Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Transition of planar Couette flow at infinite Reynolds numbers

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<105) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit. © 2013 American Physical Society.

Planar variations in normal anisotropy in mild steel strip

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THz emission from quantum dot-based THz antennas pumped by a tunable quantum-dot laser diode

The THz optoelectronics field is now maturing and semiconductor-based THz antenna devices are becoming more widely implemented as analytical tools in spectroscopy and imaging. Photoconductive (PC) THz switches/antennas are driven optically typically using either an ultrashort-pulse laser or an optical signal composed of two simultaneous longitudinal wavelengths which are beat together in the PC material at a THz difference frequency. This allows the generation of (photo)carrier pairs which are then captured over ultrashort timescales usually by defects and trapping sites throughout the active material lattice. Defect-implanted PC materials with relatively high bandgap energy are typically used and many parameters such as carrier mobility and PC gain are greatly compromised. This paper demonstrates the implementation of low bandgap energy InAs quantum dots (QDs) embedded in standard crystalline GaAs as both the PC medium and the ultrafast capture mechanism in a PC THz antenna. This semiconductor structure is grown using standard MBE methods and allows the device to be optically driven efficiently at wavelengths up to ~1.3 µm, in this case by a single tunable dual-mode QD diode laser.

Controlled growth of poly(2-(diethylamino)ethyl methacrylate) brushes via atom transfer radical polymerisation on planar silicon surfaces

Progress in making pH-responsive polyelectrolyte brushes with a range of different grafting densities is reported. Polymer brushes of poly(2-(diethylamino)ethyl methacrylate) were synthesised via atom transfer radical polymerisation on silicon wafers using a 'grafted from' approach. The [11-(2-bromo-2-methyl) propionyloxy]undecyl trichlorosilane initiator was covalently attached to the silicon via silylation, from which the brushes were grown using a catalytic system of copper(I) chloride and pentamethyldiethylenetriamine in tetrahydrofuran at 80°C. X-ray reflectivity was used to assess the initiator surfaces and an upper limit on the grafting density of the polymer was determined. The quality of the brushes produced was analysed using ellipsometry and atomic force microscopy, which is also discussed.

A flexible approach for the apodization of planar waveguide Bragg gratings

A novel single-step technique for the apodization of planar waveguide Bragg gratings based on the polarization control method is proposed. First results are presented, showing successful side-lobe suppression in the reflection spectrum of the gratings.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.

Quantum dot-based terahertz photoconductive antennas

We present novel Terahertz (THz) emitting optically pumped Quantum Dot (QD) photoconductive (PC) materials and antenna structures on their basis both for pulsed and CW pumping regimes. Full text Quantum dot and microantenna design - Presented here are design considerations for the semiconductor materials in our novel QD-based photoconductive antenna (PCA) structures, metallic microantenna designs, and their implementation as part of a complete THz source or transceiver system. Layers of implanted QDs can be used for the photocarrier lifetime shortening mechanism[1,2]. In our research we use InAs:GaAs QD structures of varying dot layer number and distributed Bragg reflector(DBR)reflectivity range. According to the observed dependence of carrier lifetimes on QD layer periodicity [3], it is reasonable to assume that electron lifetimes can be potentially reduced down to 0.45ps in such structures. Both of these features; long excitation wavelength and short carriers lifetime predict possible feasibility of QD antennas for THz generation and detection. In general, relatively simple antenna configurations were used here, including: coplanar stripline (CPS); Hertzian-type dipoles; bow-ties for broadband and log-spiral(LS)or log-periodic(LP)‘toothed’ geometriesfor a CW operation regime. Experimental results - Several lasers are used for antenna pumping: Ti:Sapphire femtosecond laser, as well as single-[4], double-[5] wavelength, and pulsed [6] QD lasers. For detection of the THz signal different schemes and devices were used, e.g. helium-cooled bolometer, Golay cell and a second PCA for coherent THz detection in a traditional time-domain measurement scheme.Fig.1shows the typical THz output power trend from a 5 um-gap LPQD PCA pumped using a tunable QD LD with optical pump spectrum shown in (b). Summary - QD-based THz systems have been demonstrated as a feasible and highly versatile solution. The implementation of QD LDs as pump sources could be a major step towards ultra-compact, electrically controllable transceiver system that would increase the scope of data analysis due to the high pulse repetition rates of such LDs [3], allowing real-time THz TDS and data acquisition. Future steps in development of such systems now lie in the further investigation of QD-based THz PCA structures and devices, particularly with regards to their compatibilitywith QD LDs as pump sources. [1]E. U. Rafailov et al., “Fast quantum-dot saturable absorber for passive mode-locking of solid-State lasers,”Photon.Tech.Lett., IEEE, vol. 16 pp. 2439-2441(2004) [2]E. Estacio, “Strong enhancement of terahertz emission from GaAs in InAs/GaAs quantum dot structures. Appl.Phys.Lett., vol. 94 pp. 232104 (2009) [3]C. Kadow et al., “Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics,” Appl. Phys. Lett., vol. 75 pp. 3548-3550 (1999) [4]T. Kruczek, R. Leyman, D. Carnegie, N. Bazieva, G. Erbert, S. Schulz, C. Reardon, and E. U. Rafailov, “Continuous wave terahertz radiation from an InAs/GaAs quantum-dot photomixer device,” Appl. Phys. Lett., vol. 101(2012) [5]R. Leyman, D. I. Nikitichev, N. Bazieva, and E. U. Rafailov, “Multimodal spectral control of a quantum-dot diode laser for THz difference frequency generation,” Appl. Phys. Lett., vol. 99 (2011) [6]K.G. Wilcox, M. Butkus, I. Farrer, D.A. Ritchie, A. Tropper, E.U. Rafailov, “Subpicosecond quantum dot saturable absorber mode-locked semiconductor disk laser, ” Appl. Phys. Lett. Vol 94, 2511 © 2014 IEEE.

Lower Bounds on the Directed Sweepwidth of Planar Shapes

We investigate a recently introduced width measure of planar shapes called sweepwidth and prove a lower bound theorem on the sweepwidth.

Assembly accuracy analysis for small components with a planar surface in large-scale metrology

Large-scale mechanical products, such as aircraft and rockets, consist of large numbers of small components, which introduce additional difficulty for assembly accuracy and error estimation. Planar surfaces as key product characteristics are usually utilised for positioning small components in the assembly process. This paper focuses on assembly accuracy analysis of small components with planar surfaces in large-scale volume products. To evaluate the accuracy of the assembly system, an error propagation model for measurement error and fixture error is proposed, based on the assumption that all errors are normally distributed. In this model, the general coordinate vector is adopted to represent the position of the components. The error transmission functions are simplified into a linear model, and the coordinates of the reference points are composed by theoretical value and random error. The installation of a Head-Up Display is taken as an example to analyse the assembly error of small components based on the propagation model. The result shows that the final coordination accuracy is mainly determined by measurement error of the planar surface in small components. To reduce the uncertainty of the plane measurement, an evaluation index of measurement strategy is presented. This index reflects the distribution of the sampling point set and can be calculated by an inertia moment matrix. Finally, a practical application is introduced for validating the evaluation index.

Optimal partisan districting on planar geographies

We show that optimal partisan districting in the plane with geographical constraints is an NP-complete problem.

Optimizing the radiation pattern of smart antennas using genetic algorithms

This work is directed towards optimizing the radiation pattern of smart antennas using genetic algorithms. The structure of the smart antennas based on Space Division Multiple Access (SDMA) is proposed. It is composed of adaptive antennas, each of which has adjustable weight elements for amplitudes and phases of signals. The corresponding radiation pattern formula available for the utilization of numerical optimization techniques is deduced. Genetic algorithms are applied to search the best phase-amplitude weights or phase-only weights with which the optimal radiation pattern can be achieved. ^ One highlight of this work is the proposed optimal radiation pattern concept and its implementation by genetic algorithms. The results show that genetic algorithms are effective for the true Signal-Interference-Ratio (SIR) design of smart antennas. This means that not only nulls can be put in the directions of the interfering signals but also simultaneously main lobes can be formed in the directions of the desired signals. The optimal radiation pattern of a smart antenna possessing SDMA ability has been achieved. ^ The second highlight is on the weight search by genetic algorithms for the optimal radiation pattern design of antennas having more than one interfering signal. The regular criterion for determining which chromosome should be kept for the next step iteration is modified so as to improve the performance of the genetic algorithm iteration. The results show that the modified criterion can speed up and guarantee the iteration to be convergent. ^ In addition, the comparison between phase-amplitude perturbations and phase-only perturbations for the radiation pattern design of smart antennas are carried out. The effects of parameters used by the genetic algorithm on the optimal radiation pattern design are investigated. Valuable results are obtained. ^

Enhancement of wireless networks with heterogeneous antennas

In recent years, wireless communication infrastructures have been widely deployed for both personal and business applications. IEEE 802.11 series Wireless Local Area Network (WLAN) standards attract lots of attention due to their low cost and high data rate. Wireless ad hoc networks which use IEEE 802.11 standards are one of hot spots of recent network research. Designing appropriate Media Access Control (MAC) layer protocols is one of the key issues for wireless ad hoc networks. ^ Existing wireless applications typically use omni-directional antennas. When using an omni-directional antenna, the gain of the antenna in all directions is the same. Due to the nature of the Distributed Coordination Function (DCF) mechanism of IEEE 802.11 standards, only one of the one-hop neighbors can send data at one time. Nodes other than the sender and the receiver must be either in idle or listening state, otherwise collisions could occur. The downside of the omni-directionality of antennas is that the spatial reuse ratio is low and the capacity of the network is considerably limited. ^ It is therefore obvious that the directional antenna has been introduced to improve spatial reutilization. As we know, a directional antenna has the following benefits. It can improve transport capacity by decreasing interference of a directional main lobe. It can increase coverage range due to a higher SINR (Signal Interference to Noise Ratio), i.e., with the same power consumption, better connectivity can be achieved. And the usage of power can be reduced, i.e., for the same coverage, a transmitter can reduce its power consumption. ^ To utilizing the advantages of directional antennas, we propose a relay-enabled MAC protocol. Two relay nodes are chosen to forward data when the channel condition of direct link from the sender to the receiver is poor. The two relay nodes can transfer data at the same time and a pipelined data transmission can be achieved by using directional antennas. The throughput can be improved significant when introducing the relay-enabled MAC protocol. ^ Besides the strong points, directional antennas also have some explicit drawbacks, such as the hidden terminal and deafness problems and the requirements of retaining location information for each node. Therefore, an omni-directional antenna should be used in some situations. The combination use of omni-directional and directional antennas leads to the problem of configuring heterogeneous antennas, i e., given a network topology and a traffic pattern, we need to find a tradeoff between using omni-directional and using directional antennas to obtain a better network performance over this configuration. ^ Directly and mathematically establishing the relationship between the network performance and the antenna configurations is extremely difficult, if not intractable. Therefore, in this research, we proposed several clustering-based methods to obtain approximate solutions for heterogeneous antennas configuration problem, which can improve network performance significantly. ^ Our proposed methods consist of two steps. The first step (i.e., clustering links) is to cluster the links into different groups based on the matrix-based system model. After being clustered, the links in the same group have similar neighborhood nodes and will use the same type of antenna. The second step (i.e., labeling links) is to decide the type of antenna for each group. For heterogeneous antennas, some groups of links will use directional antenna and others will adopt omni-directional antenna. Experiments are conducted to compare the proposed methods with existing methods. Experimental results demonstrate that our clustering-based methods can improve the network performance significantly. ^

Desenvolvimento teórico e experimental de FSS com elementos fractais de Gosper em estruturas de multicamadas

The fractal self-similarity property is studied to develop frequency selective surfaces (FSS) with several rejection bands. Particularly, Gosper fractal curves are used to define the shapes of the FSS elements. Due to the difficulty of making the FSS element details, the analysis is developed for elements with up to three fractal levels. The simulation was carried out using Ansoft Designer software. For results validation, several FSS prototypes with fractal elements were fabricated. In the fabrication process, fractals elements were designed using computer aided design (CAD) tools. The prototypes were measured using a network analyzer (N3250A model, Agilent Technologies). Matlab software was used to generate compare measured and simulated results. The use of fractal elements in the FSS structures showed that the use of high fractal levels can reduce the size of the elements, at the same time as decreases the bandwidth. We also investigated the effect produced by cascading FSS structures. The considered cascaded structures are composed of two FSSs separated by a dielectric layer, which distance is varied to determine the effect produced on the bandwidth of the coupled geometry. Particularly, two FSS structures were coupled through dielectric layers of air and fiberglass. For comparison of results, we designed, fabricated and measured several prototypes of FSS on isolated and coupled structures. Agreement was observed between simulated and measured results. It was also observed that the use of cascaded FSS structures increases the FSSs bandwidths and, in particular cases, the number of resonant frequencies, in the considered frequency range. In future works, we will investigate the effects of using different types of fractal elements, in isolated, multilayer and coupled FSS structures for applications on planar filters, high-gain microstrip antennas and microwave absorbers