Lattice Boltzmann Method

Lattice Boltzmann Method Computational Fluid Dynamics permits the analysis of the behaviour of fluid flows in virtual environments and compared to traditional experimental tests involves lower time and costs as well as a better understanding of the studied phenomenon. Indeed, once the solution is obtai- ned all the magnitudes of the fluids can be accurately computed and visualised. Moreover, with CFD there is no interference between the flow field and the measuring equipment. The main approach used to study the behaviour of a fluid is the continuum one, which uses the Navier-Stokes equations and describes the fluid through macroscopic properties as pressure temperature and density. Since it is difficult and time-consuming to solve directly the non-linear partial differential NS equations these are converted into a system of algebraic equations th- rough finite difference, finite volume or finite element methods. The fluid domain is discretized and each node or volume contains a huge number of particles, the average value of pressure, velocity density etc is computed through an iterative process until convergence is reached. An alternative approach to study the fluid characteristics is the analysis of the microscale beha- viour of the fluid particles. The forces between particles (molecules) describe and determine the flow dynamic and at each time step the position and velocity of each particle is computed using the Newtons second law of momentum conservation. From the kinetic theory macro-scale pro- perties of the fluid can be obtained. This method is clearly impractical because of the extreme number of particles that constitute even a small volume of fluid. The LBM method is in the middle of these two methodologies and focuses the attention on di- screte collections of particles whose properties are described through a probability distribution function (PDF). The PDF describes the behaviour of a large number of particles using a sta- tistical distribution. This approach hence doesnt request the knowledge of the single particles positions and velocities. The Maxwell-Boltzmann distribution function can be defined as the probability of finding particles within a certain range of velocities at a certain range of locations at a certain time f(r,c,t), where r,c,tare the position, velocity and time respectively. The spatial discretization used is named lattice and it is based on a Cartesian distribution of discrete points with discrete sets of velocity directions. The lattice is determined by the number of dimensions n and discrete velocity directions m (DnQm), a large number of velocities leads to a more precise description but also a higher computational cost. For each discrete velocity direction a PDF is defined. The Boltzmanns Transport Equation is used to describe the evolution of the PDFs and their  interactions: à ¢Ã‹â€ Ã¢â‚¬Å¡f à ¢Ã‹â€ Ã¢â‚¬Å¡t+ c ·Ãƒ ¢Ã‹â€ Ã¢â‚¬ ¡f= à ¢Ã¢â‚¬Å¾Ã‚ ¦(f) The equation states that the total derivative of the PDF equals to the collision operator à ¢Ã¢â‚¬Å¾Ã‚ ¦. This is a Lagrangian approach to the fluid dynamics while the traditional CFD methods use a Eulerian one. The collision operator depends on the distribution functions and it is very complicated to compute, a solution was founded by Bhatnagar, Gross and Krook (BGK) who replaced it with a single relaxation time (SRT) simplified model: à ¢Ã¢â‚¬Å¾Ã‚ ¦ = 1 (feqf) à Ã¢â‚¬Å¾ where feqis the local equilibrium distribution function (the distribution which represents the system equilibrium) and à Ã¢â‚¬Å¾is the relaxation time (particle collision frequency). The above equation can be written along each velocity direction and can be discretized as à ¢Ã‹â€ Ã¢â‚¬  teq fi(r+ cià ¢Ã‹â€ Ã¢â‚¬  t,t+ à ¢Ã‹â€ Ã¢â‚¬  t) = fi(r,t) + [f (r,t)f(r,t)] à Ã¢â‚¬Å¾i This equation can be used to describe many phenomena specifying the proper equilibrium di- stribution function. The two steps represented are the propagation step which models the movement of the distribution functions along discrete directions and the collision step which describes the physical phenomena. The main drawbacks using an SRT scheme are the low Mach number which can be used, the limitations imposed by the value of à Ã¢â‚¬Å¾and the Prandtl number must be near one. For these reasons a multiple relaxation time (MRT) collision operator is used, this approach involves the calculation of the collision step in the momentum space instead of the velocity space. The CFD software Xflow uses an MRT scheme which improves the stability and enhance the Mach number limitations up to Mach 0.6 for the overall fluid domain and up to Mach 1 in local regions, this means for example that a shock wave in the point of the minimum Cp value in a transonic airfoil can be captured. The lattice structure used in the software is a D3Q27 arran- ged in an octree structure. This method divides the 3D space in a tree data structure where each portion is recursively subdivided in eight equals smaller parts. In this manner, different spatial scales with different refinements can be obtained in the fluid domain. Each level has spatial and temporal scales twice as smaller than the previous one so the ratio dx/dt and the CFL condition remain constant allowing a proper time step for each node. This is an advantage towards traditional CFD method where the time step is constant and hence the calculation is inefficient for the coarse part of the mesh. Moreover, adaptive ref inement criteria based on the local vorticity level can be used to refine wake regions, free surface and interfaces. The model used to simulate subgrid turbulence is the Wall-Adapting Local Eddy (WALE) vi- scosity model. This approach is the same used for Large Eddy Simulation and introduce an artificial eddy viscosity ÃŽÂ ½t. This model appears to be more efficiently applied in the LBM me- thod because the strain rate tensor is available in the local node while it needs information from the neighbours nodes to be evaluated in traditional CFD models. Besides, the proportional aspect ratio of the lattice required for LES turbulence model is another advantage in behalf of LBM technique. The impossibility to represent the boundary layer near walls because of the isotropy of the latti- ce structure and the consequent high number of nodes requested to capture the phenomenon is overcome through the use of the Wall-Modeled LES approach (WMLES). Furthermore, as the turbolence length scale is proportional to the distance from the free surface and the boundary layer thickness is proportional to the Reynolds number, the resolution scale becomes unaccep- tably small near walls. This is why the WMLES approach uses RANS in the proximity of the walls. The discrete velocities projections are also used to calculate the distance between the lattice and the geometry in order to obtain a detailed description of the body curvature which is used in WMLES to evaluate the boundary layer behaviour.

Outline of Carbon and Molecular Diversity of Life

Chapter 4 Carbon and the Molecular Diversity of Life Lecture Outline Overview: Carbon – The Backbone of Biological Molecules * Although cells are 70–95% water, the rest consists mostly of carbon-based compounds. * Carbon is unparalleled in its ability to form large, complex, and diverse molecules. * Carbon accounts for the diversity of biological molecules and has made possible the great diversity of living things. * Proteins, DNA, carbohydrates, and other molecules that distinguish living matter from inorganic material are all composed of carbon atoms bonded to each other and to atoms of other elements. These other elements commonly include hydrogen (H), oxygen (O), nitrogen (N), sulfur (S), and phosphorus (P). (CHONPS) Concept 4. 1 Organic chemistry is the study of carbon compounds * The study of carbon compounds, organic chemistry, deals with any compound with carbon (organic compounds). *Organic compounds can range from simple molecules, such as CO2 or CH4, to compl ex molecules such as proteins, which may weigh more than 100,000 daltons. * The overall percentages of the major elements of life (C, H, O, N, S, and P) are quite uniform from one organism to another. However, because of carbon’s versatility, these few elements can be combined to build an inexhaustible variety of organic molecules. * Variations in organic molecules can distinguish even between individuals of a single species. * The science of organic chemistry began in attempts to purify and improve the yield of products obtained from other organisms. * Initially, chemists learned to synthesize simple compounds in the laboratory, but had no success with more complex compounds.The Swedish chemist Jons Jacob Berzelius was the first to make a distinction between organic compounds that seemed to arise only in living organisms and inorganic compounds that were found in the nonliving world. * This led early organic chemists to propose vitalism, the belief that physical and chemical laws did not apply to living things. * Support for vitalism began to wane as organic chemists learned to synthesize complex organic compounds in the laboratory. * In the early 1800s, the German chemist Friedrich Wohler and his students were able to synthesize urea from totally inorganic materials.In 1953, Stanley Miller at the University of Chicago set up a laboratory simulation of chemical conditions on the primitive Earth and demonstrated the spontaneous synthesis of organic compounds. * Such spontaneous synthesis of organic compounds may have been an early stage in the origin of life. * Organic chemists finally rejected vitalism and embraced mechanism, accepting that the same physical and chemical laws govern all natural phenomena including the processes of life. * Organic chemistry was redefined as the study of carbon compounds regardless of their origin. Organisms do produce the majority of organic compounds. * The laws of chemistry apply to inorganic and organic compounds ali ke. Concept 4. 2 Carbon atoms can form diverse molecules by bonding to four other atoms *With a total of 6 electrons, a carbon atom has 2 in the first electron shell and 4 in the second shell. * Carbon has little tendency to form ionic bonds by losing or gaining 4 electrons to complete its valence shell. * Instead, carbon usually completes its valence shell by sharing electrons with other atoms in four covalent bonds. This tetravalence by carbon makes large, complex molecules possible. * When carbon forms covalent bonds with four other atoms, they are arranged at the corners of an imaginary tetrahedron with bond angles of 109. 5Â °. * In molecules with multiple carbons, every carbon bonded to four other atoms has a tetrahedral shape. * However, when two carbon atoms are joined by a double bond, all bonds around those carbons are in the same plane and have a flat, three-dimensional structure. * The three-dimensional shape of an organic molecule determines its function. The electron configuration of carbon makes it capable of forming covalent bonds with many different elements. * The valences of carbon and its partners can be viewed as the building code that governs the architecture of organic molecules. *In carbon dioxide, one carbon atom forms two double bonds with two different oxygen atoms. * In the structural formula, O=C=O, each line represents a pair of shared electrons. This arrangement completes the valence shells of all atoms in the molecule. * While CO2 can be classified as either organic or inorganic, its importance to the living world is clear. CO2 is the source of carbon for all organic molecules found in organisms. It is usually fixed into organic molecules by the process of photosynthesis. * Urea, CO(NH2)2, is another simple organic molecule in which each atom forms covalent bonds to complete its valence shell. Variation in carbon skeletons contributes to the diversity of organic molecules. * Carbon chains form the skeletons of most organic mole cules. * The skeletons vary in length and may be straight, branched, or arranged in closed rings. *The carbon skeletons may include double bonds. Atoms of other elements can be bonded to the atoms of the carbon skeleton. * Hydrocarbons are organic molecules that consist of only carbon and hydrogen atoms. * Hydrocarbons are the major component of petroleum, a fossil fuel that consists of the partially decomposed remains of organisms that lived millions of years ago. * Fats are biological molecules that have long hydrocarbon tails attached to a nonhydrocarbon component. * Petroleum and fat are hydrophobic compounds that cannot dissolve in water because of their many nonpolar carbon-to-hydrogen bonds. Isomers are compounds that have the same molecular formula but different structures and, therefore, different chemical properties. * For example, butane and isobutane have the same molecular formula, C4H10, but butane has a straight skeleton and isobutane has a branched skeleton. * The tw o butanes are structural isomers, molecules that have the same molecular formula but differ in the covalent arrangement of atoms. * Geometric isomers are compounds with the same covalent partnerships that differ in the spatial arrangement of atoms around a carbon–carbon double bond. The double bond does not allow atoms to rotate freely around the bond axis. *The biochemistry of vision involves a light-induced change in the structure of rhodopsin in the retina from one geometric isomer to another. * Enantiomers are molecules that are mirror images of each other. * Enantiomers are possible when four different atoms or groups of atoms are bonded to a carbon. * In this case, the four groups can be arranged in space in two different ways that are mirror images. * They are like left-handed and right-handed versions of the molecule. * Usually one is biologically active, while the other is inactive. Even subtle structural differences in two enantiomers have important functional signi ficance because of emergent properties from specific arrangements of atoms. * One enantiomer of the drug thalidomide reduced morning sickness, the desired effect, but the other isomer caused severe birth defects. *The L-dopa isomer is an effective treatment of Parkinson’s disease, but the D-dopa isomer is inactive. Concept 4. 3 Functional groups are the parts of molecules involved in chemical reactions * The components of organic molecules that are most commonly involved in chemical reactions are known as functional groups. If we consider hydrocarbons to be the simplest organic molecules, we can view functional groups as attachments that replace one or more of the hydrogen atoms bonded to the carbon skeleton of the hydrocarbon. * Each functional group behaves consistently from one organic molecule to another. * The number and arrangement of functional groups help give each molecule its unique properties. * As an example, the basic structure of testosterone (a male sex hormone ) and estradiol (a female sex hormone) is the same. *Both are steroids with four fused carbon rings, but they differ in the functional groups attached to the rings. These functional groups interact with different targets in the body. * There are six functional groups that are most important to the chemistry of life: hydroxyl, carbonyl, carboxyl, amino, sulfhydryl, and phosphate groups. * All are hydrophilic and increase the solubility of organic compounds in water. * In a hydroxyl group (—OH), a hydrogen atom forms a polar covalent bond with an oxygen atom, which forms a polar covalent bond to the carbon skeleton. * Because of these polar covalent bonds, hydroxyl groups increase the solubility of organic molecules. Organic compounds with hydroxyl groups are alcohols, and their names typically end in -ol. * A carbonyl group (>CO) consists of an oxygen atom joined to the carbon skeleton by a double bond.* If the carbonyl group is on the end of the skeleton, the compound is a n aldehyde. * If the carbonyl group is within the carbon skeleton, then the compound is a ketone. * Isomers with aldehydes versus ketones have different properties. * A carboxyl group (—COOH) consists of a carbon atom with a double bond to an oxygen atom and a single bond to the oxygen of a hydroxyl group. * Compounds with carboxyl groups are carboxylic acids. A carboxyl group acts as an acid because the combined electronegativities of the two adjacent oxygen atoms increase the dissociation of hydrogen as an ion (H+). * An amino group (—NH2) consists of a nitrogen atom bonded to two hydrogen atoms and the carbon skeleton. * Organic compounds with amino groups are amines. * The amino group acts as a base because the amino group can pick up a hydrogen ion (H+) from the solution. * Amino acids, the building blocks of proteins, have amino and carboxyl groups. *A sulfhydryl group (—SH) consists of a sulfur atom bonded to a hydrogen atom and to the backbone. This grou p resembles a hydroxyl group in shape. * Organic molecules with sulfhydryl groups are thiols. * Two sulfhydryl groups can interact to help stabilize the structure of proteins. * A phosphate group (—OPO32? ) consists of a phosphorus atom bound to four oxygen atoms (three with single bonds and one with a double bond). * A phosphate group connects to the carbon backbone via one of its oxygen atoms. * Phosphate groups are anions with two negative charges, as two protons have dissociated from the oxygen atoms. * One function of phosphate groups is to transfer energy between organic molecules.Adenosine triphosphate, or ATP, is the primary energy-transferring molecule in living cells. These are the chemical elements of life. * Living matter consists mainly of carbon, oxygen, hydrogen, and nitrogen, with smaller amounts of sulfur and phosphorus. * These elements are linked by strong covalent bonds. * Carbon, with its four covalent bonds, is the basic building block in molecular archi tecture. * The great diversity of organic molecules with their special properties emerges from the unique arrangement of the carbon skeleton and the functional groups attached to the skeleton.

Research Proposal - 779 Words

MBA THESIS PROPOSAL GUIDELINES 1. INTRODUCTION The aim of this document is to give MBA students practical guidance about their thesis proposal. In addition to some general comments, the actual structure that should be followed in presenting the proposal is also outlined. The research proposal can serve many useful functions. The most important is that it helps the student to think out the research project he/she is about to undertake and predict any difficulties that might arise. For those who are not quite sure what their focus will be, the research proposal can be a space to explore options. Research proposals can be effective starting places to discuss projects with professors, too. A professor who is initially skeptical about a project†¦show more content†¦(3) Problem Definition From the wider background, you have just described you should select a management problem and explain it clearly. 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The Olympic Event Of Los Angeles - 1082 Words

Los Angeles is like any other major city around the world. Crowded population, busy businesses, and heavy traffic. But on the day I showed up for work in the cold morning, it was different. The streets are empty and blocked off at least one block apart, more law enforcement patrolling the streets, and people are beginning to line up on the side walk. As the sun begun to rise and the temperatures to warm up, hundreds of guests line up at the starting line. This day was no ordinary running event. Not just any marathon taken place, but qualifications to take 6 spots (three men, three women) to represent the United States for the 2016 Summer Olympics in Rio de Janeiro. Witnessing a historic event, I wonder why runners do it and what our Olympic runners will face in Rio? Through pain and sweat, the marathon runner will give their all for Olympic gold. One thing that can be observed in an Olympic event is the togetherness and unity of the population. 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