We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles inst...We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway.The model is analyzed with the use of the linear stability theory and nonlinear analysis method.The stability and neutral stability condition are obtained.We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler scheme.The results of the numerical simulation verify the validity of the new model.展开更多
The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equa...The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equation.The displacement expressions of the Scholte waves in liquid and solid were derived.Additionally,the mode of motion of Scholte waves in liquid and solid and their variation with depth was studied.The following results were obtained:The dispersion equation shows that the propagation velocity of the fundamental Scholte wave was greater than the P-wave in liquid and less than that of the Scholte wave in homogeneous elastic half-space.In contrast,the velocity of higher-order Scholte waves was greater than that of P waves in liquid and S-waves in solid.Only the fundamental Scholte wave has no cutoff frequency.The Scholte wave at the liquid surface moved only vertically,while the particles inside the liquid medium moved elliptically.The amplitude variation with depth in the solid medium caused the particle motion to change from a retrograde ellipse to a prograde ellipse.The above results imply the study of Scholte waves in the ocean and oceanic crust and help estimate ocean depths.展开更多
We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer b...We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer birth of fitness catalyzed by the population, where the fitness aggregates perform self-death process and the population aggregates perform self-birth process. The kinetic behaviors of the aggregate size distributions of the fitness and population were analyzed by the rate equation approach with their exchange rate kernel K1（k,j） = K1kj and K2（k,j） = K2kj, the fitness aggregate＇s self-death rate kernel J1 （ k ） = J1 k, population aggregate＇s self-birth rate kernel J2（ k ） = J2k and population-catalyzed fitness birth rate kernel I（k,j） = Ikj＇. The kinetic behavior of the fitness was found depending crucially on the parameter v, which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst （population） aggregate. （i） In the v ≤ 0 case, the effect of catalyzed-birth of fitness is rather weak and the exchange-driven aggregation and self-death of the fitness dominate the process, and the fitness aggregate size distribution αk（t） does not have scale form. （ii） When v ≥0, the effect of the population-catalyzed birth of fitness gets strong enough, and the catalyzed-birth and self-death of the fitness aggregates, together with the self-birth of the population aggregates dominate the evolution process of the fitness aggregates. The aggregate size distribution αk （t） approaches a generalized scaling form.展开更多
The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one th...The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one thousand times） faster than today＇s existing highest speed computers. Since one of the Milennium Prize Problems offered by Claymath asks about whether P （Deterministic Polynomial） is equal to NP （Non-Deterministic Polynomial） （what that means informally is that whether we can design a computer which can quickly solve a certain complicated problem can also verify the solution quickly （and vice versa）. Fortunately, the answer to P vs. NP problem based on my findings in certain algebraic algorythms is yes although there have been many people who claimed the answer is no. What that means is that humans can make machines that work very fast and close to human intelligence in the identification of, say, certain proteins and amino acids, in case my theory is proven to be a fact. This paper is therefore an initial stage of planting the first seeds of the process, in terms of describing how exactly this can happen, theoretically of course, since everything in Science begins with a theory based on the outcome of a hypothesis.展开更多
Ultrasonic speeds have been measured at 298.15 K and 308.15 K for mixtures of formamide ＋ 1 -propanol or 2-propanol. For an equimolar mixture, excess molar compressibility follows the sequence of l-propanol 〉 2-prop...Ultrasonic speeds have been measured at 298.15 K and 308.15 K for mixtures of formamide ＋ 1 -propanol or 2-propanol. For an equimolar mixture, excess molar compressibility follows the sequence of l-propanol 〉 2-propanol. The ultrasonic speed data are correlated by various correlations such as Nomoto＇s relation, van Dael＇s mixing relation and impedance dependence relation, and analyzed in terms of Jacobson＇s free length theory and Schaaffs collision factor theory. Excess isentropic compressibility is calculated from ex- perimental ultrasonic speed data and previously reported excess volume data. The excess molar ultrasonic speed and isentropic compressibility values are fitted to Redlich-Kister polynomial equation. Other proper- ties such as molecular association, available volume, free volume, and intermolecular free length are also calculated. The excess isentropic compressibility data are also interpreted in terms of graph theoretical ap- proach. The calculated isentropic compressibility values are well consistent with the experimental data. It is found that the interaction between formamide and propanol increases when hydroxyl group attached to a carbon atom has more -CH3 groups.展开更多
This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interio...This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results.展开更多
基金supported by National Natural Science Foundation of China under Grant No.60674062the Middle-Aged and Young Scientists Research Incentive Fund of Shandong Province under Grant No.2007BS01013
文摘We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway.The model is analyzed with the use of the linear stability theory and nonlinear analysis method.The stability and neutral stability condition are obtained.We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler scheme.The results of the numerical simulation verify the validity of the new model.
基金supported by the National Natural Science Fondation of China(Nos.42174074,41674055,41704053)the Earthquake Science Spark Program of Hebei Province(No.DZ20200827053)+1 种基金Fundamental Research Funds for the Central Universities(No.ZY20215117)the Hebei Key Laboratory of Earthquake Dynamics(No.FZ212105).
文摘The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equation.The displacement expressions of the Scholte waves in liquid and solid were derived.Additionally,the mode of motion of Scholte waves in liquid and solid and their variation with depth was studied.The following results were obtained:The dispersion equation shows that the propagation velocity of the fundamental Scholte wave was greater than the P-wave in liquid and less than that of the Scholte wave in homogeneous elastic half-space.In contrast,the velocity of higher-order Scholte waves was greater than that of P waves in liquid and S-waves in solid.Only the fundamental Scholte wave has no cutoff frequency.The Scholte wave at the liquid surface moved only vertically,while the particles inside the liquid medium moved elliptically.The amplitude variation with depth in the solid medium caused the particle motion to change from a retrograde ellipse to a prograde ellipse.The above results imply the study of Scholte waves in the ocean and oceanic crust and help estimate ocean depths.
基金National Natural Science Foundation of China under Grant Nos.10275048 and 10305009the Natural Science Foundation of Zhejiang Province of China under Grant No.102067
文摘We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer birth of fitness catalyzed by the population, where the fitness aggregates perform self-death process and the population aggregates perform self-birth process. The kinetic behaviors of the aggregate size distributions of the fitness and population were analyzed by the rate equation approach with their exchange rate kernel K1（k,j） = K1kj and K2（k,j） = K2kj, the fitness aggregate＇s self-death rate kernel J1 （ k ） = J1 k, population aggregate＇s self-birth rate kernel J2（ k ） = J2k and population-catalyzed fitness birth rate kernel I（k,j） = Ikj＇. The kinetic behavior of the fitness was found depending crucially on the parameter v, which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst （population） aggregate. （i） In the v ≤ 0 case, the effect of catalyzed-birth of fitness is rather weak and the exchange-driven aggregation and self-death of the fitness dominate the process, and the fitness aggregate size distribution αk（t） does not have scale form. （ii） When v ≥0, the effect of the population-catalyzed birth of fitness gets strong enough, and the catalyzed-birth and self-death of the fitness aggregates, together with the self-birth of the population aggregates dominate the evolution process of the fitness aggregates. The aggregate size distribution αk （t） approaches a generalized scaling form.
文摘The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one thousand times） faster than today＇s existing highest speed computers. Since one of the Milennium Prize Problems offered by Claymath asks about whether P （Deterministic Polynomial） is equal to NP （Non-Deterministic Polynomial） （what that means informally is that whether we can design a computer which can quickly solve a certain complicated problem can also verify the solution quickly （and vice versa）. Fortunately, the answer to P vs. NP problem based on my findings in certain algebraic algorythms is yes although there have been many people who claimed the answer is no. What that means is that humans can make machines that work very fast and close to human intelligence in the identification of, say, certain proteins and amino acids, in case my theory is proven to be a fact. This paper is therefore an initial stage of planting the first seeds of the process, in terms of describing how exactly this can happen, theoretically of course, since everything in Science begins with a theory based on the outcome of a hypothesis.
文摘Ultrasonic speeds have been measured at 298.15 K and 308.15 K for mixtures of formamide ＋ 1 -propanol or 2-propanol. For an equimolar mixture, excess molar compressibility follows the sequence of l-propanol 〉 2-propanol. The ultrasonic speed data are correlated by various correlations such as Nomoto＇s relation, van Dael＇s mixing relation and impedance dependence relation, and analyzed in terms of Jacobson＇s free length theory and Schaaffs collision factor theory. Excess isentropic compressibility is calculated from ex- perimental ultrasonic speed data and previously reported excess volume data. The excess molar ultrasonic speed and isentropic compressibility values are fitted to Redlich-Kister polynomial equation. Other proper- ties such as molecular association, available volume, free volume, and intermolecular free length are also calculated. The excess isentropic compressibility data are also interpreted in terms of graph theoretical ap- proach. The calculated isentropic compressibility values are well consistent with the experimental data. It is found that the interaction between formamide and propanol increases when hydroxyl group attached to a carbon atom has more -CH3 groups.
基金supported by Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105)
文摘This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results.
