Steady State
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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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Transient State
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. The time taken for the circuit to change from one steady state to another steady state is called the transient time. Examples Chemical Engineering When a chemical reactor is being brought into operation, the concentrations, temperatures, species compositions, and reaction rates are changing with time until operation reaches its nominal process variables. Electrical engineering When a switch is flipped in an appropriate electrical circuit containing a capacitor or inductor, the component draws out the resulting change in voltage or current (respectively), causing the system to take a substantial amount of time to reach a new steady state. We can define a transient by saying that when a quantity is at rest or in uniform motion and a change in time takes place , changing the existing state , a transient has taken place. W ...
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Systems Theory
Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" by expressing synergy or emergent behavior. Changing one component of a system may affect other components or the whole system. It may be possible to predict these changes in patterns of behavior. For systems that learn and adapt, the growth and the degree of adaptation depend upon how well the system is engaged with its environment and other contexts influencing its organization. Some systems support other systems, maintaining the other system to prevent failure. The goals of systems theory are to model a system's dynamics, constraints, conditions, and relations; and to elucidate principles (such as purpose, measure ...
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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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Chemical Engineering
Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials. The work of chemical engineers can range from the utilization of nanotechnology and nanomaterials in the laboratory to large-scale industrial processes that convert chemicals, raw materials, living cells, microorganisms, and energy into useful forms and products. Chemical engineers are involved in many aspects of plant design and operation, including safety and hazard assessments, process design and analysis, modeling, control engineering, chemical reaction engineering, nuclear engineering, biological engineering, construction specification, ...
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Constant Envelope
Constant envelope is achieved when a sinusoidal waveform reaches equilibrium in a specific system. This happens when negative feedback in a control system, such as in radio automatic gain control or when an amplifier reaches steady state. Steady state, as defined in electrical engineering, occurs after a system becomes settled. To be more specific, control systems are unstable until they reach a steady state. Constant envelope needs to occur for the system to be stable, where there is the least amount of noise and feedback gain has rendered the system steady. Feedback is used to create a feedback signal to control gain, reduce distortion, control output voltage, improve stability or create instability, as in an oscillator. Some examples of constant envelope modulations are as FSK, GFSK, MSK, GMSK and Feher's IJF - All constant envelope modulations allow power amplifiers to operate at or near saturation levels. Although, the power spectrum efficiency of a non-constant amplit ...
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Transient (electricity)
In electrical engineering and mechanical engineering, a transient response is the response of a system to a change from an equilibrium or a steady state. The transient response is not necessarily tied to abrupt events but to any event that affects the equilibrium of the system. The impulse response and step response are transient responses to a specific input (an impulse and a step, respectively). In electrical engineering specifically, the transient response is the circuit’s temporary response that will die out with time. It is followed by the steady state response, which is the behavior of the circuit a long time after an external excitation is applied. Damping The response can be classified as one of three types of damping that describes the output in relation to the steady-state response. ;Underdamped :An underdamped response is one that oscillates within a decaying envelope. The more underdamped the system, the more oscillations and longer it takes to reach steady-state ...
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Economic Equilibrium
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. This price is often called the competitive price or market clearing price and will tend not to change unless demand or supply changes, and quantity is called the "competitive quantity" or market clearing quantity. But the concept of ''equilibrium'' in economics also applies to imperfectly competitive markets, where it takes the form of a Nash equilibrium. Understanding economic equilibriu ...
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Depreciation (economics)
In economics, depreciation is the gradual decrease in the economic value of the capital stock of a firm, nation or other entity, either through physical depreciation, obsolescence or changes in the demand for the services of the capital in question. If the capital stock is K_t in one period t, gross (total) investment spending on newly produced capital is I_t and depreciation is D_t, the capital stock in the next period, K_, is K_t + I_t - D_t. The net increment to the capital stock is the difference between gross investment and depreciation, and is called net investment. Models In economics, the value of a capital asset may be modeled as the present value of the flow of services the asset will generate in future, appropriately adjusted for uncertainty. Economic depreciation over a given period is the reduction in the remaining value of future goods and services. Under certain circumstances, such as an unanticipated increase in the price of the services generated by an asset or a ...
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Physical Capital
Physical capital represents in economics one of the three primary factors of production. Physical capital is the apparatus used to produce a good and services. Physical capital represents the tangible man-made goods that help and support the production. Inventory, cash, equipment or real estate are all examples of physical capital. Definition N.G. Mankiw definition from the book Economics: '' Capital is the equipment and structures used to produce goods and services. Physical capital consists of man-made goods (or input into the process of production) that assist in the production process. Cash, real estate, equipment, and inventory are examples of physical capital.'' Capital goods represents one of the key factors of corporation function. Generally, capital allows a company to preserve liquidity while growing operations, it refers to physical assets in business and the way a company have reached their physical capital. While referring how companies have obtained their capital ...
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Investment (macroeconomics)
In macroeconomics, investment "consists of the additions to the nation's capital stock of buildings, equipment, software, and inventories during a year" or, alternatively, investment spending — "spending on productive physical capital such as machinery and construction of buildings, and on changes to inventories — as part of total spending" on goods and services per year. Krugman, Paul and Robin Wells (2012), 2nd ed. ''Economics'', p. 593. Worth Publishers. The types of investment include residential investment in housing that will provide a flow of housing services over an extended time, non-residential fixed investment in things such as new machinery or factories, human capital investment in workforce education, and inventory investment (the accumulation, intentional or unintentional, of goods inventories) In measures of national income and output, "gross investment" (represented by the variable ) is a component of gross domestic product (), given in the formula , where i ...
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Trevor Swan
Trevor Winchester Swan (14 January 1918 – 15 January 1989) was an Australian economist. He is best known for his work on the Solow–Swan growth model, published simultaneously by American economist Robert Solow, for his work on integrating internal and external balance as represented by the Swan Diagram, and for pioneering work in macroeconomic modeling, which predated that of Lawrence Klein but remained unpublished until 1989. Swan is widely regarded as the greatest economic theorist that Australia has produced, and as one of the finest economists not to receive a Nobel Memorial Prize in Economic Sciences. There were two independent pioneers of Neoclassical Growth Theory: Robert Solow and Trevor Swan. Solow published "A Contribution to the Theory of Economic Growth" in the February issue of the QJE in 1956, and Trevor Swan published "Economic Growth and Capital Accumulation" in the ''Economic Record'', subsequent to Solow in December 1956. Swan's contribution has been ove ...
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Robert Solow
Robert Merton Solow, GCIH (; born August 23, 1924) is an American economist whose work on the theory of economic growth culminated in the exogenous growth model named after him. He is currently Emeritus Institute Professor of Economics at the Massachusetts Institute of Technology, where he has been a professor since 1949. He was awarded the John Bates Clark Medal in 1961, the Nobel Memorial Prize in Economic Sciences in 1987, and the Presidential Medal of Freedom in 2014. Four of his PhD students, George Akerlof, Joseph Stiglitz, Peter Diamond and William Nordhaus later received Nobel Memorial Prizes in Economic Sciences in their own right. Biography Robert Solow was born in Brooklyn, New York, into a Jewish family on August 23, 1924, the oldest of three children. He regarded his parents as being very intelligent despite their not being able to attend college due to the necessity to work. He was well educated in the neighborhood public schools and excelled academically early ...
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