Lateral earth pressure - Revision history

en>Shafiq1864: /* Active and passive pressure */ Defined soil active pressure and passive resistance in a fundamentally sound manner.

2014-08-27T01:12:24Z

Active and passive pressure: Defined soil active pressure and passive resistance in a fundamentally sound manner.

← Older revision		Revision as of 03:12, 27 August 2014
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	~~Friends call him Royal~~. ~~Bookkeeping~~ is what ~~she does~~. Her ~~husband~~ and her ~~chose~~ to reside in Delaware but she needs to ~~transfer~~ because of her family~~. Camping is some thing that I've done for many years~~.<br><br>~~Here is my site~~ [http://~~Superleague.taktikfuchs~~.~~org~~/index.php?mod=users&action=view&id=~~1645~~ extended ~~auto~~ warranty]		The name of the author is Luther. Managing individuals is what I do in my working day job. To perform badminton is some thing he truly enjoys doing. Her spouse and her selected to reside in Delaware but she needs to move because of her family members.<br><br>My page: [http://Frag5.com/index.php?mod=users&action=view&id=13770 extended car warranty]

en>Blkutter at 05:10, 14 February 2014

2014-02-14T05:10:36Z

← Older revision		Revision as of 07:10, 14 February 2014
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	In [[complex network]] theory, the '''fitness model''' is a model of the evolution of a network: how the links between nodes change over time depends on the '''fitness''' of nodes. Fitter nodes attract more links at the expense of less fit nodes.		Friends call him Royal. Bookkeeping is what she does. Her husband and her chose to reside in Delaware but she needs to transfer because of her family. Camping is some thing that I've done for many years.<br><br>Here is my site [http://Superleague.taktikfuchs.org/index.php?mod=users&action=view&id=1645 extended auto warranty]

	~~It has been used to model the network structure of the [[World Wide Web]]~~.

	~~==Description of the model==~~
	~~The model~~ is ~~based on the idea of '''fitness,''' an inherent competitive factor that nodes may have, capable of affecting the network's evolution.<ref>Albert R~~. and ~~Barabási A.-L., "Statistical mechanics of complex networks", ''Reviews of Modern Physics'' 74, 47 (2002)</ref> According to this idea, the nodes' intrinsic ability~~ to ~~attract links~~ in ~~the network varies from node to node, the most efficient (or "fit") being able~~ to ~~gather more edges in the expense~~ of ~~others~~. In that sense, not all nodes are identical to each other, and they claim their degree increase according to the fitness they possess every time. The fitness factors of all the nodes composing the network may form a distribution ρ(η) characteristic of the system been studied.

	~~Bianconi and Barabási<ref>Bianconi Ginestra and Barabási A.-L., 2001a, '~~'~~Europhys. Lett.'' 54, 436.</ref> proposed a new model called Bianconi-Barabasi model, a variant to the Barabási-Albert model ([[BA model]]), where the probability~~ for ~~a node to connect to another one is supplied with a term expressing the fitness of the node involved~~. ~~The fitness parameter is time independent and is multiplicative to the probability~~

	: <~~math~~>~~\Pi_i = \frac{\eta_i k_i}{\sum_j \eta_{j}k_j}.~~<~~/math~~>

	~~Thus, the system of equations for the time evolution of the degrees <math>k_{i}</math> according to the continuum theory introduced by the same model will have the form~~

	~~: <math>\frac{\partial k_{i}}{\partial t} = m\Pi_{i} = m\frac{\eta_{i}k_{i}}{\sum_{j}\eta_{j}k_{j}}</math>~~

	where ''m'' the number of edges the newly coming node has. If we require the solution to have a similar form to the one it had without the insertion of the fitness factors (to avoid ruining the [[power-law]] [[degree distribution]] of [[~~scale-free networks]]), then the exponent of the solution has to change and become fitness dependent~~

	: ~~<math>k_{\eta}(t,t_{i}) = m\left(\frac{t}{t_i}\right)^{\beta(\eta_{i})}<~~/~~math>~~

	~~where~~

	~~: <math>\beta(\eta) = \frac{\eta}{C}\mbox{ and }C = \int\rho(\eta)\frac{\eta}{1-\beta(\eta)}\,d\eta.<~~/~~math>~~

	~~Hence, the more fit nodes increase their degree faster than the less ones~~. ~~This characteristic attributes the network with a different behavior regarding its evolution~~. Without the introduction of the fitness property, all nodes had the same exponent in the power-law degree evolution formula. This means that the older nodes in the system would have more edges compared to newcoming ones. After the fitness property is introduced, this exponent, and accordingly, the slope of <math>k(t)</~~math> change, giving thus the opportunity to newcoming nodes to dominate the system~~.

	It was seen through this example how can a network's evolution change behavior through the introduction of a new parameter in the model. However, we require the network to preserve its overall scale-free character. By forcing the fitness dependence to be accumulated in the exponent only, the degree-distribution will still be a power-law relationship, composed though by a weighted sum of different power-law in degree-evolution formulas

	~~: <math>P(k) \sim \int\rho(\eta)\frac{C}{\eta}(m/k)^{C/\eta +1}\,d\eta</math>~~

	~~where ρ(η) is the fitness distribution depending on the system's composition~~

	~~The fitness model can be extended to in corporate additional processes, such as internal edges, which affect the exponents.<ref>Ergun, G. and G. J. Rodgers, ''Physica A'' 303 (2002) 261~~&~~ndash;272</ref>~~

	==~~Fitness model and the evolution of the Web==~~

	The fitness model has been used to model the network structure of the [[World Wide Web]]. In a [[PNAS]] article,<ref>J.S. Kong, N. Sarshar, V.P. Roychowdhury, "Experience versus Talent Shapes the Structure of the Web", Proceedings of the National Academy of Sciences of the USA, September 16, 2008; 105 (37)</ref> Kong et al. extended the fitness model to include random node deletion, a common phenomena in the Web. When the deletion rate of the web pages are accounted for, they found that the overall fitness distribution is exponential. Nonetheless, even this small variance in the fitness is amplified through the [[preferential attachment]] mechanism, leading to a [[heavy-tailed distribution]] of incoming links on the Web.

	~~== See also ==~~
	* [[Bose–Einstein condensation: a network theory approach]]

	~~== References ==~~

	~~<references/>~~

	~~[[Category:Network theory]~~]

195.37.234.90: article is about silos not soils, see http://www.gbv.de/dms/tib-ub-hannover/300868936.pdf

2014-01-17T08:48:03Z

article is about silos not soils, see http://www.gbv.de/dms/tib-ub-hannover/300868936.pdf

← Older revision		Revision as of 10:48, 17 January 2014
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	~~Wilber Berryhill~~ is the ~~title his parents gave him~~ and ~~he totally digs~~ that ~~title~~. ~~Office supervising is exactly where her primary income arrives from~~. ~~What me~~ and ~~my family love is doing ballet but I~~'~~ve been taking on~~ new ~~things lately~~. ~~I've always cherished living in Mississippi~~.<br><br>~~Feel free~~ to ~~surf~~ to ~~my website online psychic~~ ([~~http~~://~~netwk~~.~~hannam~~.ac.kr/xe/~~data_2~~/~~85669 over here~~])		In [[complex network]] theory, the '''fitness model''' is a model of the evolution of a network: how the links between nodes change over time depends on the '''fitness''' of nodes. Fitter nodes attract more links at the expense of less fit nodes.

			It has been used to model the network structure of the [[World Wide Web]].

			==Description of the model==
			The model is based on the idea of '''fitness,''' an inherent competitive factor that nodes may have, capable of affecting the network's evolution.<ref>Albert R. and Barabási A.-L., "Statistical mechanics of complex networks", ''Reviews of Modern Physics'' 74, 47 (2002)</ref> According to this idea, the nodes' intrinsic ability to attract links in the network varies from node to node, the most efficient (or "fit") being able to gather more edges in the expense of others. In that sense, not all nodes are identical to each other, and they claim their degree increase according to the fitness they possess every time. The fitness factors of all the nodes composing the network may form a distribution ρ(η) characteristic of the system been studied.

			Bianconi and Barabási<ref>Bianconi Ginestra and Barabási A.-L., 2001a, ''Europhys. Lett.'' 54, 436.</ref> proposed a new model called Bianconi-Barabasi model, a variant to the Barabási-Albert model ([[BA model]]), where the probability for a node to connect to another one is supplied with a term expressing the fitness of the node involved. The fitness parameter is time independent and is multiplicative to the probability

			: <math>\Pi_i = \frac{\eta_i k_i}{\sum_j \eta_{j}k_j}.</math>

			Thus, the system of equations for the time evolution of the degrees <math>k_{i}</math> according to the continuum theory introduced by the same model will have the form

			: <math>\frac{\partial k_{i}}{\partial t} = m\Pi_{i} = m\frac{\eta_{i}k_{i}}{\sum_{j}\eta_{j}k_{j}}</math>

			where ''m'' the number of edges the newly coming node has. If we require the solution to have a similar form to the one it had without the insertion of the fitness factors (to avoid ruining the [[power-law]] [[degree distribution]] of [[scale-free networks]]), then the exponent of the solution has to change and become fitness dependent

			: <math>k_{\eta}(t,t_{i}) = m\left(\frac{t}{t_i}\right)^{\beta(\eta_{i})}</math>

			where

			: <math>\beta(\eta) = \frac{\eta}{C}\mbox{ and }C = \int\rho(\eta)\frac{\eta}{1-\beta(\eta)}\,d\eta.</math>

			Hence, the more fit nodes increase their degree faster than the less ones. This characteristic attributes the network with a different behavior regarding its evolution. Without the introduction of the fitness property, all nodes had the same exponent in the power-law degree evolution formula. This means that the older nodes in the system would have more edges compared to newcoming ones. After the fitness property is introduced, this exponent, and accordingly, the slope of <math>k(t)</math> change, giving thus the opportunity to newcoming nodes to dominate the system.

			It was seen through this example how can a network's evolution change behavior through the introduction of a new parameter in the model. However, we require the network to preserve its overall scale-free character. By forcing the fitness dependence to be accumulated in the exponent only, the degree-distribution will still be a power-law relationship, composed though by a weighted sum of different power-law in degree-evolution formulas

			: <math>P(k) \sim \int\rho(\eta)\frac{C}{\eta}(m/k)^{C/\eta +1}\,d\eta</math>

			where ρ(η) is the fitness distribution depending on the system's composition

			The fitness model can be extended to in corporate additional processes, such as internal edges, which affect the exponents.<ref>Ergun, G. and G. J. Rodgers, ''Physica A'' 303 (2002) 261–272</ref>

			==Fitness model and the evolution of the Web==

			The fitness model has been used to model the network structure of the [[World Wide Web]]. In a [[PNAS]] article,<ref>J.S. Kong, N. Sarshar, V.P. Roychowdhury, "Experience versus Talent Shapes the Structure of the Web", Proceedings of the National Academy of Sciences of the USA, September 16, 2008; 105 (37)</ref> Kong et al. extended the fitness model to include random node deletion, a common phenomena in the Web. When the deletion rate of the web pages are accounted for, they found that the overall fitness distribution is exponential. Nonetheless, even this small variance in the fitness is amplified through the [[preferential attachment]] mechanism, leading to a [[heavy-tailed distribution]] of incoming links on the Web.

			== See also ==
			* [[Bose–Einstein condensation: a network theory approach]]

			== References ==

			<references/>

			[[Category:Network theory]]

86.181.23.169: /* Rankine theory */ Equations corrected: in the Rankine formula for horizontal active pressure the first term is the square of cos beta, not cos beta.

2012-08-23T19:05:28Z

Rankine theory: Equations corrected: in the Rankine formula for horizontal active pressure the first term is the square of cos beta, not cos beta.

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Wilber Berryhill is the title his parents gave him and he totally digs that title. Office supervising is exactly where her primary income arrives from. What me and my family love is doing ballet but I've been taking on new things lately. I've always cherished living in Mississippi.<br><br>Feel free to surf to my website online psychic ([http://netwk.hannam.ac.kr/xe/data_2/85669 over here])