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In a new bottle of soda, the concentration of carbon dioxide in the liquid phase has a particular value. If half of the liquid is poured out and the bottle is sealed, carbon dioxide will leave the liquid phase at an ever-decreasing rate, and the partial pressure of carbon dioxide in the gas phase will increase until equilibrium is reached.
D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing forces of inertia which, when added to the applied forces in a system, result in dynamic equilibrium. [1] [2] D'Alembert's principle can be applied in cases of kinematic constraints that depend on velocities.
In chemistry, a steady state is a more general situation than dynamic equilibrium. While a dynamic equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in a steady state, a system that is in a steady state may not necessarily be in a state of dynamic equilibrium, because some of ...
If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change. For example, adding more S (to the chemical reaction above) from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the ...
In a linear dynamical system, the variation of a state vector (an -dimensional vector denoted ) equals a constant matrix (denoted ) multiplied by . This variation can take two forms: either as a flow , in which x {\displaystyle \mathbf {x} } varies continuously with time
Some sink, source or node are equilibrium points. 2-dimensional case refers to Phase plane. In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems.
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 ...
Chemical equilibrium is a dynamic state in which forward and backward reactions proceed at such rates that the macroscopic composition of the mixture is constant. Thus, equilibrium sign ⇌ symbolizes the fact that reactions occur in both forward ⇀ {\displaystyle \rightharpoonup } and backward ↽ {\displaystyle \leftharpoondown } directions.