Periodic performance of the chaotic spread spectrum sequence on finite precision

It is well known that the periodic performance of spread spectrum sequence heavily affects the correlative and secure characteristics of communication systems. The chaotic binary sequence is paid more and more attention since it is one kind of applicable spread spectrum sequences. However, there are unavoidable short cyclic problems for chaotic binary sequences in finite precision. The chaotic binary sequence generating methods are studied first. Then the short cyclic behavior of the chaotic sequences is analyzed in detail, which are generated by quantification approaches with finite word-length. At the same time, a chaotic similar function is defined for presenting the cyclic characteristics of the sequences. Based on these efforts, an improved method with scrambling control for generating chaotic binary sequences is proposed. To quantitatively describe the improvement of periodic performance of the sequences, an orthogonal estimator is also defined. Some simulating results are provided. From the theoretical deduction and the experimental results, it is concluded that the proposed method can effectively increase the period and raise the complexity of the chaotic sequences to some extent.

A perturbation method to the tent map based on Lyapunov exponent and its application

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function - the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation.

NANO-BEARING:THE DESIGN OF A NEW TYPE OF AIR BEARING WITH FLEXURE STRUCTURE

A new type of air bearing with flexure structure is introduced. The new bearing is designed for precision mechanical engineering devices such as mechanical watch movement. The new design uses the flexure structure to provide 3D damping to absorb shocks from all directions. Two designs are presented： one has 12 T-shape slots in the radian direction while the other has 8 spiral slots in the radian direction. Both designs have flexure mountings on the axial directions. Based on the finite element analysis （FEA）, the new bearing can reduce the vibration （displacement） by as much as 8.37% and hence, can better protect the shafts.

Transient heat conduction analysis using the NURBS-enhanced scaled boundary finite element method and modified precise integration method

The Non-uniform rational B-spline （NURBS） enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper. The scaled boundary finite element method is a semi-analytical technique, which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction. In this method, only the boundary is discretized in the finite element sense leading to a re- duction of the spatial dimension by one with no fundamental solution required. Neverthe- less, in case of the complex geometry, a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often un- avoidable in the conventional finite element approach, which leads to huge computational efforts and loss of accuracy. NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape. In the proposed methodology, the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions, while the straight part of the boundary is discretized by the conventional Lagrange shape functions. Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analy- sis and the solution is obtained using the modified precise integration method. The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion. Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method. The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.