Improving Construction for Connected Dominating Set with Steiner Tree in Wireless Sensor Networks

The connected dominating set plays an important role in ad hoc wireless networking. Many constructions for approximating the minimum connected dominating set have been proposed in the literature. In this paper, we propose a new one with Steiner tree, which produces approximation solution within a factor of 6.8 from optimal. This approximation algorithm can also be implemented distributedly.     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

Ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice observed by use of Terahertz fields

We report an experimental study indicating ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice under the action of a THz field. Our experiment was performed for an InGaAs/InAlAs superlattice with the conduction electrons undergoing miniband transport. We applied to a superlattice a dc bias that was slightly smaller than a critical bias necessary for the formation of space-charge domains caused by a static negative differential conductivity. Additionally subjecting the superlattice to a strong THz field, resulted in a dc transport governed by the formation of domains if the frequency of the field was smaller than an upper frequency limit (~3 THz). From this frequency limit for the creation and annihilation of domains we determined the characteristic time of the domain buildup. Our analysis shows that the buildup time of domains in a wide miniband and heavily doped superlattice is limited by the relaxation time due to scattering of the miniband electrons at polar optic phonons. Our results are of importance for both an understanding of ultrafast dynamics of pattern formation in nanostructures and the development of THz electronic devices.Received: 25 March 2004, Published online: 23 July 2004PACS: 72.20.Ht High-field and nonlinear effects - 72.30. + q High-frequency effects; plasma effects - 73.21.Cd SuperlatticesK.N. Alekseev: Permanent address: Department of Physical Sciences, P.O. Box 3000, University of Oulu FIN-90014, Finland.     

Constructing one-parameter families of elliptic curves with moderate rank

We give several new constructions for moderate rank elliptic curves over Q(T). In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass form) of rank 6 over Q using polynomials of degree two in T. While our method generates linearly independent points, we are able to show the rank is exactly 6 without having to verify the points are independent. The method generalizes; however, the higher rank surfaces are not rational, and we need to check that the constructed points are linearly independent.     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007     

Caratheodory interpolation kernels

Kernels over the unit disk for which a version of Carathéodory interpolation is true are characterized in a simple computationally verifiable manner.