The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in ...The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in converging channel flow were calculated, and the evolutions of the fiber alignment and the bulk effective vis-cosity were analyzed. The results showed that the bulk stress and the effective viscosity were functions of therate-of-strain tensor and the fiber orientation state ; and that the fiber suspensions evolved to steady alignment and tended to concentrate to some preferred directions close to but not same as the directions of local stream-lines. The bulk effective viscosity depended on the product of Reynolds number and time. The decrease of ef-fective viscosity near the boundary benefited the increase of the rate of flow. Finally when the fiber alignment went into steady state, the structural features of fiber suspensions were not dependent on the Reynolds numberbut on the converging channel angle.展开更多
The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In part...The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.展开更多
In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the ...In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.展开更多
A new method for determining the central axial orientation of a two-dimensional coherent magnetic flux rope(MFR)via multipoint analysis of the magnetic-field structure is developed. The method is devised under the fol...A new method for determining the central axial orientation of a two-dimensional coherent magnetic flux rope(MFR)via multipoint analysis of the magnetic-field structure is developed. The method is devised under the following geometrical assumptions:(1) on its cross section, the structure is left-right symmetric;(2) the projected structure velocity is vertical to the line of symmetry. The two conditions can be naturally satisfied for cylindrical MFRs and are expected to be satisfied for MFRs that are flattened within current sheets. The model test demonstrates that, for determining the axial orientation of such structures, the new method is more efficient and reliable than traditional techniques such as minimum-variance analysis of the magnetic field,Grad-Shafranov(GS) reconstruction, and the more recent method based on the cylindrically symmetric assumption. A total of five flux transfer events observed by Cluster are studied using the proposed approach, and the application results indicate that the observed structures, regardless of their actual physical properties, fit the assumed geometrical model well. For these events, the inferred axial orientations are all in excellent agreement with those obtained using the multi-GS reconstruction technique.展开更多
We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^- manifolds. The analytic index is the reduced η invariant of(twisted) Dirac operators and the topological index is defin...We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^- manifolds. The analytic index is the reduced η invariant of(twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer(1971)to non-orientable manifolds.展开更多
文摘The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in converging channel flow were calculated, and the evolutions of the fiber alignment and the bulk effective vis-cosity were analyzed. The results showed that the bulk stress and the effective viscosity were functions of therate-of-strain tensor and the fiber orientation state ; and that the fiber suspensions evolved to steady alignment and tended to concentrate to some preferred directions close to but not same as the directions of local stream-lines. The bulk effective viscosity depended on the product of Reynolds number and time. The decrease of ef-fective viscosity near the boundary benefited the increase of the rate of flow. Finally when the fiber alignment went into steady state, the structural features of fiber suspensions were not dependent on the Reynolds numberbut on the converging channel angle.
基金Project supported by the National Natural Science Foundation of China the Cheung-Kong Scholarship of the Ministry of Education of China the Qiu Shi Foundation and the 973 Project of the Ministry of Science and Technology of China.
文摘The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.
基金supported by the National Natural Science Foundation of China(Grant No. 10972116)
文摘In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.
基金supported by the National Natural Science Foundation of China (Grant Nos. 40774081, 41231066)Ministry of Science and Technology of China (Grant No. 2011CB811404)the Specialized Research Fund for State Key Laboratories
文摘A new method for determining the central axial orientation of a two-dimensional coherent magnetic flux rope(MFR)via multipoint analysis of the magnetic-field structure is developed. The method is devised under the following geometrical assumptions:(1) on its cross section, the structure is left-right symmetric;(2) the projected structure velocity is vertical to the line of symmetry. The two conditions can be naturally satisfied for cylindrical MFRs and are expected to be satisfied for MFRs that are flattened within current sheets. The model test demonstrates that, for determining the axial orientation of such structures, the new method is more efficient and reliable than traditional techniques such as minimum-variance analysis of the magnetic field,Grad-Shafranov(GS) reconstruction, and the more recent method based on the cylindrically symmetric assumption. A total of five flux transfer events observed by Cluster are studied using the proposed approach, and the application results indicate that the observed structures, regardless of their actual physical properties, fit the assumed geometrical model well. For these events, the inferred axial orientations are all in excellent agreement with those obtained using the multi-GS reconstruction technique.
基金supported by National Science Foundation of USA(Grant No.DMS 9022140)through a Mathematical Sciences Research Institute(MSRI)postdoctoral fellowship
文摘We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^- manifolds. The analytic index is the reduced η invariant of(twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer(1971)to non-orientable manifolds.
