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PhET Interactive Simulations is part of the University of Colorado Boulder which is a member of the Association of American Universities. [10] The team changes over time and has about 16 members consisting of professors, post-doctoral students, researchers, education specialists, software engineers (sometimes contractors), educators, and administrative assistants. [11]
In mathematics, the method of dominant balance approximates the solution to an equation by solving a simplified form of the equation containing 2 or more of the equation's terms that most influence (dominate) the solution and excluding terms contributing only small modifications to this approximate solution.
Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms. [1] During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution, [10] [11] but Gelenbe's G-network model showed this not to be the case. [12]
Consider the average number of particles with particle properties denoted by a particle state vector (x,r) (where x corresponds to particle properties like size, density, etc. also known as internal coordinates and, r corresponds to spatial position or external coordinates) dispersed in a continuous phase defined by a phase vector Y(r,t) (which again is a function of all such vectors which ...
Hybrid simulation (or combined simulation) corresponds to a mix between continuous and discrete event simulation and results in integrating numerically the differential equations between two sequential events to reduce the number of discontinuities. [10] A stand-alone simulation is a simulation running on a single workstation by itself.
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [12] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
The concept is the same as for a large mass balance, but it is performed in the context of a limiting system (for example, one can consider the limiting case in time or, more commonly, volume). A differential mass balance is used to generate differential equations that can provide an effective tool for modelling and understanding the target system.
The optimal solution to the flux-balance problem is rarely unique with many possible, and equally optimal, solutions existing. Flux variability analysis (FVA), built into some analysis software, returns the boundaries for the fluxes through each reaction that can, paired with the right combination of other fluxes, estimate the optimal solution.