Diffusion-Reaction-Models and their Application to Biological and Astrophysical Problems

In this thesis we study several problems from biophysics and astrophysics, which can be all be described by reaction-diffusion systems. The first part of this thesis is concerned with biophysical quasispecies models. These are deterministic models, describing the interaction of mutations and selection (i.e. fitness advantage by adaption). We investigate the influence of robustness against deleterious mutations on the stationary states of these models. Here, robustness means that a certain number of mutations in the individual's information string is tolerated before the fitness of the individual is diminished. The equations of state for the quasispecies models can be represented by a reaction-diffusion equation for a special type of reaction term. We give analytic results for the robustness effect on the mean fitness of a population. These results become exact in the limit of infinite information-sequence length. By exploiting a mapping to a Schr\"odinger-type equation, we find correction terms for finite sequence length, essential for applications. The provided solutions allow to answer the question under what circumstances robustness is preferable to fitness, a question often referred to as \emph{survival of the flattest}. Additionally, we investigate the occurence of the error threshold (a phase transition of the population's state) in a general class of epistatic fitness landscapes. We show that diminishing epistasis is necessary but not sufficient for the emergence of an error threshold. All analytic work is supported and verified by numerical studies. In the second part we investigate diffusion-mediated reactions on two-dimen-sional surfaces drawing on the example of hydrogen formation on interstellar dust grains. The surfaces of these dust grains play an important role in molecule production in the interstellar medium, by acting as catalysts. We are interested in the influence of (quenched) surface disorder on the production rate of molecules. As model system, we study the not yet completely understood reaction H+H -> H2 of hydrogen formation. We confirm the earlier proposed significant enhancement in the production rate of this process by disorder in the binding energies of the surface and moreover give analytic results for different distributions of binding energies. We identify the main mechanism leading to an enhanced production rate, enabling us to give temperature dependent mappings from systems with discrete and continuous binding energy distributions to effective systems with only a binary energy distribution. The analytical results on all models are confirmed by numerical solutions of the full rate equations as well as by kinetic Monte Carlo simulations

Design guidelines for spatial modulation

A new class of low-complexity, yet energyefficient Multiple-Input Multiple-Output (MIMO) transmission techniques, namely the family of Spatial Modulation (SM) aided MIMOs (SM-MIMO) has emerged. These systems are capable of exploiting the spatial dimensions (i.e. the antenna indices) as an additional dimension invoked for transmitting information, apart from the traditional Amplitude and Phase Modulation (APM). SM is capable of efficiently operating in diverse MIMO configurations in the context of future communication systems. It constitutes a promising transmission candidate for large-scale MIMO design and for the indoor optical wireless communication whilst relying on a single-Radio Frequency (RF) chain. Moreover, SM may also be viewed as an entirely new hybrid modulation scheme, which is still in its infancy. This paper aims for providing a general survey of the SM design framework as well as of its intrinsic limits. In particular, we focus our attention on the associated transceiver design, on spatial constellation optimization, on link adaptation techniques, on distributed/ cooperative protocol design issues, and on their meritorious variants

Intelligent genetic algorithms for next-generation broadband multi-carrier CDMA wireless networks

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This dissertation proposes a novel intelligent system architecture for next-generation broadband multi-carrier CDMA wireless networks. In our system, two novel and similar intelligent genetic algorithms, namely Minimum Distance guided GAs (MDGAs) are invented for both peak-to-average power ratio (PAPR) reduction at the transmitter side and multi-user detection (MUD) at the receiver side. Meanwhile, we derive a theoretical BER performance analysis for the proposed MC-CDMA system in A WGN channel. Our analytical results show that the theoretical BER performance of synchronized MC-CDMA system is the same as that of the synchronized DS-CDMA system which is also used as a theoretical guidance of our novel MUD receiver design. In contrast to traditional GAs, our MDGAs start with a balanced ratio of exploration and exploitation which is maintained throughout the process. In our algorithms, a new replacement strategy is designed which increases significantly the convergence rate and reduces dramatically computational complexity as compared to the conventional GAs. The simulation results demonstrate that, if compared to those schemes using exhaustive search and traditional GAs, (1) our MDGA-based P APR reduction scheme achieves 99.52% and 50+% reductions in computational complexity, respectively; (2) our MDGA-based MUD scheme achieves 99.54% and 50+% reductions in computational complexity, respectively. The use of one core MDGA solution for both issues can ease the hardware design and dramatically reduce the implementation cost in practice