Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Quantum Random Walks without Coin Toss

We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of classical randomised algorithms. We use this algorithm to search for a marked vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and analytical results match the scaling behaviour of earlier algorithms that use a coin toss instruction.

Symmetry in Scalar Field Topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

Topology Optimization of Micromachined Structures with Surface Micromachining Manufacturing Constraints

Topology optimization methods have been shown to have extensive application in the design of microsystems. However, their utility in practical situations is restricted to predominantly planar configurations due to the limitations of most microfabrication techniques in realizing structures with arbitrary topologies in the direction perpendicular to the substrate. This study addresses the problem of synthesizing optimal topologies in the out-of-plane direction while obeying the constraints imposed by surface micromachining. A new formulation that achieves this by defining a design space that implicitly obeys the manufacturing constraints with a continuous design parameterization is presented in this paper. This is in contrast to including manufacturing cost in the objective function or constraints. The resulting solutions of the new formulation obtained with gradient-based optimization directly provide the photolithographic mask layouts. Two examples that illustrate the approach for the case of stiff structures are included.

Topology Optimization of Electrostatically Actuated Micromechanical Structures with Accurate Electrostatic Modeling of the Interpolated Material Model

In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

High voltage DC power supply topology for pulsed load applications with converter switching synchronized to load pulses

High voltage power supplies for radar applications are investigated, which are subjected to pulsed load (125 kHz and 10% duty cycle) with stringent specifications (<0.01% regulation, efficiency>85%, droop<0.5 V/micro-sec.). As good regulation and stable operation requires the converter to be switched at much higher frequency than the pulse load frequency, transformer poses serious problems of insulation failure and higher losses. This paper proposes a methodology to tackle the problems associated with this type of application. Synchronization of converter switching with load pulses enables the converter to switch at half the load switching frequency. Low switching frequency helps in ensuring safety of HV transformer insulation and reduction of losses due to skin and proximity effect. Phase-modulated series resonant converter with ZVS is used as the power converter.

Input voltage modulated high voltage DC power supply topology for pulsed load applications

High voltage power supplies for radar applications are investigated which are subjected to pulsed load with stringent specifications. In the proposed solution, power conversion is done in two stages. A low power-high frequency converter modulates the input voltage of a high power-low frequency converter. This method satisfies all the performance specifications and takes care of the critical aspects of HV transformer.

Design of conjugate, conjoined shapes and tilings using topology optimization

We present a method for obtaining conjugate, conjoined shapes and tilings in the context of the design of structures using topology optimization. Optimal material distribution is achieved in topology optimization by setting up a selection field in the design domain to determine the presence/absence of material there. We generalize this approach in this paper by presenting a paradigm in which the material left out by the selection field is also utilised. We obtain conjugate shapes when the region chosen and the region left-out are solutions for two problems, each with a different functionality. On the other hand, if the left-out region is connected to the selected region in some pre-determined fashion for achieving a single functionality, then we get conjoined shapes. The utilization of the left-out material, gives the notion of material economy in both cases. Thus, material wastage is avoided in the practical realization of these designs using many manufacturing techniques. This is in contrast to the wastage of left-out material during manufacture of traditional topology-optimized designs. We illustrate such shapes in the case of stiff structures and compliant mechanisms. When such designs are suitably made on domains of the unit cell of a tiling, this leads to the formation of new tilings which are functionally useful. Such shapes are not only useful for their functionality and economy of material and manufacturing, but also for their aesthetic value.

A Refined Methodology for Durability-Based Service Life Estimation of Reinforced Concrete Structural Elements Considering Fuzzy and Random Uncertainties

A reliable method for service life estimation of the structural element is a prerequisite for service life design. A new methodology for durability-based service life estimation of reinforced concrete flexural elements with respect to chloride-induced corrosion of reinforcement is proposed. The methodology takes into consideration the fuzzy and random uncertainties associated with the variables involved in service life estimation by using a hybrid method combining the vertex method of fuzzy set theory with Monte Carlo simulation technique. It is also shown how to determine the bounds for characteristic value of failure probability from the resulting fuzzy set for failure probability with minimal computational effort. Using the methodology, the bounds for the characteristic value of failure probability for a reinforced concrete T-beam bridge girder has been determined. The service life of the structural element is determined by comparing the upper bound of characteristic value of failure probability with the target failure probability. The methodology will be useful for durability-based service life design and also for making decisions regarding in-service inspections.

A Five-Level Inverter Topology with Single-DC Supply by Cascading a Flying Capacitor Inverter and an H-Bridge

In this paper, a new three-phase, five-level inverter topology with a single-dc source is presented. The proposed topology is obtained by cascading a three-level flying capacitor inverter with a flying H-bridge power cell in each phase. This topology has redundant switching states for generating different pole voltages. By selecting appropriate switching states, the capacitor voltages can be balanced instantaneously (as compared to the fundamental) in any direction of the current, irrespective of the load power factor. Another important feature of this topology is that if any H-bridge fails, it can be bypassed and the configuration can still operate as a three-level inverter at its full power rating. This feature improves the reliability of the circuit. A 3-kW induction motor is run with the proposed topology for the full modulation range. The effectiveness of the capacitor balancing algorithm is tested for the full range of speed and during the sudden acceleration of the motor.

Percolation and connectivity in AB random geometric graphs

Given two independent Poisson point processes Phi((1)), Phi((2)) in R-d, the AB Poisson Boolean model is the graph with the points of Phi((1)) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Phi((2)). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d >= 2 and derive bounds fora critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and tau n in the unit cube. The AB random geometric graph is defined as above but with balls of radius r. We derive a weak law result for the largest nearest-neighbor distance and almost-sure asymptotic bounds for the connectivity threshold.

An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.