A unified approach to compute foliations, inertial manifolds, and tracking initial conditions

Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping method in [25] to compute inertial manifolds, which represents a particular leaf in the unstable foliation. Such a mapping is combined with one for the leaf in the stable foliation to compute the tracking initial condition for a given solution. The algorithms are demonstrated on the Kuramoto-Sivashinsky equation

Integrated Wireless Multimedia Turbo-Transceiver Design Approaching the Rayleigh Channel's Capacity: Interpreting Shannon's Lessons in the Turbo-Era

Claude Shannon's pioneering work quantified the performance limits of communications systems operating over classic wireline Gaussian channels. However, his source and channel coding theorems were derived for a range of idealistic conditions, which may not hold in low-delay, interactive wireless multimedia communications. Firstly, Shannon's ideal lossless source encoder, namely the entropy encoder may have an excessive codeword length, hence exhibiting a high delay and a high error sensitivity. However, in practice most multimedia source signals are capable of tolerating lossy, rather than lossless delivery to the human eye, ear and other human sensors. The corresponding lossy and preferably low-delay multimedia source codecs however exhibit unequal error sensitivity, which is not the case for Shannon's ideal entropy codec. There are further numerous differences between the Shannonian lessons originally outlined for Gaussian channels and their ramifications for routinely encountered dispersive wireless channels, where typically bursty, rather than random errors are encountered. This paper elaborates on these intriguiging lessons in the context of a few turbo-transceiver design examples, using a jointly optimised turbo transceiver capable of providing unequal error protection in the context of MPEG-4 aided wireless video telephony. The transceiver investigated consists of Space-Time Trellis Coding (STTC) invoked for the sake of mitigating the effects of fading, Trellis Coded Modulation (TCM) or Bit-Interleaved Coded Modulation (BICM) as well as two different-rate Non-Systematic Convolutional codes (NSCs) or Recursive Systematic Convolutional codes (RSCs). A single-class protection based benchmarker scheme combining STTC and NSC is used for comparison with the unequal-protection scheme advocated. The video performance of the various schemes is evaluated when communicating over uncorrelated Rayleigh fading channels. It was found that the achievable performance of the proposed scheme is within 0.99~dB of the corresponding capacity of the Rayleigh fading channel

Burst-by-Burst Adaptive Decision Feedback Equalised TCM, TTCM and BICM for H.263-Assisted Wireless Video Telephony

Decision Feedback Equaliser (DFE) aided wideband Burst-by-Burst (BbB) Adaptive Trellis Coded Modulation (TCM), Turbo Trellis Coded Modulation (TTCM) and Bit-Interleaved Coded Modulation (BICM) assisted H.263-based video transceivers are proposed and characterised in performance terms when communicating over the COST 207 Typical Urban wideband fading channel. Specifically, four different modulation modes, namely 4QAM, 8PSK, 16QAM and 64QAM are invoked and protected by the above-mentioned coded modulation schemes. The TTCM assisted scheme was found to provide the best video performance, although at the cost of the highest complexity. A range of lower-complexity arrangements will also be characterised. Finally, in order to confirm these findings in an important practical environment, we have also investigated the adaptive TTCM scheme in the CDMA-based Universal Mobile Telecommunications System's (UMTS) Terrestrial Radio Access (UTRA) scenario and the good performance of adaptive TTCM scheme recorded when communicating over the COST 207 channels was retained in the UTRA environment

Formal optimization of hovering performance using free wake lifting surface theory

Free wake techniques for performance prediction and optimization of hovering rotor are discussed. The influence functions due to vortex ring, vortex cylinder, and source or vortex sheets are presented. The vortex core sizes of rotor wake vortices are calculated and their importance is discussed. Lifting body theory for finite thickness body is developed for pressure calculation, and hence performance prediction of hovering rotors. Numerical optimization technique based on free wake lifting line theory is presented and discussed. It is demonstrated that formal optimization can be used with the implicit and nonlinear objective or cost function such as the performance of hovering rotors as used in this report

Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium

We present a new computation of S-wave color-singlet nonrelativistic QCD matrix elements for the J/psi and the eta_c. We compute the matrix elements of leading order in the heavy-quark velocity v and the matrix elements of relative order v^2. Our computation is based on the electromagnetic decay rates of the J/psi and the eta_c and on a potential model that employs the Cornell potential. We include relativistic corrections to the electromagnetic decay rates, resumming a class of corrections to all orders in v, and find that they significantly increase the values of the matrix elements of leading order in v. This increase could have important implications for theoretical predictions for a number of quarkonium decay and production processes. The values that we find for the matrix elements of relative order v^2 are somewhat smaller than the values that one obtains from estimates that are based on the velocity-scaling rules of nonrelativistic QCD.Comment: 31 pages, minor corrections, version published in Phys. Rev.