Exact dynamic and static stiffness matrices of shear deformable thin-walled beam-columns

Total potential energy of non-symmetric thin-walled beam-columns in the general form is presented by introducing the displacement field based on semitangential rotations and deriving transformation equations between displacement and force parameters defined at the arbitrary axis and the centroid-shear center axis, respectively. Next, governing equations and force-deformation relations are derived from the total potential energy for a shear-deformable, uniform beam element and a system of linear eigenproblem with non-symmetric matrices is constructed based on 14 displacement parameters. And then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force-deformatin relationships. In addition, the modified numerical method to eliminate multiple zero eigenvalues and to evaluate the exact static stiffness matrix is developed for spatial stability analysis. Finally, in order to demonstrate the validity and the accuracy of this study, the spatially coupled natural frequencies and buckling loads are evaluated and compared with analytical solutions or results analyzed by thin-walled beam elements and ABAQUS's shell elements.     

The hit problem for the Dickson algebra

Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.

     

Exclusion limits on the WIMP-nucleon cross section from the cryogenic dark matter search

The Cryogenic Dark Matter Search (CDMS) employs Ge and Si detectors to search for weakly interacting massive particles (WIMPs) via their elastic-scattering interactions with nuclei while discriminating against interactions of background particles. CDMS data, accounting for the neutron background, give limits on the spin-independent WIMP-nucleon elastic-scattering cross section that exclude unexplored parameter space above 10 GeV/c2 WIMP mass and, at >75% C.L., the entire 3sigma allowed region for the WIMP signal reported by the DAMA experiment.     

Lagrangian chaos and the effect of drag on the enstrophy cascade in two-dimensional turbulence

We investigate the effect of drag force on the enstrophy cascade of two-dimensional Navier-Stokes turbulence. We find a power law decrease of the energy wave number (k) spectrum that is faster than the classical (no-drag) prediction of k(-3). It is shown that the enstrophy cascade with drag can be analyzed by making use of a previous theory for finite lifetime passive scalars advected by a Lagrangian chaotic fluid flow. Using this we relate the power law exponent of the energy wave number spectrum to the distribution of finite time Lyapunov exponents and the drag coefficient.     

Simultaneous measurement of anomalous group-velocity dispersion and nonlinear coefficient in optical fibers using soliton-effect compression

We present a novel and simple method to measure both the value of the second-order dispersion coefficient and the nonlinear coefficient in optical fibers. This method is based on the higher-order soliton-effect pulse compression phenomenon and is valid for dispersion values greater than 0.5 ps/km/nm. A non-zero dispersion-shifted fiber, a standard single-mode fiber and a highly-dispersive highly-nonlinear fiber have been measured using this method.     

Synthesis and characterization of thiazolothiazole‐based polymers and their applications in polymer solar cells

A novel series of thiazolothiazole (Tz)‐based copolymers, poly[9,9‐didecylfluorene‐2,7‐diyl‐alt‐2,5‐bis‐(3‐hexylthiophene‐2‐yl)thiazolo[5,4‐d]thiazole] (P1), poly[9,9‐dioctyldibenzosilole‐2,7‐diyl‐alt‐2,5‐bis‐(3‐hexylthiophene‐2‐yl)thiazolo[5,4‐d]thiazole] (P2), and poly[4,4′‐bis(2‐ethylhexyl)‐dithieno[3,2‐b:2′,3′‐d]silole‐alt‐2,5‐bis‐(3‐hexylthiophene‐2‐yl)thiazolo[5,4‐d]thiazole] (P3), were synthesized for the use as donor materials in polymer solar cells (PSCs). The field‐effect carrier mobilities and the optical, electrochemical, and photovoltaic properties of the copolymers were investigated. The results suggest that the donor units in the copolymers significantly influenced the band gap, electronic energy levels, carrier mobilities, and photovoltaic properties of the copolymers. The band gaps of the copolymers were in the range of 1.80–2.14 eV. Under optimized conditions, the Tz‐based polymers showed power conversion efficiencies (PCEs) for the PSCs in the range of 2.23–2.75% under AM 1.5 illumination (100 mW/cm²). Among the three copolymers, P1, which contained a fluorene donor unit, showed a PCE of 2.75% with a short‐circuit current of 8.12 mA/cm², open circuit voltage of 0.86 V, and a fill factor (FF) of 0.39, under AM 1.5 illumination (100 mW/cm²). © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.