Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.

Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion. It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.

Robust simultaneous tracking and stabilization of wheeled mobile robots not satisfying nonholonomic constraint

A robust unified controller was proposed for wheeled mobile robots that do not satisfy the ideal rolling without slipping constraint.Practical trajectory tracking and posture stabilization were achieved in a unified framework.The design procedure was based on the transverse function method and Lyapunov redesign technique.The Lie group was also introduced in the design.The left-invariance property of the nominal model was firstly explored with respect to the standard group operation of the Lie group SE(2).Then,a bounded transverse function was constructed,by which a corresponding smooth embedded submanifold was defined.With the aid of the group operation,a smooth control law was designed,which fulfills practical tracking/stabilization of the nominal system.An additional component was finally constructed to robustify the nominal control law with respect to the slipping disturbance by using the Lyapunov redesign technique.The design procedure can be easily extended to the robot system suffered from general unknown but bounded disturbances.Simulations were provided to demonstrate the effectiveness of the robust unified controller.

Thermodynamic properties of Heisenberg magnetic systems

In this paper, we present a comprehensive investigation of the effects of the transverse correlation function （TCF） on the thermodynamic properties of Heisenberg antiferromagnetic （AFM） and ferromagnetic （FM） systems with cubic lattices. The TCF of an FM system is positive and increases with temperature, while that of an AFM system is negative and decreases with temperature. The TCF lowers internal energy, entropy and specific heat. It always raises the free energy of an FM system but raises that of an AFM system only above a specific temperature when the spin quantum number is S 〉 1. Comparisons between the effects of the TCFs on the FM and AFM systems are made where possible.