formulasearchengine - User contributions [en]

Gabor transform

2014-10-24T07:58:25Z

143.239.109.141: Clarified sentence

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Particle in a ring

2013-12-03T20:51:42Z

143.239.9.1: /* Wave function */

{{about||pain and/or loss of range of motion of a joint|joint stiffness|the term regarding the stability of a differential equation|stiff equation}}
{{redirect|Flexibility}}
[[File:Beam bending.svg|thumb|right]]
'''Stiffness''' is the rigidity of an object — the extent to which it resists [[deformation (mechanics)|deformation]] in response to an applied [[force]].<ref>{{cite journal
| title = Stiffness--an unknown world of mechanical science?
| journal = Injury
| author = Baumgart F.
| year = 2000
| volume = 31
| publisher = Elsevier
| quote = “Stiffness” = “Load” divided by “Deformation”
| url = http://www.sciencedirect.com/science/article/pii/S0020138300800406
| accessdate = 2012-05-04
| doi=10.1016/S0020-1383(00)80040-6}}</ref> The complementary concept is '''flexibility''' or pliability: the more flexible an object is, the less stiff it is.<ref>{{citation |page=126 |chapter=Stiffness and flexibility |title=200 science investigations for young students |author=Martin Wenham |year=2001 |isbn=978-0-7619-6349-3}}</ref>

==Calculations==
'''The stiffness''', ''k'', '''of a body''' is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single [[Degrees of freedom (mechanics)|degree of freedom]] (for example, stretching or compression of a rod), the stiffness is defined as

:<math>k=\frac {F} {\delta} </math>

where,

:''F'' is the force applied on the body
:δ is the [[displacement field (mechanics)|displacement]] produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring)

In the [[International System of Units]], stiffness is typically measured in [[Newton (unit)|newton]]s per metre.
In Imperial units, stiffness is typically measured in [[Pound (force)|pound]]s(lbs) per inch.

Generally speaking, [[Deflection (engineering)|deflections]] (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple [[Degrees of freedom (mechanics)|degrees of freedom]] (maximum of six DOF at a point). For example, a point on a horizontal [[Euler–Bernoulli beam equation|beam]] can undergo both a vertical [[Displacement (vector)|displacement]] and a rotation relative to its undeformed axis. When there are M degrees of freedom a M x M [[Matrix (mathematics)|matrix]] must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. In industry, the term '''influence coefficient''' is sometimes used to refer to the coupling stiffness.

It is noted that for a body with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its own direction (or degree of freedom), but also those along other directions.

For a body with multiple DOF, in order to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. Under such a condition, the above equation can be used to obtain the direct-related stiffness for the degree of freedom which is unconstrained. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses.

== Compliance ==

The [[Multiplicative inverse|inverse]] of stiffness is ''compliance'', typically measured in units of metres per newton. In rheology it may be defined as the ratio of strain to stress,<ref>V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; "Delayed flow in thermo-reversible colloidal gels"; Journal of Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. 623–644.</ref> and so take the units of reciprocal stress, ''e.g''. 1/[[pascal (unit)|Pa]].

== Rotational stiffness ==

A body may also have a rotational stiffness, ''k'', given by

:<math>k=\frac {M} {\theta} </math>

where
: ''M'' is the applied [[moment (physics)|moment]]
: ''θ'' is the rotation

In the SI system, rotational stiffness is typically measured in [[newton-metre]]s per [[radian]].

In the SAE system, rotational stiffness is typically measured in inch-[[Pound (force)|pound]]s per [[degree (angle)|degree]].

Further measures of stiffness are derived on a similar basis, including:

* shear stiffness - ratio of applied [[shear stress|shear]] force to shear deformation
* torsional stiffness - ratio of applied [[torsion (mechanics)|torsion]] moment to angle of twist

== Relationship to elasticity ==
In general, [[elastic modulus]] is not the same as stiffness. Elastic modulus is a property of the constituent material; stiffness is a property of a structure. That is, the modulus is an [[intensive and extensive properties|intensive property]] of the material; stiffness, on the other hand, is an [[intensive and extensive properties|extensive property]] of the solid body dependent on the material ''and'' the shape and boundary conditions. For example, for an element in [[tension (mechanics)|tension]] or [[compression (physical)|compression]], the axial stiffness is

:<math>k=\frac {AE} {L} </math>

where
:''A'' is the cross-sectional area,
:''E'' is the (tensile) elastic modulus (or [[Young's modulus]]),
:''L'' is the length of the element.

Similarly, the rotational stiffness is

:<math>k=\frac {nGI} {L} </math>

where
:"I" is the polar moment of inertia,
:"n" is an integer depending on the boundary condition (=4 for fixed ends)
:"G" is the rigidity modulus of the material

For the special case of unconstrained uniaxial tension or compression, [[Young's modulus]] ''can'' be thought of as a measure of the stiffness of a material.

== Use in engineering ==
The stiffness of a structure is of principal importance in many engineering applications, so the [[modulus of elasticity]] is often one of the primary properties considered when selecting a material. A high modulus of elasticity is sought when [[Deflection (engineering)|deflection]] is undesirable, while a low modulus of elasticity is required when flexibility is needed.

== See also ==
*[[Elasticity (physics)]]
*[[Elastic modulus]]
*[[Mechanical impedance]]
*[[Hardness]]
*[[Hooke's law]]
*[[Moment of inertia]]
*[[Stiffness (mathematics)]]
*[[Young's modulus]]
*[[Compliant mechanism]]

== References ==
{{Reflist}}

[[Category:Physical quantities]]
[[Category:Continuum mechanics]]
[[Category:Structural analysis]]

Chitin disaccharide deacetylase

2013-11-05T17:32:17Z

143.239.189.72:

{{Infobox enzyme
| Name = Methylenediurea deaminase
| EC_number = 3.5.3.21
| CAS_number = 205830-62-2
| IUBMB_EC_number = 3/5/3/21
| GO_code =
| image =
| width =
| caption =
}}
'''Methylenediurea deaminase''' ({{EC number|3.5.3.21}}, ''methylenediurease'') is an [[enzyme]] with system name ''methylenediurea aminohydrolase''.<ref>{{cite journal | title = Purification and characterisation of an enzyme from a strain of Ochrobactrum anthroπ that degrades condensation products of urea and formaldehyde (ureaform) |author = Jahns, T., Schepp, R., Kaltwasser, H. |journal = Can. J. Microbiol. |date = 1997 |volume = 43 |pages = 1111-1117 |pmid = }}</ref> This enzyme [[catalysis|catalyses]] the following [[chemical reaction]]

: [[methylenediurea]] + 2 H2O <math>\rightleftharpoons</math> N-(hydroxymethyl)urea + 2 NH3 + CO2 (overall reaction)
: (1a) methylenediurea + H2O <math>\rightleftharpoons</math> N-(carboxyaminomethyl)urea + NH3
: (1b) N-(carboxyaminomethyl)urea <math>\rightleftharpoons</math> N-(aminomethyl)urea + CO2 (spontaneous)
: (1c) N-(aminomethyl)urea + H2O <math>\rightleftharpoons</math> N-(hydroxymethyl)urea + NH3 (spontaneous)

Methylenediurea is [[hydrolysed]] and [[decarboxylated]] to give an aminated methylurea.

== References ==
{{reflist}}

== External links ==
* {{MeshName|Methylenediurea+deaminase}}

[[Category:EC 3.5.3]]

Dynamical billiards

2012-07-17T17:58:19Z

143.239.66.52: /* Applications */

It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible. Here are some common dental emergencies: Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached. At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN. Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours. Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary. Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital. Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital. Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief. In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off. If you loved this write-up and you would certainly such as to obtain even more info concerning [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC] kindly browse through our own web-page.

Koebe quarter theorem

2012-07-03T11:23:10Z

143.239.76.69:

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