Steady State
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Steady State
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: : \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, 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. For example, see ' for the derivation of the steady state. In many systems, a steady state is not achieved until some time after the system is started or initiated. This initial sit ...
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Systems Theory
Systems theory is the Transdisciplinarity, transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. 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" when it expresses 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, Theory of constraints, constraints, conditions, and relations; and to ...
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Dynamic Equilibrium
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. 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 partial pressure of carbon dioxide in the gas phase will increase until equilibrium is reached. At that point, due to thermal motion, a molecule of CO2 may leave the liquid phase, but within a very short time another molecule of CO2 will pass from the gas to the liquid, and vice versa. At equilibrium, the rate of tran ...
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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-st ...
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Electronic Engineering
Electronic engineering is a sub-discipline of electrical engineering that emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current flow. Previously electrical engineering only used passive devices such as mechanical switches, resistors, inductors, and capacitors. It covers fields such as analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. It is also involved in many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, photonics and robotics. The Institute of Electrical and Electronics Engineers (IEEE) is one of the most important professional bodies for electronics engineers in the US; the equivalent body in the UK is the Institution of Engin ...
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Electrical Engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after the commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, Electromagnetism, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control ...
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Economic Equilibrium
In economics, economic equilibrium is a situation in which the economic forces of supply and demand are balanced, meaning that economic variables will no longer change. 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. Understanding economic equilibrium An economic equilibrium is a situation when the economic agent cannot change the situation by adopting any strategy. The concept has been borrowed from the physical sciences. Take a system where physical forces are balanced for instance.This economically interpreted means no further change ensues. Properties of equilibrium Three basic prope ...
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Depreciation (economics)
In economics, depreciation is the gradual decrease in the economic value theory, 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 investment, 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 (economics), 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 th ...
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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 ...
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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. "accounting" 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 fo ...
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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 (; August 23, 1924 – December 21, 2023) was an American economist who received the 1987 Nobel Memorial Prize in Economic Sciences, and whose work on the theory of economic growth culminated in the exogenous growth model named after him. He was Institute Professor Emeritus of Economics at the Massachusetts Institute of Technology, where he was a professor from 1949 on. 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 attended local public school and excelled academically early in life. In September 1940, Solow went to Harvard College with ...
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Economic Growth
In economics, economic growth is an increase in the quantity and quality of the economic goods and Service (economics), services that a society Production (economics), produces. It can be measured as the increase in the inflation-adjusted Output (economics), output of an economy in a given year or over a period of time. The rate of growth is typically calculated as List of countries by real GDP growth rate, real gross domestic product (GDP) growth rate, List of countries by real GDP per capita growth, real GDP per capita growth rate or List of countries by GNI per capita growth, GNI per capita growth. The "rate" of economic growth refers to the Exponential growth, geometric annual rate of growth in GDP or GDP per capita between the first and the last year over a period of time. This growth rate represents the trend in the average level of GDP over the period, and ignores any fluctuations in the GDP around this trend. Growth is usually calculated in "real" value, which is real v ...
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