This paper proposes an approach for rendering breaking waves out of large-scale of particle-based simulation. Moving particle semi-implicit (MPS) is used to solve the governing equation, and 2D simulation is expanded ...This paper proposes an approach for rendering breaking waves out of large-scale of particle-based simulation. Moving particle semi-implicit (MPS) is used to solve the governing equation, and 2D simulation is expanded to 3D representation by giving motion variation using fractional Brownian motion (fBm). The waterbody surface is reconstructed from the outlines of 2D simulation. The splashing effect is computed according to the properties of the particles. Realistic features of the wave are ren-dered on GPU, including the reflective and refractive effect and the effect of splash. Experiments showed that the proposed method can simulate large scale breaking waves efficiently.展开更多
Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutio...Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.展开更多
In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonli...In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.展开更多
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and othe...In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.展开更多
In this paper, function characteristics of dispersion of ocean wave in finite depth water were analyzed systematically. The functional form of the fitting function is reasonably proposed, in which the parame- ters are...In this paper, function characteristics of dispersion of ocean wave in finite depth water were analyzed systematically. The functional form of the fitting function is reasonably proposed, in which the parame- ters are optimally determined by the least square method (LSM). For infinitely deep and extremely shallow water, the fitting function fits strictly the dispersion to be fitted. A new technique is presented in application of LSM. An empirical formula with maximum error of less than 0.5% for computing wavelength in finite depth water is presented for practical applications.展开更多
We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the...We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.展开更多
The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown th...The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.展开更多
Today cooperative banks belong to the most significant financial institution in the world. Moreover, they can compete with commercial banks. The own funds of the cooperative bank are important in their activity. The m...Today cooperative banks belong to the most significant financial institution in the world. Moreover, they can compete with commercial banks. The own funds of the cooperative bank are important in their activity. The main goal of this paper is to investigate how much the level of the own funds of the Polish cooperative banks influenced their efficiency. The research pertained to operating cooperative banks in Poland. The following measures of the efficiency were used in the research： return on Equity （ROE）, net profit, index C/I, and financial margin. The results of the study indicate that banks from the Quartile III （highest aggregate own funds）, had the highest net profits, the highest ROE, the lowest C/I value, the lowest ROE, and the lowest financial markups. On this basis, it remains to be recommended that banks of highest aggregate own funds continue expansion of own funds which will increase lending capacity and subsequently contribute to higher effectiveness.展开更多
基金Project partly supported by the National Institute of Information andCommunication Technology (NICT), Japan
文摘This paper proposes an approach for rendering breaking waves out of large-scale of particle-based simulation. Moving particle semi-implicit (MPS) is used to solve the governing equation, and 2D simulation is expanded to 3D representation by giving motion variation using fractional Brownian motion (fBm). The waterbody surface is reconstructed from the outlines of 2D simulation. The splashing effect is computed according to the properties of the particles. Realistic features of the wave are ren-dered on GPU, including the reflective and refractive effect and the effect of splash. Experiments showed that the proposed method can simulate large scale breaking waves efficiently.
基金The project supported by National Natural Science Foundation of China under Grant No.10771196the Natural Science Foundation of Zhejiang Province under Grant No.Y605044
文摘Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.
基金The project supported by National Natural Science Foundation of China under Grant No.40305006the Ministry of Science and Technology of China through Special Public Welfare Project under Grant No.2002DIB20070
文摘In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
基金The project supported by National Natural Science Foundation of China, the Natural Science Foundation of Shandong Province of China, and the Natural Science Foundation of Liaocheng University .
文摘In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.
基金This study was financially supported by Key Technologies R & D Programme of China (No.2001BA603B-01).
文摘In this paper, function characteristics of dispersion of ocean wave in finite depth water were analyzed systematically. The functional form of the fitting function is reasonably proposed, in which the parame- ters are optimally determined by the least square method (LSM). For infinitely deep and extremely shallow water, the fitting function fits strictly the dispersion to be fitted. A new technique is presented in application of LSM. An empirical formula with maximum error of less than 0.5% for computing wavelength in finite depth water is presented for practical applications.
基金Project supported by the National Natural Science Foundation of China （Grant No 60508005） and the Scientific Foundation for Returned 0verseas Scholars of Heilongjiang Province, China （Grant No LC05C02）.
文摘We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.
文摘The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.
文摘Today cooperative banks belong to the most significant financial institution in the world. Moreover, they can compete with commercial banks. The own funds of the cooperative bank are important in their activity. The main goal of this paper is to investigate how much the level of the own funds of the Polish cooperative banks influenced their efficiency. The research pertained to operating cooperative banks in Poland. The following measures of the efficiency were used in the research： return on Equity （ROE）, net profit, index C/I, and financial margin. The results of the study indicate that banks from the Quartile III （highest aggregate own funds）, had the highest net profits, the highest ROE, the lowest C/I value, the lowest ROE, and the lowest financial markups. On this basis, it remains to be recommended that banks of highest aggregate own funds continue expansion of own funds which will increase lending capacity and subsequently contribute to higher effectiveness.
