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Tellegen's Theorem
Tellegen's theorem is one of the most powerful theorems in network theory. Most of the energy distribution theorems and extremum principles in network theory can be derived from it. It was published in 1952 by Bernard Tellegen. Fundamentally, Tellegen's theorem gives a simple relation between magnitudes that satisfy Kirchhoff's laws of electrical circuit theory. The Tellegen theorem is applicable to a multitude of network systems. The basic assumptions for the systems are the conservation of flow of extensive quantities (Kirchhoff's current law, KCL) and the uniqueness of the potentials at the network nodes (Kirchhoff's voltage law, KVL). The Tellegen theorem provides a useful tool to analyze complex network systems including electrical circuits, biological and metabolic networks, pipeline transport networks, and chemical process networks. The theorem Consider an arbitrary lumped network that has b branches and n nodes. In an electrical network, the branches are two-termin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Metabolic Network
A metabolic network is the complete set of metabolic and physical processes that determine the physiological and biochemical properties of a cell. As such, these networks comprise the chemical reactions of metabolism, the metabolic pathways, as well as the regulatory interactions that guide these reactions. With the sequencing of complete genomes, it is now possible to reconstruct the network of biochemical reactions in many organisms, from bacteria to human. Several of these networks are available online: Kyoto Encyclopedia of Genes and Genomes ( KEGG), EcoCyc, BioCyc and metaTIGER. Metabolic networks are powerful tools for studying and modelling metabolism. Uses Metabolic networks can be used to detect comorbidity patterns in diseased patients. Certain diseases, such as obesity and diabetes, can be present in the same individual concurrently, sometimes one disease being a significant risk factor for the other disease. The disease phenotypes themselves are normally the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Incidence Matrix
In mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation. If the first class is ''X'' and the second is ''Y'', the matrix has one row for each element of ''X'' and one column for each mapping from ''X'' to ''Y''. The entry in row ''x'' and column ''y'' is 1 if the vertex ''x'' is part of (called ''incident'' in this context) the mapping that corresponds to ''y'', and 0 if it is not. There are variations; see below. Graph theory Incidence matrix is a common graph representation in graph theory. It is different to an adjacency matrix, which encodes the relation of vertex-vertex pairs. Undirected and directed graphs In graph theory an undirected graph has two kinds of incidence matrices: unoriented and oriented. The ''unoriented incidence matrix'' (or simply ''incidence matrix'') of an undirected graph is a n\times m matrix ''B'', where ''n'' and ''m'' are the numbers of vertices and ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Laplace Transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex-valued frequency domain, also known as ''s''-domain, or ''s''-plane). The transform is useful for converting derivative, differentiation and integral, integration in the time domain into much easier multiplication and Division (mathematics), division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic equation, algebraic polynomial equations, and by simplifyin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nonlinear Circuit
A linear circuit is an electronic circuit which obeys the superposition principle. This means that the output of the circuit ''F(x)'' when a linear combination of signals ''ax1(t) + bx2(t)'' is applied to it is equal to the linear combination of the outputs due to the signals ''x1(t)'' and ''x2(t)'' applied separately: :F(ax_1 + bx_2) = aF(x_1) + bF(x_2)\, It is called a linear circuit because the output voltage and current of such a circuit are linear functions of its input voltage and current. This kind of linearity is not the same as that of straight-line graphs. In the common case of a circuit in which the components' values are constant and don't change with time, an alternate definition of linearity is that when a sinusoidal input voltage or current of frequency ''f'' is applied, any steady-state output of the circuit (the current through any component, or the voltage between any two points) is also sinusoidal with frequency ''f''. A linear circuit with constant comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Lumped-element Model
The lumped-element model (also called lumped-parameter model, or lumped-component model) is a simplified representation of a physical system or circuit that assumes all components are concentrated at a single point and their behavior can be described by idealized mathematical models. The lumped-element model simplifies the system or circuit behavior description into a topology. It is useful in electrical systems (including electronics), mechanical multibody systems, heat transfer, acoustics, etc. This is in contrast to distributed parameter systems or models in which the behaviour is distributed spatially and cannot be considered as localized into discrete entities. The simplification reduces the state space of the system to a finite dimension, and the partial differential equations (PDEs) of the continuous (infinite-dimensional) time and space model of the physical system into ordinary differential equations (ODEs) with a finite number of parameters. Electrical systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chemical Process
In a scientific sense, a chemical process is a method or means of somehow changing one or more chemicals or chemical compounds. Such a chemical process can occur by itself or be caused by an outside force, and involves a chemical reaction of some sort. In an "engineering" sense, a chemical process is a method intended to be used in manufacturing or on an industrial scale (see Industrial process) to change the composition of chemical(s) or material(s), usually using technology similar or related to that used in chemical plants or the chemical industry. Neither of these definitions are exact in the sense that one can always tell definitively what is a chemical process and what is not; they are practical definitions. There is also significant overlap in these two definition variations. Because of the inexactness of the definition, chemists and other scientists use the term "chemical process" only in a general sense or in the engineering sense. However, in the "process (engine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pipeline Transport
A pipeline is a system of Pipe (fluid conveyance), pipes for long-distance transportation of a liquid or gas, typically to a market area for consumption. The latest data from 2014 gives a total of slightly less than of pipeline in 120 countries around the world. The United States had 65%, Russia had 8%, and Canada had 3%, thus 76% of all pipeline were in these three countries. The main attribute to pollution from pipelines is caused by corrosion and leakage. ''Pipeline and Gas Journal''s worldwide survey figures indicate that of pipelines are planned and under construction. Of these, represent projects in the planning and design phase; reflect pipelines in various stages of construction. Liquids and gases are transported in pipelines, and any chemically stable substance can be sent through a pipeline. Pipelines exist for the transport of crude and refined petroleum, fuels—such as oil, natural gas and biofuels—and other fluids including sewage, slurry, water, beer, hot wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Biological Network
A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. In general, networks or graphs are used to capture relationships between entities or objects. A typical Graph theory, graphing representation consists of a set of Vertex (graph theory), nodes connected by Glossary of graph theory, edges. History of networks As early as 1736 Leonhard Euler analyzed a real-world issue known as the Seven Bridges of Königsberg, which established the foundation of graph theory. From the 1930s-1950s the study of random graphs were developed. During the mid 1990s, it was discovered that many different types of "real" networks have structural properties quite different from random networks. In the late 2000's, scale-free and small-world networks began shaping the emergence of systems biology, network biology, and network medicine. In 2014, graph theoretical methods were used by Frank Emmert-Streib to an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Network Theory
In mathematics, computer science, and network science, network theory is a part of graph theory. It defines networks as Graph (discrete mathematics), graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or directed graph, asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience. Applications of network theory include Logistics, logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.; see List of network theory topics for more examples. Euler's solution of the Seven Bridges of Königsberg, Seven Bridges of Königsberg problem is c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kirchhoff's Voltage Law
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of curre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kirchhoff's Current Law
Kirchhoff's circuit laws are two Equality (mathematics), equalities that deal with the Electric current, current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for Network analysis (electrical circuits), network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
