Bühlmann Decompression Algorithm
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Bühlmann Decompression Algorithm
The Bühlmann decompression algorithm is a mathematical model (algorithm) of the way in which inert gases enter and leave the human body as the ambient pressure changes. Versions are used to create Bühlmann decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time. These decompression tables allow divers to plan the depth and duration for dives and the required decompression stops. The algorithm was developed by Swiss physician Dr. Albert A. Bühlmann, who did research into decompression theory at the Laboratory of Hyperbaric Physiology at the University Hospital in Zürich, Switzerland. The results of Bühlmann's research that began in 1959 were published in a 1983 German book whose English translation was entitled ''Decompression-Decompression Sickness''. The book was regarded as the most complete public reference on decompression calculations and was used soon after in dive computer algorithms. The ...
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Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ...
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Exponential Decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N. The solution to this equation (see derivation below) is: :N(t) = N_0 e^, where is the quantity at time , is the initial quantity, that is, the quantity at time . Measuring rates of decay Mean lifetime If the decaying quantity, ''N''(''t''), is the number of discrete elements in a certain set, it is possible to compute the average length of time that an element remains in the set. This is called the mean lifetime (or simply the lifetime), where the exponential time constant, \tau, relates to the decay rate constant, λ, in the following way: :\tau = \frac. The mean lifetime can be looked at as a ...
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No Decompression Limit
The practice of decompression by divers comprises the planning and monitoring of the profile indicated by the algorithms or tables of the chosen decompression model, to allow asymptomatic and harmless release of excess inert gases dissolved in the tissues as a result of breathing at ambient pressures greater than surface atmospheric pressure, the equipment available and appropriate to the circumstances of the dive, and the procedures authorized for the equipment and profile to be used. There is a large range of options in all of these aspects. Decompression may be continuous or staged, where the ascent is interrupted by stops at regular depth intervals, but the entire ascent is part of the decompression, and ascent rate can be critical to harmless elimination of inert gas. What is commonly known as no-decompression diving, or more accurately no-stop decompression, relies on limiting ascent rate for avoidance of excessive bubble formation. Staged decompression may include deep st ...
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Sub-Aqua Association
The Sub-Aqua Association or SAA is a diver training organization for scubadivers in the United Kingdom. The SAA and other UK-based diving groups have traditionally used a club-based system with unpaid instructors, while other training agencies organise most of their training programs through professional instructors and dive shops. The other major club-based diving organizations in the UK are the British Sub-Aqua Club (BSAC) and the Scottish Sub Aqua Club, and the principal non-club-based organisation is PADI. History The Sub-Aqua Association was created in 1976 to represent diving clubs outside of the BSAC branch structure. Its training structure is based on the BSAC levels and offers a full range of diving qualifications. The association is made up of independent clubs, while the BSAC is a single club with many branches. Training Sub-Aqua Association member clubs maintain their independence and individual clubs organize diving programs and instruction according to the nat ...
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Gradient Factor
Decompression theory is the study and modelling of the transfer of the inert gas component of breathing gases from the gas in the lungs to the tissues and back during exposure to variations in ambient pressure. In the case of underwater diving and compressed air work, this mostly involves ambient pressures greater than the local surface pressure, but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure, are generally exposed to ambient pressures less than standard sea level atmospheric pressure. In all cases, the Decompression sickness, symptoms caused by decompression occur during or within a relatively short period of hours, or occasionally days, after a significant pressure reduction. The term "decompression" derives from the reduction in ambient pressure experienced by the organism and refers to both the reduction in pressure and the process of allowing dissolved inert gases to be eliminated from the Tissue (biolog ...
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Decompression Practice
The practice of decompression by divers comprises the planning and monitoring of the profile indicated by the algorithms or tables of the chosen decompression model, to allow asymptomatic and harmless release of excess inert gases dissolved in the tissues as a result of breathing at ambient pressures greater than surface atmospheric pressure, the equipment available and appropriate to the circumstances of the dive, and the procedures authorized for the equipment and profile to be used. There is a large range of options in all of these aspects. Decompression may be continuous or staged, where the ascent is interrupted by stops at regular depth intervals, but the entire ascent is part of the decompression, and ascent rate can be critical to harmless elimination of inert gas. What is commonly known as no-decompression diving, or more accurately no-stop decompression, relies on limiting ascent rate for avoidance of excessive bubble formation. Staged decompression may include deep st ...
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Mediterranean Sea
The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin and almost completely enclosed by land: on the north by Western and Southern Europe and Anatolia, on the south by North Africa, and on the east by the Levant. The Sea has played a central role in the history of Western civilization. Geological evidence indicates that around 5.9 million years ago, the Mediterranean was cut off from the Atlantic and was partly or completely desiccated over a period of some 600,000 years during the Messinian salinity crisis before being refilled by the Zanclean flood about 5.3 million years ago. The Mediterranean Sea covers an area of about , representing 0.7% of the global ocean surface, but its connection to the Atlantic via the Strait of Gibraltar—the narrow strait that connects the Atlantic Ocean to the Mediterranean Sea and separates the Iberian Peninsula in Europe from Morocco in Africa—is only wide. The Mediterranean Sea e ...
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Half Time (physics)
In several team sports, matches are played in two halves. Half-time (also written halftime or half time) is the name given to the interval between the two halves of the match. Typically, after half-time, teams swap ends of the field of play in order to reduce any advantage that may be gained from wind or a slope to the playing surface, for example. While it exists mainly to allow competitors to rest briefly and recover from the play of the first half, half-time also serves a number of other purposes. It also serves as an intermission for spectators, and it often features entertainment, such as cheerleading performances, tifos, performances by school marching bands (particularly in high school and collegiate sports in North America), or concerts featuring popular music acts (particularly in major events such as the Super Bowl). On games that are broadcast on television and radio, it also provides broadcasters with an opportunity to give a recap of the first half of the game, air ...
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Shell Oil Company
Shell USA, Inc. (formerly Shell Oil Company, Inc.) is the United States-based wholly owned subsidiary of Shell plc, a UK-based transnational corporation " oil major" which is amongst the largest oil companies in the world. Approximately 18,000 Shell employees are based in the U.S. Its U.S. headquarters are in Houston, Texas. Shell USA, including its consolidated companies and its share in equity companies, is one of America's largest oil and natural gas producers, natural gas marketers, gasoline marketers and petrochemical manufacturers. History In 1997, Shell and Texaco entered into two refining/marketing joint ventures. One combined their Midwestern and Western operations and was known as Equilon. The other, known as Motiva Enterprises, combined the Eastern and Gulf Coast operations of Shell Oil and Star Enterprise, itself a joint venture between Saudi Aramco and Texaco. After Texaco merged with Chevron in 2001, Shell purchased Texaco's shares in the joint ventures. In 2002 ...
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John Scott Haldane
John Scott Haldane (; 2 May 1860 – 14/15 March 1936) was a British physician and physiologist famous for intrepid self-experimentation which led to many important discoveries about the human body and the nature of gases. He also experimented on his son, the celebrated and polymathic biologist J. B. S. Haldane, even when he was quite young. Haldane locked himself in sealed chambers breathing potentially lethal cocktails of gases while recording their effect on his mind and body. Haldane visited the scenes of many mining disasters and investigated their causes. When the Germans used poison gas in World War I, Haldane went to the front at the request of Lord Kitchener and attempted to identify the gases being used. One outcome of this was his invention of the first respirator. Haldane's investigations into decompression sickness resulted in the first reasonably reliable decompression tables, and his mathematical model is still used in highly modified forms for computing d ...
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Decompression Theory
Decompression theory is the study and modelling of the transfer of the inert gas component of breathing gases from the gas in the lungs to the tissues and back during exposure to variations in ambient pressure. In the case of underwater diving and compressed air work, this mostly involves ambient pressures greater than the local surface pressure, but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure, are generally exposed to ambient pressures less than standard sea level atmospheric pressure. In all cases, the symptoms caused by decompression occur during or within a relatively short period of hours, or occasionally days, after a significant pressure reduction. The term "decompression" derives from the reduction in ambient pressure experienced by the organism and refers to both the reduction in pressure and the process of allowing dissolved inert gases to be eliminated from the tissues during and after this reduct ...
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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ...
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