In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:
In discrete time, it means that the first difference of each property is zero and remains so:
Convection is single or multiphase fluid flow that occurs spontaneously through the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.
Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see convection cell). The convection may be due to gravitational, electromagnetic or fictitious body forces. Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its mantle. Discrete convective cells in the atmosphere can be identified by clouds, with stronger convection resulting in thunderstorms. Natural convection also plays a role in stellar physics. Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection.
In scientific ecology, climax community or climatic climax community is a historic term for a community of plants, animals, and fungi which, through the process of ecological succession in the development of vegetation in an area over time, have reached a steady state. This equilibrium was thought to occur because the climax community is composed of species best adapted to average conditions in that area. The term is sometimes also applied in soil development. Nevertheless, it has been found that a "steady state" is more apparent than real, particularly across long timescales.
The idea of a single climax, which is defined in relation to regional climate, originated with Frederic Clements in the early 1900s. The first analysis of succession as leading to something like a climax was written by Henry Cowles in 1899, but it was Clements who used the term "climax" to describe the idealized endpoint of succession.
In systems theory, a system is said to be transient or in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state. In electrical engineering, the time taken for an electronic circuit to change from one steady state to another steady state is called the transient time.
A fusion energy gain factor, usually expressed with the symbol Q, is the ratio of fusion power produced in a nuclear fusion reactor to the power required to maintain the plasma in a steady state. The condition of Q = 1, when the power being released by the fusion reactions is equal to the required heating power, is referred to as breakeven, or in some sources, scientific breakeven.
The energy given off by the fusion reactions may be captured within the fuel, leading to self-heating. Most fusion reactions release at least some of their energy in a form that cannot be captured within the plasma, so a system at Q = 1 will cool without external heating. With typical fuels, self-heating in fusion reactors is not expected to match the external sources until at least Q ≈ 5. If Q increases past this point, increasing self-heating eventually removes the need for external heating. At this point the reaction becomes self-sustaining, a condition called ignition, and is generally regarded as highly desirable for practical reactor designs. Ignition corresponds to infinite Q.
In chemistry, a dynamic equilibrium exists once a reversible reaction occurs. Substances initially transition between the reactants and products at different rates until the forward and backward reaction rates eventually equalize, meaning there is no net change. Reactants and products are formed at such a rate that the concentration of neither changes. It is a particular example of a system in a steady state.
A tetanic contraction (also called tetanized state, tetanus, or physiologic tetanus, the latter to differentiate from the disease called tetanus) is a sustained muscle contraction evoked when the motor nerve that innervates a skeletal muscle emits action potentials at a very high rate. During this state, a motor unit has been maximally stimulated by its motor neuron and remains that way for some time. This occurs when a muscle's motor unit is stimulated by multiple impulses at a sufficiently high frequency. Each stimulus causes a twitch. If stimuli are delivered slowly enough, the tension in the muscle will relax between successive twitches. If stimuli are delivered at high frequency, the twitches will overlap, resulting in tetanic contraction. A tetanic contraction can be either unfused (incomplete) or fused (complete). An unfused tetanus is when the muscle fibers do not completely relax before the next stimulus because they are being stimulated at a fast rate; however there is a partial relaxation of the muscle fibers between the twitches. Fused tetanus is when there is no relaxation of the muscle fibers between stimuli and it occurs during a high rate of stimulation. A fused tetanic contraction is the strongest single-unit twitch in contraction. When tetanized, the contracting tension in the muscle remains constant in a steady state. This is the maximal possible contraction. During tetanic contractions, muscles can shorten, lengthen or remain constant length.
Tetanic contraction is usually normal (such as when holding up a heavy box). Muscles often exhibit some level of tetanic activity, leading to muscle tone, in order to maintain posture; for example, in a crouching position, some muscles require sustained contraction to hold the position. Tetanic contraction can exist in a variety of states, including isotonic and isometric forms—for example, lifting a heavy box off the floor is isotonic, but holding it at the elevated position is isometric. Isotonic contractions place muscles in a constant tension but the muscle length changes, while isometric contractions hold a constant muscle length.