3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects

We present a new data structure for a set of n convex simply-shaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting—preprocess a set of n non-intersecting convex simply-shaped flat objects in 3-space, whose xy-projections are fat, for efficient vertical ray shooting queries, (ii) point enclosure—preprocess a set C of n convex simply-shaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) bounded-size range searching— preprocess a set C of n convex fat polygons, so that the k objects intersecting a “not-too-large” query polygon can be reported efficiently, and (iv) bounded-size segment shooting—preprocess a set C as in (iii), so that the first object (if exists) hit by a “not-too-long” oriented query segment can be found efficiently. For the first three problems we construct data structures of size O(λ_s(n)log³n), where s is the maximum number of intersections between the boundaries of the (xy-projections) of any pair of objects, and λ_s(n) is the maximum length of (n, s) Davenport-Schinzel sequences. The data structure for the fourth problem is of size O(λ_s(n)log²n). The query time in the first problem is O(log⁴n), the query time in the second and third problems is O(log³n + klog²n), and the query time in the fourth problem is O(log³n).

We also present a simple algorithm for computing a depth order for a set as in (i), that is based on the solution to the vertical ray shooting problem. (A depth order for , if exists, is a linear order of , such that, if K₁, K₂ and K₁ lies vertically above K₂, then K₁ precedes K₂.) Unlike the algorithm of Agarwal et al. (1995) that might output a false order when a depth order does not exist, the new algorithm is able to determine whether such an order exists, and it is often more efficient in practical situations than the former algorithm.     

双层桥梁耦合系统的强迫振动

本文研究作为双层桥模型的梁方程耦合系统，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了一个关于这种系统的解的存在性定理，它类似于ＭｃＫｅｎｎａ和Ｗａｌｔｅｒ文２中关于吊桥方程的一个定理。     

Mass transport in metals under intensive impulse reactions

An unusually high mobility of atoms under intensive impulse reactions is explained by the behavior of point defects at the shock wave front. It is shown that either a shock wave front or moving dislocations can capture the interstitials, or they can be thermally activated in the direction of the shock wave propagation.     

Electronic transport properties of bismuth nanobridges through silicon-nitride membranes

The electronic transport through nanostructured bismuth nanobridges has been investigated at low temperatures (T<2 K) and in magnetic fields B up to 8.5 T. The samples show reproducible resistance fluctuations as a function of B, superimposed on a large magnetoresistance of up to 50%. In addition, time-dependent resistance fluctuations in zero magnetic field demonstrate the presence of bistable scatterers in the constriction region of our samples, which are described by two-level systems. Their dynamics are shown to be sensitive to subtle modifications of the static scatterer configuration in their vicinity, which cannot be detected in the sample magnetofingerprint.     

Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001     

Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems

Some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second-order Hamiltonian systems by the minimax methods in critical point theory.     

An experiment with arithmetic precision in linear algebra computations

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation. Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.     

Vortices in Bose-Einstein condensates: A review of the experimental results

Rotating dilute Bose-Einstein condensates (BEC) of alkali atoms offer a testing ground for theories of vortices in weakly interacting superfluids. In a rotating super-fluid, quantised vortices, with a vorticity h/m, form above a critical velocity. Such vortices have been generated in BEC of alkali atoms by different techniques such as (a) wave function engineering of a two-component BEC, (b) decay of solitons, (c) rotation of a thermal cloud before cooling it below the condensation temperature, (d) stirring with an ‘optical’ spoon, (e) rotating a deformation in the anisotropic trap in which the condensate is trapped and (f) by creating Berry phase by adiabatically reversing the axial magnetic field. Since the core of a vortex is a fraction of a micrometer in diameter, it cannot be directly imaged optically. The condensate with vortices is allowed to ballistically expand till the size increases by one order before the vortices are imaged. Surface wave spectroscopy and the change in aspect ratio of a rotating cloud are the other techniques used. Studies have been made on the creation and dynamics of single vortex and on systems with more than a hundred vortices. Results have been obtained on vortex nucleation, stability of vortex structures, nature of the vortex lattice and defects in such a lattice. Important results are: (a) evidence exists that vortex nucleation takes place by a surface mode instability; but this is not the only mechanism; (b) the vortex lattice is perfectly triangular right up to the edge; (c) in the initial stages of rotation of the cloud a tangled web of vortices is seen; it takes a few hundred milliseconds before the vortices arrange themselves in a lattice; this time appears to be independent of temperature; (d) the decay of vortices appears to arise from the transfer of energy to the rotating thermal component and is dependent on temperature; (e) defects in the lattices such as dislocations and grain boundaries are seen; (f) transverse oscillations (Tkachenko modes) of the vortex lattice have been observed; and (g) giant vortices have been produced. These will be discussed.