Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.

Coexistence curve of acetonitrile and cyclohexane liquid system

The paper reports a detailed determination of the coexistence curve for the binary liquid system acetonitrile+cyclohexane, which have very closely matched densities and the data points get affected by gravity only for t=(Tc−T)/ Tc[approximately-equal-to]10−6. About 100 samples were measured over the range 10−6asymptotic region, give an exponent of 0.9 for the diameter in keeping with the (1−alpha) exponent theoretically predicted, the value of alpha being 0.11 in binary liquids. The extrapolation properties of the Wegner expansion procedure is somewhat inferior to the extrapolation obtained using a renormalization group (RG) crossover expansion. The use of the new variables proposed by Johnston et al. and Vnuk in making the coexistence curve appear symmetric in the new variables is pointed out. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Plasma assisted surface modification of organic biopolymers to prevent bacterial attachment

Despite many synthetic biomaterials having physical properties that are comparable or even superior to those of natural body tissues, they frequently fail due to the adverse physiological reactions they cause within the human body, such as infection and inflammation. The surface modification of biomaterials is an economical and effective method by which biocompatibility and biofunctionality can be achieved while preserving the favorable bulk characteristics of the biomaterial, such as strength and inertness. Amongst the numerous surface modification techniques available, plasma surface modification affords device manufacturers a flexible and environmentally friendly process that enables tailoring of the surface morphology, structure, composition, and properties of the material to a specific need. There are a vast range of possible applications of plasma modification in biomaterial applications, however, the focus of this review paper is on processes that can be used to develop surface morphologies and chemical structures for the prevention of adhesion and proliferation of pathogenic bacteria on the surfaces of in-dwelling medical devices. As such, the fundamental principles of bacterial cell attachment and biofilm formation are also discussed. Functional organic plasma polymerised coatings are also discussed for their potential as biosensitive interfaces, connecting inorganic/metallic electronic devices with their physiological environments.

Design of Multiloop Controllers for an Ammonia Reactor

The specific objective of this paper is to develop multiloop controllers that would achieve asymptotic regulation in the presence of parameter variations and disturbance inputs for a tubular reactor used in ammonia synthesis. The dynamic model considered here has nine state variables, two control inputs, and two outputs. A systematic procedure for pairing the two inputs with the corresponding two outputs is presented. The two multiloop proportional controllers so configured are designed via the parameter plane method. This economic configuration of controllers maintains the temperature profile almost at the optimal value whereas the point controllers fail to do so.

A convenient sample preparation protocol for scanning electron microscope examination of xylem-occluding bacterial biofilm on cut flowers and foliage

Microbes and their exopolysaccharides (EPS) can block xylem vessels, thereby increasing the hydraulic resistance and decreasing the vase life of cut flowers and foliage. Scanning electron microscopy (SEM) provides a powerful tool for investigation of bacteria-induced xylem occlusion. However, conventional preparation protocols for SEM involving chemicals can cause loss of hydrated EPS material, and thereby damage the bacterial biofilms during dehydration. A modified chemical fixation protocol involving pre-fixation with 75 mM lysine plus 2.5% glutaraldehyde followed by the normal fixation in 3% glutaraldehyde was, therefore, tested for improved preservation of bacterial biofilm at the stem-ends of cut Acacia holosericea foliage stems. Stem-end segments with different stages of bacterial growth were obtained from stems stood into water. The lysine-based protocol was compared with four other processing protocols of critical point drying (CPD) without fixation (control), freeze-drying (FD), conventional chemical fixation followed by drying with hexamethyldisilazane (HMDS), and conventional chemical fixation with CPD. The non-fixed control. FD and the glutaraldehyde fixation with HMDS drying gave poor preservation of hydrated material, including bacterial EPS. Conventional glutaraldehyde fixation followed by CPD was superior to these three methods in terms of better preserving the EPS. However, this fourth method gave condensation of biofilms during dehydration. In contrast, the modified lysine-based protocol resulted in superior preservation of EPS and biofilm structure. Thus, this fifth method was the most appropriate for examination of bacterial stem-end blockage in cut ornamentals. (C) 2012 Elsevier B.V. All rights reserved.

Structure of shock waves at re-entry speeds

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

Relaminarization in highly accelerated turbulent boundary layers

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

Uusmaalaisten viljelijöiden arviot uudesta ympäristötuesta

The agro-environmental subsidy scheme is the most important agricultural environmental policy instrument used in Finland. The principal aim of the agro-environmental subsidy is to reimburse farmer the costs of using environmentally sounder farming practices and the measures that aim for preserving the environment. It also serves as an economic incentive for ensuring the large enough participation. The agro-environmental subsidy scheme is to be reformed in 2007. The main question answered in thesis was that whether farmers in Uusimaa region are ready to participate in the environmental subsidy scheme on the basis of the economical reasons or not. The focus is on farmers' opinions about how difficult it is to carry out measures of new environmental subsidy and do these measures change their ways of farming. The analysis is based on an empirical study of the farmers attitudes towards the new environmental subsidy scheme. The theoretical framework of this thesis is based on principal-agent theory and on the theory of the firm. In principal-agent theory environmental subsidy is interpreted as a deal in which farmers function as agents and government as a principal. Theory of the firm provides a theoretical framework for the analysis, through which we aim to analyse how rationally behaving farmer makes decisions by economical reasons to participate in the environment subsidy scheme. The thesis points out that presumably the participation percentage will stay high during the period of the new environmental subsidy scheme.

Dissipativeness and Stability of a Class of Distributed Parameter Systems

Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected. (C) 2013 Elsevier B.V. All rights reserved.

Detecting rare events using Kullback-Leibler divergence: A weakly supervised approach

Video surveillance infrastructure has been widely installed in public places for security purposes. However, live video feeds are typically monitored by human staff, making the detection of important events as they occur difficult. As such, an expert system that can automatically detect events of interest in surveillance footage is highly desirable. Although a number of approaches have been proposed, they have significant limitations: supervised approaches, which can detect a specific event, ideally require a large number of samples with the event spatially and temporally localised; while unsupervised approaches, which do not require this demanding annotation, can only detect whether an event is abnormal and not specific event types. To overcome these problems, we formulate a weakly-supervised approach using Kullback-Leibler (KL) divergence to detect rare events. The proposed approach leverages the sparse nature of the target events to its advantage, and we show that this data imbalance guarantees the existence of a decision boundary to separate samples that contain the target event from those that do not. This trait, combined with the coarse annotation used by weakly supervised learning (that only indicates approximately when an event occurs), greatly reduces the annotation burden while retaining the ability to detect specific events. Furthermore, the proposed classifier requires only a decision threshold, simplifying its use compared to other weakly supervised approaches. We show that the proposed approach outperforms state-of-the-art methods on a popular real-world traffic surveillance dataset, while preserving real time performance.

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.