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Trip Distribution
Trip distribution (or destination choice or zonal interchange analysis) is the second component (after trip generation, but before mode choice and route assignment) in the traditional four-step transportation forecasting model. This step matches tripmakers’ origins and destinations to develop a “trip table”, a matrix that displays the number of trips going from each origin to each destination. Historically, this component has been the least developed component of the transportation planning model. Where: ''T'' ''ij'' = trips from origin ''i'' to destination ''j''. Note that the practical value of trips on the diagonal, e.g. from zone 1 to zone 1, is zero since no intra-zonal trip occurs. Work trip distribution is the way that travel demand models understand how people take jobs. There are trip distribution models for other (non-work) activities such as the choice of location for grocery shopping, which follow the same structure. History Over the years, model ...
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IMG SignR4492829
img or IMG is an abbreviation for image. img or IMG may also refer to: * IMG (company), global sports and media business headquartered in New York City but with its main offices in Cleveland, originally known as the "International Management Group", with divisions including: ** IMG Academy, an athletic training complex in Bradenton, Florida with facilities for multiple sports ** IMG Artists, a performing arts management company with multiple worldwide offices ** IMG College, a college sports marketing agency based in Winston-Salem, North Carolina ** IMG Models, a modeling agency based in New York * IMG (file format), the file extension of several different disk image formats which store a full digital representation (image) of disk drive or storage media * IMG, a prefix for camera image file names commonly used in Design rule for Camera File system * mg/code>, a tag used in BBCode to place an image * , an HTML element used to place an image; see * IMG Worlds of Adventure, the l ...
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Demographic Gravitation
Demographic gravitation is a concept of "social physics", introduced by Princeton University astrophysicist John Quincy Stewart in 1947.Stewart, John Q., "Demographic Gravitation: Evidence and Applications," ''Sociometry'', Vol. 11, No. 1/2. (February–May 1948), pp. 31–58. It is an attempt to use equations and notions of classical physics, such as gravity, to seek simplified insights and even laws of demographic behaviour for large numbers of human beings. A basic conception within it is that large numbers of people, in a city for example, actually behave as an attractive force for other people to migrate there. It has been related to W. J. Reilly's law of retail gravitation, George Kingsley Zipf's Demographic Energy, and to the theory of trip distribution through gravity models. Writing in the journal '' Sociometry'', Stewart set out an "agenda for social physics." Comparing the microscopic versus macroscopic viewpoints in the methodology of formulating physical laws ...
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Journal Of The American Institute Of Planners
The American Planning Association (APA) is a professional organization representing the field of urban planning in the United States. APA was formed in 1978, when two separate professional planning organizations, the American Institute of Planners and the American Society of Planning Officials, were merged into a single organization. The American Institute of Certified Planners is now the organization's professional branch. Functions Like many professional organizations, the American Planning Association's main function is to serve as a forum for the exchange of ideas between people who work in the field of urban planning. The organization keeps track of the various improvement efforts underway around the country, which may include the improvement or construction of new parks, highways and roads, or residential developments. The organization is also a starting point for people looking for employment. The association also publishes the ''Journal of the American Planning Asso ...
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Hypermobility (travel)
Hypermobile travelers are "highly mobile individuals" who take "frequent trips, often over great distances." They "account for a large share of the overall kilometres travelled, especially by air." These people contribute significantly to the overall amount of airmiles flown within a given society. Although concerns over hypermobility apply to several modes of transport, the environmental impact of aviation and especially its greenhouse gas emissions have brought particular focus on flying. Among the reasons for this focus is that these emissions, because they are made at high altitude, have a climate impact that is commonly estimated to be 2.7 higher than the same emissions if made at ground-level. Although the amount of time people have spent in motion has remained constant since 1950, the shift from feet and bicycles to cars and planes has increased the speed of travel fivefold. This results in the twin effects of wider and shallower regions of social activity around each person ...
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Environmental Impact Of Aviation
Like other emissions resulting from fossil fuel combustion, aircraft engines produce gases, noise, and particulates, raising environmental concerns over their global effects and their effects on local air quality. Jet airliners contribute to climate change by emitting carbon dioxide (), the best understood greenhouse gas, and, with less scientific understanding, nitrogen oxides, contrails and particulates. Their radiative forcing is estimated at 1.3–1.4 that of alone, excluding induced cirrus cloud with a very low level of scientific understanding. In 2018, global commercial operations generated 2.4% of all emissions. Jet airliners have become 70% more fuel efficient between 1967 and 2007, and emissions per revenue ton-kilometer (RTK) in 2018 were 47% of those in 1990. In 2018, emissions averaged 88 grams of per revenue passenger per km. While the aviation industry is more fuel efficient, overall emissions have risen as the volume of air travel has increas ...
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Marchetti's Constant
Marchetti's constant is the average time spent by a person for commuting each day. Its value is approximately one hour, or half an hour for a one-way trip. It is named after Italian physicist Cesare Marchetti, though Marchetti himself attributed the "one hour" finding to transportation analyst and engineer Yacov Zahavi. Marchetti posits that although forms of urban planning and transport may change, and although some live in villages and others in cities, people gradually adjust their lives to their conditions (including location of their homes relative to their workplace) such that the average travel time stays approximately constant. Ever since Neolithic times, people have kept the average time spent per day for travel the same, even though the distance may increase due to the advancements in the means of transportation. In his 1934 book '' Technics and Civilization'', Lewis Mumford attributes this observation to Bertrand Russell: :Mr. Bertrand Russell has noted that each impr ...
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Lowry Model
Land-use forecasting undertakes to project the distribution and intensity of trip generating activities in the urban area. In practice, land-use models are demand-driven, using as inputs the aggregate information on growth produced by an aggregate economic forecasting activity. Land-use estimates are inputs to the transportation planning process. The discussion of land-use forecasting to follow begins with a review of the Chicago Area Transportation Study (CATS) effort. CATS researchers did interesting work, but did not produce a transferable forecasting model, and researchers elsewhere worked to develop models. After reviewing the CATS work, the discussion will turn to the first model to be widely known and emulated: the Lowry model developed by Ira S. Lowry when he was working for the Pittsburgh Regional Economic Study. Second and third generation Lowry models are now available and widely used, as well as interesting features incorporated in models that are not widely use ...
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Stirling's Approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of n. It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: \ln(n!) = n\ln n - n +O(\ln n), where the big O notation means that, for all sufficiently large values of n, the difference between \ln(n!) and n\ln n-n will be at most proportional to the logarithm. In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to use instead the binary logarithm, giving the equivalent form \log_2 (n!) = n\log_2 n - n\log_2 e +O(\log_2 n). The error term in either base can be expressed more precisely as \tfrac12\log(2\pi n)+O(\tfrac1n), corresponding to an approximate formula for the factorial itself, n! \sim \sqrt\left(\frac\r ...
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Lagrangian Multipliers
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function. The method can be summarized as follows: in order to find the maximum or minimum of a function f(x) subjected to the equality constraint g(x) = 0, form the Lagrangian function :\mathcal(x, \lambda) = f(x) + \lambda g(x) and find the stationary points of \mathcal considered as a function of x and the Lagrange mu ...
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Boltzmann's Law
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerner, G. L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid. In the modern literature the term Boltzmann equation is often used in a more general sense, referring to any kinetic equation that describes the change of a macroscopic quantity in a thermodynamic system, such as energy, charge or particle number. The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the position ...
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Iterative Proportional Fitting
The iterative proportional fitting procedure (IPF or IPFP, also known as biproportional fitting or biproportion in statistics or economics (input-output analysis, etc.), RAS algorithm in economics, raking in survey statistics, and matrix scaling in computer science) is the operation of finding the fitted matrix X which is the closest to an initial matrix Z but with the row and column totals of a target matrix Y (which provides the constraints of the problem; the interior of Y is unknown). The fitted matrix being of the form X=PZQ, where P and Q are diagonal matrices such that X has the margins (row and column sums) of Y. Some algorithms can be chosen to perform biproportion. We have also the entropy maximization, information loss minimization (or cross-entropy) or RAS which consists of factoring the matrix rows to match the specified row totals, then factoring its columns to match the specified column totals; each step usually disturbs the previous step’s match, so these steps are ...
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Distance Decay
Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the distance is outside of the two locales' activity space, their interactions begin to decrease. It is thus an assertion that the mathematics of the inverse square law in physics can be applied to many geographic phenomena, and is one of the ways in which physics principles such as gravity are often applied metaphorically to geographic situations. Mathematical models Distance decay is graphically represented by a curving line that swoops concavely downward as distance along the x-axis increases. Distance decay can be mathematically represented as an inverse-square law by the expression I = const. \times d^ or I \propto 1/d^2, where is interaction and is distance. In practice, it is often parameterized to fit a specific situation, such ...
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