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Lattice Boltzmann Methods
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy- Pomeau-Pazzis and Frisch- Hasslacher- Pomeau models), is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equations directly, a fluid density on a lattice is simulated with streaming and collision (relaxation) processes. The method is versatile as the model fluid can straightforwardly be made to mimic common fluid behaviour like vapour/liquid coexistence, and so fluid systems such as liquid droplets can be simulated. Also, fluids in complex environments such as porous media can be straightforwardly simulated, whereas with complex boundaries other CFD methods can be hard to work with. Algorithm Unlike CFD methods that solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Gas Automata
Lattice gas automata (LGCA), or lattice gas cellular automata, are a type of cellular automaton used to simulate fluid flows, pioneered by Hardy–Pomeau–de Pazzis and Frisch– Hasslacher– Pomeau. They were the precursor to the lattice Boltzmann methods. From lattice gas automata, it is possible to derive the macroscopic Navier–Stokes equations. Interest in lattice gas automaton methods levelled off in the early 1990s, as the interest in the lattice Boltzmann started to rise. However, an LGCA variant, termed BIO-LGCA, is still widely used to model collective migration in biology. Basic principles As a cellular automaton, these models comprise a lattice, where the sites on the lattice can take a certain number of different states. In lattice gas, the various states are particles with certain velocities. Evolution of the simulation is done in discrete time steps. After each time step, the state at a given site can be determined by the state of the site itself and neighbori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of State
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Though there are many equations of state, none accurately predicts properties of substances under all conditions. The quest for a universal equation of state has spanned three centuries. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the Motion (physics), physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamics (mechanics), dynamic "evolution" of the system. In the most common version, the trajectory, trajectories of atoms and molecules are determined by Numerical integration, numerically solving Newton's laws of motion, Newton's equations of motion for a system of interacting particles, where Force (physics), forces between the particles and their potential energy, potential energies are often calculated using interatomic potentials or molecular mechanics, molecular mechanical Force field (chemistry), force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analyt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Diffusion
Reaction may refer to a process or to a response to an action, event, or exposure. Physics and chemistry *Chemical reaction *Nuclear reaction *Reaction (physics), as defined by Newton's third law * Chain reaction (other) Biology and medicine *Adverse drug reaction *Allergic reaction *Reflex, neural reaction *Hypersensitivity, immune reaction *Intolerance (other) * Light reaction (other) Psychology *Emotional, reaction * Reactivity *Proactivity, opposite of reactive behaviour *Reactive attachment disorder Politics and culture *Reactionary, a political tendency *Reaction video *Commentary (other) Proper names and titles * ''Reaction'' (album), a 1986 album by American R&B singer Rebbie Jackson ** "Reaction" (song), the title song from the Rebbie Jackson album *"Reaction", a single by Dead Letter Circus *''Reactions'', a 2018 album by The Mods *ReAction GUI, a GUI toolkit used on AmigaOS * Reaction.life, a political news and commentary web ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar flow, laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulence, turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (Eddy (fluid dynamics), eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar–turbulent transition, laminar to turbulent flow and is used in the scaling of similar but different-sized fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Noise
In statistics, the fraction of variance unexplained (FVU) in the context of a regression task is the fraction of variance of the regressand (dependent variable) ''Y'' which cannot be explained, i.e., which is not correctly predicted, by the explanatory variables ''X''. Formal definition Suppose we are given a regression function f yielding for each y_i an estimate \widehat_i = f(x_i) where x_i is the vector of the ''i''th observations on all the explanatory variables. We define the fraction of variance unexplained (FVU) as: :\begin \text & = = = \left( = 1- , \text\right) \\ pt & = 1 - R^2 \end where ''R''2 is the coefficient of determination and ''VAR''err and ''VAR''tot are the variance of the residuals and the sample variance of the dependent variable. ''SS''''err'' (the sum of squared predictions errors, equivalently the residual sum of squares), ''SS''''tot'' (the total sum of squares), and ''SS''''reg'' (the sum of squares of the regression, equivalently the expla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galilean Invariance
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described this principle in 1632 in his ''Dialogue Concerning the Two Chief World Systems'' using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary. Formulation Specifically, the term ''Galilean invariance'' today usually refers to this principle as applied to Newtonian mechanics, that is, Newton's laws of motion hold in all frames related to one another by a Galilean transformation. In other words, all frames related to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called ''Newtonian relativity''. Among the axioms from Newton's theory are: #There exists an '' absolute space'', in which Newton's laws are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Number
In thermodynamics, the particle number (symbol ) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental thermodynamic property which is conjugate to the chemical potential. Unlike most physical quantities, the particle number is a dimensionless quantity, specifically a countable quantity. It is an extensive property, as it is directly proportional to the size of the system under consideration and thus meaningful only for closed systems. A constituent particle is one that cannot be broken into smaller pieces at the scale of energy involved in the process (where is the Boltzmann constant and is the temperature). For example, in a thermodynamic system consisting of a piston containing water vapour, the particle number is the number of water molecules in the system. The meaning of constituent particles, and thereby of particle numbers, is thus temperature-dependent. Determining the particle number The concept of pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Gas Automaton
Lattice gas automata (LGCA), or lattice gas cellular automata, are a type of cellular automaton used to simulate fluid flows, pioneered by Hardy–Pomeau–de Pazzis and Frisch– Hasslacher– Pomeau. They were the precursor to the lattice Boltzmann methods. From lattice gas automata, it is possible to derive the macroscopic Navier–Stokes equations. Interest in lattice gas automaton methods levelled off in the early 1990s, as the interest in the lattice Boltzmann started to rise. However, an LGCA variant, termed BIO-LGCA, is still widely used to model collective migration in biology. Basic principles As a cellular automaton, these models comprise a lattice, where the sites on the lattice can take a certain number of different states. In lattice gas, the various states are particles with certain velocities. Evolution of the simulation is done in discrete time steps. After each time step, the state at a given site can be determined by the state of the site itself and neighbori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aerodynamics
Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an important domain of study in aeronautics. The term ''aerodynamics'' is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving Aircraft#Heavier-than-air – aerodynes, heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
