Invariants of differential equations defined by vector fields

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the second order. A result on the characterization of classes of these equations by the invariant functions is also given.Comment: 13 page

Application of convolve-multiply-convolve SAW processor for satellite communications

There is a need for a satellite communications receiver than can perform simultaneous multi-channel processing of single channel per carrier (SCPC) signals originating from various small (mobile or fixed) earth stations. The number of ground users can be as many as 1000. Conventional techniques of simultaneously processing these signals is by employing as many RF-bandpass filters as the number of channels. Consequently, such an approach would result in a bulky receiver, which becomes impractical for satellite applications. A unique approach utilizing a realtime surface acoustic wave (SAW) chirp transform processor is presented. The application of a Convolve-Multiply-Convolve (CMC) chirp transform processor is described. The CMC processor transforms each input channel into a unique timeslot, while preserving its modulation content (in this case QPSK). Subsequently, each channel is individually demodulated without the need of input channel filters. Circuit complexity is significantly reduced, because the output frequency of the CMC processor is common for all input channel frequencies. The results of theoretical analysis and experimental results are in good agreement

Intersubband transitions in pseudomorphic InGaAs/GaAs/AlGaAs multiple step quantum wells

Intersubband transitions from the ground state to the first and second excited states in pseudomorphic AlGaAs/InGaAs/GaAs/AlGaAs multiple step quantum wells have been observed. The step well structure has a configuration of two AlGaAs barriers confining an InGaAs/GaAs step. Multiple step wells were grown on GaAs substrate with each InGaAs layer compressively strained. During the growth, a uniform growth condition was adopted so that inconvenient long growth interruptions and fast temperature ramps when switching the materials were eliminated. The sample was examined by cross‐sectional transmission electron microscopy, an x‐ray rocking curve technique, and the results show good crystal quality using this simple growth method. Theoretical calculations were performed to fit the intersubband absorption spectrum. The calculated energies are in good agreement with the observed peak positions for both the 1→2 and 1→3 transitions

A cooperative design approach to the design of interactive devices for small, specialized user groups

University of Technology, Sydney. Faculty of Engineering and Information Technology.This research considers a cooperative design approach to the design, development and implementation of interactive devices catering to small, specialised user groups. Conventional methods of mass production used in the manufacture of interactive devices demand medium to large volume production runs of 10,000 to 100,000 + units for products to remain cost effective. This drives the need for products to appeal to large user groups, which means product implementation catering to small user groups is limited. However there is a need for interactive devices catering to small user groups in industries that require specialised devices to do specific tasks. Such industries include mining, health care and aged care to name a few. Recent advancements in Additive Manufacturing technology combined with the availability of Open Source Hardware + Software offer the possibility to develop and implement interactive devices for low-volume production starting as low as one unit produced. Conventional User Centred Design approaches used in Industrial Design are tailored towards high-volume production, however for small-volume production a cooperative design (co-design) approach may be more relevant. To investigate this a study was conducted by devising a co-design approach and applying it to the design, development and implementation of an Operator Control Unit (OCU). This OCU was designed to control a semi-autonomous robotic Grit-blasting Assistive Device (GAD) that was deployed on the Sydney Harbour Bridge (SHB). The purpose of the SHB GAD is to remove old paint and rust from the Harbour Bridge steel structure by blasting it with grit. The development of the SHB GAD, including its OCU, is a joint project between Roads and Maritime Services (RMS) and the University of Technology Sydney’s Centre for Autonomous Systems. The project was chosen for the study because the SHB GAD is a tool developed specifically for the Sydney Harbour Bridge and is to be used by a small user group of ten users. The study was conducted by designing and developing the OCU cooperatively with five users, who are employees of RMS. Upon implementation of the OCU resulting from the study, a review of the co-design approach was conducted, by interviewing the five users and asking them to reflect on the process. The results revealed that this research is able to make contributions that will assist in furthering knowledge in this area. Furthermore the results led to a set of conclusions, of which one is that a co-design approach adds value to a project at a personal, team and company level. The resulting OCU was also compared to two commercially available OCUs. This comparison demonstrated, that the resulting OCU could be identified as a robotic OCU even though the users involved in the co-design approach had no previous design or robotics experience. The contributions and conclusions may provide new ways of structuring Industrial Design and Human Robot Interaction approaches to the design of interactive devices for small, specialised user groups

Exchange coupling between two ferromagnetic electrodes separated by a graphene nanoribbon

In this study, based on the self-energy method and the total energy calculation, the indirect exchange coupling between two semi-infinite ferromagnetic strips (FM electrodes) separated by metallic graphene nanoribbons (GNRs) is investigated. In order to form a FM/GNR/FM junction, a graphitic region of finite length is coupled to the FM electrodes along graphitic zigzag or armchair interfaces of width $N$. The numerical results show that, the exchange coupling strength which can be obtained from the difference between the total energies of electrons in the ferromagnetic and antiferromagnetic couplings, has an oscillatory behavior, and depends on the Fermi energy and the length of the central region.Comment: 4 pages, 6 figures, International Conference on Theoretical Physics 'Dubna-Nano2008

Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

SiGeC alloy layer formation by high-dose C + implantations into pseudomorphic metastable Ge0.08Si0.92 on Si(100)

Dual-energy carbon implantation (1 × 1016/cm2 at 150 and at 220 keV) was performed on 260-nm-thick undoped metastable pseudomorphic Si(100)/ Ge0.08Si0.92 with a 450-nm-thick SiO2 capping layer, at either room temperature or at 100 °C. After removal of the SiO2 the samples were measured using backscattering/channeling spectrometry and double-crystal x-ray diffractometry. A 150-nm-thick amorphous layer was observed in the room temperature implanted samples. This layer was found to have regrown epitaxially after sequential annealing at 550 °C for 2 h plus at 700 °C for 30 min. Following this anneal, tensile strain, believed to result from a large fraction of substitutional carbon in the regrown layer, was observed. Compressive strain, that presumably arises from the damaged but nonamorphized portion of the GeSi layer, was also observed. This strain was not significantly affected by the annealing treatment. For the samples implanted at 100 °C, in which case no amorphous layer was produced, only compressive strain was observed. For samples implanted at both room temperature and 100 °C, the channelled backscattering yield from the Si substrate was the same as that of the virgin sample

A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation x¨+f(x)x˙+g(x)=0\ddot{x}+f(x)\dot{x}+g(x) = 0 : Part II: Equations having Maximal Lie Point Symmetries

In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Li\'enard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.Comment: Accepted for publication in Journal of Mathematical Physic