Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Fluid mechanics-non-linear waves studies on korteweg-de vries equations

In this thesis the author has presented qualitative studies of certain Kdv equations with variable coefficients. The well-known KdV equation is a model for waves propagating on the surface of shallow water of constant depth. This model is considered as fitting into waves reaching the shore. Renewed attempts have led to the derivation of KdV type equations in which the coefficients are not constants. Johnson's equation is one such equation. The researcher has used this model to study the interaction of waves. It has been found that three-wave interaction is possible, there is transfer of energy between the waves and the energy is not conserved during interaction.

Numerical Simulation of Two-Part Underwater Towing System

The motion instability is an important issue that occurs during the operation of towed underwater vehicles (TUV), which considerably affects the accuracy of high precision acoustic instrumentations housed inside the same. Out of the various parameters responsible for this, the disturbances from the tow-ship are the most significant one. The present study focus on the motion dynamics of an underwater towing system with ship induced disturbances as the input. The study focus on an innovative system called two-part towing. The methodology involves numerical modeling of the tow system, which consists of modeling of the tow-cables and vehicles formulation. Previous study in this direction used a segmental approach for the modeling of the cable. Even though, the model was successful in predicting the heave response of the tow-body, instabilities were observed in the numerical solution. The present study devises a simple approach called lumped mass spring model (LMSM) for the cable formulation. In this work, the traditional LMSM has been modified in two ways. First, by implementing advanced time integration procedures and secondly, use of a modified beam model which uses only translational degrees of freedoms for solving beam equation. A number of time integration procedures, such as Euler, Houbolt, Newmark and HHT-α were implemented in the traditional LMSM and the strength and weakness of each scheme were numerically estimated. In most of the previous studies, hydrodynamic forces acting on the tow-system such as drag and lift etc. are approximated as analytical expression of velocities. This approach restricts these models to use simple cylindrical shaped towed bodies and may not be applicable modern tow systems which are diversed in shape and complexity. Hence, this particular study, hydrodynamic parameters such as drag and lift of the tow-system are estimated using CFD techniques. To achieve this, a RANS based CFD code has been developed. Further, a new convection interpolation scheme for CFD simulation, called BNCUS, which is blend of cell based and node based formulation, was proposed in the study and numerically tested. To account for the fact that simulation takes considerable time in solving fluid dynamic equations, a dedicated parallel computing setup has been developed. Two types of computational parallelisms are explored in the current study, viz; the model for shared memory processors and distributed memory processors. In the present study, shared memory model was used for structural dynamic analysis of towing system, distributed memory one was devised in solving fluid dynamic equations.

‘Driving Forces of Investment Decisions in Mutual Funds’

Unfortunately, in India it is a fact that most of the investors are not interested in mutual funds. Those who are investing, they are investing only very small amounts. But what is important to be noted here is that when compared to other financial instruments, investments in mutual funds are safer and also yields more returns on the investment portfolio. Moreover as an investment avenue mutual fund is available for those investors who are not willing to take any exposure directly in the security market. It also helps such investors to build their wealth over a period of time. At the retail level, investors are unique and are highly heterogeneous, and the mutual fund schemes' selection will also differ depends on their expectations. Hence, investors’ expectation is a very important factor in this regard that needs to be analysed by all the investment houses. Hence, the factors that drive the investment decisions of individual investors to meet their expectations by investing money in mutual funds need an in-depth analysis. These driving forces include the preference of investors on mutual fund compared to various available avenues of financial investments, risk attitude of investors, influence of characteristics of instruments of mutual funds on investors, the investment specific attitudes of investors, and influence of qualities of fund management on investors. The success of any mutual fund, a popular means of investment, depends on how effectively an Asset Management Company has been able to understand the level of influence of these factors on the decision of investors to invest in mutual funds. For a substantial growth in the mutual fund market, there must be a high level precision in the design and marketing of the products of mutual funds taking into account these driving forces by the Asset Management Companies. Therefore, there is a need to conduct a detailed study on investments in mutual funds in this direction. A review of available literature also revealed that no detailed study on mutual funds has so far been attempted in this direction; hence the present study on Driving Forces of Investment Decisions in Mutual Funds is undertaken.

Some conservation laws of fluid mechanics

This thesis contains a study of conservation laws of fluid mechanics. These conservation laws though classical, have been put to extensive studies in t:he past many decades

Virtual Model Control of a Biped Walking Robot

The transformation from high level task specification to low level motion control is a fundamental issue in sensorimotor control in animals and robots. This thesis develops a control scheme called virtual model control which addresses this issue. Virtual model control is a motion control language which uses simulations of imagined mechanical components to create forces, which are applied through joint torques, thereby creating the illusion that the components are connected to the robot. Due to the intuitive nature of this technique, designing a virtual model controller requires the same skills as designing the mechanism itself. A high level control system can be cascaded with the low level virtual model controller to modulate the parameters of the virtual mechanisms. Discrete commands from the high level controller would then result in fluid motion. An extension of Gardner's Partitioned Actuator Set Control method is developed. This method allows for the specification of constraints on the generalized forces which each serial path of a parallel mechanism can apply. Virtual model control has been applied to a bipedal walking robot. A simple algorithm utilizing a simple set of virtual components has successfully compelled the robot to walk eight consecutive steps.

An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.

Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.

Peeling, healing and bursting in a lubricated elastic sheet

We consider the dynamics of an elastic sheet lubricated by the flow of a thin layer of fluid that separates it from a rigid wall. By considering long wavelength deformations of the sheet, we derive an evolution equation for its motion, accounting for the effects of elastic bending, viscous lubrication and body forces. We then analyze various steady and unsteady problems for the sheet such as peeling, healing, levitating and bursting using a combination of numerical simulation and dimensional analysis. On the macro-scale, we corroborate our theory with a simple experiment, and on the micro-scale, we analyze an oscillatory valve that can transform a continuous stream of fluid into a series of discrete pulses.

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent years but at the moment few applications concern the description of natural phenomena with this type of probability models, as well as the interpretation of their parameters. The skew–normal distributions family represents an extension of the normal family to which a parameter (λ) has been added to regulate the skewness. The development of this theoretical field has followed the general tendency in Statistics towards more flexible methods to represent features of the data, as adequately as possible, and to reduce unrealistic assumptions as the normality that underlies most methods of univariate and multivariate analysis. In this paper an investigation on the shape of the frequency distribution of the logratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells, has been performed. Samples have been collected around the active center of Vulcano island (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals of about six months. Data of the logratio have been tentatively modeled by evaluating the performance of the skew–normal model for each well. Values of the λ parameter have been compared by considering temperature and spatial position of the sampling points. Preliminary results indicate that changes in λ values can be related to the nature of environmental processes affecting the data

Thermodynamics and log–contrast analysis in fluid geochemistry

There are two principal chemical concepts that are important for studying the natural environment. The first one is thermodynamics, which describes whether a system is at equilibrium or can spontaneously change by chemical reactions. The second main concept is how fast chemical reactions (kinetics or rate of chemical change) take place whenever they start. In this work we examine a natural system in which both thermodynamics and kinetic factors are important in determining the abundance of NH+4 , NO−2 and NO−3 in superficial waters. Samples were collected in the Arno Basin (Tuscany, Italy), a system in which natural and antrophic effects both contribute to highly modify the chemical composition of water. Thermodynamical modelling based on the reduction-oxidation reactions involving the passage NH+4 -> NO−2 -> NO−3 in equilibrium conditions has allowed to determine the Eh redox potential values able to characterise the state of each sample and, consequently, of the fluid environment from which it was drawn. Just as pH expresses the concentration of H+ in solution, redox potential is used to express the tendency of an environment to receive or supply electrons. In this context, oxic environments, as those of river systems, are said to have a high redox potential because O2 is available as an electron acceptor. Principles of thermodynamics and chemical kinetics allow to obtain a model that often does not completely describe the reality of natural systems. Chemical reactions may indeed fail to achieve equilibrium because the products escape from the site of the rection or because reactions involving the trasformation are very slow, so that non-equilibrium conditions exist for long periods. Moreover, reaction rates can be sensitive to poorly understood catalytic effects or to surface effects, while variables as concentration (a large number of chemical species can coexist and interact concurrently), temperature and pressure can have large gradients in natural systems. By taking into account this, data of 91 water samples have been modelled by using statistical methodologies for compositional data. The application of log–contrast analysis has allowed to obtain statistical parameters to be correlated with the calculated Eh values. In this way, natural conditions in which chemical equilibrium is hypothesised, as well as underlying fast reactions, are compared with those described by a stochastic approach

Short-term storage and mental speed account for the relationship between working memory and fluid intelligence. 'El almacenamiento a corto plazo y la velocidad mental dan cuenta de la relaci??n entre memoria de trabajo e inteligencia fluida'

Resumen tomado de la publicaci??n

Viscous Flow and Fluid Dynamics

Exam questions and solutions for a third year maths course. Diagrams for the questions are all together in the support.zip file, as .eps files

El taulell de forces com a eina de laboratori a l'Ensenyament Mitjà. 'La tabla de fuerzas como un instrumento de laboratorio en las Enseñanzas Medias'.

Experimentar la utilización de la 'tabla de fuerzas' en la enseñanza de la Física de BUP como herramienta de laboratorio. 68 alumnos de segundo de BUP del curso 1986/87. Se parte de las conclusiones extraídas de otra investigación realizada por el mismo autor (estudio de las cualidades que tiene de obtener el material de prácticas de laboratorio de Física y Química); en él se constata la existencia de graves deficiencias en el material de prácticas de Física que normalmente se utiliza, especialmente el material experimental de Mecánica. En consecuencia se lleva a cabo la construcción de una tabla de fuerzas. Paralelamente se proponen una serie de prácticas teniendo en cuenta las instrucciones para el uso de dicha tabla. Material didáctico. Consulta de libros. Cuestionario ad hoc. Trabajos. -47 trabajos pueden considerarse correctos: 69'1 por ciento. - 9 trabajos presentan pequeñas desviaciones debidas a incorrectas compensaciones: 13'3 por ciento. - 12 trabajos presentan pequeñas desviaciones en la dirección de la resultante: 17'6 por ciento. El alumno participa de una manera activa en la experiencia y, manipulando las pinzas y las pesas, deviene el protagonista. Ha mejorado la habilidad del alumno por el trabajo experimental y su capacidad de extraer conclusiones. Ha mejorado el cálculo vectorial y tiene los conceptos de magnitud escalar y vectorial más claros.