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Virtual displacements be zero on the part of the surface that has prescribed displacements, and thus the work done by the reactions is zero. There remains only external surface forces on the part that do work. The virtual work equation then becomes the principle of virtual displacements:
The balancing of rotating bodies is important to avoid vibration. In heavy industrial machines such as gas turbines and electric generators, vibration can cause catastrophic failure, as well as noise and discomfort. In the case of a narrow wheel, balancing simply involves moving the center of gravity to the centre of rotation
These balance equations were first considered by Peter Whittle. [8] [9] The resulting equations are somewhere between detailed balance and global balance equations. Any solution to the local balance equations is always a solution to the global balance equations (we can recover the global balance equations by summing the relevant local balance ...
Strictly speaking the above equation holds also for systems with chemical reactions if the terms in the balance equation are taken to refer to total mass, i.e. the sum of all the chemical species of the system. In the absence of a chemical reaction the amount of any chemical species flowing in and out will be the same; this gives rise to an ...
Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting from grams to moles using molar mass as the conversion factor, or from grams to milliliters using density. For example, to find the amount of NaCl (sodium chloride) in 2.00 g, one would do the following:
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 [13] =, 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 ...
Load balancing can optimize response time and avoid unevenly overloading some compute nodes while other compute nodes are left idle. Load balancing is the subject of research in the field of parallel computers. Two main approaches exist: static algorithms, which do not take into account the state of the different machines, and dynamic ...
where {HG} is the thermodynamic activity of the complex at equilibrium. {H} represents the activity of the host and {G} the activity of the guest. The quantities [], [] and [] are the corresponding concentrations and is a quotient of activity coefficients.