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Avrami Equation
The Avrami equation describes how solids transform from one phase to another at constant temperature. It can specifically describe the kinetics of crystallisation, can be applied generally to other changes of phase in materials, like chemical reaction rates, and can even be meaningful in analyses of ecological systems. The equation is also known as the Johnson– Mehl– Avrami–Kolmogorov (JMAK) equation. The equation was first derived by Johnson, Mehl, Avrami and Kolmogorov (in russian) in a series of articles published in the Journal of Chemical Physics between 1939 and 1941. Moreover, Kolmogorov treated statistically the crystallization of a solid in 1937 (in russian, Kolmogorov, A. N., Izv. Akad. Nauk. SSSR., 1937, 3, 355). Transformation kinetics Transformations are often seen to follow a characteristic s-shaped, or sigmoidal, profile where the transformation rates are low at the beginning and the end of the transformation but rapid in between. The initial slow rate c ...
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Avrami Equation
The Avrami equation describes how solids transform from one phase to another at constant temperature. It can specifically describe the kinetics of crystallisation, can be applied generally to other changes of phase in materials, like chemical reaction rates, and can even be meaningful in analyses of ecological systems. The equation is also known as the Johnson– Mehl– Avrami–Kolmogorov (JMAK) equation. The equation was first derived by Johnson, Mehl, Avrami and Kolmogorov (in russian) in a series of articles published in the Journal of Chemical Physics between 1939 and 1941. Moreover, Kolmogorov treated statistically the crystallization of a solid in 1937 (in russian, Kolmogorov, A. N., Izv. Akad. Nauk. SSSR., 1937, 3, 355). Transformation kinetics Transformations are often seen to follow a characteristic s-shaped, or sigmoidal, profile where the transformation rates are low at the beginning and the end of the transformation but rapid in between. The initial slow rate c ...
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Grain Boundary
In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship. High and low angle boundaries It is convenient to categorize grain boundaries according to the extent of misorientation between the two grains. ''Low-angle grain boundaries'' (''LAGB'') or ''subgrain boundaries'' are those with a misorientation less than about 15 degrees. Generally speaking they are composed of a ...
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Fractal Geometry
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere is ...
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Gastric Cancer
Stomach cancer, also known as gastric cancer, is a cancer that develops from the lining of the stomach. Most cases of stomach cancers are gastric carcinomas, which can be divided into a number of subtypes, including gastric adenocarcinomas. Lymphomas and mesenchymal tumors may also develop in the stomach. Early symptoms may include heartburn, upper abdominal pain, nausea, and loss of appetite. Later signs and symptoms may include weight loss, yellowing of the skin and whites of the eyes, vomiting, difficulty swallowing, and blood in the stool, among others. The cancer may spread from the stomach to other parts of the body, particularly the liver, lungs, bones, lining of the abdomen, and lymph nodes. The most common cause is infection by the bacterium ''Helicobacter pylori'', which accounts for more than 60% of cases. Certain types of ''H. pylori'' have greater risks than others. Smoking, dietary factors such as pickled vegetables and obesity are other risk factors. About 10% ...
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Neoplastic Transformation
Carcinogenesis, also called oncogenesis or tumorigenesis, is the formation of a cancer, whereby normal cells are transformed into cancer cells. The process is characterized by changes at the cellular, genetic, and epigenetic levels and abnormal cell division. Cell division is a physiological process that occurs in almost all tissues and under a variety of circumstances. Normally, the balance between proliferation and programmed cell death, in the form of apoptosis, is maintained to ensure the integrity of tissues and organs. According to the prevailing accepted theory of carcinogenesis, the somatic mutation theory, mutations in DNA and epimutations that lead to cancer disrupt these orderly processes by interfering with the programming regulating the processes, upsetting the normal balance between proliferation and cell death. This results in uncontrolled cell division and the evolution of those cells by natural selection in the body. Only certain mutations lead to cancer ...
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Mutation
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitosis, or meiosis or other types of damage to DNA (such as pyrimidine dimers caused by exposure to ultraviolet radiation), which then may undergo error-prone repair (especially microhomology-mediated end joining), cause an error during other forms of repair, or cause an error during replication (translesion synthesis). Mutations may also result from insertion or deletion of segments of DNA due to mobile genetic elements. Mutations may or may not produce detectable changes in the observable characteristics (phenotype) of an organism. Mutations play a part in both normal and abnormal biological processes including: evolution, cancer, and the development of the immune system, including junctional diversity. Mutation is the ultimate source o ...
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Gompertz Curve
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the curve than the left-side or lower valued asymptote. This is in contrast to the Logistic function, simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regard to detailing populations. History Benjamin Gompertz (1779–1865) was an actuary in London who was privately educated. He was elected a fellow of the Royal Society in 1819. The function was first presented in his June 16, 1825 paper at the bottom of page 518. The G ...
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Biophysics
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology. The term ''biophysics'' was originally introduced by Karl Pearson in 1892.Roland Glaser. Biophysics: An Introduction'. Springer; 23 April 2012. . The term ''biophysics'' is also regularly used in academia to indicate the study of the physical quantities (e.g. electric current, temperature, stress, entropy) in biological systems. Other biological sciences also perform research on the biophysical properties of living organisms including molecular biology, cell biology, chemical biology, and biochemistry. Overview ...
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Cancer
Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body. These contrast with benign tumors, which do not spread. Possible signs and symptoms include a lump, abnormal bleeding, prolonged cough, unexplained weight loss, and a change in bowel movements. While these symptoms may indicate cancer, they can also have other causes. Over 100 types of cancers affect humans. Tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity or excessive drinking of alcohol. Other factors include certain infections, exposure to ionizing radiation, and environmental pollutants. In the developing world, 15% of cancers are due to infections such as ''Helicobacter pylori'', hepatitis B, hepatitis C, human papillomavirus infection, Epstein–Barr virus and human immunodeficiency virus (HIV). These factors act, at least partly, by changing the genes of ...
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Nucleation
In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled (at atmospheric pressure) below 0°C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0°C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay. Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immedi ...
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Phase (matter)
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See ) The term ''phase'' is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the term ''phase'' is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Bec ...
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Nucleation
In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled (at atmospheric pressure) below 0°C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0°C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay. Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immedi ...
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