Size-dependent chemical transformation,structural phase change,and optical properties of nanowires

Nanowires offer a unique approach for the bottom-up assembly of electronic and photonic devices with the potential of integrating photonics with existing technologies. The anisotropic geometry and mesoscopic length scales of nanowires also make them very interesting systems to study a variety of size-dependent phenomenon where finite-size effects become important. We will discuss the intriguing size-dependent properties of nanowire systems with diameters in the 5–300?nm range, where finite-size and interfacial phenomena become more important than quantum mechanical effects. The ability to synthesize and manipulate nanostructures by chemical methods allows tremendous versatility in creating new systems with well-controlled geometries, dimensions, and functionality, which can then be used for understanding novel processes in finite-sized systems and devices.     

Dynamic Point Location in General Subdivisions

The dynamic planar point location problem is the task of maintaining a dynamic set S of n nonintersecting (except possibly at endpoints) line segments in the plane under the following operations:

• Locate (: point): Report the segment immediately above , i.e., the first segment intersected by an upward vertical ray starting at ;

• Insert (: segment): Add segment to the collection of segments;

• Delete (: segment): Remove segment from the collection of segments.

We present a solution which requires space O(n) and has query and insertion time O(log n log log n) and deletion time O(log²n). The bounds for insertions and deletions are amortized. A query time below O(log²n) was previously only known for monotone subdivisions and subdivisions consisting of horizontal segments and required nonlinear space.     

A remark on nilpotent Lie Algebras

Letf(n) denoted the number of essential parameters which are needed to classifyn-dimensional nilpotent Lie Algebras over the complex number field. Then $f(2n) \geqslant \tfrac{{n(n2 - 7)}}{6} - 2$ .     

Charged particle multiplicity distributions ine + e − annihilation at 29 GeV: a comparison with hadronic data

The charged particle multiplicity distributions for two-jet events ine ⁺ e ^? annihilation at 29 GeV have been measured using the High Resolution Spectrometer at PEP. A Poisson distribution describes the data for both the complete event and for the single jets. In addition, no correlation is observed between the multiplicities in the two jets of an event. For fixed values of the prong number of the complete event, the multiplicity sharing between the two jets is in good agreement with a binomial distribution. The rapidity gap distribution is exponential with a slope equal to the mean rapidity density. These observations, which are consistent with a picture of independent emission of single particles, are contrasted to the results from soft hadronic collisions and conclusions are drawn about the nature of clusters.     

Absolute triple differential cross sections for electron impact ionization of helium: Comparison between experimental and theoretical results at 256 eV collision energy

Triple differential cross sections have been measured for electron impact ionization of helium at 256 eV collision energy, 3 eV energy of the slow outgoing electrons and scattering angles of the fast outgoing electrons of 4°, 6°, 8°, and 10°. The data have been put on absolute scale by extrapolating the generalized oscillator strength to zero momentum transfer. In this optical limit the triple differential cross sections can be normalized by using the well-known cross sections for photoionization. The experimental data are compared with results of different theoretical approaches. For nearly all calculated curves rather good agreement with the measurements is obtained for the relative shape of the binary peak, while often its absolute cross section is overestimated. Concerning the recoil peak, larger discrepancies are found with respect to both, relative shapes and cross sections. A perceptible improvement can be stated for calculations which have been performed in a distorted wave approximation and in second Born approximation.     

Correlation functions and correlation times for models with multiplicative white noise

Correlation functions and correlation times for the Stratonovich and Verhulst model are investigated. By transforming the Fourier transform of the corresponding Fokker-Planck equation into a tridiagonal vector recurrence relation, the Fourier transform of the correlation function and the correlation time are expressed in terms of matrix continued fractions or by similar iterations and are thus obtained numerically. By using the inverse Fourier transform, the correlation function itself is calculated. Furthermore an analytic expression in terms of an integral is obtained for the correlation time, which is evaluated exactly in the Verhulst model and asymptotically for large and weak noise strength in the Stratonovich model. A Padé expansion approximating the correlation time for all noise strength is also given.