Modular lambda function - Revision history

183.32.240.237: /* Other elliptic functions */

2014-10-18T13:53:51Z

Other elliptic functions

← Older revision		Revision as of 15:53, 18 October 2014
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en>Titus III: /* Other elliptic functions */ Wiki-link to j-invariant

2014-02-19T03:23:53Z

Other elliptic functions: Wiki-link to j-invariant

← Older revision		Revision as of 05:23, 19 February 2014
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	~~'''Kramers' opacity law''' describes~~ the ~~[[opacity (optics)\|opacity]] of a medium in terms of~~ the ~~ambient [[density]]~~ and ~~[[temperature]], assuming that the opacity is dominated by [[ionization\|bound-free absorption]] (the absorption~~ of ~~light during ionization of a bound [[electron]]) or [[free-free absorption]] (~~the ~~absorption of light when scattering a free ion, also called [[bremsstrahlung]])~~.~~<ref>Phillips (1999), p. 92.</ref>~~ It ~~is often used~~ to ~~model [[radiative transfer]], particularly in [[stellar atmosphere]]s~~.<~~ref~~>~~Carroll (1996), p. 274–276.~~<~~/ref~~> ~~The relation~~ is ~~named after~~ the ~~[[Dutch people\|Dutch]] [[physicist]] [[Hendrik Kramers]], who first derived~~ the ~~form in 1923~~.~~<ref name="Carroll274">Carroll (1996), p~~. ~~274~~.~~</ref>~~		We reserve the right to include advertising on our site, including Kontera links and Google Ads. Use them at the beginning and end of your paragraphs. It may take several versions before the true story emerges and then you can distill it to word length requirements. It will help you to become a more effective writer. After jotting down all the points they should be elaborated throughout the content. <br><br>For now you need to understand exactly what the question is asking you. You can expect the grade you get to be based on the quality. Even the last moment suggestions of the students are not ignored. The introduction should be one that immediately grabs your reader's attention. The main idea of your whole essay will be your thesis statement. <br><br>At the same time, you will be assigned one writer or a team of writers, according to the difficulty of your project and the time frame you want it done in. If you have any inquiries regarding where and ways to use [http://www.lvlywallpapers.com/profile/emoua writing my paper], you could contact us at our web site. Buy APA legitimate custom economic papers, MLA economic essays and other internationally recognized formats. Essay writing in the university will enable students to develop research techniques. Clients are assured to get all writing services regardless of their geographical locations since nowadays internet can be accessible in any corners of the planet as long as there is an internet connection within the client’s locale. Obviously it's best to write your own essays; don't let laziness goad you into taking a shortcut. <br><br>Supporting Paragraphs Supporting paragraphs is the whole body of your essay. Our writing company is the best there is and any one intending to have someone else do any academic writing for them should visit our site for online order applications. This is carried out in order to make sure that the essays have acquired the expected high quality standards. Essay writing is a major constant in a students academic life. For your assistance, we have divided the formula into eight paragraphs that will be consuming assumable 2000 words. <br><br>And a great essay might just be what turns a 'maybe' into an 'admit. Like icing on a cake, the lacquer object, when set, were ornamented. Thanks to the Internet - research has become much easier and more fun that it was in past generations. The writers ensure the high school essay meets the instructors plagiarism and originality requirements. Certainly while drafting essays, the first thought that will come to your mind is the latest event that you have experienced.

	The ~~general functional form~~ of ~~the opacity law is~~

	<~~math~~>
	~~\bar{\kappa} \propto \rho T^{-7/2},~~
	<~~/math~~>

	~~where <math>\bar{\kappa}</math> is~~ the ~~resulting average opacity~~, ~~<math>\rho</math> is the density and <math>T</math>~~ the ~~temperature~~ of ~~the medium. Often the overall opacity is inferred from observations,~~ and ~~this form of~~ the ~~relation describes how changes~~ in ~~the density or temperature will affect the opacity~~.

	~~==Calculation==~~

	~~The specific forms for bound-free~~ and ~~free-free are~~

	~~Bound-free~~:
	~~<math>~~
	~~\bar{\kappa}_{bf} = 4.34 \times 10^{25} \frac{g_{bf}}{t}Z(1+X) \frac{\rho}{\rm g~~/~~cm^3} \left(\frac{T}{\rm K}\right)^{-7~~/~~2} {\rm \, cm^2 \, g^{-1}},~~
	~~</math>~~

	~~[[Bremsstrahlung\|Free-free]]:~~
	~~<math>~~
	~~\bar{\kappa}_{ff} = 3~~.~~68 \times 10^{22} g_{ff}(1 - Z)(1 + X) \frac{\rho}{\rm g~~/~~cm^3} \left(\frac{T}{\rm K}\right)^{-7~~/~~2} {\rm \~~, ~~cm^2 \~~, ~~g^{-1}}~~.
	~~</math>~~

	~~[[Thomson scattering\|Electron-scattering]]:~~
	~~<math>~~
	~~\bar{\kappa}_{es} = 0~~.~~2 (1+X) {\rm \, cm^2 \, g^{-1}}~~
	~~</math>~~

	~~Here, <math>g_{bf}</math> and <math>g_{ff}</math>~~ are the ~~[[Gaunt factor]]~~s ~~(quantum mechanical correction terms) associated with bound-free and free-free transitions respectively~~. ~~The~~ <~~math~~>t<~~/math~~> is ~~an additional correction factor, typically having a value between 1 and 100~~. ~~The opacity depends on~~ the ~~number density of electrons~~ and ~~ions~~ in the ~~medium, described by~~ the ~~fractional abundance (by mass) of elements heavier than [[hydrogen]] <math>Z</math>~~, ~~and~~ the ~~fractional abundance (by mass) of hydrogen~~ <~~math~~>X<~~/math~~>.~~<ref name="Carroll274"/>~~

	~~==References==~~
	~~{{Reflist}}~~

	~~==Bibliography==~~
	*{{Cite book
	~~\| author=Carroll~~, ~~Bradley; Ostlie~~, ~~Dale~~
	~~\| year=1996~~
	~~\| title=Modern Astrophysics~~
	~~\| publisher=Addison-Wesley~~
	~~\| location=~~
	~~\| url=http://books.google.com/books?id=yXR_QgAACAAJ}}~~
	*{{Cite book
	~~\| author = Phillips~~, A. C.
	~~\| year = 1999~~
	~~\| title =~~ The ~~Physics of Stars~~
	~~\| publisher = Wiley~~
	~~\| url = http://books~~.~~google~~.~~com/books?id=4CZpQgAACAAJ}}~~

	~~{{DEFAULTSORT:Kramers' Opacity Law}}~~
	~~[[Category:Scattering, absorption and radiative transfer (optics)]]~~

en>Titus III: For consistency, expressed the q-expansion in terms of the nome.

2012-12-31T16:46:37Z

For consistency, expressed the q-expansion in terms of the nome.

← Older revision		Revision as of 18:46, 31 December 2012
Line 1:		Line 1:
	~~Visit our essay writing company~~ and ~~enjoy quality services. When you cherished this short article and you would like to acquire more information regarding~~ [~~http://lovebear94.cafe24.com/s1/10570 buy essay plagiarism free~~] ~~generously visit our website. • Are you intending to tell~~ the ~~narrative objectively. Attaining proficiency in writing~~ is ~~not an easy thing and it takes considerable time to attain mastery in~~ the ~~writing~~ of ~~essays. This is important as if~~ the ~~essays assigned are not submitted on time~~, ~~students will fail the class. Custom essay writing services do just what they say---they write customized essays for you~~. <br><br>~~e articles that have been submitted several times to the site but are not 100% unique. We have been writing critical essays for a while and the experience has gotten our writers get~~ used to ~~writing these essays. If you practice this regularly~~, ~~then one day surely you will improve yourself. This doesn’t mean that spell check leaves words incorrectly spelled; it means that the word that you intended may not be the word that is included~~ in ~~the paper. Students use academic writing services because such services are extremely helpful to them in their studies~~. <br><br>The ~~main target~~ is ~~within~~ the ~~language being an result of your context~~, ~~and hence~~ the ~~beginning level for that instructing and mastering of writing abilities will be the last product or service~~. ~~We strive to treat all our customers with respect and integrity~~. ~~As a result you can get custom essays~~ of ~~outstanding quality which are just tailor made for you. Before medicine essays are delivered to customers~~, ~~they have to be proof read by a panel of editors. When such a company must write my essay for me I make certain that I buy~~ the ~~best offer.~~ <br><br>~~Supporting Paragraphs Supporting paragraphs~~ is the ~~whole body~~ of ~~your essay~~. ~~Here in~~ this ~~article you can get some~~ of the ~~important tips that can help you to write an effective essay; effective~~ in the ~~sense that the reader~~ will ~~get attracted towards~~ the ~~writing, so your writing should be in so much expert format~~. ~~Due to strict completion among writing service providers it is a win~~-~~win situation for students because they get premium quality service at very competitive rates that~~ are ~~usually defined as per the complexity level of student~~. ~~Essay writing is a major constant in a students academic life~~. ~~Adult material relating to sex~~, ~~sex toys~~, ~~escorts or prostitution~~. <br><br>~~Afore we mentioned the professors resorting to online grading services~~, ~~but there also is~~ the ~~well~~-~~known fact that students often address the online writing services for completion of their assignments~~. ~~Are you looking for excellent value in movies online. While writing~~ an ~~essay~~, ~~you just need to focus on 3 parts like introduction, body~~ and ~~conclusion~~. The ~~writers ensure~~ the ~~high school essay meets~~ the ~~instructors plagiarism~~ and ~~originality requirements~~. ~~Here are some~~ of ~~the main points which would definitely help you out in writing a good essay~~.		'''Kramers' opacity law''' describes the [[opacity (optics)\|opacity]] of a medium in terms of the ambient [[density]] and [[temperature]], assuming that the opacity is dominated by [[ionization\|bound-free absorption]] (the absorption of light during ionization of a bound [[electron]]) or [[free-free absorption]] (the absorption of light when scattering a free ion, also called [[bremsstrahlung]]).<ref>Phillips (1999), p. 92.</ref> It is often used to model [[radiative transfer]], particularly in [[stellar atmosphere]]s.<ref>Carroll (1996), p. 274–276.</ref> The relation is named after the [[Dutch people\|Dutch]] [[physicist]] [[Hendrik Kramers]], who first derived the form in 1923.<ref name="Carroll274">Carroll (1996), p. 274.</ref>

			The general functional form of the opacity law is

			<math>
			\bar{\kappa} \propto \rho T^{-7/2},
			</math>

			where <math>\bar{\kappa}</math> is the resulting average opacity, <math>\rho</math> is the density and <math>T</math> the temperature of the medium. Often the overall opacity is inferred from observations, and this form of the relation describes how changes in the density or temperature will affect the opacity.

			==Calculation==

			The specific forms for bound-free and free-free are

			Bound-free:
			<math>
			\bar{\kappa}_{bf} = 4.34 \times 10^{25} \frac{g_{bf}}{t}Z(1+X) \frac{\rho}{\rm g/cm^3} \left(\frac{T}{\rm K}\right)^{-7/2} {\rm \, cm^2 \, g^{-1}},
			</math>

			[[Bremsstrahlung\|Free-free]]:
			<math>
			\bar{\kappa}_{ff} = 3.68 \times 10^{22} g_{ff}(1 - Z)(1 + X) \frac{\rho}{\rm g/cm^3} \left(\frac{T}{\rm K}\right)^{-7/2} {\rm \, cm^2 \, g^{-1}}.
			</math>

			[[Thomson scattering\|Electron-scattering]]:
			<math>
			\bar{\kappa}_{es} = 0.2 (1+X) {\rm \, cm^2 \, g^{-1}}
			</math>

			Here, <math>g_{bf}</math> and <math>g_{ff}</math> are the [[Gaunt factor]]s (quantum mechanical correction terms) associated with bound-free and free-free transitions respectively. The <math>t</math> is an additional correction factor, typically having a value between 1 and 100. The opacity depends on the number density of electrons and ions in the medium, described by the fractional abundance (by mass) of elements heavier than [[hydrogen]] <math>Z</math>, and the fractional abundance (by mass) of hydrogen <math>X</math>.<ref name="Carroll274"/>

			==References==
			{{Reflist}}

			==Bibliography==
			*{{Cite book
			\| author=Carroll, Bradley; Ostlie, Dale
			\| year=1996
			\| title=Modern Astrophysics
			\| publisher=Addison-Wesley
			\| location=
			\| url=http://books.google.com/books?id=yXR_QgAACAAJ}}
			*{{Cite book
			\| author = Phillips, A. C.
			\| year = 1999
			\| title = The Physics of Stars
			\| publisher = Wiley
			\| url = http://books.google.com/books?id=4CZpQgAACAAJ}}

			{{DEFAULTSORT:Kramers' Opacity Law}}
			[[Category:Scattering, absorption and radiative transfer (optics)]]

76.120.181.41: edit

2012-08-30T17:40:14Z

edit

New page

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