Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

A Study of Single Stage Semi‐Dry Anaerobic Digestion of Organic Fraction of Municipal Solid Waste

Solid waste generation is a natural consequence of human activity and is increasing along with population growth, urbanization and industrialization. Improper disposal of the huge amount of solid waste seriously affects the environment and contributes to climate change by the release of greenhouse gases. Practicing anaerobic digestion (AD) for the organic fraction of municipal solid waste (OFMSW) can reduce emissions to environment and thereby alleviate the environmental problems together with production of biogas, an energy source, and digestate, a soil amendment. The amenability of substrate for biogasification varies from substrate to substrate and different environmental and operating conditions such as pH, temperature, type and quality of substrate, mixing, retention time etc. Therefore, the purpose of this research work is to develop feasible semi-dry anaerobic digestion process for the treatment of OFMSW from Kerala, India for potential energy recovery and sustainable waste management. This study was carried out in three phases in order to reach the research purpose. In the first phase, batch study of anaerobic digestion of OFMSW was carried out for 100 days at 32°C (mesophilic digestion) for varying substrate concentrations. The aim of this study was to obtain the optimal conditions for biogas production using response surface methodology (RSM). The parameters studied were initial pH, substrate concentration and total organic carbon (TOC). The experimental results showed that the linear model terms of initial pH and substrate concentration and the quadratic model terms of the substrate concentration and TOC had significant individual effect (p < 0.05) on biogas yield. However, there was no interactive effect between these variables (p > 0.05). The optimum conditions for maximizing the biogas yield were a substrate concentration of 99 g/l, an initial pH of 6.5 and TOC of 20.32 g/l. AD of OFMSW with optimized substrate concentration of 99 g/l [Total Solid (TS)-10.5%] is a semi-dry digestion system .Under the optimized condition, the maximum biogas yield was 53.4 L/kg VS (volatile solid).. In the second phase, semi-dry anaerobic digestion of organic solid wastes was conducted for 45 days in a lab-scale batch experiment for substrate concentration of 100 g/l (TS-11.2%) for investigating the start-up performances under thermophilic condition (50°C). The performance of the reactor was evaluated by measuring the daily biogas production and calculating the degradation of total solids and the total volatile solids. The biogas yield at the end of the digestion was 52.9 L/kg VS for the substrate concentration of 100 g/l. About 66.7% of volatile solid degradation was obtained during the digestion. A first order model based on the availability of substrate as the limiting factor was used to perform the kinetic studies of batch anaerobic digestion system. The value of reaction rate constant, k, obtained was 0.0249 day-1. A laboratory bench scale reactor with a capacity of 36.8 litres was designed and fabricated to carry out the continuous anaerobic digestion of OFMSW in the third phase. The purpose of this study was to evaluate the performance of the digester at total solid concentration of 12% (semi-dry) under mesophlic condition (32°C). The digester was operated with different organic loading rates (OLRs) and constant retention time. The performance of the reactor was evaluated using parameters such as pH, volatile fatty acid (VFA), alkalinity, chemical oxygen demand (COD), TOC and ammonia-N as well as biogas yield. During the reactor’s start-up period, the process is stable and there is no inhibition occurred and the average biogas production was 14.7 L/day. The reactor was fed in continuous mode with different OLRs (3.1,4.2 and 5.65 kg VS/m3/d) at constant retention time of 30 days. The highest volatile solid degradation of 65.9%, with specific biogas production of 368 L/kg VS fed was achieved with OLR of 3.1 kg VS/m3/d. Modelling and simulation of anaerobic digestion of OFMSW in continuous operation is done using adapted Anaerobic Digestion Model No 1 (ADM1).The proposed model, which has 34 dynamic state variables, considers both biochemical and physicochemical processes and contains several inhibition factors including three gas components. The number of processes considered is 28. The model is implemented in Matlab® version 7.11.0.584(R2010b). The model based on adapted ADM1 was tested to simulate the behaviour of a bioreactor for the mesophilic anaerobic digestion of OFMSW at OLR of 3.1 kg VS/m3/d. ADM1 showed acceptable simulating results.

Body mass index as a standard of living measure: a different interpretation for the case of Colombia

We analyze the Body Mass Index (BMI) in a distinct way of its traditional use and it lets us use it as a proxy of standard of living for the case of Colombia. Our approach is focused on studying how far the people are from the normal range and not on the score of each one and this lets us to treat equally extreme cases as severe thinness and obesity. We use a probabilistic model (Ordered Probit) that evaluates the probability of being within the normal range or another level. We found that socioeconomic variables have a significant effect on the dependent variable and that there are no linear effects. Besides, people with difficulties for walking and adults have less probability of having a normal BMI.

Linear and nonlinear microrheology of dense colloidal suspensions

The length and time scales accessible to optical tweezers make them an ideal tool for the examination of colloidal systems. Embedded high-refractive-index tracer particles in an index-matched hard sphere suspension provide 'handles' within the system to investigate the mechanical behaviour. Passive observations of the motion of a single probe particle give information about the linear response behaviour of the system, which can be linked to the macroscopic frequency-dependent viscous and elastic moduli of the suspension. Separate 'dragging' experiments allow observation of a sample's nonlinear response to an applied stress on a particle-by particle basis. Optical force measurements have given new data about the dynamics of phase transitions and particle interactions; an example in this study is the transition from liquid-like to solid-like behaviour, and the emergence of a yield stress and other effects attributable to nearest-neighbour caging effects. The forces needed to break such cages and the frequency of these cage breaking events are investigated in detail for systems close to the glass transition.

Sequence-selective assembly of tweezer-molecules on linear templates enables frameshift-reading of sequence information

Monomer-sequence information in synthetic copolyimides can be recognised by tweezer-type molecules binding to adjacent triplet-sequences on the polymer chains. In the present paper different tweezer-molecules are found to have different sequence-selectivities, as demonstrated in solution by 1H NMR spectroscopy and in the solid state by single crystal X-ray analyses of tweezer-complexes with linear and macrocyclic oligo-imides. This work provides clear-cut confirmation of polyimide chain-folding and adjacent-tweezer-binding. It also reveals a new and entirely unexpected mechanism for sequence-recognition which, by analogy with a related process in biomolecular information processing, may be termed "frameshift-reading". The ability of one particular tweezer-molecule to detect, with exceptionally high sensitivity, long-range sequence-information in chain-folding aromatic copolyimides, is readily explained by this novel process.

Alternatives to linear analysis of energy balance data from lactating dairy cows

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Linkage disequilibrium assessment via log-linear modeling of SNP haplotype frequencies

Analyses of high-density single-nucleotide polymorphism (SNP) data, such as genetic mapping and linkage disequilibrium (LD) studies, require phase-known haplotypes to allow for the correlation between tightly linked loci. However, current SNP genotyping technology cannot determine phase, which must be inferred statistically. In this paper, we present a new Bayesian Markov chain Monte Carlo (MCMC) algorithm for population haplotype frequency estimation, particulary in the context of LD assessment. The novel feature of the method is the incorporation of a log-linear prior model for population haplotype frequencies. We present simulations to suggest that 1) the log-linear prior model is more appropriate than the standard coalescent process in the presence of recombination (>0.02cM between adjacent loci), and 2) there is substantial inflation in measures of LD obtained by a "two-stage" approach to the analysis by treating the "best" haplotype configuration as correct, without regard to uncertainty in the recombination process. Genet Epidemiol 25:106-114, 2003. (C) 2003 Wiley-Liss, Inc.

Solid phase microextraction of volatile oxidation compounds in oil-in-water emulsions

Headspace solid phase microextraction (HS-SPME) has been used to isolate the headspace volatiles formed during oxidation of oil-in-water emulsions. Qualitative and quantitative analyses with an internal standard were performed by GC-FID. Four sample temperatures for adsorption (30, 40, 50 and 60 C) and adsorption times in the range 10-25 min were tested to determine the conditions for the volatile concentration to reach equilibrium. The optimum conditions were at 50 C for 20 min. The method was applied to monitor changes in volatile composition during oxidation of an o/w emulsion. SPME was a simple, reproducible and sensitive method for the analysis of volatile oxidation products in oil-in-water emulsions. (c) 2004 Elsevier Ltd. All rights reserved.

Linear predicted two-pass hexagonal algorithm with parallel implementation for motion estimation

This paper presents a paralleled Two-Pass Hexagonal (TPA) algorithm constituted by Linear Hashtable Motion Estimation Algorithm (LHMEA) and Hexagonal Search (HEXBS) for motion estimation. In the TPA., Motion Vectors (MV) are generated from the first-pass LHMEA and are used as predictors for second-pass HEXBS motion estimation, which only searches a small number of Macroblocks (MBs). We introduced hashtable into video processing and completed parallel implementation. We propose and evaluate parallel implementations of the LHMEA of TPA on clusters of workstations for real time video compression. It discusses how parallel video coding on load balanced multiprocessor systems can help, especially on motion estimation. The effect of load balancing for improved performance is discussed. The performance or the algorithm is evaluated by using standard video sequences and the results are compared to current algorithms.

Linear predicted hexagonal search algorithm with moments

A novel Linear Hashtable Method Predicted Hexagonal Search (LHMPHS) method for block based motion compensation is proposed. Fast block matching algorithms use the origin as the initial search center, which often does not track motion very well. To improve the accuracy of the fast BMA's, we employ a predicted starting search point, which reflects the motion trend of the current block. The predicted search centre is found closer to the global minimum. Thus the center-biased BMA's can be used to find the motion vector more efficiently. The performance of the algorithm is evaluated by using standard video sequences, considers the three important metrics: The results show that the proposed algorithm enhances the accuracy of current hexagonal algorithms and is better than Full Search, Logarithmic Search etc.

Linear algorithm and hexagonal search based two-pass algorithm for motion estimation

This paper presents a novel two-pass algorithm constituted by Linear Hashtable Motion Estimation Algorithm (LHMEA) and Hexagonal Search (HEXBS) for block base motion compensation. On the basis of research from previous algorithms, especially an on-the-edge motion estimation algorithm called hexagonal search (HEXBS), we propose the LHMEA and the Two-Pass Algorithm (TPA). We introduced hashtable into video compression. In this paper we employ LHMEA for the first-pass search in all the Macroblocks (MB) in the picture. Motion Vectors (MV) are then generated from the first-pass and are used as predictors for second-pass HEXBS motion estimation, which only searches a small number of MBs. The evaluation of the algorithm considers the three important metrics being time, compression rate and PSNR. The performance of the algorithm is evaluated by using standard video sequences and the results are compared to current algorithms, Experimental results show that the proposed algorithm can offer the same compression rate as the Full Search. LHMEA with TPA has significant improvement on HEXBS and shows a direction for improving other fast motion estimation algorithms, for example Diamond Search.

Alignment of a model amyloid peptide fragment in bulk and at a solid surface

The alignment of model amyloid peptide YYKLVFFC is investigated in bulk and at a solid surface using a range of spectroscopic methods employing polarized radiation. The peptide is based on a core sequence of the amyloid beta (A beta) peptide, KLVFF. The attached tyrosine and cysteine units are exploited to yield information on alignment and possible formation of disulfide or dityrosine links. Polarized Raman spectroscopy on aligned stalks provides information on tyrosine orientation, which complements data from linear dichroism (LD) on aqueous solutions subjected to shear in a Couette cell. LD provides a detailed picture of alignment of peptide strands and aromatic residues and was also used to probe the kinetics of self-assembly. This suggests initial association of phenylalanine residues, followed by subsequent registry of strands and orientation of tyrosine residues. X-ray diffraction (XRD) data from aligned stalks is used to extract orientational order parameters from the 0.48 nm reflection in the cross-beta pattern, from which an orientational distribution function is obtained. X-ray diffraction on solutions subject to capillary flow confirmed orientation in situ at the level of the cross-beta pattern. The information on fibril and tyrosine orientation from polarized Raman spectroscopy is compared with results from NEXAFS experiments on samples prepared as films on silicon. This indicates fibrils are aligned parallel to the surface, with phenyl ring normals perpendicular to the surface. Possible disulfide bridging leading to peptide dimer formation was excluded by Raman spectroscopy, whereas dityrosine formation was probed by fluorescence experiments and was found not to occur except under alkaline conditions. Congo red binding was found not to influence the cross-beta XRD pattern.

Principles and calibration of solid phase microextraction fibre (passive sampler) for measurements of airflow and air infiltration in dwellings

Tracer gas techniques have been the most appropriate experimental method of determining airflows and ventilation rates in houses. However, current trends to reduce greenhouse gas effects have prompted the need for alternative techniques, such as passive sampling. In this research passive sampling techniques have been used to demonstrate the potential to fulfil these requirements by using solutions of volatile organic compounds (VOCs) and solid phase microextraction (SPME) fibres. These passive sampling techniques have been calibrated against tracer gas decay techniques and measurements from a standard orifice plate. Two constant sources of volatile organic compounds were diffused into two sections of a humidity chamber and sampled using SPME fibres. From a total of four SPME fibres (two in each section), reproducible results were obtained. Emission rates and air movement from one section to the other were predicted using developed algorithms. Comparison of the SPME fibre technique with that of the tracer gas technique and measurements from an orifice plate showed similar results with good precision and accuracy. With these fibres, infiltration rates can be measured over grab samples in a time weighted averaged period lasting from 10 minutes up to several days. Key words: passive samplers, solid phase microextraction fibre, tracer gas techniques, airflow, air infiltration, houses.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.

A critique of neural networks for discrete-time linear control

This paper discusses the use of multi-layer perceptron networks for linear or linearizable, adaptive feedback.control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parametrization. A comparison is made with standard, non-perceptron algorithms, e.g. self-tuning control, and it is shown how gross over-parametrization can occur in the neural network case. Because of the resultant heavy computational burden and poor controller convergence, a strong case is made against the use of neural networks for discrete-time linear control.