62 research outputs found
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
ニュートン流体における粉体の二相動力学
Many scientific and technical problems which concern the dynamics of complex fluids such as multi-phase-flow and realistic flow in porous and granular media deal with the interaction between fluids and particles, rather than with the dynamics of the fluid alone. The research of how the surrounding fluid affects the dynamics of particles, or how to deal with the problem computationally for the microscopic level is still at the beginning. The aim of this study is to develop a microscopic simulation method (fluid goes around the particles) where granular particles can be simulated inside fluids to study those problems. This is done by combining the simulation method for granular particles with the simulation method for the incompressible Newtonian fluid. The granular particles are implemented via the discrete element method (DEM) where the elastic contact force between two undeformed contacting polygonal particles is proportional to the overlap area ("hard particle, soft contact"). The Gear Predictor-Corrector of 2nd-order (BDF2) is used as the time integrator to solve the equations of motion of the particles. For the fluid phase, the implementation of the incompressible Navier-Stokes equations via the Galerkin finite element method (FEM) is formulated as differential algebraic equations (DAE) with the pressures as the Lagrange parameters. The time integration is again via the BDF2 while the resulting non-linear equations are solved via the Newton-Raphson methods. The spatial discretization is via the Taylor-Hood elements from Delaunay triangulations with additional post-processing with the relaxation algorithm. The coupling of the DEM for the granular particles and the FEM for the fluid is via appropriate boundary conditions and the drag force (computed by the integration of the fluid stress tensor over the particle\u27s surface). This is being verified via the computation of wall correction factors of a sinking particle. The fluid simulation is extended to a simulation of free surfaces where the motion of the surface is integrated out according to the velocity on the surface which is obtained from the FEM-scheme. The second-order Adams-Bashforth method turns out to be the most suitable integrator for the surface motion. Compared to conventional efforts, which try to solve partial differential equations for the motion of the surface, the additional effort in our method with respect to new data structures etc. is minimal. The free surfaces code is verified by simulating the collapse of a water column. For the speed of the wavefronts, excellent agreement is obtained for large viscosity with the lubrication approximation. The agreement of the results with the experimental data for water is a further gratifying result. Two numerical experiments are conducted using the DEM-FEM code: one with a rather slow dynamics, another one relatively more "violent". The compaction simulation has shown that the addition of fluid to a granular assembly can increase the sound velocity in the system, compared to the dry case. The high viscosity slowed down the compaction, irrespective whether the system was tapped only on the ground or on the whole boundary. The granular column simulations show that for systems immersed under fluids, rolling of particles becomes less important than for the corresponding dry systems.電気通信大学201
Block methods for direct solution of higher order ordinary differential equations using interpolation and collocation approach
Countless problems in real life situations involve rates of change of one or more independent variables. These rates of change can be expressed in terms of derivatives which lead to differential equations. Conventionally, initial value problems of higher order ordinary differential equations are solved by first reducing the equations to their equivalent systems of first order ordinary differential equations. Then, suitable existing numerical methods for first order ordinary
differential equations will be employed to solve the resulting equations. However, this approach will enlarge the equations and thus increases computational burden which may jeopardise the accuracy of the solution. In overcoming the setbacks, direct methods were proposed. Disappointedly, most of the existing direct methods
approximate the numerical solution at one point at a time. Block methods were then introduced with the aim of approximating numerical solutions at many points concurrently. Several new block methods using interpolation and collocation approach for solving initial value problems of higher order ordinary differential equations directly were developed in this study to increase the accuracy of the solution. In developing these methods, a power series was used as an approximate solution to the problems of ordinary differential equations of order d. The power series was interpolated at d points before the last two points while its highest
derivative was collocated at all grid points in deriving the new block methods. In addition, the properties of the new methods such as order, error constant, zerostability, consistency, convergence and region of absolute stability were also
investigated. The developed methods were then applied to solve several initial value problems of higher order ordinary differential equations. The numerical results indicated that the new methods produced better accuracy than the existing methods
when solving the same problems. Therefore, this study has successfully produced new methods for solving initial value problems of higher order ordinary differential equations
Dynamical systems : mechatronics and life sciences
Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications"
summarize 164 and the Springer Proceedings summarize 60 best papers of university
teachers and students, researchers and engineers from whole the world. The papers were
chosen by the International Scientific Committee from 315 papers submitted to the
conference. The reader thus obtains an overview of the recent developments of dynamical
systems and can study the most progressive tendencies in this field of science
Dynamical Systems
Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...
Computational fluid dynamics and experimental study of the hydrodynamics of a bubble column and an air-water jet-stirred cell
A large number of flows encountered in nature and in many industrial processes areintrinsically multiphase flows. The efficiency and the effectiveness of multiphase flow
processes strongly depend on the ability to model the fluid flow behaviour. Thus, a robust and accurate description of multiphase flow can lead to an increase in performance, a
reduction in cost, and an improvement in safety for engineering systems. In recent years, Computational Fluid Dynamics (CFD) has become an indispensable predictive tool for gathering information to be used for design and optimization for fluid systems. In this thesis the hydrodynamics of two bubbly flow systems, a bubble column and a waterjet-agitated flotation cell (Hydrojet cell), were studied by means of numerical simulations. In
order to validate the bubble column CFD simulations Particle Image Velocimetry (PIV) was used. An experimental investigation about bubble size distribution (BSD) along a water jet was carried out by means of image analysis. Because of high gas fraction and high velocity of
the air/water streams used to agitate the Hydrojet cell, with the available equipment, no experimental measurements could be done to evaluate the velocity field of the cell.
The thesis consists of three parts: theoretical part, bubble column study and Hydrojet cell study. In the theoretical part, first, a summary of fluid dynamics principles and an overview of the principal issues related to multiphase flow modelling were presented. Then a brief
introduction to PIV and its application to two phase bubbly flow were given. Finally a review of the principle of the flotation process and its modelling were done in order to highlight the reasons for the low recovery of fine particles. Then the potentialities offered by the use of
waterjets to fine particles flotation were presented.
In the second part experimental and numerical studies of a bubble column were presented. PIV technique was used to determine the velocity field of a laboratory bubble column. A separation method for multiphase PIV was developed and tested. By means of the proposed method, the acquired mixed-fluid images were processed to obtain two sets of single phase images before PIV analysis. The velocity field was determined using a multi-pass crosscorrelation.
Following three-dimensional time-dependent CFD simulations of a lab-scale bubble column were presented. The simulations were carried out using the Euler - Euler
approach. Two different multiphase turbulence models, Shear Stress Transport (SST) and Large Eddy Simulation (LES), were tested, and different interfacial closure models reported in the literature were examined. When LES were used to model the turbulence instead of the
SST model, much better agreement with the experimental data was found, provided that the drag, lift and virtual mass forces were taken into account. In the third part a preliminary experimental study, carried out in a rectangular flat cell, was presented. It was carried out to investigate the size distribution of bubbles generated by a
moderate pressure water jet, by means of image analysis. This study showed the ability of water jets at moderate pressure to break an air stream into small bubbles. Increasing the pressure of the pump, smaller and more uniform bubbles were obtained. Then three-dimensional CFD simulations of the Hydrojet cell are presented. The Hydrojet
cell, due to the exceeding computational burden, was simulated as a two-phase (gas-liquid) system, although actually it is a three-phase (gas-liquid-solid) system. Also in this case simulations were carried out using the Euler - Euler approach. The turbulence of the liquid
phase was modelled with the SST model. The single reference frame technique was used to describe the movement of the waterjet lance. To achieve a homogeneous aeration in the
region near the inlets different inlet velocity and rotational speed were tested. The results gave useful indications about the role of the four principal operating parameters: nozzles diameter, velocity of rotation of the lance, speed of the water jets and then pressure of the
pump and inlet air flow rate. What emerges is the need of high rotational speed of the waterjet lance in order to ensure an uniform gas distribution within the mixing zone. This is not possible with the current apparatus. Thus in order to make the system suitable to produce an appropriate environment for the full development of the flotation process it is necessary to modify the system
Computational fluid dynamics and experimental study of the hydrodynamics of a bubble column and an air-water jet-stirred cell
A large number of flows encountered in nature and in many industrial processes areintrinsically multiphase flows. The efficiency and the effectiveness of multiphase flow
processes strongly depend on the ability to model the fluid flow behaviour. Thus, a robust and accurate description of multiphase flow can lead to an increase in performance, a
reduction in cost, and an improvement in safety for engineering systems. In recent years, Computational Fluid Dynamics (CFD) has become an indispensable predictive tool for gathering information to be used for design and optimization for fluid systems. In this thesis the hydrodynamics of two bubbly flow systems, a bubble column and a waterjet-agitated flotation cell (Hydrojet cell), were studied by means of numerical simulations. In
order to validate the bubble column CFD simulations Particle Image Velocimetry (PIV) was used. An experimental investigation about bubble size distribution (BSD) along a water jet was carried out by means of image analysis. Because of high gas fraction and high velocity of
the air/water streams used to agitate the Hydrojet cell, with the available equipment, no experimental measurements could be done to evaluate the velocity field of the cell.
The thesis consists of three parts: theoretical part, bubble column study and Hydrojet cell study. In the theoretical part, first, a summary of fluid dynamics principles and an overview of the principal issues related to multiphase flow modelling were presented. Then a brief
introduction to PIV and its application to two phase bubbly flow were given. Finally a review of the principle of the flotation process and its modelling were done in order to highlight the reasons for the low recovery of fine particles. Then the potentialities offered by the use of
waterjets to fine particles flotation were presented.
In the second part experimental and numerical studies of a bubble column were presented. PIV technique was used to determine the velocity field of a laboratory bubble column. A separation method for multiphase PIV was developed and tested. By means of the proposed method, the acquired mixed-fluid images were processed to obtain two sets of single phase images before PIV analysis. The velocity field was determined using a multi-pass crosscorrelation.
Following three-dimensional time-dependent CFD simulations of a lab-scale bubble column were presented. The simulations were carried out using the Euler - Euler
approach. Two different multiphase turbulence models, Shear Stress Transport (SST) and Large Eddy Simulation (LES), were tested, and different interfacial closure models reported in the literature were examined. When LES were used to model the turbulence instead of the
SST model, much better agreement with the experimental data was found, provided that the drag, lift and virtual mass forces were taken into account. In the third part a preliminary experimental study, carried out in a rectangular flat cell, was presented. It was carried out to investigate the size distribution of bubbles generated by a
moderate pressure water jet, by means of image analysis. This study showed the ability of water jets at moderate pressure to break an air stream into small bubbles. Increasing the pressure of the pump, smaller and more uniform bubbles were obtained. Then three-dimensional CFD simulations of the Hydrojet cell are presented. The Hydrojet
cell, due to the exceeding computational burden, was simulated as a two-phase (gas-liquid) system, although actually it is a three-phase (gas-liquid-solid) system. Also in this case simulations were carried out using the Euler - Euler approach. The turbulence of the liquid
phase was modelled with the SST model. The single reference frame technique was used to describe the movement of the waterjet lance. To achieve a homogeneous aeration in the
region near the inlets different inlet velocity and rotational speed were tested. The results gave useful indications about the role of the four principal operating parameters: nozzles diameter, velocity of rotation of the lance, speed of the water jets and then pressure of the
pump and inlet air flow rate. What emerges is the need of high rotational speed of the waterjet lance in order to ensure an uniform gas distribution within the mixing zone. This is not possible with the current apparatus. Thus in order to make the system suitable to produce an appropriate environment for the full development of the flotation process it is necessary to modify the system
Rheological chaos and elastic turbulence in a generalised Maxwell model for viscoelastic fluid flow
This work presents a new extension to a generalised nonlinear Maxwell model for the theoty of viscoelastic material flow. Nonlinear terms within this constitutive model are used to replicate many experimental phenomena such as shear-thickening/thinning, shear banding and dynamic stress responses found in complex materials such as polymers, Micelles, colloidal dispersions and even granular media. Numerical simulations of the stress tensor under spatially homogeneous plane Couette flow reveal a range of solutions from steady state to chaotic, chosen in part by the strength of nonlinear terms. Bifurcation and stability analysis reveal the onset of chaotic flow and are used to study the various transitions to chaos. A detailed phase space diagram is produced to categorise different dynamical regimes by determining the Lyapunov exponent under variation of two main model parameters. The route to chaos is identified primarily as a Hopf bifurcation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Mathematical modelling of hepatopancreatic digestive cell of the blue mussel
The lysosomal system of the hepatopancreatic digestive cell of the
mussel (Mytilus sp.) is critical in intracellular food degradation, toxic
responses and internal cellular turnover. Mathematical and numerical
models are developed to simulate the responses of this system to varying
conditions, dietary and toxicological. The model evolution encompasses:
inclusion of glycogen/lipid storage forms; extrapolation to include nitrogen
metabolism; development of rate of endocytosis and food signal; increased
functionality of endo/lysosomes; shift to protein/carbohydrate/lipid based
model; and the incorporation of the cost of normal Sanction and
replacement of damaged components. Control is asserted through control
of cytosolic concentrations: the intial assumption of constant carbon
concentration is shown to be unacceptable for later models. A control
algorithm is developed which regulates cell volume by the ratio of
proteinaceous material to energy forms.
Endocytosis is shown to be the main determinant behind routine
cellular behaviour. Observed phasic behaviour of the digestive tubules is
incorporated into the cellular behavioural pattern. A probability-based
model for the rate of endocytosis is developed.
Increased autophagy as the sole response to toxic injury is found to
be inadequate to explain observed responses. It is proposed to complement
this response with impairment of lysosomal efficiency to explain this
inadequacy. Toxic injury is implemented through an increase in the rates of
damage to cellular components. Within the lysosome this leads to a
reduction in the concentration of digestive enzymes inhibiting lysosomal
performance and, in conjunction with the enhanced autophagy due to
increased cytosolic damage, invoking the lysosomal swelling commonly
observed.Plymouth Marine Laborator
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