A nonlinear theory for a flexible unsteady wing

This paper extends the previous studies by Wu [Wu TY (2001) Adv Appl Mech 38:291–353; Wu TY (2005) Advances in engineering mechanics—reflections and outlooks. World Scientific; Wu TY (2006) Struct Control Health Monit 13:553–560] to present a fully nonlinear theory for the evaluation of the unsteady flow generated by a two-dimensional flexible lifting surface moving in an arbitrary manner through an incompressible and inviscid fluid for modeling bird/insect flight and fish swimming. The original physical concept founded by Theodore von Kármán and William R. Sears [von Kármán T, Sears WR (1938) J Aero Sci 5:379–390] in describing the complete vortex system of a wing and its wake in non-uniform motion for their linear theory is adapted and extended to a fully nonlinear consideration. The new theory employs a joint Eulerian and Lagrangian description of the wing motion to establish a fully nonlinear theory for a flexible wing moving with arbitrary variations in wing shape and trajectory, and obtain a fully nonlinear integral equation for the wake vorticity in generalizing Herbert Wagner’s [Wagner H (1925) ZAMM 5:17–35] linear version for an efficient determination of exact solutions in general

A nonlinear unsteady flexible wing theory

This paper extends a previous study by Wu (Adv. Appl. Mech. 2001; 38:291-353) to continue developing a fully non-linear theory for calculation of unsteady flow generated by a two-dimensional flexible lifting surface moving in arbitrary manner through an incompressible and inviscid fluid for modelling bird/insect flight and fish swimming. The original physical concept elucidated by von Kármán and Sears (J. Aeronau Sci. 1938; 5:379-390) in describing the complete vortex system of a wing and its wake in non-uniform motion for their linear theory is adapted and applied to a fully non-linear consideration. The new theory employs a joint Eulerian and Lagrangian description of the lifting-surface movement to facilitate the formulation. The present investigation presents further analysis for addressing arbitrary variations in wing shape and trajectory to achieve a non-linear integral equation akin to Wagner's (Z. Angew. Math. Mech. 1925; 5:17-35) linear version for accurate computation of the entire system of vorticity distribution

Generalized reduction criterion for separability of quantum states

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new separability criterion naturally generalizes the reduction separability criterion introduced independently in previous work of [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C. Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partial transposition criterion [K. Chen and L.A. Wu, Phys. Lett. A 306, 14 (2002)]. The criterion involves only simple matrix manipulations and can therefore be easily applied.Comment: 17 pages, 2 figure

Spatial Geometry and the Wu-Yang Ambiguity

We display continuous families of SU(2) vector potentials $A_i^a(x)$ in 3 space dimensions which generate the same magnetic field $B^{ai}(x)$ (with det $B\neq 0$). These Wu-Yang families are obtained from the Einstein equation $R_{ij}=-2G_{ij}$ derived recently via a local map of the gauge field system into a spatial geometry with $2$-tensor $G_{ij}=B^a{}_i B^a{}_j\det B$ and connection $\Gamma_{jk}^i$ with torsion defined from gauge covariant derivatives of $B$.Comment: Based on talks given by R. Khuri at PASCOS-94, Syracuse University, May 1994 and at Gursey Memorial Conference I, Istanbul, June 1994, 7 pages, TeX (typo in first Author's name is corrected.

Stability of Non-Abelian Black Holes

Two types of self-gravitating particle solutions found in several theories with non-Abelian fields are smoothly connected by a family of non-trivial black holes. There exists a maximum point of the black hole entropy, where the stability of solutions changes. This criterion is universal, and the changes in stability follow from a catastrophe-theoretic analysis of the potential function defined by black hole entropy.Comment: 4 Figures to be sent on request,8 pages, WU-AP/33/9

Totally geodesic surfaces with arbitrarily many compressions

A closed totally geodesic surface in the figure eight knot complement remains incompressible in all but finitely many Dehn fillings. In this paper, we show that there is no universal upper bound on the number of such fillings, independent of the surface. This answers a question of Ying-Qing Wu