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Steady State (other)
Steady state may refer to: *Steady state (systems) an operating condition in thermodynamic and other systems or processes when variables stay constant as time passes. ** Steady-state economy, an economy made up of a constant population size and a constant stock of physical wealth (capital). ** Steady-state equilibrium (monetary theory), an economic situation where neutrality of money coincides with zero population growth. ** Steady-state rate of growth (neoclassical growth theory), an economy featuring an equi-proportionate increase in capital and labour ** Steady state (electronics), a state existing in a circuit or network when all transients have died away. **Steady state (chemistry), a term in chemical kinetics meaning the situation in which all state variables of an open system are constant in time. ** Steady state (biochemistry), a situation in which certain parameters of cells or organs, usually concentrations of molecules, are constant in time ** Steady state (physiology), al ...
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Steady State
In systems theory, a system or a Process theory, 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: : \frac = 0 \quad \text t. In discrete time, it means that the first difference of each property is zero and remains so: :p_t-p_=0 \quad \text t. The concept of a steady state has relevance in many fields, in particular thermodynamics, Steady state economy, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various states will be repeated will remain constant. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state. In many systems, a steady state i ...
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Thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ...
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Steady-state Economy
A steady-state economy is an economy made up of a constant stock of physical wealth (capital) and a constant population size. In effect, such an economy does not grow in the course of time. The term usually refers to the national economy of a particular country, but it is also applicable to the economic system of a city, a region, or the entire world. Early in the history of economic thought, classical economist Adam Smith of the 18th century developed the concept of a ''stationary state'' of an economy: Smith believed that any national economy in the world would sooner or later settle in a final state of stationarity. Since the 1970s, the concept of a steady-state economy has been associated mainly with the work of leading ecological economist Herman Daly. As Daly's concept of a ''steady-state'' includes the ecological analysis of natural resource flows through the economy, his concept differs from the original classical concept of a ''stationary state''. One other ...
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Neutrality Of Money
Neutral or neutrality may refer to: Mathematics and natural science Biology * Neutral organisms, in ecology, those that obey the unified neutral theory of biodiversity Chemistry and physics * Neutralization (chemistry), a chemical reaction in which an acid and a base react quantitatively with each other * Neutral solution, a chemical solution which is neither acidic nor basic * Neutral particle, a particle without electrical charge Mathematics * Neutral element or identity element, in mathematics, a special element with respect to a binary operation, such that if the operation is applied to any element in a set, that element is unchanged * Neutral vector, a multivariate random variable that exhibits a particular type of statistical independence (Dirichlet distribution) Philosophy * Neutrality (philosophy), the absence of declared or intentional bias * Neutrality (psychoanalysis) * Neutral level, the physical or material traces of esthesic and poietic processes identified i ...
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Solow–Swan Model
The Solow–Swan model or exogenous growth model is an economic model of long-run economic growth. It attempts to explain long-run economic growth by looking at capital accumulation, labor or population growth, and increases in productivity largely driven by technological progress. At its core, it is an aggregate production function, often specified to be of Cobb–Douglas type, which enables the model "to make contact with microeconomics". The model was developed independently by Robert Solow and Trevor Swan in 1956,The idea of using a Cobb–Douglas production function at the core of a growth model dates back to . See and superseded the Keynesian Harrod–Domar model. Mathematically, the Solow–Swan model is a nonlinear system consisting of a single ordinary differential equation that models the evolution of the ''per capita'' stock of capital. Due to its particularly attractive mathematical characteristics, Solow–Swan proved to be a convenient starting point for various ext ...
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Steady State (electronics)
In electronics, steady state is an equilibrium condition of a circuit or network that occurs as the effects of transients are no longer important. Steady state is reached (attained) after transient (initial, oscillating or turbulent) state has subsided. During steady state, a system is in relative stability. Steady state determination is an important topic, because many design specifications of electronic systems are given in terms of the steady-state characteristics. Periodic steady-state solution is also a prerequisite for small signal dynamic modeling. Steady-state analysis is therefore an indispensable component of the design process. Calculation methods Steady state calculation methods can be sorted into time-domain algorithms (time domain sensitivities, shooting) and frequency-domain algorithms (harmonic balance) methods, are the best choice for most microwave circuits excited with sinusoidal signals (e.g. mixers, power amplifiers). Time domain methods Time domain metho ...
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Steady State (chemistry)
In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, there must be a flow through the system (compare mass balance). A simple example of such a system is the case of a bathtub with the tap running but with the drain unplugged: after a certain time, the water flows in and out at the same rate, so the water level (the state variable Volume) stabilizes and the system is in a steady state. The steady state concept is different from chemical equilibrium. Although both may create a situation where a concentration does not change, in a system at chemical equilibrium, the net reaction rate is zero (products transform into reactants at the same rate as reactants transform into products), while no such limitation exists in the steady state concept. Indeed, there does not have to be a reaction at all ...
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Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.C.M. Guldberg and P. Waage,"Studies Concerning Affinity" ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864), 35P. W ...
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Open System (thermodynamics)
A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are not thermodynamic systems. A wall of a thermodynamic system may be purely notional, when it is described as being 'permeable' to all matter, all radiation, and all forces. A state of a thermodynamic system can be fully described in several different ways, by several different sets of thermodynamic state variables. A widely used distinction is between ''isolated'', ''closed'', and ''open'' thermodynamic systems. An isolated thermodynamic system has walls that are non-conductive of heat and perfectly reflective of all radiation, that are rigid and immovable, and that are impermeable to all forms of matter and all forces. (Some writers use the word 'closed' when here the word 'isolated' is being used.) A closed thermodynamic system is c ...
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Steady State (biochemistry)
In biochemistry, steady state refers to the maintenance of constant internal concentrations of molecules and ions in the cells and organs of living systems. Living organisms remain at a dynamic steady state where their internal composition at both cellular and gross levels are relatively constant, but different from equilibrium concentrations. A continuous flux of mass and energy results in the constant synthesis and breakdown of molecules via chemical reactions of biochemical pathways. Essentially, steady state can be thought of as homeostasis at a cellular level. Maintenance of steady state Metabolic regulation achieves a balance between the rate of input of a substrate and the rate that it is degraded or converted, and thus maintains steady state. The rate of metabolic flow, or flux, is variable and subject to metabolic demands. However, in a metabolic pathway, steady state is maintained by balancing the rate of substrate provided by a previous step and the rate that th ...
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Homeostasis
In biology, homeostasis (British English, British also homoeostasis) Help:IPA/English, (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physics, physical, and chemistry, chemical conditions maintained by organism, living systems. This is the condition of optimal functioning for the organism and includes many variables, such as body temperature and fluid balance, being kept within certain pre-set limits (homeostatic range). Other variables include the pH of extracellular fluid, the concentrations of sodium, potassium and calcium ions, as well as that of the blood sugar level, and these need to be regulated despite changes in the environment, diet, or level of activity. Each of these variables is controlled by one or more regulators or homeostatic mechanisms, which together maintain life. Homeostasis is brought about by a natural resistance to change when already in the optimal conditions, and equilibrium is maintained by many regulatory mechanisms: it is thought to be ...
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Dynamic Equilibrium
In chemistry, a dynamic equilibrium exists once a reversible reaction occurs. Substances transition between the reactants and products at equal rates, 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. In physics, concerning thermodynamics, a closed system is in thermodynamic equilibrium when reactions occur at such rates that the composition of the mixture does not change with time. Reactions do in fact occur, sometimes vigorously, but to such an extent that changes in composition cannot be observed. Equilibrium constants can be expressed in terms of the rate constants for reversible reactions. Examples 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 p ...
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