In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are uniform. Examples of physical properties include density, index of refraction and chemical composition. A simple description is that a phase is a region of material, chemically uniform, physically distinct, 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, the humid air is a third phase over the ice and water; the glass of the jar is another separate phase. 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; 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. Because phase boundaries relate to changes in the organization of matter, such as a change from liquid to solid or a more subtle change from one crystal structure to another, this latter usage is similar to the use of "phase" as a synonym for state of matter.
However, the state of matter and phase diagram usages are not commensurate with the formal definition given above and the intended meaning must be determined in part from the context in which the term is used. Distinct phases may be described as different states of matter such as gas, solid, plasma or Bose–Einstein condensate. Useful mesophases between solid and liquid form other states of matter. Distinct phases may exist within a given state of matter; as shown in the diagram for iron alloys, several phases exist for both the liquid states. Phases may be differentiated based on solubility as in polar or non-polar. A mixture of water and oil will spontaneously separate into two phases. Water has a low solubility in oil, oil has a low solubility in water. Solubility is the maximum amount of a solute that can dissolve in a solvent before the solute ceases to dissolve and remains in a separate phase. A mixture can separate into more than two liquid phases and the concept of phase separation extends to solids, i.e. solids can form solid solutions or crystallize into distinct crystal phases.
Metal pairs that are mutually soluble can form alloys, whereas metal pairs that are mutually insoluble cannot. As many as eight immiscible liquid phases have been observed. Mutually immiscible liquid phases are formed from water, hydrophobic organic solvents, silicones, several different metals, from molten phosphorus. Not all organic solvents are miscible, e.g. a mixture of ethylene glycol and toluene may separate into two distinct organic phases. Phases do not need to macroscopically separate spontaneously. Emulsions and colloids are examples of immiscible phase pair combinations that do not physically separate. Left to equilibration, many compositions will form a uniform single phase, but depending on the temperature and pressure a single substance may separate into two or more distinct phases. Within each phase, the properties are uniform but between the two phases properties differ. Water in a closed jar with an air space over it forms a two phase system. Most of the water is in the liquid phase, where it is held by the mutual attraction of water molecules.
At equilibrium molecules are in motion and, once in a while, a molecule in the liquid phase gains enough kinetic energy to break away from the liquid phase and enter the gas phase. Every once in a while a vapor molecule collides with the liquid surface and condenses into the liquid. At equilibrium and condensation processes balance and there is no net change in the volume of either phase. At room temperature and pressure, the water jar reaches equilibrium when the air over the water has a humidity of about 3%; this percentage increases. At 100 °C and atmospheric pressure, equilibrium is not reached. If the liquid is heated a little over 100 °C, the transition from liquid to gas will occur not only at the surface, but throughout the liquid volume: the water boils. For a given composition, only certain phases are possible at pressure; the number and type of phases that will form is hard to predict and is determined by experiment. The results of such experiments can be plotted in phase diagrams; the phase diagram shown here is for a single component system.
In this simple system, which phases that are possible depends only on pressure and temperature. The markings show points. At temperatures and pressures away from the markings, there will be only one phase at equilibrium. In the diagram, the blue line marking the boundary between liquid and gas does not continue indefinitely, but terminates at a point called the critical point; as the temperature and pressure approach the critical point, the properties of the liquid and gas become progressively more similar. At the critical point, the liquid and gas become indistinguishable. Above the critical point, there are no longer separate liquid and gas phases: there is only a generic fluid phase referred to as a supercritical fluid. In water, the critical point occurs at 22.064 MPa. An unusual feature of the water phase diagram is that the solid–liquid phase line has a negative slope. For most substances, the slope is positive; this unusual feature of water is related to ice having a lowe
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883. Through consideration of this set and others helped lay the foundations of modern point-set topology. Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle third of a line segment and repeating the process with the remaining shorter segments. Cantor himself mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set, nowhere dense; the Cantor ternary set C is created by iteratively deleting the open middle third from a set of line segments. One starts by deleting the open middle third from the interval, leaving two line segments: ∪. Next, the open middle third of each of these remaining segments is deleted, leaving four line segments: ∪ ∪ ∪.
This process is continued ad infinitum, where the nth set is C n = C n − 1 3 ∪ for n ≥ 1, C 0 =. The Cantor ternary set contains all points in the interval that are not deleted at any step in this infinite process: C:= ⋂ n = 1 ∞ C n; the first six steps of this process are illustrated below. Using the idea of self-similar transformations, T L = x / 3, T R = / 3 and C n = T L ∪ T R, the explicit closed formulas for the Cantor set are C = ∖ ⋃ n = 1 ∞ ⋃ k = 0 3 n − 1, where every middle third is removed as the open interval from the closed interval = surrounding it, or C = ⋂ n = 1 ∞ ⋃ k = 0 3 n − 1 − 1 ( ∪ [ 3 k + 2
Diffusion-limited aggregation is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T. A. Witten Jr. and L. M. Sander in 1981, is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, dielectric breakdown; the clusters formed in DLA processes are referred to as Brownian trees. These clusters are an example of a fractal. In 2D these fractals exhibit a dimension of 1.71 for free particles that are unrestricted by a lattice, however computer simulation of DLA on a lattice will change the fractal dimension for a DLA in the same embedding dimension. Some variations are observed depending on the geometry of the growth, whether it be from a single point radially outward or from a plane or line for example. Two examples of aggregates generated using a microcomputer by allowing random walkers to adhere to an aggregate are shown on the right.
Computer simulation of DLA is one of the primary means of studying this model. Several methods are available to accomplish this. Simulations can be done on a lattice of any desired geometry of embedding dimension or the simulation can be done more along the lines of a standard molecular dynamics simulation where a particle is allowed to random walk until it gets within a certain critical range whereupon it is pulled onto the cluster. Of critical importance is that the number of particles undergoing Brownian motion in the system is kept low so that only the diffusive nature of the system is present; the intricate and organic forms that can be generated with diffusion-limited aggregation algorithms have been explored by artists. Simutils, part of the toxiclibs open source library for the Java programming language developed by Karsten Schmidt, allows users to apply the DLA process to pre-defined guidelines or curves in the simulation space and via various other parameters dynamically direct the growth of 3D forms.
A collision is the event in which two or more bodies exert forces on each other in about a short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force; some examples of physical interactions that scientists would consider collisions are the following: When an insect lands on a plant's leaf, its legs are said to collide with the leaf. When a cat strides across a lawn, each contact that its paws make with the ground is considered a collision, as well as each brush of its fur against a blade of grass; when a boxer throws a punch, their fist is said to collide with the opponent's body. When an astronomical object merges with a black hole, they are considered to collide; some colloquial uses of the word collision are the following: A traffic collision involves at least one automobile. A mid-air collision occurs between airplanes. A ship collision involves at least two moving maritime vessels hitting each other.
Collision is short-duration interaction between two bodies or more than two bodies causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces; the magnitude of the velocity difference just before impact is called the closing speed. All collisions conserve momentum. What distinguishes different types of collisions is whether they conserve kinetic energy; the Line of impact is the line, colinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, Newton's coefficient of restitution is defined only along this line. Collisions are of three types, they are: 1.perfectly elastic collision 2.inelastic collision 3.perfectly inelastic collision. Collisions can either be elastic, meaning they conserve both momentum and kinetic energy, or inelastic, meaning they conserve momentum but not kinetic energy. An inelastic collision is sometimes called a plastic collision.
A “perfectly inelastic” collision is a limiting case of inelastic collision in which the two bodies stick together after impact. The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution, a value that ranges between zero and one. A elastic collision has a coefficient of restitution of one. There are two types of collisions between two bodies - 1) Head-on collisions or one-dimensional collisions - where the velocity of each body just before impact is along the line of impact, 2) Non-head-on collisions, oblique collisions or two-dimensional collisions - where the velocity of each body just before impact is not along the line of impact. According to the coefficient of restitution, there are two special cases of any collision as written below: A elastic collision is defined as one in which there is no loss of kinetic energy in the collision. In reality, any macroscopic collision between objects will convert some kinetic energy to internal energy and other forms of energy, so no large-scale impacts are elastic.
However, some problems are sufficiently close to elastic that they can be approximated as such. In this case, the coefficient of restitution equals one. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. In this case, coefficient of restitution does not equal one. In any type of collision there is a phase when for a moment colliding bodies have the same velocity along the line of impact; the kinetic energy of bodies reduces to its minimum during this phase and may be called a maximum deformation phase for which momentarily the coefficient of restitution becomes one. Collisions in ideal gases approach elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force; some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are elastic.
Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions. In maritime law, it is desirable to distinguish between the situation of a vessel striking a moving object, that of it striking a stationary object; the word "allision" is used to mean the striking of a stationary object, while "collision" is used to mean the striking of a moving object. So when two vessels run against each other, it is called collision whereas when one vessel ran against another, it is considered allision; the fixed object could include a bridge or dock. While there is no huge difference between the two terminologies and they are used interchangeably, it is important to determine the difference because it helps clarify the circumstances of emergencies and adapt accordingly. In the case of Vane Line Bunkering, Inc. v. Natalie D M/V, it was established that there was the presumption that the moving vessel is at fault, stating that "presumption derives from the common-sense observation that moving vessels do not collide with stationary objects unless the vessel is mishandled in
In mathematics, more in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern changes with the scale at which it is measured. It has been characterized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently from the space it is embedded in; the essential idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions. In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastline's measured length changes with the length of the measuring stick used. In terms of that notion, the fractal dimension of a coastline quantifies how the number of scaled measuring sticks required to measure the coastline changes with the scale applied to the stick. There are several formal mathematical definitions of fractal dimension that build on this basic concept of change in detail with change in scale.
The term fractal dimension became the phrase that Mandelbrot himself became most comfortable with respect to encapsulating the meaning of the word fractal, a term he created. After several iterations over years, Mandelbrot settled on this use of the language: "...to use fractal without a pedantic definition, to use fractal dimension as a generic term applicable to all the variants."One non-trivial example is the fractal dimension of a Koch snowflake. It has a topological dimension of 1, but it is by no means a rectifiable curve: the length of the curve between any two points on the Koch snowflake is infinite. No small piece of it is line-like, but rather it is composed of an infinite number of segments joined at different angles; the fractal dimension of a curve can be explained intuitively thinking of a fractal line as an object too detailed to be one-dimensional, but too simple to be two-dimensional. Therefore its dimension might best be described not by its usual topological dimension of 1 but by its fractal dimension, a number between one and two.
A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. Several types of fractal dimension can be measured empirically. Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract to practical phenomena, including turbulence, river networks, urban growth, human physiology and market trends; the essential idea of fractional or fractal dimensions has a long history in mathematics that can be traced back to the 1600s, but the terms fractal and fractal dimension were coined by mathematician Benoit Mandelbrot in 1975. Fractal dimensions were first applied as an index characterizing complicated geometric forms for which the details seemed more important than the gross picture. For sets describing ordinary geometric shapes, the theoretical fractal dimension equals the set's familiar Euclidean or topological dimension. Thus, it is 0 for sets describing points.
But this changes for fractal sets. If the theoretical fractal dimension of a set exceeds its topological dimension, the set is considered to have fractal geometry. Unlike topological dimensions, the fractal index can take non-integer values, indicating that a set fills its space qualitatively and quantitatively differently from how an ordinary geometrical set does. For instance, a curve with a fractal dimension near to 1, say 1.10, behaves quite like an ordinary line, but a curve with fractal dimension 1.9 winds convolutedly through space nearly like a surface. A surface with fractal dimension of 2.1 fills space much like an ordinary surface, but one with a fractal dimension of 2.9 folds and flows to fill space rather nearly like a volume. This general relationship can be seen in the two images of fractal curves in Fig.2 and Fig. 3 – the 32-segment contour in Fig. 2, convoluted and space filling, has a fractal dimension of 1.67, compared to the perceptibly less complex Koch curve in Fig. 3, which has a fractal dimension of 1.26.
The relationship of an increasing fractal dimension with space-filling might be taken to mean fractal dimensions measure density, but, not so. Instead, a fractal dimension measures complexity, a concept related to certain key features of fractals: self-similarity and detail or irregularity; these features are evident in the two examples of fractal curves. Both are curves with topological dimension of 1, so one might hope to be able to measure their length or slope, as with ordinary lines, but we cannot do either of these things, because fractal curves have complexity in the form of self-similarity and detail that ordinary lines lack. The self-similarity lies in the infinite scaling, the detail in the defining elements of each set; the length between any two points on these curves is undefined because the curves are theoretical constructs that never stop repeating themselves. Every smaller piece is composed of an infinite number of scaled segments that look like the first iteration; these are not rectifiable curves, meaning they cannot be measured by being broken down into many segments approximating their respective lengths.
They cannot be cha
International Standard Serial Number
An International Standard Serial Number is an eight-digit serial number used to uniquely identify a serial publication, such as a magazine. The ISSN is helpful in distinguishing between serials with the same title. ISSN are used in ordering, interlibrary loans, other practices in connection with serial literature; the ISSN system was first drafted as an International Organization for Standardization international standard in 1971 and published as ISO 3297 in 1975. ISO subcommittee TC 46/SC 9 is responsible for maintaining the standard; when a serial with the same content is published in more than one media type, a different ISSN is assigned to each media type. For example, many serials are published both in electronic media; the ISSN system refers to these types as electronic ISSN, respectively. Conversely, as defined in ISO 3297:2007, every serial in the ISSN system is assigned a linking ISSN the same as the ISSN assigned to the serial in its first published medium, which links together all ISSNs assigned to the serial in every medium.
The format of the ISSN is an eight digit code, divided by a hyphen into two four-digit numbers. As an integer number, it can be represented by the first seven digits; the last code digit, which may be 0-9 or an X, is a check digit. Formally, the general form of the ISSN code can be expressed as follows: NNNN-NNNC where N is in the set, a digit character, C is in; the ISSN of the journal Hearing Research, for example, is 0378-5955, where the final 5 is the check digit, C=5. To calculate the check digit, the following algorithm may be used: Calculate the sum of the first seven digits of the ISSN multiplied by its position in the number, counting from the right—that is, 8, 7, 6, 5, 4, 3, 2, respectively: 0 ⋅ 8 + 3 ⋅ 7 + 7 ⋅ 6 + 8 ⋅ 5 + 5 ⋅ 4 + 9 ⋅ 3 + 5 ⋅ 2 = 0 + 21 + 42 + 40 + 20 + 27 + 10 = 160 The modulus 11 of this sum is calculated. For calculations, an upper case X in the check digit position indicates a check digit of 10. To confirm the check digit, calculate the sum of all eight digits of the ISSN multiplied by its position in the number, counting from the right.
The modulus 11 of the sum must be 0. There is an online ISSN checker. ISSN codes are assigned by a network of ISSN National Centres located at national libraries and coordinated by the ISSN International Centre based in Paris; the International Centre is an intergovernmental organization created in 1974 through an agreement between UNESCO and the French government. The International Centre maintains a database of all ISSNs assigned worldwide, the ISDS Register otherwise known as the ISSN Register. At the end of 2016, the ISSN Register contained records for 1,943,572 items. ISSN and ISBN codes are similar in concept. An ISBN might be assigned for particular issues of a serial, in addition to the ISSN code for the serial as a whole. An ISSN, unlike the ISBN code, is an anonymous identifier associated with a serial title, containing no information as to the publisher or its location. For this reason a new ISSN is assigned to a serial each time it undergoes a major title change. Since the ISSN applies to an entire serial a new identifier, the Serial Item and Contribution Identifier, was built on top of it to allow references to specific volumes, articles, or other identifiable components.
Separate ISSNs are needed for serials in different media. Thus, the print and electronic media versions of a serial need separate ISSNs. A CD-ROM version and a web version of a serial require different ISSNs since two different media are involved. However, the same ISSN can be used for different file formats of the same online serial; this "media-oriented identification" of serials made sense in the 1970s. In the 1990s and onward, with personal computers, better screens, the Web, it makes sense to consider only content, independent of media; this "content-oriented identification" of serials was a repressed demand during a decade, but no ISSN update or initiative occurred. A natural extension for ISSN, the unique-identification of the articles in the serials, was the main demand application. An alternative serials' contents model arrived with the indecs Content Model and its application, the digital object identifier, as ISSN-independent initiative, consolidated in the 2000s. Only in 2007, ISSN-L was defined in the
Marian Smoluchowski was a Polish physicist who worked in the Polish territories of the Austro-Hungarian Empire. He was a pioneer of statistical physics, an avid mountaineer. Born into an upper-class family in Vorder-Brühl, near Vienna, Smoluchowski studied physics at the University of Vienna, his teachers included Joseph Stefan. Ludwig Boltzmann held a position at Munich University during Smoluchowski's studies in Vienna, Boltzmann returned to Vienna in 1894 when Smoluchowski was serving in the Austrian army, they had no direct contact, although Smoluchowski's work follows in the tradition of Boltzmann's ideas. After several years at other universities, in 1899 Smoluchowski moved to Lwów, where he took a position at the University of Lwów, he was president of the Polish Copernicus Society of Naturalists, 1906–7. In 1913 Smoluchowski moved to Kraków to take over a chair in the Experimental Physics Department, succeeding August Witkowski, who had long envisioned Smoluchowski as his successor; when World War I began the following year, the work conditions became unusually difficult, as the spacious and modern Physics Department building, built by Witkowski a short time before, was turned into a military hospital.
The possibility of working in that building had been one of the reasons Smoluchowski had decided to move to Kraków. Smoluchowski was now forced to work in the apartment of the late Professor Karol Olszewski. During his lectures in experimental physics, use of the simplest demonstration equipment was impossible. Smoluchowski lectured in experimental physics. Smoluchowski was a member of the Copernicus Society of Natural Scientists and the Polish Academy of Sciences and Letters, his non-professional interests included skiing, mountain climbing in the Alps and the Tatra Mountains, watercolor painting, playing the piano. Smoluchowski died in Kraków in victim of a dysentery epidemic. Professor Władysław Natanson wrote in an obituary of Smoluchowski: "With great pleasure I recall the charm of his life, his noble cordiality, combined with exquisite kindness. I wish I could render the curious appeal of his personality, recall how temperate he was, how modest and elegantly diffident, yet always full of a pure, spontaneous joy."In 1901 he had married Zofia Baraniecka, who survived him.
They had Aldona Smoluchowska and Roman Smoluchowski. Roman became a notable physicist who worked in Poland, after World War II settled in the United States. Smoluchowski conducted fundamental research on the kinetic theory of matter. In 1904 he discovered density fluctuations in the gas phase, in 1908 he was the first physicist to ascribe the phenomenon of critical opalescence to large density fluctuations, his investigations explained the blue color of the sky as a consequence of light scattering in the atmosphere. In 1906, shortly after Albert Einstein, he independently explained Brownian motion. Smoluchowski presented an equation. In 1916 he proposed the equation for diffusion in an external potential field; this equation bears his name. Einstein–Smoluchowski relation Feynman-Smoluchowski ratchet List of Poles Probability Smoluchowski coagulation equation Smoluchowski factor Statistics A. Teske, Marian Smoluchowski, Leben und Werk. Polish Academy of Sciences, Warsaw, 1977. A. Einstein and M. von Smoluchowski: "Untersuchungen über die Theorie der Brownschen Bewegung.
Abhandlung über die Brownsche Bewegung und verwandte Erscheinungen", Harri Deutsch, 1997.. ISBN 3-8171-3207-7. S. Chandrasekhar, M. Kac, R. Smoluchowski, "Marian Smoluchowski - his life and scientific work", ed. by R. S. Ingarden, PWN, Warszawa 1999. E. Seneta Marian Smoluchowski, Statisticians of the Centuries pp. 299–302. New York: Springer. S. Ulam Marian Smoluchowski and the Theory of Probabilities in Physics, American Journal of Physics, 25, 475-481. Abraham Pais, Subtle is the chapter 5, section 5e. Einstein and Smoluchowski. Umcs.lublin.pl Chronological Table of Marian Smoluchowski's Life, M. Smoluchowski's Writings in 3 Volumes O'Connor, John J.. A. Fuliński: On Marian Smoluchowski's life and contribution to physics pdf file, Acta Phys. Polonica B, Vol. 29, No 6, pp. 1523–1537 internet version of Wielka Encyklopedia Tatrzańska, entry Marian Smoluchowski, after Zofia i Witold H. Paryscy, Wielka Encyklopedia Tatrzańska, 1995, 2004, ISBN 83-7104-009-1 Media related to Marian Smoluchowski at Wikimedia Commons