Chen Benyong

Hamilton formalism and noether symmetry for mechanico—electrical systems with fractional derivatives

This paper presents extensions to the traditional calculus of variations for mechanico—electrical systems containing fractional derivatives. The Euler—Lagrange equations and the Hamilton formalism of the mechanico—electrical systems with fractional derivatives are established. The definition and the criteria for the fractional generalized Noether quasi-symmetry are presented. Furthermore, the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations. An example is presented to illustrate the application of the results.

Noether symmetries of discrete mechanico–electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.

Lie symmetries and conserved quantities for a two-dimentional nonlinear diffusion equation of concentration

The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.

Influence of colloidal particle transfer on the quality of self-assembling colloidal photonic crystal under confined condition

The relationship between colloidal particle transfer and the quality of colloidal photonic crystal (CPC) is investigated by comparing colloidal particle self-assembling under the vertical channel (VC) and horizontal channel (HC) conditions. Both the theoretical analyses and the experimental measurements indicate that crystal quality depends on the stability of mass transfer. For the VC, colloidal particle transfer takes place in a stable laminar flow, which is conducive to forming high-quality crystal. In contrast, it happens in an unstable turbulent flow for the HC. Crystals with cracks and an uneven surface formed under the HC condition can be seen from the images of a field emission scanning electron microscope (SEM) and a three-dimensional (3D) laser scanning microscope (LSM), respectively.

Large-scale photonic crystals with inserted defects and their optical properties

Deliberately introducing defects into photonic crystals is an important way to functionalize the photonic crystals. We prepare a special large-scale three-dimensional (3D) photonic crystal (PC) with designed defects by an easy and low-cost method. The defect layer consists of photoresist strips or air-core strips. Field emission scanning electron microscopy (FESEM) shows that the 3D PC is of good quality and the defect layer is uniform. Different defect states shown in the ultraviolet-visible spectra are induced by the photoresist strip layer and air-core strip layer. The special large-scale 3D PC can be tested for integrated optical circuits, and the defects can act as optical waveguides.

A new type of conserved quantity of Mei symmetry for the motion of mechanico—electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico-electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico—electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.

An Energy-Work Relationship Integration Scheme for Nonconservative Hamiltonian Systems

This letter focuses on studying a new energy-work relationship numerical integration scheme of nonconservative Hamiltonian systems. The signal-stage, multistage, and parallel composition numerical integration schemes are presented for this system. The high-order energy-work relation scheme of the system is constructed by a parallel connection of 𝑛 multistage scheme of order 2 which its order of accuracy is 2𝑛. The connection, which is discrete analog of usual case, between the change of energy and work of nonconservative force is obtained for nonconservative Hamiltonian systems.This letter also shows that the more the stages of the schemes are, the less the error rate of the scheme is for nonconservative Hamiltonian systems. Finally, an applied example is discussed to illustrate these results.

Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler–Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.