For example, the graph contains the points ( 1, 1 ), ( 2, 0. 5 ), ( 5, 0. 2 ), ( 10, 0. 1 ), ... As the values of x become larger and larger, say 100, 1000, 10, 000 ..., putting them far to the right of the illustration, the corresponding values of y,. 01,. 001,. 0001, ..., become infinitesimal relative to the scale shown.

where B is the magnitude of the magnetic field ( the magnetic flux density ) having the unit of Wb / m < sup > 2 </ sup > ( Tesla ), S is the area of the surface, and θ is the angle between the magnetic field lines and the normal ( perpendicular ) to S. For a varying magnetic field, we first consider the magnetic flux through an infinitesimal area element dS, where we may consider the field to be constant:

For example, the Laurent series consisting only of the constant term 1 is identified with the real number 1, and the series with only the linear term x is thought of as the simplest infinitesimal, from which the other infinitesimals are constructed.

For example, the basic infinitesimal x has a square root.

For a homogeneous system, with a well-defined temperature and pressure, the expression for dU can be written in terms of exact differentials, if the work that the system does is equal to its pressure times the infinitesimal increase in its volume.

For infinitesimal deformations of a continuum body, in which the displacements and the displacement gradients are small compared to unity, i. e., and, it is possible to perform a geometric linearisation of the Lagrangian finite strain tensor, and the Eulerian finite strain tensor.

For infinitesimal strains then we have

For example, in the infinitesimal expression, the contractile work energy associated with a thermodynamic system that is a contractile fiber that shortens by an amount − dl under a force f would result in a term fdl being added.

For a point dipole, the distance is infinitesimal, Taking into account that the two charges have opposite signs, the force takes the form

For example will be used to denote an infinitesimal increment of work.

For example, an infinitesimal compression of a gas in a cylinder where there exists friction between the piston and the cylinder is a quasistatic, but not reversible process.

For example one may talk about an infinitesimal rotation of a rigid body, in three-dimensional space.

For example, in the case of infinitesimal rotations, the Lie algebra structure is that provided by the cross product, once a skew-symmetric matrix has been identified with a 3-vector.

For an infinitesimal element, and assuming continuity on the displacement field, it is possible to use a Taylor series expansion around point, neglecting higher-order terms, to approximate the components of the relative displacement vector for the neighboring particle as

For infinitesimal strains ()

For FMJ bullets mounted in bottle neck cases, roll crimping is generally not ever used unless a cannelure is present on the bullet, to prevent causing bullet deformation when crimping.

For a four-dimensional spherical uncharged black hole, the deformation of the horizon is similar to the type of deformation which describes the emission and absorption of particles on a string-theory world sheet.

For example an F < sub > 2 </ sub > fold, with an S < sub > 2 </ sub > axial plane foliation would be the result of a D < sub > 2 </ sub > deformation.

For this reason wormholes have been defined geometrically, as opposed to topologically, as regions of spacetime that constrain the incremental deformation of closed surfaces.

He claimed, “ the best sites for ‘ earth art ’ are sites that have been disrupted by industry, reckless urbanization, or nature ’ s own devastation .” While in earlier 18th-century formal characterizations of the pastoral and the sublime, something like a “ gash in the ground ” if encountered by a “ leveling improver ”, as described by Price, would have been smoothed over and the whole composition returned to a more aesthetically pleasing contour For Smithson, however, it was not necessary that the deformation become a visual aspect of a landscape ; by his anti-formalist logic, more important was the temporal scar worked over by natural or human intervention.

For many applications, plastic deformation is unacceptable, and is used as the design limitation.

For nuclei near these magic numbers, the shell correction creates a second minimum in the energy as a function of deformation.

Also, starting with any compact real form of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain solvable Lie algebra ( the Iwasawa decomposition ), and this provides a canonical bicrossproduct quantum group associated to g. For su ( 2 ) one obtains a quantum group deformation of the Euclidean group E ( 3 ) of motions in 3 dimensions.

For example, in Riemann surface theory, the deformation theory of complex structures is studied classically by means of quadratic differentials ( namely sections of L ( K < sup > 2 </ sup >)).

For example when a body is moved rapidly through a fluid it causes more rapid deformation of fluid element than one moving slowly.

For example, tungsten requires a temperature in the thousands of degrees before creep deformation can occur while ice will creep near 0 ° C ( 32 ° F ).

For example, during earthquakes, reinforced concrete members may experience lateral deformation of the longitudinal reinforcing bars.

For example, ΣΤΗΡΟΣΣΥ on his Hermaeus coins is thought to be a deformation of ΣΩΤΗΡΟΣ ( Sotiros ), the traditional title of Hermaeus on his coins.

For the special case of plane strain deformation, becomes and is considered a material property.

For the general linear group, this decomposition is the QR decomposition, and the deformation retraction is the Gram-Schmidt process.

For metal objects designed to flex, such as springs, specialized alloys are usually employed in order to avoid work hardening ( a result of plastic deformation ) and metal fatigue, with specific heat treatments required to obtain the necessary characteristics.

For instance, having a single point as a deformation retract would imply a space is path connected ( in fact, it would imply contractibility of the space ).

For example, cranial deformation is evident in the skulls of the Maya, where a straight line between nose and forehead may have been preferred over an angle or slope.

For Newtonian fluids, the pressure drop increases linearly with flow rate and the measured viscosity does not depend upon applied deformation rate or stress.

For a pure shear deformation

For prescribed strain components the strain tensor equation represents a system of six differential equations for the determination of three displacements components, giving an over-determined system.

For virtual displacements only, the differential form of the constraint is

For example, to derive the principle of virtual displacements in variational notations for supported bodies, we specify:

For that particular site, “ Predicted seabed soil displacements beneath the maximum ice keel gouge depth ( 3. 5 ft ) yielded a 7-ft minimum depth of cover for pipe bending strains up to 1. 4 %” ( Lanan et al.

When gravitation waves with frequencies around 3, 000 Hz pass through the MiniGRAIL ball, it will vibrate with displacements on the order of 10 < sup >− 20 </ sup > m. For comparison, the cross-section of a single proton ( the nucleus of a hydrogen atom ), is 10 < sup >− 15 </ sup > m ( 1 fm ).

For example a 1 MeV neutron striking graphite will create 900 displacements, however not all displacements will create defects because some of the struck atoms will find and fill the vacancies that were either small pre-existing voids or vacancies newly formed by the other struck atoms.