages and disadvantages of the solution.
文摘Design of waste rock barriers forming safety berms for haul trucks requires knowledge of complex interactions which cannot readily be tested by physical means.An advanced numerical model based on non-smooth multi-domain mechanics is presented together with model calibration using limited fullscale experimental data.Waste rock is represented by spherical particles with rolling resistance,and an ultra-class haul truck is represented by a rigid multibody system interconnected with mechanical joints.The model components are first calibrated and then the calibrated model is used for simulating various collision scenarios with different approach conditions and safety berm geometries.Numerical predictions indicate that the width of the berm is most critical for efficiently stopping a runaway truck.The model can also predict if a certain berm geometry is capable of stopping a runaway truck.Results are summarised in a series of diagrams intended for use as design guidelines by practitioners and engineers.
基金supported by the National Natural Science Foundation of China under Grant(11601085)the Natural Science Foundation of Fujian Province(2017J01400,2018J01664)the Scientific Research Foundation of Fuzhou University(GXRC-17026).
文摘In this paper we propose a discrete logistic system with pure delays. By giving the detail analysis of the right-hand side functional of the system, we consider its permanence property which is one of the most important topic in the study of population dynamics. The results obtained in this paper are good extensions of the existing results to the discrete case. Also we give an example to show the feasibility of our main results.
基金the Natural Science Foundation of China under Grant Nos.91441120,51806116,11875001,and 11602162the China Postdoctoral Science Foundation under Grant No.2017M620757+2 种基金the Center for Combustion Energy at Tsinghua Universitythe Natural Science Foundation of Hebei Province under Grant Nos.A2017409014,ZD2017001,and A201500111the UK Engineering and Physical Sciences Research Council under Project UK Consortium on Mesoscale Engineering Sciences (UKCOMES)under Grant Nos.EP/L00030X/1and EP/R029598/1.
文摘The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability(KHI). It is found that, the relaxation time always strengthens the global nonequilibrium(GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are:(i) Initially,binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate.(ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI.(iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy(light) medium reduces(increases), because the heavy(light) medium has a relatively small(large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.
基金financially supported by the National Key R&D Program of China(2018YFC1504905)the Funds for Creative Research Groups of China(41521002)the National Natural Science Foundation of China(41772317 and 41372306).
文摘Recently, various toppling slopes have emerged with the development of hydropower projects in the western mountainous regions of China. The slope on the right bank of the Laxiwa Hydropower Station, located on the mainstream of the Yellow River in the Qinghai Province of Northwest China, is a typical hard rock slope. Further, its deformation characteristics are different from those of common natural hard rock toppling. Because this slope is located close to the dam of the hydropower station, its deformation mechanism has a practical significance. Based on detailed geological engineering surveys, four stages of deformation have been identified using discrete element numerical software and geological engineering analysis methods, including toppling creep, initial toppling deformation, intensified toppling deformation, and current slope formation. The spatial and time-related deformation of this site also exhibited four stages, including initial toppling, toppling development, intensification of toppling, and disintegration and collapse. Subsequently, the mechanism of toppling and deformation of the bank slope were studied. The results of this study exhibit important reference value for developing the prevention–control design of toppling and for ensuring operational safety in the hydropower reservoir area.
基金MATH-AmSud 18- MATH-07 SaSMoTiDep Project and HERMES project 41305. S. Torres is partially supported by the Project ECOS-CONICYT C15E05, REDES 15003& MATH-AmSud 18-MATH-07 SaSMoTiDep Project and Fondecyt (1171335)S. Tindel is supported by NSF (Grant DMS-1613163).
文摘In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.
基金the Natural Science Foundation of Shandong Province of China(Grant No.ZR2014AM001).
文摘We demonstrate that the new hierarchy of integrable lattice equations in Chin. Phys. B 21 090202(2012) can be changed into the integrable lattice hierarchy in Chin. Phys. B 13 1009(2004) by using a very simple transformation.
基金supported by Spanish Government Grant(Grant No. MTM2016-79436-P)supported by Nazarbayev University Social Policy Grant.
文摘In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.