formulasearchengine - User contributions [en]

Turbulence

2014-02-03T08:10:18Z

50.0.121.102: /* Further reading */ add McDonough lecture notes

The '''heat index''' ('''HI''') or '''humiture''' or '''humidex''' (not to be confused with the [[humidex|Canadian humidex]]) is an index that combines [[air]] [[temperature]] and [[relative humidity]] in an attempt to determine the human-perceived equivalent temperature—how hot it feels. The result is also known as the "felt air temperature" or "[[apparent temperature]]". For example, when the temperature is {{j|90 °F}} {{j|(32 °C)}} with very high humidity, the heat index can be about {{j|105 °F (41 °C).}}

The human body normally cools itself by [[perspiration]], or sweating. [[Heat]] is removed from the body by [[evaporation]] of that sweat. However, relative humidity reduces the evaporation rate because the higher vapor content of the surrounding air does not allow the maximum amount of evaporation from the body to occur. This results in a lower rate of heat removal from the body, hence the sensation of being overheated. This effect is subjective; its measurement has been based on subjective descriptions of how hot subjects feel for a given temperature and humidity. This results in a heat index that relates one combination of temperature and humidity to another one at higher temperature and lower humidity.

== History ==
The heat index was developed in 1978 by [[George Winterling]] as the "humiture" and was adopted by the USA's [[National Weather Service]] a year later.<ref>[http://www.news4jax.com/news/19262258/detail.html George Winterling: A Lifelong Passion For Weather] [[WJXT]], April 23, 2009</ref> It is derived from work carried out by Robert G. Steadman.<ref name=SteadmanI>The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science, R. G. Steadman, Journal of Applied Meteorology, July 1979, Vol 18 No7, pp861-873 {{doi|10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2}} [http://journals.ametsoc.org/doi/pdf/10.1175/1520-0450%281979%29018%3C0861%3ATAOSPI%3E2.0.CO%3B2]</ref><ref>The Assessment of Sultriness. Part II: Effects of Wind, Extra Radiation and Barometric Pressure on Apparent Temperature Journal of Applied Meteorology, R. G. Steadman, July 1979, Vol 18 No7, pp874-885</ref> Like the [[wind chill]] index, the heat index contains assumptions about the human body mass and height, clothing, amount of physical activity, thickness of blood, sunlight and ultraviolet radiation exposure, and the wind speed. Significant deviations from these will result in heat index values which do not accurately reflect the perceived temperature.<ref>[http://www.slate.com/id/2123486/fr/rss/ How do they figure the heat index? - By Daniel Engber - Slate Magazine]</ref>

In [[Canada]], the similar [[humidex]] is used in place of the heat index. While both the humidex and the heat index are calculated using dew point, the humidex uses a dew point of {{convert|45|°F|°C}} as a base, whereas the heat index uses a dew point base of {{convert|57|°F|°C}}. Further, the heat index uses heat balance equations which account for many variables other than vapor pressure, which is used exclusively in the humidex calculation. A joint committee formed by the United States and Canada to resolve differences has since been disbanded.

The heat index is defined so as to equal the actual air temperature when the [[partial pressure]] of [[water vapor]] is equal to a baseline value of 1.6 [[Pascal (unit)|kPa]]. At [[standard atmospheric pressure]] (101.325 kPa), this baseline corresponds to a [[dew point]] of {{j|14 °C}} {{j|(57 °F)}} and a [[mixing ratio]] of 0.01 (10 g of water vapor per kilogram of dry air).<ref name=SteadmanI/> This corresponds to an air temperature of {{j|25 °C}} {{j|(77 °F)}} and relative humidity of 50% in the sea-level [[psychrometric chart]].

At high temperatures, the level of ''relative'' humidity needed to make the heat index higher, than the actual temperature, is lower than at cooler temperatures. For example, at approximately {{j|27 °C}} {{j|(80 °F)}}, the heat index will agree with the actual temperature if the relative humidity is 45%, but at about {{j|43 °C (110 °F),}} any relative-humidity reading above 17% will make the heat index higher than {{j|43 °C}}.

The formula described is considered valid only if the actual temperature is above {{j|27 °C}} {{j|(80 °F)}}, dew point temperatures greater than {{j|12 °C (54 °F),}} and relative humidities higher than 40%.<ref>[http://www.campbellsci.com/documents/technical-papers/heatindx.pdf Heat Index Campbell Scientific Inc.] (PDF file), CampbellSci.com.</ref> The heat index and humidex figures are based on temperature measurements taken in the shade and not the sun, so extra care must be taken while in the sun. The heat index also does not factor in the effects of wind, which lowers the apparent temperature.

Sometimes the heat index and the [[wind chill]] are denoted collectively by the single term "apparent temperature", "relative outdoor temperature", or "feels like".

==Meteorological considerations==

Outdoors in open conditions, as the relative humidity increases, first haze and ultimately a thicker cloud cover develops, reducing the amount of direct sunlight reaching the surface. Thus, there is an inverse relationship between maximum potential temperature and maximum potential relative humidity. Because of this factor, it was once believed that the highest heat index reading actually attainable anywhere on Earth is approximately {{convert|71|°C|°F|abbr=on}}. However, in [[Dhahran]], [[Saudi Arabia]] on July 8, 2003, the [[dew point]] was {{convert|35|°C|°F|abbr=on}} while the temperature was {{convert|42|°C|°F|abbr=on}}, resulting in a heat index of {{convert|78|°C|°F|abbr=on}}. This is comparable to the temperatures that are recommended to kill bacteria in many meat products, and it is common in a [[sauna]]. High heat-index values also indicate that intense thunderstorms are approaching, depending on the intensity of the cold front, causing more violent storms.<ref>
{{cite book
| last = Burt | first = Christopher C.
| authorlink =
| title = Extreme Weather: A Guide & Record Book
| url = http://books.google.com/books?id=NuP7ATq9nWgC&dq=extreme+weather+a+guide+%26+record+book&printsec=frontcover#PPA28,M1
| publisher = W. W. Norton & Company
| year = 2004 | pages = 28
| doi =
| isbn = 0-393-32658-6 }}</ref>

==Table of Heat Index values==
This table is from the U.S. [[National Oceanic and Atmospheric Administration]].
{{HeatTable}}

To find the Heat Index temperature, look at the Heat Index chart above. For example, if the air temperature is 96°F and the relative humidity is 65%, the heat index—how hot it feels—is 121°F.

This table is an approximation of the Heat Index, using the formula and first set of constants below, converted to Celsius.
{{HeatTableC}}

==Effects of the heat index (shade values)==
{| class="wikitable"
|-
! Celsius || Fahrenheit || Notes
|-
| 27–32 °C || 80–90 °F
| Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in [[heat cramp]]s.
|-
| 32–41 °C || 90–105 °F
| Extreme caution: [[heat cramp]]s and [[heat exhaustion]] are possible. Continuing activity could result in [[heat stroke]].
|-
| 41–54 °C || 105–130 °F
| Danger: [[heat cramp]]s and [[heat exhaustion]] are likely; [[heat stroke]] is probable with continued activity.
|-
| over 54 °C || over 130 °F
| Extreme danger: [[heat stroke]] is imminent.
|-
|}

Exposure to full sunshine can increase heat index values by up to 8 °C (14 °F).<ref name=Pueblo>[http://web.archive.org/web/20110629041320/http://www.crh.noaa.gov/pub/heat.php Heat Index] on the website of the Pueblo, CO United States National Weather Service.</ref>

==Formula==
The formula below approximates the heat index in degrees Fahrenheit, to within ±1.3 °F. It is the result of a multivariate fit (temperature equal to or greater than 80°F and relative humidity equal to or greater than 40%) to a model of the human body.<ref>Lans P. Rothfusz. "The Heat Index 'Equation' (or, More Than You Ever Wanted to Know About Heat Index)", Scientific Services Division (NWS Southern Region Headquarters), 1 July 1990 [http://www.srh.noaa.gov/images/ffc/pdf/ta_htindx.PDF]</ref><ref>R.G. Steadman, 1979. "The assessment of sultriness. Part I: A temperature-humidity index based on human physiology and clothing science," J. Appl. Meteor., 18, 861-873</ref> This equation reproduces the above NOAA National Weather Service table (except the values at 90°F & 45%/70% relative humidity vary unrounded by less than -1/+1, respectively).
:<math>\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2R + c_8 T R^2 + c_9 T^2 R^2\ \, </math>

where
:<math>\mathrm{HI}\,\!</math> = heat index (in degrees Fahrenheit)
:<math>T\,\!</math> = ambient [[dry-bulb temperature]] (in degrees Fahrenheit)
:<math>R\,\!</math> = relative humidity (percentage value between 0 and 100)
:<math>c_1 = -42.379, \,\!</math> <math>c_2 = 2.04901523, \,\!</math> <math>c_3 = 10.14333127,\,\!</math> <math>c_4 = -0.22475541, \,\!</math> <math>c_5 = -6.83783 \times 10^{-3},\,\!</math> <math>c_6 = -5.481717 \times 10^{-2},\,\!</math> <math>c_7 = 1.22874 \times 10^{-3}, \,\!</math> <math>c_8 = 8.5282 \times 10^{-4}, \,\!</math> <math>c_9 = -1.99 \times 10^{-6}.\,\!</math>

An alternative set of constants for this equation that is within 3 degrees of the NWS master table for all humidities from 0 to 80% and all temperatures between 70 and 115 °F and all heat indexes < 150 °F is
:<math>c_1 = 0.363445176, \,\!</math> <math> c_2 = 0.988622465, \,\!</math> <math> c_3 = 4.777114035, \,\!</math> <math> c_4 = -0.114037667, \,\!</math> <math> c_5 = -0.000850208, \,\!</math> <math> c_6 = -0.020716198, \,\!</math> <math> c_7 = 0.000687678, \,\!</math> <math> c_8 = 0.000274954, \,\!</math> <math> c_9 = 0 \,\!</math> <math>(c_9 \,\!</math> <math>unused).</math>

A further alternate is this:<ref>
{{cite book
| last = Stull | first = Richard
| authorlink =
| title = Meteorology for Scientists and Engineers, Second Edition
| url = http://books.google.com/books?ei=r_D5T9XTBIrOqAHe_c2LCQ&id=QrYRAQAAIAAJ&dq=Meteorology+for+Scientists+and+Engineers&q=5.37941#search_anchor
| publisher = Brooks/Cole
| year = 2000 | page = 60
| doi =
| isbn = 9780534372149 }}</ref>
:<math>\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2 + c_{10} T^3 + c_{11} R^3 + c_{12} T^3 R + c_{13} T R^3 + c_{14} T^3 R^2 + c_{15} T^2 R^3 + c_{16} T^3 R^3\ \, </math>
where
:<math>c_1 = 16.923, \,\!</math> <math>c_2 = 0.185212, \,\!</math> <math>c_3 = 5.37941,\,\!</math> <math>c_4 = -0.100254, \,\!</math> <math>c_5 = 9.41695 \times 10^{-3},\,\!</math> <math>c_6 = 7.28898 \times 10^{-3},\,\!</math> <math>c_7 = 3.45372\times 10^{-4}, \,\!</math> <math>c_8 = -8.14971 \times 10^{-4}, \,\!</math> <math>c_9 = 1.02102 \times 10^{-5},\,\!</math> <math>c_{10} = -3.8646 \times 10^{-5},\,\!</math> <math>c_{11} = 2.91583 \times 10^{-5},\,\!</math> <math>c_{12} = 1.42721 \times 10^{-6},\,\!</math> <math>c_{13} = 1.97483 \times 10^{-7},\,\!</math> <math>c_{14} = -2.18429 \times 10^{-8},\,\!</math> <math>c_{15} = 8.43296 \times 10^{-10},\,\!</math> <math>c_{16} = -4.81975 \times 10^{-11}.\,\!</math>

For example, using this last formula, with temperature {{convert|90|F|C}} and relative humidity (RH) of 85%, the result would be: {{heat index|90|85}}.

== See also ==
* [[Apparent temperature]]
* [[Humidex]]
* [[Wind chill]]

==References==
{{Reflist}}

== External links ==
*[http://www.bom.gov.au/info/thermal_stress/ Description of wind chill & apparent temperature] Formulae in metric units
*[http://www.wpc.ncep.noaa.gov/html/heatindex.shtml Heat Index Calculator] Calculates both °F and °C

{{Meteorological variables}}

{{DEFAULTSORT:Heat Index}}
[[Category:Atmospheric thermodynamics]]
[[Category:Weather]]

Weil restriction

2014-01-03T04:20:25Z

50.0.121.102: add cryptography application

The '''negentropy''', also '''negative entropy''' or '''syntropy''' or '''extropy''' or '''entaxy''',<ref>Wiener, Norbert</ref> of a [[living system]] is the [[entropy]] that it exports to keep its own entropy low; it lies at the intersection of [[entropy and life]]. The concept and phrase "negative entropy" were introduced by [[Erwin Schrödinger]] in his 1944 popular-science book ''[[What is Life? (Schrödinger)|What is Life?]]''<ref>Schrödinger, Erwin, ''What is Life - the Physical Aspect of the Living Cell'', Cambridge University Press, 1944</ref> Later, [[Léon Brillouin]] shortened the phrase to ''negentropy'',<ref>Brillouin, Leon: (1953) "Negentropy Principle of Information", ''J. of Applied Physics'', v. '''24(9)''', pp. 1152-1163
</ref><ref>Léon Brillouin, ''La science et la théorie de l'information'', Masson, 1959</ref> to express it in a more "positive" way: a living system imports negentropy and stores it.<ref>Mae-Wan Ho, [http://www.i-sis.org.uk/negentr.php What is (Schrödinger's) Negentropy?], Bioelectrodynamics Laboratory, Open university Walton Hall, Milton Keynes</ref> In 1974, [[Albert Szent-Györgyi]] proposed replacing the term ''negentropy'' with ''syntropy''. That term may have originated in the 1940s with the Italian mathematician [[Luigi Fantappiè]], who tried to construct a unified theory of [[biology]] and [[physics]]. [[Buckminster Fuller]] tried to popularize this usage, but ''negentropy'' remains common.

In a note to [[What is Life?]] Schrödinger explained his use of this phrase.
{{cquote|[...] if I had been catering for them [physicists] alone I should have let the discussion turn on ''[[Thermodynamic free energy|free energy]]'' instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to ''[[energy]]'' for making the average reader alive to the contrast between the two things.}}

Indeed, negentropy has been used by biologists as the basis for purpose or direction in life, namely cooperative or moral instincts.<ref>[[Jeremy Griffith]]. 2011. ''What is the Meaning of Life?''. In ''The Book of Real Answers to Everything!'' ISBN 9781741290073. From http://www.worldtransformation.com/what-is-the-meaning-of-life/</ref>

In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos.<ref>Mahulikar, S.P. & Herwig, H.: (2009) "Exact thermodynamic principles for dynamic order existence and evolution in chaos", ''Chaos, Solitons & Fractals'', v. '''41(4)''', pp. 1939-1948</ref> Thus, negentropy has units [J/kg-K] when defined based on specific entropy per unit mass, and [K<sup>−1</sup>] when defined based on specific entropy per unit energy. This definition enabled: ''i'') scale-invariant thermodynamic representation of dynamic order existence, ''ii'') formulation of physical principles exclusively for dynamic order existence and evolution, and ''iii'') mathematical interpretation of Schrödinger's negentropy debt.

==Information theory==
In [[information theory]] and [[statistics]], negentropy is used as a measure of distance to normality.<ref>Aapo Hyvärinen, [http://www.cis.hut.fi/aapo/papers/NCS99web/node32.html Survey on Independent Component Analysis, node32: Negentropy], Helsinki University of Technology
Laboratory of Computer and Information Science</ref><ref>Aapo Hyvärinen and Erkki Oja, [http://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/node14.html Independent Component Analysis: A Tutorial, node14: Negentropy], Helsinki University of Technology
Laboratory of Computer and Information Science</ref><ref>Ruye Wang, [http://fourier.eng.hmc.edu/e161/lectures/ica/node4.html Independent Component Analysis, node4: Measures of Non-Gaussianity]</ref> Out of all [[Distribution (mathematics)|distributions]] with a given mean and variance, the normal or [[Gaussian distribution]] is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes [[if and only if]] the signal is Gaussian.

Negentropy is defined as

:<math>J(p_x) = S(\phi_x) - S(p_x)\,</math>

where <math>S(\phi_x)</math> is the [[differential entropy]] of the Gaussian density with the same [[mean]] and [[variance]] as <math>p_x</math> and <math>S(p_x)</math> is the differential entropy of <math>p_x</math>:

:<math>S(p_x) = - \int p_x(u) \log p_x(u) du</math>

Negentropy is used in [[statistics]] and [[signal processing]]. It is related to network [[Information entropy|entropy]], which is used in [[Independent Component Analysis]].<ref>P. Comon, Independent Component Analysis - a new concept?, ''Signal Processing'', '''36''' 287-314, 1994.</ref><ref>Didier G. Leibovici and Christian Beckmann, [http://www.fmrib.ox.ac.uk/analysis/techrep/tr01dl1/tr01dl1/tr01dl1.html An introduction to Multiway Methods for Multi-Subject fMRI experiment], FMRIB Technical Report 2001, Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB), Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital, Headley Way, Headington, Oxford, UK.</ref>

==Correlation between statistical negentropy and Gibbs' free energy==
[[File:Wykres Gibbsa.svg|275px|thumb|right|[[Willard Gibbs]]’ 1873 '''available energy''' ([[Thermodynamic free energy|free energy]]) graph, which shows a plane perpendicular to the axis of ''v'' ([[volume]]) and passing through point A, which represents the initial state of the body. MN is the section of the surface of [[dissipated energy]]. Qε and Qη are sections of the planes ''η'' = 0 and ''ε'' = 0, and therefore parallel to the axes of ε ([[internal energy]]) and η ([[entropy]]) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its ''available energy'' ([[Gibbs free energy]]) and its ''capacity for entropy'' (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.]]
There is a physical quantity closely linked to [[Thermodynamic free energy|free energy]] ([[free enthalpy]]), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, [[Josiah Willard Gibbs|Willard Gibbs]] created a diagram illustrating the concept of free energy corresponding to [[free enthalpy]]. On the diagram one can see the quantity called [[capacity for entropy]]. The said quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume.<ref>Willard Gibbs, [http://www.ufn.ru/ufn39/ufn39_4/Russian/r394b.pdf A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces], ''Transactions of the Connecticut Academy'', 382-404 (1873)</ref> In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by [[François Jacques Dominique Massieu|Massieu]] for the [[isothermal process]] <ref>Massieu, M. F. (1869a). Sur les fonctions caractéristiques des divers fluides.
''C. R. Acad. Sci.'' LXIX:858-862.</ref><ref>Massieu, M. F. (1869b). Addition au precedent memoire sur les fonctions
caractéristiques. ''C. R. Acad. Sci.'' LXIX:1057-1061.</ref><ref>Massieu, M. F. (1869), ''Compt. Rend.'' '''69''' (858): 1057.</ref> (both quantities differs just with a figure sign) and then [[Max Planck|Planck]] for the [[Isothermal process|isothermal]]-[[Isobaric process|isobaric]] process <ref>Planck, M. (1945). ''Treatise on Thermodynamics''. Dover, New York.</ref> More recently, the Massieu-Planck [[thermodynamic potential]], known also as ''[[free entropy]]'', has been shown to play a great role in the so-called entropic formulation of [[statistical mechanics]],<ref>Antoni Planes, Eduard Vives, [http://www.ecm.ub.es/condensed/eduard/papers/massieu/node2.html Entropic Formulation of Statistical Mechanics], Entropic variables and Massieu-Planck functions 2000-10-24 Universitat de Barcelona</ref> applied among the others in molecular biology<ref>John A. Scheilman, [http://www.biophysj.org/cgi/reprint/73/6/2960.pdf Temperature, Stability, and the Hydrophobic Interaction], ''Biophysical Journal'' '''73''' (December 1997), 2960-2964, Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403 USA</ref> and thermodynamic non-equilibrium processes.<ref>Z. Hens and X. de Hemptinne, [http://arxiv.org/pdf/chao-dyn/9604008 Non-equilibrium Thermodynamics approach to Transport Processes in Gas Mixtures], Department of Chemistry, Catholic University of Leuven,
Celestijnenlaan 200 F, B-3001 Heverlee, Belgium</ref>

::'''<math>J = S_\max - S = -\Phi = -k \ln Z\,</math>'''

::where:
::<math>J</math> - negentropy (Gibbs "capacity for entropy")
::<math>\Phi</math> – [[Free entropy|Massieu potential]]
::<math>Z</math> - [[Partition function (statistical mechanics)|partition function]]
::<math>k</math> - [[Boltzmann constant]]

==Risk management==

In [[risk management]], negentropy is the force that seeks to achieve effective organizational behavior and lead to a steady predictable state.<ref>[http://www.kent.ac.uk/scarr/events/Grinberg-%20(2).pdf Pedagogical Risk and Governmentality: Shantytowns in Argentina in the 21st Century] (see p. 4).</ref>

==Brillouin's negentropy principle of information==

In 1953, Brillouin derived a general equation<ref>Leon Brillouin, The negentropy principle of information, ''J. Applied Physics'' '''24''', 1152-1163 1953</ref> stating that the changing of an information bit value requires at least kT ln(2) energy. This is the same energy as the work [[Leo Szilard]]'s engine produces in the idealistic case. In his book,<ref>Leon Brillouin, ''Science and Information theory'', Dover, 1956</ref> he further explored this problem concluding that any cause of this bit value change (measurement, decision about a yes/no question, erasure, display, etc) will require the same amount of energy.

==Notes==
{{reflist}}

==See also==
* [[Ectropy]]
* [[Exergy]]
* [[Extropy]]
* [[Free entropy]]
* [[Entropy in thermodynamics and information theory]]

==External links==
Eschatos ♦ [http://knol.google.com/k/eschatos/information/1zm6ikqu62pfl/20 Information]

[[Category:Thermodynamic entropy]]
[[Category:Entropy and information]]
[[Category:Statistical deviation and dispersion]]