An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Positional Consensus of Multi-Agent Systems Using Linear Programming Based Decentralized Control with Rectilinear Decision Domain

In this paper we develop a Linear Programming (LP) based decentralized algorithm for a group of multiple autonomous agents to achieve positional consensus. Each agent is capable of exchanging information about its position and orientation with other agents within their sensing region. The method is computationally feasible and easy to implement. Analytical results are presented. The effectiveness of the approach is illustrated with simulation results.

Geometrically non-linear dynamics of composite four-bar mechanisms

This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.

Measurement Based Impromptu Deployment of a Multi-Hop Wireless Relay Network

We study the problem of optimal sequential (''as-you-go'') deployment of wireless relay nodes, as a person walks along a line of random length (with a known distribution). The objective is to create an impromptu multihop wireless network for connecting a packet source to be placed at the end of the line with a sink node located at the starting point, to operate in the light traffic regime. In walking from the sink towards the source, at every step, measurements yield the transmit powers required to establish links to one or more previously placed nodes. Based on these measurements, at every step, a decision is made to place a relay node, the overall system objective being to minimize a linear combination of the expected sum power (or the expected maximum power) required to deliver a packet from the source to the sink node and the expected number of relay nodes deployed. For each of these two objectives, two different relay selection strategies are considered: (i) each relay communicates with the sink via its immediate previous relay, (ii) the communication path can skip some of the deployed relays. With appropriate modeling assumptions, we formulate each of these problems as a Markov decision process (MDP). We provide the optimal policy structures for all these cases, and provide illustrations of the policies and their performance, via numerical results, for some typical parameters.

Linear and nonlinear intersubband optical properties in a step quantum well with an applied electric field

Within the framework of the effective-mass envelope-function theory, the field-dependent intersubband optical properties of a Al0.4Ga0.6As/Al0.2Ga0.8As/GaAs step quantum well are investigated theoretically based on the periodic boundary condition. A very large Stark shift occurs when the lowest subband electron remains confined to the small well while the higher subband electron confined to the big well. The optical nonlinearity in a step well due to resonant intersubband transition (ISBT) is analyzed using a density-matrix approach. The second-harmonic generation coefficient chi(2 omega)((2)) and nonlinear optical rectification chi(0)((2)) have also been investigated theoretically. The results show that the ISBT in a step well can generate very large second order optical nonlinearities, chi(0)((2)) and chi(2 omega)((2)) can be tuned by the electric field over a wide range.

The mean value concept in mono-linear regression of multi-variables and its application to trace studies in geosciences

IEECAS SKLLQG

A method for semi-automated objective quantification of linear bedforms from multi-scale Digital Elevation Models

The increasing availability of large, detailed digital representations of the Earth’s surface demands the application of objective and quantitative analyses. Given recent advances in the understanding of the mechanisms of formation of linear bedform features from a range of environments, objective measurement of their wavelength, orientation, crest and trough positions, height and asymmetry is highly desirable. These parameters are also of use when determining observation-based parameters for use in many applications such as numerical modelling, surface classification and sediment transport pathway analysis. Here, we (i) adapt and extend extant techniques to provide a suite of semi-automatic tools which calculate crest orientation, wavelength, height, asymmetry direction and asymmetry ratios of bedforms, and then (ii) undertake sensitivity tests on synthetic data, increasingly complex seabeds and a very large-scale (39 000km2) aeolian dune system. The automated results are compared with traditional, manually derived,measurements at each stage. This new approach successfully analyses different types of topographic data (from aeolian and marine environments) from a range of sources, with tens of millions of data points being processed in a semi-automated and objective manner within minutes rather than hours or days. The results from these analyses show there is significant variability in all measurable parameters in what might otherwise be considered uniform bedform fields. For example, the dunes of the Rub’ al Khali on the Arabian peninsula are shown to exhibit deviations in dimensions from global trends. Morphological and dune asymmetry analysis of the Rub’ al Khali suggests parts of the sand sea may be adjusting to a changed wind regime from that during their formation 100 to 10 ka BP.

Improved Linear Transmit Processing for Single-User and Multi-User MIMO Communications Systems

In this paper, we propose a novel linear transmit precoding strategy for multiple-input, multiple-output (MIMO) systems employing improper signal constellations. In particular, improved zero-forcing (ZF) and minimum mean square error (MMSE) precoders are derived based on modified cost functions, and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders. The superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results. The novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi-user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi-user channels. In both cases, the improved precoding schemes yield significant performance gain compared to the conventional counterparts.

Improvement in clinical step and shoot intensity modulated radiation therapy delivery accuracy on an integrated linear accelerator control system

Purpose: The dose delivery accuracy of 30 clinical step and shoot intensity modulated radiation therapy plans was investigated using the single integrated multileaf collimator controller of the Varian Truebeam linear accelerator (linac) (Varian Medical Systems, Palo Alto, CA) and compared with the dose delivery accuracy on a previous generation Varian 2100CD C-Series linac.

Methods and Materials: Ten prostate, 10 prostate and pelvic node, and 10 head-and-neck cases were investigated in this study. Dose delivery accuracy on each linac was assessed using Farmer ionization chamber point dose measurements, 2-dimensional planar ionization chamber array measurements, and the corresponding Varian dynamic log files. Absolute point dose measurements, fluence delivery accuracy, leaf position accuracy, and the overshoot effect were assessed for each plan.

Results: Absolute point dose delivery accuracy increased by 1.5% on the Truebeam compared with the 2100CD linac. No improvement in fluence delivery accuracy between the linacs, at a gamma criterion of 3%/3 mm was measured using the 2-dimensional ionization chamber array, with median (interquartile range) gamma passing rates of 98.99% (97.70%-99.72%) and 99.28% (98.26%-99.75%) for the Truebeam and 2100CD linacs, respectively. Varian log files also showed no improvement in fluence delivery between the linacs at 3%/3 mm, with median gamma passing rates of 99.97% (99.93%-99.99%) and 99.98% (99.94%-100%) for the Truebeam and 2100CD linacs, respectively. However, log files revealed improved leaf position accuracy and fluence delivery at 1%/1 mm criterion on the Truebeam (99.87%; 99.78%-99.94%) compared with the 2100CD linac (97.87%; 91.93%-99.49%). The overshoot effect, characterized on the 2100CD linac, was not observed on the Truebeam.

Conclusions: The integrated multileaf collimator controller on the Varian Truebeam improves clinical treatment delivery accuracy of step and shoot intensity modulated radiation therapy fields compared with delivery on a Varian C-series linac. © 2014.

Enhancing Linear Programming with Motion Modeling for Multi-target Tracking

In this paper we extend the minimum-cost network flow approach to multi-target tracking, by incorporating a motion model, allowing the tracker to better cope with longterm occlusions and missed detections. In our new method, the tracking problem is solved iteratively: Firstly, an initial tracking solution is found without the help of motion information. Given this initial set of tracklets, the motion at each detection is estimated, and used to refine the tracking solution.
Finally, special edges are added to the tracking graph, allowing a further revised tracking solution to be found, where distant tracklets may be linked based on motion similarity. Our system has been tested on the PETS S2.L1 and Oxford town-center sequences, outperforming the baseline system, and achieving results comparable with the current state of the art.