Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams

A new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial. These new shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. The natural frequencies predicted by the proposed element are compared with an element with stiff-string, cubic polynomial and quintic polynomial shape functions. It is found that the new element exhibits superior convergence compared to the other basis functions.

Implications of gain functions in fisheries management

The appealing concept of optimal harvesting is often used in fisheries to obtain new management strategies. However, optimality depends on the objective function, which often varies, reflecting the interests of different groups of people. The aim of maximum sustainable yield is to extract the greatest amount of food from replenishable resources in a sustainable way. Maximum sustainable yield may not be desirable from an economic point of view. Maximum economic yield that maximizes the profit of fishing fleets (harvesting sector) but ignores socio-economic benefits such as employment and other positive externalities. It may be more appropriate to use the maximum economic yield that which is based on the value chain of the overall fishing sector, to reflect better society's interests. How to make more efficient use of a fishery for society rather than fishing operators depends critically on the gain function parameters including multiplier effects and inclusion or exclusion of certain costs. In particular, the optimal effort level based on the overall value chain moves closer to the optimal effort for the maximum sustainable yield because of the multiplier effect. These issues are illustrated using the Australian Northern Prawn Fishery.

Deep inelastic electroproduction structure functions for polarized and unpolarized proton targets

Following Ioffe's method of QCD sum rules the structure functions F2(x) for deep inelastic ep and en scattering are calculated. Valence u-quark and d-quark distributions are obtained in the range 0.1 less, approximate x <0.4 and compared with data. In the case of polarized targets the structure function g1(x) and the asymmetry Image Full-size image are calculated. The latter is in satisfactory agreement in sign and magnitude with experiments for x in the range 0.1< x < 0.4.

Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

Do H-functions always increase during Violent Relaxation

Recent work on the violent relaxation of collisionless stellar systems has been based on the notion of a wide class of entropy functions. A theorem concerning entropy increase has been proved. We draw attention to some underlying assumptions that have been ignored in the applications of this theorem to stellar dynamical problems. Once these are taken into account, the use of this theorem is at best heuristic. We present a simple counter-example.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

Testing threshold functions using implied minterm structure

A geometrical structure called the implied minterm structure (IMS) has been developed from the properties of minterms of a threshold function. The IMS is useful for the manual testing of linear separability of switching functions of up to six variables. This testing is done just by inspection of the plot of the function on the IMS.

Transmission loss analysis of rectangular expansion chamber with arbitrary location of inlet/outlet by means of Green's functions

Transmission loss of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed here based on the Green's function of a rectangular cavity with homogeneous boundary conditions. The rectangular chamber Green's function is expressed in terms of a finite number of rigid rectangular cavity mode shapes. The inlet and outlet ports are modeled as uniform velocity pistons. If the size of the piston is small compared to wavelength, then the plane wave excitation is a valid assumption. The velocity potential inside the chamber is expressed by superimposing the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from velocity potentials using linear momentum equation. The average pressure acting on the pistons at the inlet and outlet locations is estimated by integrating the acoustic pressure over the piston area in the two constituent configurations. The transfer matrix is derived from the average pressure values and thence the transmission loss is calculated. The results are verified against those in the literature where use has been made of modal expansions and also numerical models (FEM fluid). The transfer matrix formulation for yielding wall rectangular chambers has been derived incorporating the structural–acoustic coupling. Parametric studies are conducted for different inlet and outlet configurations, and the various phenomena occurring in the TL curves that cannot be explained by the classical plane wave theory, are discussed.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Application of Haar functions for transmission line and transformer differential protection

The development of algorithms, based on Haar functions, for extracting the desired frequency components from transient power-system relaying signals is presented. The applications of these algorithms to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. For transmission line protection, three modes of application of the Haar algorithms are described: a full-cycle window algorithm, an approximate full-cycle window algorithm, and a half-cycle window algorithm. For power transformer differential protection, the combined second and fifth harmonic magnitude of the differential current is compared with that of fundamental to arrive at a trip decision. The proposed line protection algorithms are evaluated, under different fault conditions, using realistic relaying signals obtained from transient analysis conducted on a model 400 kV, 3-phase system. The transformer differential protection algorithms are also evaluated using a variety of simulated inrush and internal fault signals.

Cholesterol Disturbances in Inherited Neurodegenerative Diseases : Studies on Npc1, Ppt1 and Ctsd deficient mice

The central nervous system (CNS) is the most cholesterol-rich organ in the body. Cholesterol is essential to CNS functions such as synaptogenesis and formation of myelin. Significant differences exist in cholesterol metabolism between the CNS and the peripheral organs. However, the regulation of cholesterol metabolism in the CNS is poorly understood compared to our knowledge of the regulation of cholesterol homeostasis in organs reached by cholesterol-carrying lipoprotein particles in the circulation. Defects in CNS cholesterol homeostasis have been linked to a variety of neurodegenerative diseases, including common diseases with complex pathogenetic mechanisms such as Alzheimer s disease. In spite of intense effort, the mechanisms which link disturbed cholesterol homeostasis to these diseases remain elusive. We used three inherited recessive neurodegenerative disorders as models in the studies included in this thesis: Niemann-Pick type C (NPC), infantile neuronal ceroid lipofuscinosis and cathepsin D deficiency. Of these three, NPC has previously been linked to disturbed intracellular cholesterol metabolism. Elucidating the mechanisms with which disturbances of cholesterol homeostasis link to neurodegeneration in recessive inherited disorders with known genetic lesions should shed light on how cholesterol is handled in the healthy CNS and help to understand how these and more complex diseases develop. In the first study we analyzed the synthesis of sterols and the assembly and secretion of lipoprotein particles in Npc1 deficient primary astrocytes. We found that both wild type and Npc1 deficient astrocytes retain significant amounts of desmosterol and other cholesterol precursor sterols as membrane constituents. No difference was observed in the synthesis of sterols and the secretion of newly synthesized sterols between Npc1 wild type, heterozygote or knockout astrocytes. We found that the incorporation of newly synthesized sterols into secreted lipoprotein particles was not inhibited by Npc1 mutation, and the lipoprotein particles were similar to those excreted by wild type astrocytes in shape and size. The bulk of cholesterol was found to be secreted independently of secreted NPC2. These observations demonstrate the ability of Npc1 deficient astrocytes to handle de novo sterols, and highlight the unique sterol composition in the developing brain. Infantile neuronal ceroid lipofuscinosis is caused by the deficiency of a functional Ppt1 enzyme in the cells. In the second study, global gene expression studies of approximately 14000 mouse genes showed significant changes in the expression of 135 genes in Ppt1 deficient neurons compared to wild type. Several genes encoding for enzymes of the mevalonate pathway of cholesterol biosynthesis showed increased expression. As predicted by the expression data, sterol biosynthesis was found to be upregulated in the knockout neurons. These data link Ppt1 deficiency to disturbed cholesterol metabolism in CNS neurons. In the third study we investigated the effect of cathepsin D deficiency on the structure of myelin and lipid homeostasis in the brain. Our proteomics data, immunohistochemistry and western blotting data showed altered levels of the myelin protein components myelin basic protein, proteolipid protein and 2 , 3 -cyclic nucleotide 3 phosphodiesterase in the brains of cathepsin D deficient mice. Electron microscopy revealed altered myelin structure in cathepsin D deficient brains. Additionally, plasmalogen-derived alkenyl chains and 20- and 24-carbon saturated and monounsaturated fatty acids typical for glycosphingolipids were found to be significantly reduced, but polyunsaturated species were significantly increased in the knockout brains, pointing to a decrease in white matter. The levels of ApoE and ABCA1 proteins linked to cholesterol efflux in the CNS were found to be altered in the brains of cathepsin D deficient mice, along with an accumulation of cholesteryl esters and a decrease in triglycerols. Together these data demonstrate altered myelin architecture in cathepsin D deficient mice and link cathepsin D deficiency to aberrant cholesterol metabolism and trafficking. Basic research into rare monogenic diseases sheds light on the underlying biological processes which are perturbed in these conditions and contributes to our understanding of the physiological function of healthy cells. Eventually, understanding gained from the study of disease models may contribute towards establishing treatment for these disorders and further our understanding of the pathogenesis of other, more complex and common diseases.