|
Random Sequential Adsorption
Random sequential adsorption (RSA) refers to a process where particles are randomly introduced in a system, and if they do not overlap any previously adsorbed particle, they adsorb and remain fixed for the rest of the process. RSA can be carried out in computer simulation, in a mathematical analysis, or in experiments. It was first studied by one-dimensional models: the attachment of pendant groups in a polymer chain by Paul Flory, and the car-parking problem by Alfréd Rényi. Other early works include those of Benjamin Widom. In two and higher dimensions many systems have been studied by computer simulation, including in 2d, disks, randomly oriented squares and rectangles, aligned squares and rectangles, various other shapes, etc. An important result is the maximum surface coverage, called the saturation coverage or the packing fraction. On this page we list that coverage for many systems. The blocking process has been studied in detail in terms of the ''random sequential a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic scale, microscopic particles like atoms and molecules, to macroscopic scale, macroscopic particles like powder (substance), powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion (physics), motion. The term ''particle'' is rather general in meaning, and is refined as needed by various scientific fields. Anything that is composed of particles may be referred to as being particulate. However, the noun ''particulates, particulate'' is most frequently ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions. Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compounds, produces unique physical properties including toughness, high elasticity, viscoelasticity, and a tendency to form amorphous and semicrystalline structures rather than crystals. The term "polymer" derives from the Greek word πολύς (''polus'', meaning "many, much") and μέρος (''meros'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Flory
Paul John Flory (June 19, 1910 – September 9, 1985) was an American chemist and Nobel laureate who was known for his work in the field of polymers, or macromolecules. He was a leading pioneer in understanding the behavior of polymers in solution, and won the Nobel Prize in Chemistry in 1974 "for his fundamental achievements, both theoretical and experimental, in the physical chemistry of macromolecules". Biography Personal life Flory was born in Sterling, Illinois, on June 19, 1910. He was raised by Ezra Flory and Nee Martha Brumbaugh. His father worked as a clergyman-educator, and his mother was a school teacher. He first gained his interest in science from Carl W Holl, who was a professor in chemistry. Holl was employed in Indiana at Manchester College as a chemistry professor. In 1936, he married Emily Catherine Tabor. He and Emily had three children together; Susan Springer, Melinda Groom and Paul John Flory jr. They also had five grandchildren. All of his children purs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic Bernhard Alexander; his uncle was Franz Alexander, a Hungarian-American psychoanalyst and physician. He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point, he was drafted to forced labour service, from which he escaped. He then completed his PhD in 1947 at the University of Szeged, under the advisement of Frigyes Riesz. He married Katalin Schulhof (who used Kató Rényi as her married name), herself a mathematician, in 1946; their daughter Zsuzsanna was bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benjamin Widom
Benjamin Widom (born 13 October 1927) is the Goldwin Smith Professor of Chemistry at Cornell University. His research interests include physical chemistry and statistical mechanics. In 1998, Widom was awarded the Boltzmann Medal "for his illuminating studies of the statistical mechanics of fluids and fluid mixtures and their interfacial properties, especially his clear and general formulation of scaling hypotheses for the equation of state and surface tensions of fluids near critical points." Academic background Widom was born in Newark, New Jersey. He graduated from New York City's Stuyvesant High School in 1945, and received his BA from Columbia University in 1949, followed by his PhD from Cornell in 1953. He became an instructor of chemistry at Cornell in 1954, was appointed assistant professor in 1955 and a full professor in 1963. He was chair of the chemistry department between 1978 and 1981. He was elected a member of the National Academy of Sciences in 1974 and a fell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Sequential Adsorption Disks1
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable.Strictly speaking, the frequency of an outcome will converge almost surely to a predictable value as the number of trials becomes arbitrarily large. Non-convergence or convergence to a different value is possible, but has probability zero. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy. The fields ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ilona Palásti
Ilona Palásti (1924–1991) was a Hungarian mathematician who worked at the Alfréd Rényi Institute of Mathematics. She is known for her research in discrete geometry, geometric probability, and the theory of random graphs. With Alfréd Rényi and others, she was considered to be one of the members of the Hungarian School of Probability. Contributions In connection to the Erdős distinct distances problem, Palásti studied the existence of point sets for which the ith least frequent distance occurs i times. That is, in such points there is one distance that occurs only once, another distance that occurs exactly two times, a third distance that occurs exactly three times, etc. For instance, three points with this structure must form an isosceles triangle. Any n evenly-spaced points on a line or circular arc also have the same property, but Paul Erdős asked whether this is possible for points in general position (no three on a line, and no four on a circle). Palásti found an eigh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Threshold
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in Randomness, random systems. Below the threshold a giant connected component (graph theory), connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified Lattice model (physics), lattice models of random systems or networks (Graph (discrete mathematics), graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability ''p'', or more generally a critical surface for a group of parameters ''p''1, ''p''2, ..., such that infinite connectivity (''percolation'') first occurs. Percolation models The most common percolation model is to take a regular lattice, like a squar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Sequential Adsorption Of Line Segments
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable.Strictly speaking, the frequency of an outcome will converge almost surely to a predictable value as the number of trials becomes arbitrarily large. Non-convergence or convergence to a different value is possible, but has probability zero. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy. The fields of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adsorption
Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a fluid (the ''absorbate'') is dissolved by or permeates a liquid or solid (the ''absorbent''). Adsorption is a '' surface phenomenon'', while absorption involves the whole volume of the material, although adsorption does often precede absorption. The term ''sorption'' encompasses both processes, while ''desorption'' is the reverse of it. Like surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent or metallic) of the constituent atoms of the material are fulfilled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Deposition
Particle deposition is the spontaneous attachment of particles to surfaces. The particles in question are normally colloidal particles, while the surfaces involved may be planar, curved, or may represent particles much larger in size than the depositing ones (e.g., sand grains). Deposition processes may be triggered by appropriate hydrodynamic flow conditions and favorable particle-surface interactions. Depositing particles may just form a monolayer which further inhibits additional particle deposition, and thereby one refers to ''surface blocking''. Initially attached particles may also serve as seeds for further particle deposition, which leads to the formation of thicker particle deposits, and this process is termed as ''surface ripening'' or ''fouling''. While deposition processes are normally irreversible, initially deposited particles may also detach. The latter process is known as ''particle release'' and is often triggered by the addition of appropriate chemicals or a modific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
