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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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System
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα"
Henry George Liddell, Robert Scott, ''
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Growth Curve (statistics)
The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as seen in the definition. Definition Growth curve model: Let X be a ''p''×''n'' random matrix corresponding to the observations, A a ''p''×''q'' within design matrix with ''q'' ≤ ''p'', B a ''q''×''k'' parameter matrix, C a ''k''×''n'' between individual design matrix with rank(''C'') + ''p'' ≤ ''n'' and let Σ be a positive-definite ''p''×''p'' matrix. Then : X=ABC+\Sigma^E defines the growth curve model, where A and C are known, B and Σ are unknown, and E is a random matrix distributed as ''N''''p'',''n''(0,''I''''p'',''n''). This differs from standard MANOVA by the addition of C, a "postmatrix". History Many writers have considered the growth curve analysis, among them Wishart (1938), Box (1950) and Rao (1958). Potthoff and Roy in 19 ...
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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, measur ...
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Steady State Theory
In cosmology, the steady-state model, or steady state theory is an alternative to the Big Bang theory of evolution of the universe. In the steady-state model, the density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that asserts that the observable universe is practically the same at any time and any place. While from the 1940s to the 1960s the astrophysical community was equally divided between supporters of the Big Bang theory and supporters of the steady-state theory, it is now rejected by the vast majority of cosmologists, astrophysicists and astronomers, as the observational evidence points to a hot Big Bang cosmology with a finite age of the universe, which the steady-state model does not predict. History In the 13th century, Siger of Brabant authored the thesis ''The Eternity of the World'', which argued that there was no first man, and no first specimen ...
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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 di ...
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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. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state. In many systems, a steady state is not achieved until some time afte ...
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State Function
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system (e.g. gas, liquid, solid, crystal, or emulsion), not the path which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example. In this law, one state variable (e.g., pressure, volume, temperature, or the amount of substance in a gaseous equilibrium system) is a function of other state variables so is regarded as a state function. A state fu ...
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Simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games. Simulation is also used with scientific modelling of natural systems or human systems to gain insight into their functioning, as in economics. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not ...
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Race Condition
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is Sequential logic, dependent on the sequence or timing of other uncontrollable events. It becomes a software bug, bug when one or more of the possible behaviors is undesirable. The term ''race condition'' was already in use by 1954, for example in David A. Huffman's doctoral thesis "The synthesis of sequential switching circuits". Race conditions can occur especially in logic gate, logic circuits, thread (computing), multithreaded, or distributed computing, distributed software programs. In electronics A typical example of a race condition may occur when a logic gate combines signals that have traveled along different paths from the same source. The inputs to the gate can change at slightly different times in response to a change in the source signal. The output may, for a brief period, change to an unwanted state before settling back to the d ...
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Population Dynamics
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years,Malthus, Thomas Robert. An Essay on the Principle of Population: Library of Economics although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model. According to Malthus, assuming that the conditions (the environment) remain constant (''ceteris paribus''), a population will grow (or decline) exponentially. This principle provided the basis for the subsequent predictive theories, such as the demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic mode ...
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Limits To Growth
''The Limits to Growth'' (''LTG'') is a 1972 report that discussed the possibility of exponential economic and population growth with finite supply of resources, studied by computer simulation. The study used the World3 computer model to simulate the consequence of interactions between the earth and human systems. The model was based on the work of Jay Forrester of MIT, as described in his book ''World Dynamics''. Commissioned by the Club of Rome, the findings of the study were first presented at international gatherings in Moscow and Rio de Janeiro in the summer of 1971. The report's authors are Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III, representing a team of 17 researchers. The report concludes that, without substantial changes in resource consumption, "the most probable result will be a rather sudden and uncontrollable decline in both population and industrial capacity". Although its methods and premises were heavily challenged on ...
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Limit Cycle
In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of a great many real-world oscillatory systems. The study of limit cycles was initiated by Henri Poincaré (1854–1912). Definition We consider a two-dimensional dynamical system of the form x'(t)=V(x(t)) where V : \R^2 \to \R^2 is a smooth function. A ''trajectory'' of this system is some smooth function x(t) with values in \mathbb^2 which satisfies this differential equation. Such a trajectory is called ''closed'' (or ''periodic'') if it is not constant but returns to its starting point, i.e. if there exists some t_0>0 such that x(t + t_0) = x(t) for all t \in \R. An orbit is the image of a t ...
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