Fiber bundle - Revision history

en>IkamusumeFan: /* Formal definition */ Update a SVG version of the local triviality.

2014-11-04T07:44:27Z

Formal definition: Update a SVG version of the local triviality.

← Older revision		Revision as of 09:44, 4 November 2014
Line 1:		Line 1:
	~~{{refimprove\|date=April 2013}}~~		"After 7 years of trying other methods, I finally got pregnant, 4 weeks after applying these holistic methods at the age of 44, thank you". Do we require to keep on obtaining possibly a lot more, or less, ordinary sex. s body approaches the time when she is most fertile to conceive naturally, the amount of cervical mucous discharge by the vagina increases. Fertility experts are also a good path to take and can significantly increase the multiple birth rates. Relax and you will see that everything will be fine and the pregnancy will come. <br><br>Coffee, soda, and chocolate can reduce the quality of sperm and egg cells. Sims are able to have sex with members of the opposite sex as well as members of the same sex. If it is greater than 28 days, you'll ovulate later. If all these statements fit you, then all you have to have can be a small know-how regarding how to get pregnant inside a proper way. The mobility of the sperm can be affected by the lubricants. <br><br>This kind of meat is also a great source of vitamin B12 which is essential to maintain and develop the nervous system. Epididymals obstruction is defined as the blockage of the passage of sperm to **** leading to low sperm count and increases the risk of infertility. Instead, go for doggy, missionary, spoon, as long as you. Living a healthier lifestyle can prevent you from having miscarriages and stillbirths. Snooki's son Lorenzo is going to have a BFF in Baby Mathews, that's for sure. <br><br>There are also some things you need to know and follow to help boost your chances of getting pregnant fast naturally. ' Diet - Each partners ought to eat properly-balanced meals, including meals eminent in anti-oxidants (vegatables and fruits) and iron (poultry and meat). When you are in great shape, your body can do what it is designed to do without a problem. The luteal phase and begins the day of ovulation and ends on the day you begin to menstruate. Drink lots of water to rid off toxins in your body. <br><br>And these two divisions of the same type of DNA, this means the children of the same sex, and appearance. A detailed understanding of the many factors that cause infertility is the foundation on which a successful conception can be made to occur. In this position, the gravity will aid the sperm in making its way to the fallopian tube to meet the ovary. That is why it is vital that couples do things to mitigate stress. Since every female is different from one another, this includes her hormone balance which in turn affects her period cycles, there is no exact science saying when a woman is fertile and when one is not.<br><br>If you have any thoughts relating to in which and how to use [http://www.quebec-1759.info/ best sex positions to get pregnant fast], you can call us at the webpage.
	~~'''Soap films''' are thin layers~~ of ~~[[liquid]] (usually water-based) surrounded by air. For example, if two [[soap bubble]]s come into contact~~, ~~they merge and a thin film is created in between. Thus~~, ~~[[foam]]s are composed~~ of ~~a network of films connected by [[Plateau's laws\|Plateau borders]]. Films are used as model systems for minimal surfaces~~, ~~which are widely used in mathematics~~.

	~~== Stability of soap films ==~~
	~~[[File:SchemeSoapFilm.png\|left\|thumb\|Figure 1: Organisation of surfactants at both surfaces of the soap film]]~~
	~~[[File:MarangoniInSoapFilms.png\|thumb\|Figure 2: Marangoni surface forces due~~ to ~~inhomogeneities in surfactants concentration~~. ~~The arrows represent~~ the ~~force direction]]~~

	~~Daily experience shows that soap bubble formation~~ is ~~not feasible with water or with any pure liquid. Actually~~, the ~~presence~~ of ~~soap, which is composed at~~ a ~~molecular scale of [[surfactants]], is necessary~~ to ~~stabilize~~ the ~~film~~. ~~Most of~~ the ~~time~~, ~~surfactants are [[amphiphile\|amphiphilic]]~~, ~~which means they are molecules with both a [[hydrophobic]]~~ and ~~a [[hydrophilic]] part~~. ~~Thus, they~~ are ~~arranged preferentially at~~ the ~~air/water interface (see figure 1).~~

	~~Surfactants stabilize films because they create a repulsion between both surfaces~~ of the ~~film~~, ~~preventing it from thinning and consequentially bursting~~. ~~This~~ can be ~~shown quantitatively through calculations relating~~ to ~~[[disjoining pressure]]~~. The ~~main repulsion mechanisms are steric (~~the ~~surfactants~~ can ~~not interlace) and electrostatic (if surfactants are charged).~~

	~~Moreover, surfactants make the film more stable toward thickness fluctuations due to~~ the ~~[[Marangoni effect]]~~. This ~~gives some elasticity to the interface: if surface concentrations are not homogeneously dispersed at the surface, Marangoni forces will tend to re-homogenize the surface concentration (see figure 2).~~

	~~Even in the presence~~ of ~~stabilizing surfactants,~~ a ~~soap film does not last forever. Water evaporates with time depending on the humidity~~ of the ~~atmosphere~~. ~~Moreover,~~ as ~~soon as a film is not perfectly horizontal,~~ the ~~liquid flows toward~~ the ~~bottom due~~ to ~~gravity~~ and the ~~liquid accumulates at the bottom~~. ~~At the top~~, ~~the film thins and bursts.~~

	~~== Importance of surface tension: minimal surfaces ==~~

	~~From a mathematical point of view~~, ~~soap films are considered~~ as ~~[[minimal surface]]s~~. ~~See for instance the approximate numerical method for minimal surfaces form finding at [[Stretched grid method]]~~. ~~[[Surface tension]], which measures the energy needed~~ to ~~create~~ a ~~surface indeed acts as a physical surface minimizer: since surface energy is proportional to the soap film surface~~, ~~the film deforms to minimize its surface and, thus its energy~~.<~~ref name=Ball61~~>~~Ball, 2009. pp. 61–67~~<~~/ref~~>

	~~Depending on the support provided, the soap film~~ naturally ~~takes the minimal surface~~. ~~On a flat support, the soap film is usually flat. But~~, ~~on more complicate supports, it takes the minimal achievable surface.<ref name=Ball61/>~~

	~~== Colours of a soap film ==~~

	~~[[File:thinfilmbubble.jpg\|thumb\|left\|Figure 3: thin film interference~~ in ~~a soap bubble. Notice the golden yellow colour near the top where the film is thin~~ and ~~a few even thinner black spots]]~~

	~~The [[iridescence\|iridescent]] colours of a soap film are caused by [[Interference (wave propagation~~)~~\|interfering]] of~~ (~~internally~~ and ~~externally~~) ~~reflected light waves~~, a ~~process called [[Thin-film interference\|thin film interference]]~~ and ~~are determined by~~ the ~~thickness~~ of the ~~film~~. ~~This phenomenon is not~~ the same ~~as the origin~~ of ~~[[rainbow]] colours (caused by~~ the ~~[[refraction]]~~ of ~~internally reflected light), but rather is~~ the same as the ~~phenomenon causing~~ the ~~colours in an oil slick~~ on a ~~wet road.~~

	~~==Drainage of a soap film==~~

	~~If surfactants are well chosen<ref name=Ball61/> and the atmospheric humidity and air movements are suitably controlled, a horizontal soap film~~ can ~~last from minutes~~ to ~~hours~~. In ~~contrast~~, ~~a vertical soap film is affected by [[~~gravity~~]] and so~~ the ~~liquid tends~~ to ~~drain, causing~~ the ~~soap film~~ to ~~thin at~~ the ~~top~~. ~~Colour depends on film thickness, which accounts for the coloured interference fringes~~ that ~~can be seen at the top of figure 4.~~

	~~[[File:GenerationSoapFilm.jpg\|thumb\|upright\|Figure 4: Picture of a film taken during its generation~~. ~~The film~~ is ~~pulled out of a soapy solution and drains~~ from ~~the top.]]~~

	~~==Bursting of a soap film==~~

	~~If a soap film is unstable~~, ~~it ends by bursting. A hole is created somewhere~~ in ~~the film and opens very rapidly. [[Surface tension]] indeed leads to surface minimization and~~, ~~thus, to film disappeance. The hole operture~~ is ~~not instantaneous~~ and is ~~slowed down by the liquid inertia~~. ~~The balance between the forces of inertia~~ and ~~surface tension leads~~ to ~~the opening velocity~~:~~<ref>{{cite article \|last1=Culick\|first1=F~~.~~E.C~~. ~~\|authorlink1= \|last2= \|first2= \|journal=Journal of Applied Physics \|volume=31(6) \|date= \|year= 1960\|month= \|origyear= \|publisher= \|location= \|isbn= \|oclc= \|doi= \|id= \|page=1128–1129}}<~~/~~ref>~~
	~~<math>V=\sqrt{\frac{2\gamma}{\rho h}}</math> where <math>\gamma</math> is the liquid surface tension~~, ~~<math>\rho</math> is~~ the ~~liquid density and <math>h</math> is the film thickness~~.

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

	~~==Sources==~~

	* {{cite book \| title=Shapes. Nature's Patterns: a tapestry in three parts \| publisher=Oxford University Press \| author=Ball, Philip \| year=2009 \| pages=61-67, 81-97, 291-292 \| isbn=978-0-19-960486-9}}

	~~{{Foam scales and properties}}~~

	~~[[Category:Minimal surfaces]]~~
	~~[[Category:Bubbles]]~~

	~~[[he:קרום סבון]]~~

en>Churchill17 at 21:33, 15 January 2014

2014-01-15T21:33:59Z

← Older revision		Revision as of 23:33, 15 January 2014
Line 1:		Line 1:
	~~Were you~~ in a ~~relationship with a man with whom you had ardentfervent feelings~~ for ~~plus he broke up with you? Do you say to yourself all time "I desire my spouse back"? If this really is the case then read on to find out what you~~ are ~~able to do to get ex back~~.~~<br><br>We~~ [~~http~~:~~//safedietplans~~.~~com/bmr-calculator bmr calculator~~] ~~could really wish To look wonderful for~~ the ~~family~~ or ~~school reunion~~, ~~plus certain persons believe~~ a ~~need for them~~ to ~~loseweight super Fast~~.~~While this is pretty widespread~~, it~~'s right~~ to ~~go at your weight, plus choose a moderate program~~. The ~~next time we go we~~ can ~~still look perfect~~, ~~plus~~ the ~~regimen will be~~ more ~~lengthy expression~~.~~<br><br>We~~ are ~~all topic~~ to ~~what exactly is called~~ the ~~basal metabolic rate~~. ~~This is~~ the ~~amount~~ of ~~calories every living individual demands to survive~~. ~~It is based found~~ on the ~~amount~~ of ~~calories required~~ to ~~keep our organs functioning~~. ~~Even strolling to~~ the ~~fridge for certain tempting snack or~~ a ~~cold 1~~, ~~plus then back to~~ the ~~sofa~~ for the ~~next TV show would be considered 'exercise' whenever computing~~ a ~~BMR. It~~ is the ~~amount of calories you'll burn if you remain inside bed all day long~~ and ~~do nothing~~.<br><br>~~We've all heard~~ the ~~tales of celebrities who drank nothing however lemonade with maple syrup plus cayenne pepper to promptly slim down for~~ a ~~character~~. ~~What you don't hear about is~~ the ~~aftermath: Those same celebrities regained all fat as soon as they ended their fast weight loss diets~~.<br>~~<br>To eat enough, find~~ a ~~Activity level on~~ the ~~chart. When you have chosen an honest level~~, ~~take~~ a ~~bmr~~ and ~~Multiply it~~ by ~~a BMR~~. This ~~can give~~ a ~~estimated calorie expenditure~~. ~~Note that this really is merely~~ a ~~"ball park" figure plus~~ the ~~actual requirements can be almost depending on your true activity level~~ and ~~body fat percentage. As both~~ are ~~stochastic plus adaptive~~, ~~you will want~~ to ~~consistently revisit your BMR~~ to ~~get an honest and honest amount~~ to ~~effectively eat~~ the ~~correct amount of calories~~.~~<br><br>What is a protein? Proteins~~, that ~~become amino acids inside~~ the ~~digestive program, are mandatory to rebuild all~~ of ~~the cells inside your body~~. ~~Without adequate daily protein, over time the body usually wither and die~~. ~~It is critically important for the health~~ of ~~your body to receive adequate protein~~. The ~~body cannot manufacture "amino acid"~~ from ~~either carbs or fats~~.~~<br><br>Frankly, because~~ a ~~pharmacist~~, ~~I am not persuaded~~ by ~~strong healthcare evidence which they~~ in ~~actual fact do what they claim~~ to ~~do. Many are stimulants which may be dangerous~~ to ~~some individuals~~. ~~Others merely work~~ by ~~decreasing~~ the ~~appetite temporarily~~. ~~Sometimes they "work" simply because you merely invested $40.00 on~~ the ~~bottle~~ of ~~pills~~...~~plus we don~~'~~t have enough income left to purchase junk food!~~		{{refimprove\|date=April 2013}}
			'''Soap films''' are thin layers of [[liquid]] (usually water-based) surrounded by air. For example, if two [[soap bubble]]s come into contact, they merge and a thin film is created in between. Thus, [[foam]]s are composed of a network of films connected by [[Plateau's laws\|Plateau borders]]. Films are used as model systems for minimal surfaces, which are widely used in mathematics.

			== Stability of soap films ==
			[[File:SchemeSoapFilm.png\|left\|thumb\|Figure 1: Organisation of surfactants at both surfaces of the soap film]]
			[[File:MarangoniInSoapFilms.png\|thumb\|Figure 2: Marangoni surface forces due to inhomogeneities in surfactants concentration. The arrows represent the force direction]]

			Daily experience shows that soap bubble formation is not feasible with water or with any pure liquid. Actually, the presence of soap, which is composed at a molecular scale of [[surfactants]], is necessary to stabilize the film. Most of the time, surfactants are [[amphiphile\|amphiphilic]], which means they are molecules with both a [[hydrophobic]] and a [[hydrophilic]] part. Thus, they are arranged preferentially at the air/water interface (see figure 1).

			Surfactants stabilize films because they create a repulsion between both surfaces of the film, preventing it from thinning and consequentially bursting. This can be shown quantitatively through calculations relating to [[disjoining pressure]]. The main repulsion mechanisms are steric (the surfactants can not interlace) and electrostatic (if surfactants are charged).

			Moreover, surfactants make the film more stable toward thickness fluctuations due to the [[Marangoni effect]]. This gives some elasticity to the interface: if surface concentrations are not homogeneously dispersed at the surface, Marangoni forces will tend to re-homogenize the surface concentration (see figure 2).

			Even in the presence of stabilizing surfactants, a soap film does not last forever. Water evaporates with time depending on the humidity of the atmosphere. Moreover, as soon as a film is not perfectly horizontal, the liquid flows toward the bottom due to gravity and the liquid accumulates at the bottom. At the top, the film thins and bursts.

			== Importance of surface tension: minimal surfaces ==

			From a mathematical point of view, soap films are considered as [[minimal surface]]s. See for instance the approximate numerical method for minimal surfaces form finding at [[Stretched grid method]]. [[Surface tension]], which measures the energy needed to create a surface indeed acts as a physical surface minimizer: since surface energy is proportional to the soap film surface, the film deforms to minimize its surface and, thus its energy.<ref name=Ball61>Ball, 2009. pp. 61–67</ref>

			Depending on the support provided, the soap film naturally takes the minimal surface. On a flat support, the soap film is usually flat. But, on more complicate supports, it takes the minimal achievable surface.<ref name=Ball61/>

			== Colours of a soap film ==

			[[File:thinfilmbubble.jpg\|thumb\|left\|Figure 3: thin film interference in a soap bubble. Notice the golden yellow colour near the top where the film is thin and a few even thinner black spots]]

			The [[iridescence\|iridescent]] colours of a soap film are caused by [[Interference (wave propagation)\|interfering]] of (internally and externally) reflected light waves, a process called [[Thin-film interference\|thin film interference]] and are determined by the thickness of the film. This phenomenon is not the same as the origin of [[rainbow]] colours (caused by the [[refraction]] of internally reflected light), but rather is the same as the phenomenon causing the colours in an oil slick on a wet road.

			==Drainage of a soap film==

			If surfactants are well chosen<ref name=Ball61/> and the atmospheric humidity and air movements are suitably controlled, a horizontal soap film can last from minutes to hours. In contrast, a vertical soap film is affected by [[gravity]] and so the liquid tends to drain, causing the soap film to thin at the top. Colour depends on film thickness, which accounts for the coloured interference fringes that can be seen at the top of figure 4.

			[[File:GenerationSoapFilm.jpg\|thumb\|upright\|Figure 4: Picture of a film taken during its generation. The film is pulled out of a soapy solution and drains from the top.]]

			==Bursting of a soap film==

			If a soap film is unstable, it ends by bursting. A hole is created somewhere in the film and opens very rapidly. [[Surface tension]] indeed leads to surface minimization and, thus, to film disappeance. The hole operture is not instantaneous and is slowed down by the liquid inertia. The balance between the forces of inertia and surface tension leads to the opening velocity:<ref>{{cite article \|last1=Culick\|first1=F.E.C. \|authorlink1= \|last2= \|first2= \|journal=Journal of Applied Physics \|volume=31(6) \|date= \|year= 1960\|month= \|origyear= \|publisher= \|location= \|isbn= \|oclc= \|doi= \|id= \|page=1128–1129}}</ref>
			<math>V=\sqrt{\frac{2\gamma}{\rho h}}</math> where <math>\gamma</math> is the liquid surface tension, <math>\rho</math> is the liquid density and <math>h</math> is the film thickness.

			==References==
			{{Reflist}}

			==Sources==

			* {{cite book \| title=Shapes. Nature's Patterns: a tapestry in three parts \| publisher=Oxford University Press \| author=Ball, Philip \| year=2009 \| pages=61-67, 81-97, 291-292 \| isbn=978-0-19-960486-9}}

			{{Foam scales and properties}}

			[[Category:Minimal surfaces]]
			[[Category:Bubbles]]

			[[he:קרום סבון]]

en>Mgvongoeden: /* See also */ I-bundle added

2012-07-07T14:30:12Z