en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (8853)

2013-01-10T03:38:04Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (8853)

← Older revision		Revision as of 05:38, 10 January 2013
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			[[Image:ResistorsNetwork.jpg\|right\|200px\|thumb\|The driving induces transitions between levels of a closed system, leading to diffusion in energy space and, hence, an associated heating. The diffusion coefficient can be calculated using a resistor network analogy.]]

			<div align="justify">
			'''Semi-linear response theory (SLRT)''' is an extension of [[linear response theory]] (LRT) for [[mesoscopic]] circumstances: LRT applies if the driven transitions are much weaker/slower than the environmental relaxation/dephasing effect, while SLRT assumes the opposite conditions. SLRT uses a resistor network analogy (see illustration) in order to calculate the rate of energy absorption: The driving induces transitions between energy levels, and connected sequences of transitions are essential in order to have a non-vanishing result, as in the theory of percolation.
			</div>

	~~There are also many businesses that are now offering~~ the ~~fixed gear bike~~, ~~kromica fixie and takara fixie bikes~~, ~~much to the delight of many biking aficionados. Above the very last ten many years the trails of this place have become smaller and scaled-down~~. ~~When you loved this information and you would love to receive more info with regards to [http://www~~.~~bataviarr~~.~~com~~/~~profile/sahoule Womens mountain bike sizing~~.~~] kindly visit our webpage~~. ~~Check out bicycle repair tool reviews of the most popular tools that provide the best value for your dollar~~. ~~Generally speaking, a good~~, ~~durable mountain bike starts at about $600 and goes up from there~~. ~~Look at what other riders appreciate about their bikes~~. <br><br>~~The prices offered by these online stores are very competitive and realistic according to the market~~. ~~"Before breathing exercises it took me 45 minutes to really get into my stride when off road mountain biking~~. ~~You can also purchase helmets and other safety equipment~~, ~~lights~~, ~~locks~~, ~~saddles~~, ~~racks~~, ~~packs~~, ~~trainers~~, ~~bike maintenance gear~~, ~~trailers~~, ~~team wear~~, ~~Trek souvenirs~~, ~~and even computers for your bike~~. ~~- Get a bike that is lightweight and made out~~ of ~~carbon fiber materials~~. ~~UST kits can also improve sturdiness~~ of ~~UST wheels with added sealing capacity~~ in ~~case of any punctures~~. <br>~~<br>They are electricity assisted~~, ~~meaning electric power is used in response to the rider's pedaling power~~, ~~with pedaling staying the key driver~~. ~~Never miss the chance to experience mountain biking~~. ~~Buy~~ a ~~bike~~ that has a ~~top quality body made outside~~ of ~~steel, aluminum, carbon fiber or titanium~~. In ~~no time you'll be cruising through~~ the ~~woods and getting into great shape. Re-lube the chain carefully, making sure each link~~ is ~~covered with oil, spin the pedals backwards a few times, then wipe off any excess oil~~ from the ~~chain with an old rag~~. <br><br>~~Decide how and where you want to ride, then choose~~ a ~~mountain bike that fits your personal style, rather than that~~ of the ~~sales staff.~~ In ~~between~~, ~~the biker~~ can ~~perform whatever new trick he or she has learnt up and this trick is known~~ as the ~~gap jump~~. ~~But older children may have more adventurous tastes~~, and ~~want for toys that are~~ - ~~well~~, still ~~miniatures~~, but ~~are flashier, more expensive, and more functional~~. ~~The internet will do just fine, maybe even better, as there are countless of online stores and biking websites from which you may get~~ the ~~information you need~~. ~~To find out~~ the ~~latest News and Tips on folding bikes~~, ~~visit Best Folding Bikes at bestfoldingbikes~~. <br><br>~~When~~ the ~~helmet~~ is in the ~~correct position on the head~~, the ~~straps can be adjusted so that they~~ are ~~snug across the side of the head and under the chin. Try finding the best bike for yourself at local shops~~, ~~where you can take a test ride before you finally decide. Usually~~, ~~alloy stems tend to be the more cost~~-~~effective of the two~~, ~~however~~ the ~~high end~~ of ~~the level~~, ~~aluminum stems which have been produced from high-grade alloys could be more expensive than carbon counterparts because they~~ are ~~lighter plus~~ more ~~responsive~~. ~~Originally founded in 1962, Kenda spent a most of the last one~~-~~hundred years focused on cycling. Some riders advocate the additional technical the trail the greater a hardtail mountain bikeis sought after.~~		==Applications==
			The original motivation for introducing SLRT was the study of mesosopic conductance
			<ref>D. Cohen, T. Kottos, H. Schanz, J. Phys. A 39, 11755 (2006)</ref>
			<ref>S. Bandopadhyay, Y. Etzioni and D. Cohen, Europhys. Lett. 76, 739 (2006)</ref>
			<ref>A. Stotland, R. Budoyo, T. Peer, T. Kottos, D. Cohen, J. Phys. A 41, 262001(FTC) (2008)</ref>
			.<ref>A. Stotland, T. Kottos, D. Cohen, Phys. Rev. B 81, 115464 (2010)</ref>
			The term SLRT has been coined in
			<ref>M. Wilkinson, B. Mehlig, D. Cohen, Europhys. Lett. 75, 709 (2006)</ref>
			where it has been applied to the calculation of energy absorption by metallic grains.
			Later the theory has been applied for analysing the rate of heating of atoms in vibrating traps
			.<ref>A. Stotland, D. Cohen, N. Davidson, Europhys. Lett. 86, 10004 (2009)</ref>

			==Definition of semilinear response==
			Consider a system that is driven by a source <math>f(t)</math> that has
			a power spectrum <math>\tilde{S}(\omega)</math>. The latter is defined
			as the Fourier transform of <math>\langle f(t)f(0)\rangle</math>.
			In linear response theory (LRT) the driving source induces a steady state
			which is only slightly different from the equilibrium state.
			In such circumstances the response (<math>G</math>) is a linear functional of the power spectrum:

			: <math>
			G = G[\tilde{S}(\omega)] = \int_{-\infty}^\infty \eta(\omega) \tilde{S}(\omega) \, d\omega
			</math>

			In the traditional LRT context <math>G</math> represents the rate of heating,
			and <math>\eta(\omega)</math> can be defined as the absorption coefficient.
			Whenever such relation applies

			: <math>
			[A] \ \ \ \ \tilde{S}(\omega) \mapsto \lambda \tilde{S}(\omega) \text{ implies } G \mapsto \lambda G
			</math>

			: <math>
			[B] \ \ \ \ \tilde{S}(\omega) \mapsto \tilde{S}_1(\omega) + \tilde{S}_2(\omega) \text{ implies } G \mapsto G_1 + G_2
			</math>

			If the driving is very strong the response becomes non-linear, meaning that both properties [A] and [B] do not hold. But there is a class of systems whose response becomes semi-linear, i.e. the first property [A] still holds, but not [B].

			==Resistor network modeling==
			SLRT applies whenever the driving is strong enough such that relaxation to the steady state is slow compared with the driven dynamics. Yet one assumes that the system can be modeled as a resistor network, mathematically expressed as <math>G=[[G_{nm}]]</math>.
			The notation <math>[[G_{nm}]]</math> stands for the usual electrical engineering calculation of a two terminal conductance of a given resistor network. For example parallel connections imply <math>G = \sum_{nm} G_{nm}</math>, while serial connections imply <math>G=\left[\sum_{nm} G_{nm}^{-1}\right]^{-1}</math>. Resistor network calculation is manifestly semi-linear because it satisfies <math>[[\lambda A]]=\lambda [[A]]</math>, but in general <math>[[A+B]]\ne[[A]]+[[B]]</math>.

			==Fermi golden rule picture==
			In the quantum mechanical calculation of energy absorption, the <math>G_{nm}</math> represent Fermi-golden-rule transition rates between energy levels. If only neighboring levels are coupled, serial addition implies

			: <math>
			G = G[\tilde{S}(\omega)] = \left[\int_{-\infty}^\infty \mu(\omega) \tilde{S}(\omega)^{-1} \, d\omega\right]^{-1}
			</math>

			which is manifestly semi-linear. Results for sparse networks, that are encountered in the analysis of weakly chaotic driven systems,
			are more interesting and can be obtained using a generalized variable range hopping (VRH) scheme.

			== References ==
			{{Reflist}}

			{{DEFAULTSORT:Semilinear Response}}
			[[Category:Quantum mechanics]]
			[[Category:Statistical mechanics]]
			[[Category:Non-equilibrium thermodynamics]]

en>ChrisGualtieri: /* Availability */Typo fixing, typos fixed: ie → i.e. using AWB

2012-08-09T04:22:03Z

Availability: Typo fixing, typos fixed: ie → i.e. using AWB

New page

There are also many businesses that are now offering the fixed gear bike, kromica fixie and takara fixie bikes, much to the delight of many biking aficionados. Above the very last ten many years the trails of this place have become smaller and scaled-down. When you loved this information and you would love to receive more info with regards to [http://www.bataviarr.com/profile/sahoule Womens mountain bike sizing.] kindly visit our webpage. Check out bicycle repair tool reviews of the most popular tools that provide the best value for your dollar. Generally speaking, a good, durable mountain bike starts at about $600 and goes up from there. Look at what other riders appreciate about their bikes. The prices offered by these online stores are very competitive and realistic according to the market. "Before breathing exercises it took me 45 minutes to really get into my stride when off road mountain biking. You can also purchase helmets and other safety equipment, lights, locks, saddles, racks, packs, trainers, bike maintenance gear, trailers, team wear, Trek souvenirs, and even computers for your bike. - Get a bike that is lightweight and made out of carbon fiber materials. UST kits can also improve sturdiness of UST wheels with added sealing capacity in case of any punctures. They are electricity assisted, meaning electric power is used in response to the rider's pedaling power, with pedaling staying the key driver. Never miss the chance to experience mountain biking. Buy a bike that has a top quality body made outside of steel, aluminum, carbon fiber or titanium. In no time you'll be cruising through the woods and getting into great shape. Re-lube the chain carefully, making sure each link is covered with oil, spin the pedals backwards a few times, then wipe off any excess oil from the chain with an old rag. Decide how and where you want to ride, then choose a mountain bike that fits your personal style, rather than that of the sales staff. In between, the biker can perform whatever new trick he or she has learnt up and this trick is known as the gap jump. But older children may have more adventurous tastes, and want for toys that are - well, still miniatures, but are flashier, more expensive, and more functional. The internet will do just fine, maybe even better, as there are countless of online stores and biking websites from which you may get the information you need. To find out the latest News and Tips on folding bikes, visit Best Folding Bikes at bestfoldingbikes. When the helmet is in the correct position on the head, the straps can be adjusted so that they are snug across the side of the head and under the chin. Try finding the best bike for yourself at local shops, where you can take a test ride before you finally decide. Usually, alloy stems tend to be the more cost-effective of the two, however the high end of the level, aluminum stems which have been produced from high-grade alloys could be more expensive than carbon counterparts because they are lighter plus more responsive. Originally founded in 1962, Kenda spent a most of the last one-hundred years focused on cycling. Some riders advocate the additional technical the trail the greater a hardtail mountain bikeis sought after.

Dependability state model - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (8853)

en>ChrisGualtieri: /* Availability */Typo fixing, typos fixed: ie → i.e. using AWB