Similar to the well-known phases of SLE, the Loewner differential equation with Lip(1/2) driving terms is known to have a phase transition at norm 4, when traces change from simple to non-simple curves. We establish the deterministic analog of the second phase transition of SLE, where traces change to space-filling curves: There is a constant C > 4 such that a Loewner driving term whose trace i...

Data is always stored in secondary storage Devices due to its volume. When it is stored in secondary storage devices, it is required that the access time is as minimal as possible. Most of the queries issued for providing location based services, result in accessing nearest point. This paper provides an algorithm to store the data efficiently so that accessing time is reduced for answering such...

This paper presents a variety of novel uses of space-filling curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes – both structured and unstructured. We demonstrate the use of single O ( N log N ) SFC-based reordering to produce single-pass ( O ( N )) algorithms for ...

Space-filling curves(SFC) have been widely accepted as an easy technique to generate good quality mesh partitions. In this work, we discuss the limitations of some of the existing methods for generating SFCs and propose a recursive algorithm for constructing a general SFC that works for a range of meshes in 2D and 3D. All of our test cases for the 2D SFC come from the meshes used in Community E...

The introduction of next generation sequencing methods in genome studies has made it possible to shift research from a gene-centric approach to a genome wide view. Although methods and tools to detect single nucleotide polymorphisms are becoming more mature, methods to identify and visualize structural variation (SV) are still in their infancy. Most genome browsers can only compare a given sequ...

Swarms of mobile robots can be tasked with searching a geographic region for targets of interest, such as buried land mines. We assume that the individual robots are equipped with sensors tuned to the targets of interest, that these sensors have limited range, and that the robots can communicate with one another to enable cooperation. How can a swarm of cooperating sensate robots efficiently se...

This paper presents bounds on the quality of partitions induced by space-filling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than...

In this paper, we present a parallel multigrid PDE solver working on adaptive hierarchical cartesian grids. The presentation is restricted to the linear elliptic operator of second order, but extensions are possible and have already been realised as prototypes. Within the solver the handling of the vertices and the degrees of freedom associated to them is implemented solely using stacks and ite...

The paper presents a new combination of two methods for tool path generation for five-axis machining proposed earlier by the authors. The first method is based on the grid generation technologies whereas the second method exploits the space-filling curve approach. Combination of the two techniques is superior with regard to the conventional methods and with regard to the case when the two metho...