The differential equation and the general solution. The Bosanquet model applies for a simple liquid as in most situations the ink’s continuous phase can be. solutions to the Bosanquet and the Washburn equations were given by Schoelkopf et al. (15) for a range of capillary radii and for fluids of different properties. of Sorbie et al. by applying the equation of Bosanquet to a three-dimensional network model, Pore-Cor. All authors agree that, with the inclusion of inertial terms.
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In the theory of capillarity, Bosanquet equation is an improved modification of the simpler Lucas—Washburn theory for the motion of a liquid in a thin capillary tube or a porous material that can be approximated as a large collection of capillaries. In the Lucas—Washburn model, the inertia of the fluid is ignored, leading to the assumption that flow is continuous under constant viscous laminar Poiseuille flow conditions without considering effects of mass transport bosxnquet acceleration occurring at the start of flow and at points of changing internal capillary geometry.
The Bosanquet equation is a differential equation that is second-order in the time derivative, similar to Newton’s Second Lawand therefore takes into account the fluid inertia. Equations of motion, like the Washburn’s equation, that attempt to explain a velocity instead of acceleration as proportional to a driving force are often described with the term Aristotelian mechanics.
The solution of the Bosanquet equation can be split into two timescales, firstly to account for the initial motion of the fluid by considering a solution in the limit of time approaching 0 giving the form . For the condition of short time this shows a eqiation front position proportional to time rather than the Lucas-Washburn square root of time, and the independence of viscosity demonstrates plug flow.
As time increases after the initial time of acceleration, the equation decays to the familiar Lucas-Washburn form dependent on viscosity and the square root of time.
The Bosanquet equation is a differential equation that is second-order in the time derivative, similar to Newton’s Second Law, and therefore takes into account the equarion inertia. In physics, Washburn’s equation describes capillary flow in a bundle of parallel cylindrical tubes; it is extended with some issues also to imbibition into porous materials.
The equation is named after Edward Wight Washburn; also known as Lucas—Washburn equation, considering that Richard Lucas wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.
Cameron’s discovery of the form of the equation in This relationship, which holds true for a variety of situations, captures the essence of Lucas and Washburn’s equation and shows that capillary penetration and fluid transport squation porous Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits.
It is defined as the ratio of magnetomotive force mmf to magnetic flux. It represents equqtion opposition to magnetic flux, and depends on the geometry and composition of an object.
Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure bosanuet the vosanquet to the electric current. The definition of bosanqyet reluctance is analogous to Ohm’s law in this respect. However, magnetic flux bisanquet through a reluctance does not give rise to dissipation of heat as it does for current through a resistance.
Bsanquet, the analogy cannot be used for modelling energy flow in systems where energy crosses between the magnetic and electrical domains. An alternative analogy to the reluctance model which does correctly represent energy flows is the gyrator—capacitor model. Magnetic reluctance is a scalar extensive quantity, akin to electrical resistance. In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material.
As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media.
The permeability is a function of material type, and also varies with stress, temperature, etc.
Industrial air pollution source Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that include algorithms to solve the mathematical equations that govern the pollutant dispersion. The dispersion models are used to estimate the downwind ambient concentration of air pollutants or toxins emitted from sources such as industrial plants, vehicular traffic or accidental chemical releases.
They can also be used to predict future concentrations under specific scenarios i. Therefore, they are the dominant type of model used in air quality policy making. They are most useful for pollutants that are dispersed over large distances and that may react in the atmosphere.
For pollutants that have a very high spatio-temporal variability i. The ENIAC main control panel at the Moore School of Electrical Engineering The history of numerical weather prediction considers how current weather conditions as input into mathematical models of the atmosphere and oceans to predict the weather and future sea state the process of numerical weather prediction has changed over the years.
Though first attempted manually in the s, it was not until the advent of the computer and computer simulation that computation time was reduced to less than the forecast period itself. ENIAC was used to create the first forecasts via computer inand over the years more powerful computers have been used to increase the size of initial datasets as well as include more complicated versions of the equations of motion.
The development of global forecasting models led to the first climate models. The development of limited area regional models facilitated advances in forecasting the tracks of tropical cyclone as well as air quality in the s and s.
Roadway air dispersion is applied to highway segments Roadway air dispersion modeling is the study of air pollutant transport from a roadway or other linear emitter. Computer models are required to conduct this analysis, because of the complex variables involved, including vehicle emissions, vehicle speed, meteorology, and terrain geometry. Line source dispersion has been studied since at least the s, when the regulatory framework in the United States began requiring quantitative analysis of the air pollution consequences of major roadway and airport projects.
By the early s this subset of atmospheric dispersion models were being applied to real world cases of highway planning, even including some controversial court cases. How the model works The basic concept of the roadway air dispersion model is to calculate air pollutant levels in the vicinity of a highway or arterial roadway by considering them as line sources.
The model takes into account source characteristics such as traffic volume, vehicl Arcadia is a play by Tom Stoppard concerning the relationship between past and present, order and disorder, certainty and uncertainty. It has been praised by many critics as the finest play from one of the most significant contemporary playwrights in the English language. The activities of two modern scholars and the house’s current residents are juxtaposed with those of the people who lived there in the earlier period.
InThomasina Coverly, the daughter of the house, is a precocious teenager with ideas about mathematics, nature and physics well ahead of her time.
She studies with her tutor Septimus Hodge, a friend of Lord Byron an unseen guest in the house.
In the present, writer Hannah Jarvis and literature profe A cycloidal pendulum is isochronous, a fact discovered and proved by Christiaan Huygens under certain mathematical assumptions. Surprisingly, many of their discoveries later played prominent roles in physical theories, as in the case of the conic sections in celestial mechanics. The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since Antiquity, and more recently also by historians and educators.
In monetary economics the real bills doctrine refers to various theories in support of generally unrestricted issuing of ‘real bills’. They can be invoices for raw or wholesale goods to be paid to a supplier within a certain time window, i. Thus, they allow a manufacturer or retailer time eqjation receive income from the goods without the need for upfront payment or the need to borrow from a bank.
Bosanqhet the ‘real bills’ are sold on to a third party it is usually at a discount. It is part of debate on whether banks should be involved in controlling the money supply. Social liberalism also known as modern liberalism  is a political ideology and a variety of liberalism that endorses a market economy and the expansion bosanque civil and political rights while also believing that the legitimate role of the government includes addressing economic and social issues such as poverty, health care and education.
From a young age, Aris was interested in chemistry. Aris’s father owned a photo-finishing works, where he would experiment with chemicals and reactions. He attended St Martin’s, a small local kindergarten and moved to St Wulfran’s, a local preparatory school, now Queen Elizabeth’s School.
Here, he studied Latin, a skill much used later by him and he was encouraged to continue pursuit of his interest in chemistry. Because of his achievements, he was referred to the Reverend C. Canning, Headmaster of Canford School, a well-known public school, equahion to Wimborne. On the strength of this interview, equatlon was given a place in the newly created house that the school had provided for day-boarders.
The University of Oxford is bossanquet collegiate research university in Oxford, England. There is evidence of teaching as far back as , making it the oldest university in the English-speaking world and the world’s second-oldest university in continuous operation. The history and influence of the University of Oxford has made it one of the most prestigious universities in the world. The original cover of Thomas Hobbes’s work Leviathanin which he discusses the concept of the social contract theory In both moral and political philosophy, the social contract is a theory or model that originated during the Age of Enlightenment and usually concerns the legitimacy of the authority of the state over the individual.
Therefore, the relation between natural and legal rights is often a topic of social contract theory. The term takes its name from Bisanquet Social Bpsanquet French: Du contrat social ou Principes du droit politiquea book by Jean-Jacques Rousseau that discussed this concept. Although the antecedents of social contract theory are found in antiquity, in Greek and Stoic philosophy and Roman and Canon Law, An eponym is a person real or fictitious from whom something is said to take its name.
The word is back-formed from “eponymous”, from the Greek “eponymos” bosanqjet “giving name”. Here is a list of eponyms: A powder x-ray diffractometer in motion X-ray crystallography XRC is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal.
From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information. Since many materials can form crystals—such as salts, metals, minerals, semiconductors, as well as various inorganic, organic, and biological molecules—X-ray crystallography has been fundamental in the development of many scientific fields.
In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences among v The following outline is presented as an overview and topical guide to air pollution dispersion: Air pollution equuation — distribution of air pollution into the atmosphere. Air pollution is the introduction of particulates, biological molecules, or other harmful materials into Earth’s atmosphere, causing disease, death to humans, damage to other living organisms such as food crops, or the natural or built environment.
Air pollution may come from anthropogenic or equaiton sources. Dispersion refers to what happens to the pollution during and after its introduction; understanding this may help in identifying and controlling it. Air pollution dispersion has become the focus of environmental conservationists and governmental environmental protection agencies local, state, province and national of many countries which have adopted and used much of the terminology of this field in their laws and regulations regarding air pollution control.
Air pollution emission plumes Visualization of a buoyant Gaussian Socialism is a range of economic and social systems characterised by social ownership and workers’ self-management of the means of production as well as the political theories and movements associated with them.
Common ownership, where the entire society shares things Citizen ownership of equity, where the government or employee pension organizations own the stock of corporations in a market socialist ec Jeremy Bentham ; 15 February [O.
He advocated for individual and economic freedoms, the separation of church and state, freedom of expression, equal rights for women, the right to divorce, and the decriminalising of homosexual acts. Gottfried Wilhelm von Leibniz sometimes spelled Leibnitz ; German: Godefroi Guillaume Leibnitz; 1 July [O.
His most notable accomplishment was conceiving the ideas of differential and integral calculus, independently of Isaac Newton’s contemporaneous developments. It was only in bosajquet 20th century that Leibniz’s law of continuity and transcendental law of homogeneity found mathematical implementation by means of non-standard analysis. He became one of the most prolific inventors in the field of mechanical calculators.
While working on adding automatic multiplication and division to Pascal’s calculator, he was the first to describe a pinwheel calculator in  and invented the Leibn Hayek, was an Austrian economist and philosopher best known for his defense of classical liberalism. Hayek shared the Nobel Memorial Prize in Economic Sciences with Gunnar Myrdal for his equayion work in the theory of money and economic fluctuations and [