3613:
3197:
3608:{\displaystyle {\begin{aligned}\mathbf {P} (\mathbf {r} ,t)&=\varepsilon _{0}\int {\rm {d}}^{3}\mathbf {r} '{\rm {d}}t'\;{\hat {\chi }}_{e}\left(\mathbf {r} ,\mathbf {r} ',t,t';\mathbf {E} \right)\,\mathbf {E} \left(\mathbf {r} ',t'\right)\\\mathbf {M} (\mathbf {r} ,t)&={\frac {1}{\mu _{0}}}\int {\rm {d}}^{3}\mathbf {r} '{\rm {d}}t'\;{\hat {\chi }}_{m}\left(\mathbf {r} ,\mathbf {r} ',t,t';\mathbf {B} \right)\,\mathbf {B} \left(\mathbf {r} ',t'\right),\end{aligned}}}
2306:
1988:. In the context of electromagnetism, this remark applies to not only the dynamics of free charges and currents (which enter Maxwell's equations directly), but also the dynamics of bound charges and currents (which enter Maxwell's equations through the constitutive relations). As a result, various approximation schemes are typically used.
2100:
1118:
If the material is close to elastic, but the applied force induces additional time-dependent resistive forces (i.e. depend on rate of change of extension/compression, in addition to the extension/compression). Metals and ceramics have this characteristic, but it is usually negligible, although not so
790:
This can be applied to static friction (friction preventing two stationary objects from slipping on their own), kinetic friction (friction between two objects scraping/sliding past each other), or rolling (frictional force which prevents slipping but causes a torque to exert on a round object).
6839:
3748:
In practice, some materials properties have a negligible impact in particular circumstances, permitting neglect of small effects. For example: optical nonlinearities can be neglected for low field strengths; material dispersion is unimportant when frequency is limited to a narrow
4868:
1746:
3743:
2301:{\displaystyle {\begin{aligned}\mathbf {D} (\mathbf {r} ,t)&=\varepsilon _{0}\mathbf {E} (\mathbf {r} ,t)+\mathbf {P} (\mathbf {r} ,t)\\\mathbf {H} (\mathbf {r} ,t)&={\frac {1}{\mu _{0}}}\mathbf {B} (\mathbf {r} ,t)-\mathbf {M} (\mathbf {r} ,t),\end{aligned}}}
1056:
2804:
165:
advanced the use of constitutive equations, clarifying their classification and the role of invariance requirements, constraints, and definitions of terms like "material", "isotropic", "aeolotropic", etc. The class of "constitutive relations" of the form
2564:
2416:
1244:
2917:
2661:
3146:
7159:
1616:
6579:
2075:, before doing calculations in electromagnetism (i.e. applying Maxwell's macroscopic equations). These equations specify the response of bound charge and current to the applied fields and are called constitutive relations.
5538:
6972:
6716:
4623:
5132:
1815:
6447:
3817:
The local fields differ from the applied fields due to the fields produced by the polarization and magnetization of nearby material; an effect which also needs to be modeled. Further, real materials are not
7588:
Inverse problems, multi-scale analysis and effective medium theory : workshop in Seoul, Inverse problems, multi-scale analysis, and homogenization, June 22ā24, 2005, Seoul
National University, Seoul,
6184:
5762:
4767:
1494:
5633:
1627:
5984:
5383:
1110:
If the time-dependent resistive contributions are large, and cannot be neglected. Rubbers and plastics have this property, and certainly do not satisfy Hooke's law. In fact, elastic hysteresis occurs.
5041:
3669:
161:. Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
5436:
3202:
2105:
417:
6274:
1380:
3806:. Other forces may need to be modeled as well such as lattice vibrations in crystals or bond forces. Including all of the forces leads to changes in the molecule which are used to calculate
5689:
5220:
4232:
941:
4985:
4046:
7083:
6086:
4512:
4427:
2688:
4325:
4141:
926:
336:
490:
5893:
4715:
573:
2489:
785:
2814:
For real-world materials, the constitutive relations are not linear, except approximately. Calculating the constitutive relations from first principles involves determining how
3035:
931:
In general, forces which deform solids can be normal to a surface of the material (normal forces), or tangential (shear forces), this can be described mathematically using the
6035:
5837:
646:
6233:
6134:
869:
7228:
charges and currents is dealt with using grosser methods subsumed under the notions of magnetization and polarization. Depending upon the problem, one may choose to have
4927:
The relative refractive index is defined as the ratio of the two refractive indices. Absolute is for one material, relative applies to every possible pair of interfaces;
3182:, or most commonly in the situation where there are simply multiple materials occupying different regions of space. Or it could be due to a time varying medium or due to
272:
2349:
7292:
1174:
1929:
7828:
2859:
698:
6708:
5296:
121:. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as
2835:
2605:
1094:
The applied force induces non-recoverable deformations in the material when the stress (or elastic strain) reaches a critical magnitude, called the yield point.
3822:; the local fields of real materials vary wildly on the atomic scale. The fields need to be averaged over a suitable volume to form a continuum approximation.
7092:
1530:
3877:
The theoretical modeling of the continuum-approximation properties of many real materials often rely upon experimental measurement as well. For example,
6514:
6291:
There are several laws which describe the transport of matter, or properties of it, in an almost identical way. In every case, in words they read:
1991:
For example, in real materials, complex transport equations must be solved to determine the time and spatial response of charges, for example, the
6670:
6660:
6046:
5848:
7783:
6834:{\displaystyle {\frac {\partial V}{\partial x_{j}}}=\rho _{ji}J_{i}\,\rightleftharpoons \,J_{i}=\sigma _{ij}{\frac {\partial V}{\partial x_{j}}}}
2038:
These complex theories provide detailed formulas for the constitutive relations describing the electrical response of various materials, such as
5482:
7319:
7182:
3846:
2948:
2032:
6904:
7477:
7385:
6621:
5995:
3802:. In general, the constitutive equations are theoretically determined by calculating how a molecule responds to the local fields through the
7418:
4555:
5078:
1757:
129:. However, it is often necessary to account for the directional dependence of the material, and the scalar parameter is generalized to a
6379:
3794:
The theoretical calculation of a material's constitutive equations is a common, important, and sometimes difficult task in theoretical
7767:
7720:
7624:
7597:
7505:
7439:
7338:
7263:
7192:
6140:
4863:{\displaystyle n={\frac {c_{0}}{c}}={\sqrt {\frac {\varepsilon \mu }{\varepsilon _{0}\mu _{0}}}}={\sqrt {\varepsilon _{r}\mu _{r}}}}
3175:
1249:
which depends on the materials A and B are made from, since the collision involves interactions at the surfaces of A and B. Usually
7253:
5716:
1741:{\displaystyle e_{ij}={\frac {1}{2}}\left({\frac {\partial v_{i}}{\partial x_{j}}}+{\frac {\partial v_{j}}{\partial x_{i}}}\right)}
2327:
field which are defined in terms of microscopic bound charges and bound current respectively. Before getting to how to calculate
1450:
5595:
3738:{\displaystyle \mathbf {D} =\varepsilon \mathbf {E} +\xi \mathbf {H} \,,\quad \mathbf {B} =\mu \mathbf {H} +\zeta \mathbf {E} .}
5918:
5342:
3866:
2679:
2043:
1960:
7493:
5008:
3789:
1128:
7539:
7007:
5389:
7614:
7823:
7818:
6472:
5308:
3750:
381:
7757:
6239:
1113:
6308:
In general the constant must be replaced by a 2nd rank tensor, to account for directional dependences of the material.
2961:
2000:
1051:{\displaystyle \sigma _{ij}=C_{ijkl}\,\varepsilon _{kl}\,\rightleftharpoons \,\varepsilon _{ij}=S_{ijkl}\,\sigma _{kl}}
2054:
1326:
7710:
7658:
1996:
5656:
5160:
4178:
4933:
2799:{\displaystyle \varepsilon /\varepsilon _{0}=\varepsilon _{r}=\chi _{e}+1,\quad \mu /\mu _{0}=\mu _{r}=\chi _{m}+1}
1165:
1161:
103:
3985:
3838:
107:
7049:
6979:
6058:
4468:
4383:
3842:
2847:
2028:
190:
186:
4271:
4087:
3964:
3882:
3834:
3795:
2839:
2024:
1306:
182:
138:
7586:
901:
304:
5905:
3944:
3620:
3616:
2588:
2584:
2559:{\displaystyle \mathbf {P} =\varepsilon _{0}\chi _{e}\mathbf {E} ,\quad \mathbf {M} =\chi _{m}\mathbf {H} ,}
2047:
1964:
889:
815:
in a scalar equation, stating the tensile/compressive force is proportional to the extended (or contracted)
444:
292:
158:
122:
7659:"Multiresolution Homogenization of Field and Network Formulations for Multiscale Laminate Dielectric Slabs"
7404:, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3
5860:
4667:
3857:
1978:
513:
114:
1396:
depends on the geometry of the object and the drag forces at the interface between the fluid and object.
751:
5797:
4433:
3633:
2960:
are functions of frequency. (Causality does not permit materials to be nondispersive; see, for example,
2831:
1985:
1981:
1122:
816:
7791:
6007:
5809:
600:
133:. Constitutive relations are also modified to account for the rate of response of materials and their
7673:
7454:
The generalization to non-isotropic materials is straight forward; simply replace the constants with
6893:
6868:
6853:
6601:
5584:
5549:
4070:
3830:
3615:
in which the permittivity and permeability functions are replaced by integrals over the more general
2316:
2012:
2004:
1272:
1097:
6214:
6115:
1153:
of an object A after a collision with another object B is related to the relative speed of approach
6097:
3906:
3819:
2944:
2843:
1089:
828:
91:
87:
47:
2830:. These relations may be empirical (based directly upon measurements), or theoretical (based upon
2411:{\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} ,\quad \mathbf {H} =\mathbf {B} /\mu _{0}}
7730:
7348:
7273:
7187:
6636:
5644:
3624:
1992:
932:
875:
732:
243:
222:
175:
51:
3753:; material absorption can be neglected for wavelengths for which a material is transparent; and
1239:{\displaystyle e={\frac {|\mathbf {v} |_{\text{separation}}}{|\mathbf {v} |_{\text{approach}}}}}
882:
428:
7763:
7716:
7620:
7593:
7501:
7473:
7435:
7414:
7381:
7334:
7259:
6997:
6503:
5450:
5143:
3826:
3799:
3762:
2912:{\displaystyle \mathbf {D} =\varepsilon \mathbf {E} ,\quad \mathbf {H} =\mu ^{-1}\mathbf {B} }
2444:
2436:
2023:. An entire physical apparatus for dealing with these matters has developed. See for example,
2016:
1970:
1852:
1074:
1066:
7413:
Essential
Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray,
7224:
law and this response is calculated at a fundamental level using mechanics. The response of
738:
at a point of contact between two interfaces through a dimensionless coefficient of friction
7681:
7375:
6847:
6611:
6347:
4743:
4735:
4728:
4147:
4052:
3777:
3171:
2980:
1899:
1386:
1119:
much when heating due to friction occurs (such as vibrations or shear stresses in machines).
95:
5154:, which are coupled by a fourth-rank tensor called the piezooptic coefficient Ī (units K):
2656:{\displaystyle \mathbf {D} =\varepsilon \mathbf {E} ,\quad \mathbf {H} =\mathbf {B} /\mu ,}
2343:
In the absence of magnetic or dielectric materials, the constitutive relations are simple:
669:
7742:
7706:
7565:
7360:
7285:
6684:
6650:
5272:
4921:
4747:
4352:
3954:
3902:
3141:{\displaystyle D_{i}=\sum _{j}\varepsilon _{ij}E_{j},\quad B_{i}=\sum _{j}\mu _{ij}H_{j}.}
2020:
1974:
1865:
1400:
808:
800:
657:
366:
126:
118:
99:
79:
67:
63:
7677:
7401:
7154:{\displaystyle I=\varepsilon \sigma \left(T_{\text{ext}}^{4}-T_{\text{sys}}^{4}\right)}
6640:
6454:
4999:
4991:
4629:
4518:
3623:
susceptibilities. In homogeneous materials, dependence on other locations is known as
3179:
3004:
2973:
2065:
2008:
1299:
1143:
804:
154:
17:
7812:
7221:
6368:
6326:
5259:
4254:
3803:
3010:
2324:
1984:, which are almost always too complicated to be solved exactly, even at the level of
1873:
1830:
1611:{\displaystyle \tau _{ij}=2\mu \left(e_{ij}-{\frac {1}{3}}\Delta \delta _{ij}\right)}
1422:
1295:
501:
2475:, the constitutive relations are also straightforward. In terms of the polarization
3890:
3773:
2675:
2039:
1956:
1939:
1411:
1283:
1105:
584:
150:
75:
6586:
6574:{\displaystyle q_{j}=-{\frac {\kappa }{\mu }}{\frac {\partial P}{\partial x_{j}}}}
7545:
7568:, "Local-field effects and effective-medium theory: A microscopic perspective",
3977:
3932:
1418:
171:
162:
35:
2682:, respectively, of the material. These are related to the susceptibilities by:
7613:
O. C. Zienkiewicz; Robert Leroy Taylor; J. Z. Zhu; Perumal
Nithiarasu (2005).
7035:
3871:
3766:
3183:
1441:
731:
between the interface of two materials can be modelled as proportional to the
134:
55:
7313:
3864:) are based upon approximation of an inhomogeneous material by a homogeneous
7685:
7306:
6878:
6482:
6330:
6196:
5573:
4653:
3758:
3016:
2456:
1404:
83:
1515:. In general, for a Newtonian fluid, the relationship between the elements
7689:
5533:{\displaystyle \left({\frac {\partial V}{\partial T}}\right)_{p}=\gamma V}
27:
Relation between two physical quantities which is specific to a substance
7318:
Clifford
Truesdell & Walter Noll ā Stuart S. Antman (editor) (2004).
7197:
3861:
1425:
724:
720:
227:
7643:(Kluwer: Dordrecht, 1989); V. V. Jikov, S. M. Kozlov and O. A. Oleinik,
6967:{\displaystyle q_{i}=-\lambda _{ij}{\frac {\partial T}{\partial x_{j}}}}
6303:, the constant of proportionality is the characteristic of the material.
4895:
are the relative permeability of the medium. The vacuum permittivity is
1524:
of the shear stress tensor and the deformation of the fluid is given by
1085:
Several classes of deformations in elastic materials are the following:
66:, and approximates its response to external stimuli, usually as applied
7252:
Clifford
Truesdell & Walter Noll; Stuart S. Antman, editor (2004).
6591:, defines electric conductivity (and hence resistivity and resistance)
4445:
3881:
of an insulator at low frequencies can be measured by making it into a
2078:
Determining the constitutive relationship between the auxiliary fields
31:
7520:
Note that the 'magnetic susceptibility' term used here is in terms of
7167:ā¤ 1; 0 for perfect reflector, 1 for perfect absorber (true black body)
4618:{\displaystyle E_{i}=-\beta _{ij}{\frac {\partial T}{\partial x_{j}}}}
2094:
fields starts with the definition of the auxiliary fields themselves:
874:
meaning the material responds linearly. Equivalently, in terms of the
7455:
3029:
2853:
In general, the constitutive relations can usually still be written:
2440:
130:
59:
7619:(Sixth ed.). Oxford UK: Butterworth-Heinemann. p. 550 ff.
2850:, depending upon the level necessary to the problem under scrutiny.
1127:
The applied force induces displacements in the material following a
149:
The first constitutive equation (constitutive law) was developed by
5127:{\displaystyle c_{0}={\frac {1}{\sqrt {\varepsilon _{0}\mu _{0}}}}}
1810:{\displaystyle \Delta =\sum _{k}e_{kk}={\text{div}}\;\mathbf {v} ,}
3754:
71:
7645:
Homogenization of
Differential Operators and Integral Functionals
6442:{\displaystyle J_{i}=-D_{ij}{\frac {\partial C}{\partial x_{j}}}}
7715:. Singapore: World Scientific Publishing Company. p. 155.
3780:
are designed to have customized permittivity and permeability.
2930:
are not, in general, simple constants, but rather functions of
2591:
susceptibilities of a given material respectively. In terms of
6179:{\displaystyle R_{\text{m}}={\frac {\mathcal {M}}{\Phi _{B}}}}
7592:. Providence RI: American Mathematical Society. p. 282.
5757:{\displaystyle R={\frac {1}{U}}={\frac {\Delta x}{\lambda }}}
2964:.) Neither do the fields need to be in phase, which leads to
6220:
6160:
6121:
3765:
with infinite conductivity (forming hard barriers with zero
2938:, position and time, and tensorial in nature. Examples are:
1951:
Constitutive equations in electromagnetism and related areas
278:
is the perpendicular component of the force applied to area
7657:
Vitaliy
Lomakin; Steinberg BZ; Heyman E; Felsen LB (2003).
3632:
As a variation of these examples, in general materials are
1489:{\displaystyle \tau =\mu {\frac {\partial u}{\partial y}},}
1102:
The material recovers its initial shape after deformation.
7541:
Electromagnetic
Anisotropy and Bianisotropy: A Field Guide
7524:
and is different from the standard definition in terms of
5628:{\displaystyle \lambda =-{\frac {\mathbf {q} }{\nabla T}}}
3825:
These continuum approximations often require some type of
7434:. Cambridge University Press. pp. 10 & 122ā124.
5979:{\displaystyle \rho -\rho _{0}=\rho _{0}\alpha (T-T_{0})}
5378:{\displaystyle {\frac {\partial L}{\partial T}}=\alpha L}
3856:(evolving from a tradition in treating materials such as
2674:
are constants (which depend on the material), called the
7712:
Topics in
Analysis and Its Applications: Selected Theses
6774:
995:
7220:
charges and currents respond to the fields through the
5775:
Definitions (electrical/magnetic properties of matter)
5036:{\displaystyle c={\frac {1}{\sqrt {\varepsilon \mu }}}}
4742:(dimensionless) is an inherently important property of
3897:
Thermoelectric and electromagnetic properties of matter
1851:
are the components of the strain rate tensor, Ī is the
5431:{\displaystyle \varepsilon _{ij}=\alpha _{ij}\Delta T}
5325:, coefficient linear thermal expansion (dimensionless)
90:
the response of a crystal to an electric field, or in
7641:
Homogenization: Averaging
Processes in Periodic Media
7095:
7052:
6907:
6719:
6687:
6517:
6382:
6242:
6217:
6143:
6118:
6061:
6010:
5921:
5863:
5812:
5719:
5659:
5598:
5485:
5392:
5345:
5275:
5163:
5081:
5011:
4936:
4770:
4670:
4558:
4471:
4386:
4274:
4181:
4090:
3988:
3672:
3200:
3038:
2862:
2691:
2608:
2492:
2352:
2335:
it is useful to examine the following special cases.
2103:
1902:
1877:
is a constitutive relation in the sense the pressure
1760:
1630:
1533:
1453:
1329:
1177:
944:
904:
831:
754:
672:
603:
516:
447:
384:
307:
246:
7323:(Originally published as Volume III/3 of the famous
4750:
defined as the ratio of the luminal speed in vacuum
185:, the constitutive equation plays a major role. See
168:
stress rate = f (velocity gradient, stress, density)
3757:with finite conductivity often are approximated at
3166:at other locations and times. This could be due to
412:{\displaystyle E_{\text{mod}}=\sigma /\varepsilon }
74:. They are combined with other equations governing
7153:
7077:
6966:
6833:
6702:
6573:
6441:
6269:{\displaystyle \Lambda ={\frac {1}{R_{\text{m}}}}}
6268:
6227:
6178:
6128:
6080:
6029:
5978:
5887:
5831:
5756:
5683:
5627:
5532:
5430:
5377:
5290:
5214:
5126:
5035:
4979:
4884:the relative permittivity of the medium, likewise
4862:
4709:
4617:
4506:
4421:
4319:
4226:
4135:
4040:
3889:at optical-light frequencies is often measured by
3874:much larger than the scale of the inhomogeneity).
3737:
3607:
3140:
2911:
2798:
2655:
2558:
2410:
2300:
1923:
1809:
1740:
1610:
1488:
1374:
1238:
1050:
920:
863:
779:
723:is a complicated phenomenon. Macroscopically, the
692:
640:
567:
484:
411:
330:
266:
2053:It is necessary to specify the relations between
1977:, the precise dynamics of a system form a set of
7310:The naturalization and apotheosis of Walter Noll
1375:{\displaystyle D={\frac {1}{2}}c_{d}\rho Av^{2}}
3901:These constitutive equations are often used in
5684:{\displaystyle U={\frac {\lambda }{\delta x}}}
5215:{\displaystyle a_{ij}=\Pi _{ijpq}\sigma _{pq}}
4227:{\displaystyle \varepsilon _{ij}=d_{ijk}E_{k}}
58:quantities) that is specific to a material or
7666:IEEE Transactions on Antennas and Propagation
7377:Quantum Field Theory of Nonequilibrium States
4980:{\displaystyle n_{AB}={\frac {n_{A}}{n_{B}}}}
8:
807:. In its simplest form, the law defines the
799:The stress-strain constitutive relation for
7762:. London UK: Academic Press. p. 1114.
5236:Definitions (thermal properties of matter)
4041:{\displaystyle E_{k}=\rho _{kij}J_{i}H_{j}}
78:to solve physical problems; for example in
7331:The Non-linear Field Theories of Mechanics
7316:and the classic treatise by both authors:
7255:The Non-linear Field Theories of Mechanics
7078:{\displaystyle I=\varepsilon \sigma T^{4}}
7028:, temperature of external surroundings (K)
6081:{\displaystyle \sigma ={\frac {1}{\rho }}}
4507:{\displaystyle \Delta S=p_{i}\Delta E_{i}}
4422:{\displaystyle \Delta P_{j}=p_{j}\Delta T}
3488:
3286:
1798:
745:, which depends on the pair of materials:
7291:CS1 maint: multiple names: authors list (
7140:
7135:
7122:
7117:
7094:
7069:
7051:
6955:
6937:
6928:
6912:
6906:
6822:
6804:
6795:
6782:
6777:
6773:
6767:
6754:
6738:
6720:
6718:
6686:
6562:
6544:
6534:
6522:
6516:
6430:
6412:
6403:
6387:
6381:
6258:
6249:
6241:
6219:
6218:
6216:
6168:
6159:
6157:
6148:
6142:
6120:
6119:
6117:
6068:
6060:
6017:
6009:
5967:
5945:
5932:
5920:
5870:
5862:
5819:
5811:
5739:
5726:
5718:
5666:
5658:
5610:
5608:
5597:
5515:
5491:
5484:
5413:
5397:
5391:
5346:
5344:
5274:
5203:
5184:
5168:
5162:
5115:
5105:
5095:
5086:
5080:
5018:
5010:
4969:
4959:
4953:
4941:
4935:
4852:
4842:
4836:
4823:
4813:
4797:
4783:
4777:
4769:
4701:
4688:
4675:
4669:
4606:
4588:
4579:
4563:
4557:
4498:
4485:
4470:
4407:
4394:
4385:
4320:{\displaystyle M_{i}=q_{ijk}\sigma _{jk}}
4308:
4292:
4279:
4273:
4218:
4202:
4186:
4180:
4173:, direct piezoelectric coefficient (Cā
N)
4136:{\displaystyle P_{i}=d_{ijk}\sigma _{jk}}
4124:
4108:
4095:
4089:
4082:, direct piezoelectric coefficient (Cā
N)
4032:
4022:
4006:
3993:
3987:
3727:
3716:
3705:
3700:
3695:
3684:
3673:
3671:
3573:
3562:
3561:
3551:
3522:
3513:
3502:
3491:
3490:
3474:
3473:
3464:
3457:
3451:
3450:
3438:
3429:
3408:
3400:
3371:
3360:
3359:
3349:
3320:
3311:
3300:
3289:
3288:
3272:
3271:
3262:
3255:
3249:
3248:
3238:
3213:
3205:
3201:
3199:
3129:
3116:
3106:
3093:
3079:
3066:
3056:
3043:
3037:
2904:
2895:
2883:
2874:
2863:
2861:
2784:
2771:
2758:
2749:
2730:
2717:
2704:
2695:
2690:
2642:
2637:
2629:
2620:
2609:
2607:
2548:
2542:
2530:
2521:
2515:
2505:
2493:
2491:
2402:
2393:
2388:
2380:
2371:
2365:
2353:
2351:
2277:
2269:
2252:
2244:
2236:
2227:
2206:
2198:
2180:
2172:
2155:
2147:
2141:
2116:
2108:
2104:
2102:
1901:
1799:
1793:
1781:
1771:
1759:
1724:
1709:
1699:
1687:
1672:
1662:
1647:
1635:
1629:
1594:
1577:
1565:
1538:
1532:
1511:in the cross-flow (transverse) direction
1463:
1452:
1366:
1350:
1336:
1328:
1227:
1222:
1216:
1211:
1203:
1198:
1192:
1187:
1184:
1176:
1039:
1034:
1019:
1003:
998:
994:
985:
980:
965:
949:
943:
914:
903:
855:
836:
830:
765:
753:
682:
671:
627:
613:
602:
554:
540:
529:
515:
471:
457:
446:
401:
389:
383:
320:
306:
256:
245:
7470:Spatial dispersion in solids and plasmas
7400:Encyclopaedia of Physics (2nd Edition),
7333:(3rd ed.). Springer. p. xiii.
6310:
5773:
5451:Volumetric thermal expansion coefficient
5234:
4998:As a consequence of the definition, the
4331:
3911:
2435:are two universal constants, called the
2339:Without magnetic or dielectric materials
200:
7759:Handbook of Optical Constants of Solids
7709:(Ronald R Coifman, Editor) (May 2000).
7244:
7209:
6356:, diffusion flux of substance (molā
mā
s)
1264:for completely elastic collisions, and
921:{\displaystyle \sigma =E\,\varepsilon }
331:{\displaystyle \varepsilon =\Delta D/D}
113:Some constitutive equations are simply
7829:Electric and magnetic fields in matter
7738:
7728:
7432:Fluid Mechanics and Transfer Processes
7356:
7346:
7281:
7271:
7183:Defining equation (physical chemistry)
4341:Stimuli/response parameters of system
3921:Stimuli/response parameters of system
485:{\displaystyle Y=\sigma /(\Delta L/L)}
7019:, temperature of radiating system (K)
5888:{\displaystyle \rho ={\frac {RA}{l}}}
4529:, electric field strength (Nā
C = Vā
m)
3913:Electromagnetic properties of solids
3784:Calculation of constitutive relations
1507:) the variation of the flow velocity
7:
7585:Habib Ammari; Hyeonbae Kang (2006).
5711:, displacement of heat transfer (m)
4710:{\displaystyle q_{j}=\Pi _{ji}J_{i}}
4333:Thermoelectric properties of solids
4266:, piezomagnetic coefficient (Aā
Nā
m)
568:{\displaystyle G=(F/A)/(\Delta x/L)}
7784:"2. Physical Properties as Tensors"
6491:, discharge flux of substance (mā
s)
5474:, constant pressure of surroundings
4463:, pyroelectric coefficient (Cā
mā
K)
4378:, pyroelectric coefficient (Cā
mā
K)
3814:as a function of the local fields.
2033:Green's function (many-body theory)
780:{\displaystyle F=\mu _{\text{f}}R.}
7544:. World Scientific. Archived from
6948:
6940:
6815:
6807:
6731:
6723:
6555:
6547:
6423:
6415:
6243:
6165:
5742:
5616:
5502:
5494:
5422:
5357:
5349:
5181:
4685:
4599:
4591:
4491:
4472:
4413:
4387:
3475:
3452:
3273:
3250:
1761:
1717:
1702:
1680:
1665:
1587:
1474:
1466:
1312:moving through a fluid of density
621:
548:
465:
344:, dimension (length, area, volume)
314:
46:is a relation between two or more
25:
7756:Edward D. Palik; Ghosh G (1998).
7500:(3rd ed.). New York: Wiley.
7193:Principle of material objectivity
5150:to the dielectric impermeability
4363:, (dielectric) polarization (Cā
m)
351:, change in dimension of material
94:, the connection between applied
6334:, defines diffusion coefficient
6030:{\displaystyle G={\frac {1}{R}}}
5908:, linear temperature dependence
5832:{\displaystyle R={\frac {V}{I}}}
5611:
4646:, electric current density (Aā
m)
3772:Some man-made materials such as
3728:
3717:
3706:
3696:
3685:
3674:
3574:
3563:
3552:
3523:
3514:
3465:
3409:
3401:
3372:
3361:
3350:
3321:
3312:
3263:
3214:
3206:
2976:. This also leads to absorption.
2905:
2884:
2875:
2864:
2638:
2630:
2621:
2610:
2599:the constitutive relations are:
2549:
2531:
2522:
2494:
2389:
2381:
2372:
2354:
2278:
2270:
2253:
2245:
2207:
2199:
2181:
2173:
2156:
2148:
2117:
2109:
1800:
1217:
1193:
1166:Newton's experimental impact law
641:{\displaystyle B=P/(\Delta V/V)}
7639:N. Bakhvalov and G. Panasenko,
7538:TG Mackay; A Lakhtakia (2010).
5331:, strain tensor (dimensionless)
5146:relates the stresses in solids
4640:, electric field strength (Nā
C)
4454:, electric field strength (Nā
C)
4164:, electric field strength (Nā
C)
3704:
3088:
2882:
2745:
2628:
2529:
2379:
1961:Permeability (electromagnetism)
1885:are related to the temperature
191:Nonlinear correlation functions
145:Mechanical properties of matter
7380:. Cambridge University Press.
6457:for fluid flow in porous media
6371:gradient of substance (molā
dm)
6228:{\displaystyle {\mathcal {P}}}
6129:{\displaystyle {\mathcal {R}}}
5973:
5954:
4344:Constitutive tensor of system
3924:Constitutive tensor of system
3790:Computational electromagnetics
3496:
3419:
3405:
3294:
3224:
3210:
2842:). The detail employed may be
2288:
2274:
2263:
2249:
2217:
2203:
2191:
2177:
2166:
2152:
2127:
2113:
1855:rate (or dilatation rate) and
1223:
1212:
1199:
1188:
1129:strain energy density function
635:
618:
562:
545:
537:
523:
479:
462:
174:'s dissertation in 1954 under
1:
5309:thermal expansion coefficient
5267:, heat capacity of substance
4662:Ī , Peltier coefficient (Wā
A)
4148:Converse Piezoelectric Effect
2447:of free space, respectively.
864:{\displaystyle F_{i}=-kx_{i}}
187:Linear constitutive equations
7472:. Amsterdam: North-Holland.
7086:For a temperature difference
5046:for special case of vacuum;
3870:(valid for excitations with
1833:vector in the corresponding
157:. It deals with the case of
7305:See Truesdell's account in
4902:and vacuum permeability is
4053:Direct Piezoelectric Effect
1417:is linearly related to the
1286:(or explosive) collisions.
267:{\displaystyle \sigma =F/A}
7845:
3787:
2451:Isotropic linear materials
1954:
1889:, via the number of moles
1829:are the components of the
1162:coefficient of restitution
137:behavior. See the article
117:; others are derived from
7647:(Springer: Berlin, 1994).
7616:The Finite Element Method
7498:Classical Electrodynamics
7008:StefanāBoltzmann constant
6319:
6316:
6313:
5791:
5788:
5785:
5782:
5780:Quantity (common name/s)
5779:
5252:
5249:
5246:
5243:
5241:Quantity (common name/s)
5240:
4346:
4343:
4340:
4337:
3926:
3923:
3920:
3917:
3839:density functional theory
3761:or longer wavelengths as
3652:, through the additional
2822:are created from a given
2459:) linear material, where
811:(or elasticity constant)
215:
212:
209:
206:
204:Quantity (common name/s)
203:
84:flow of a fluid in a pipe
54:quantities as related to
7232:free charges whatsoever.
6643:) through material (Vā
m)
5319:, length of material (m)
4888:is the permeability and
4877:is the permittivity and
4158:, Strain (dimensionless)
3965:magnetic field intensity
3883:parallel-plate capacitor
3835:condensed matter physics
3796:condensed-matter physics
2962:KramersāKronig relations
2840:condensed matter physics
1320:(relative to the fluid)
1081:Solid-state deformations
183:condensed matter physics
159:linear elastic materials
139:Linear response function
7686:10.1109/TAP.2003.816356
7325:Encyclopedia of Physics
7258:. Springer. p. 4.
6982:of black-body radiation
6712:More general forms are:
6459:, defines permeability
6047:Electrical conductivity
5906:temperature coefficient
3945:electric field strength
3769:of field penetration).
2001:NavierāStokes equations
1965:Electrical conductivity
1842:coordinate directions,
123:electrical conductivity
7468:Halevi, Peter (1992).
7374:JĆørgen Rammer (2007).
7155:
7079:
7045:For a single radiator:
6968:
6881:through material (Wā
m)
6835:
6704:
6653:through material (Aā
m)
6589:of electric conduction
6575:
6443:
6270:
6229:
6180:
6130:
6082:
6031:
5996:Electrical conductance
5980:
5889:
5833:
5758:
5685:
5629:
5576:through material (W/m)
5534:
5468:, volume of object (m)
5432:
5379:
5292:
5216:
5128:
5037:
4981:
4864:
4757:to that in the medium
4711:
4619:
4508:
4423:
4321:
4228:
4137:
4042:
3854:homogenization methods
3739:
3609:
3194:can be calculated as:
3142:
2913:
2800:
2657:
2560:
2479:and the magnetization
2412:
2302:
2025:linear response theory
1997:FokkerāPlanck equation
1982:differential equations
1925:
1924:{\displaystyle pV=nRT}
1811:
1742:
1612:
1490:
1376:
1240:
1052:
922:
865:
781:
694:
642:
569:
486:
413:
332:
268:
18:Constitutive relations
7575:, pp. 704ā709 (1982).
7156:
7080:
6984:, defines emmisivity
6969:
6850:of thermal conduction
6836:
6705:
6576:
6444:
6348:diffusion coefficient
6299:is proportional to a
6271:
6230:
6181:
6131:
6083:
6032:
5981:
5890:
5834:
5798:Electrical resistance
5759:
5686:
5630:
5535:
5433:
5380:
5293:
5217:
5129:
5038:
4982:
4865:
4712:
4620:
4509:
4434:Electrocaloric effect
4424:
4322:
4238:Piezomagnetic effect
4229:
4138:
4043:
3740:
3610:
3168:spatial inhomogeneity
3143:
2914:
2832:statistical mechanics
2801:
2658:
2561:
2413:
2303:
1986:statistical mechanics
1926:
1812:
1743:
1613:
1491:
1377:
1290:Deformation of fluids
1275:. It is possible for
1241:
1053:
923:
866:
803:is commonly known as
782:
711:Deformation of solids
695:
693:{\displaystyle C=1/B}
643:
570:
487:
414:
333:
269:
44:constitutive relation
40:constitutive equation
7824:Equations of physics
7819:Elasticity (physics)
7093:
7050:
6980:StefanāBoltzmann law
6905:
6894:temperature gradient
6871:of material (Wā
mā
K )
6869:thermal conductivity
6854:thermal conductivity
6717:
6703:{\displaystyle V=IR}
6685:
6614:through material (A)
6602:potential difference
6515:
6380:
6240:
6215:
6141:
6116:
6059:
6008:
5919:
5861:
5810:
5717:
5657:
5596:
5585:temperature gradient
5550:Thermal conductivity
5483:
5390:
5343:
5291:{\displaystyle q=CT}
5273:
5161:
5079:
5009:
4934:
4768:
4668:
4556:
4550:, thermopower (Vā
K)
4469:
4384:
4272:
4179:
4088:
3986:
3843:GreenāKubo relations
3837:. See, for example,
3831:quantum field theory
3670:
3198:
3036:
3020:) which occurs when
2860:
2689:
2606:
2490:
2350:
2101:
2029:GreenāKubo relations
2013:electrohydrodynamics
2005:magnetohydrodynamics
1900:
1758:
1628:
1531:
1451:
1327:
1273:inelastic collisions
1175:
942:
902:
829:
752:
670:
601:
514:
445:
382:
305:
244:
7678:2003ITAP...51.2761L
7494:Jackson, John David
7145:
7127:
6098:Magnetic reluctance
5776:
5700:Thermal resistance
5645:Thermal conductance
5237:
5226:Transport phenomena
4334:
3914:
3907:solid-state physics
3852:A different set of
3170:; for example in a
2471:is proportional to
2463:is proportional to
2003:. For example, see
170:was the subject of
92:structural analysis
88:solid state physics
48:physical quantities
7741:has generic name (
7430:Kay, J.M. (1985).
7359:has generic name (
7284:has generic name (
7188:Governing equation
7151:
7131:
7113:
7075:
6964:
6831:
6700:
6637:potential gradient
6571:
6439:
6266:
6225:
6176:
6126:
6078:
6027:
5976:
5885:
5829:
5786:Defining equation
5783:(Common) symbol/s
5774:
5754:
5681:
5625:
5530:
5428:
5375:
5288:
5247:Defining equation
5244:(Common) symbol/s
5235:
5212:
5124:
5033:
4977:
4860:
4707:
4615:
4541:, displacement (m)
4504:
4419:
4332:
4317:
4224:
4133:
4038:
3912:
3827:quantum mechanical
3735:
3654:coupling constants
3625:spatial dispersion
3605:
3603:
3172:domained structure
3138:
3111:
3061:
2909:
2838:or other tools of
2796:
2653:
2556:
2408:
2298:
2296:
2055:displacement field
1993:Boltzmann equation
1921:
1807:
1776:
1738:
1608:
1486:
1372:
1307:cross-section area
1236:
1048:
918:
861:
777:
690:
638:
565:
482:
409:
328:
264:
210:Defining equation
207:(Common) symbol/s
176:Clifford Truesdell
7479:978-0-444-87405-4
7387:978-0-521-87499-1
7174:
7173:
7138:
7120:
6998:radiant intensity
6962:
6896:in material (Kā
m)
6829:
6745:
6680:Simplest form is:
6673:of material (Ī©ā
m)
6663:of material (Ī©ā
m)
6569:
6542:
6504:pressure gradient
6437:
6284:
6283:
6264:
6261:
6174:
6151:
6076:
6025:
5883:
5827:
5772:
5771:
5752:
5734:
5679:
5623:
5587:in material (Kā
m)
5509:
5364:
5144:piezooptic effect
5138:Piezooptic effect
5122:
5121:
5031:
5030:
4975:
4858:
4831:
4830:
4792:
4720:
4719:
4613:
4535:, temperature (K)
4369:, temperature (K)
4330:
4329:
3829:analysis such as
3800:materials science
3778:photonic crystals
3499:
3444:
3297:
3102:
3052:
2992:are functions of
2242:
2017:superconductivity
1853:volumetric strain
1796:
1767:
1731:
1694:
1655:
1585:
1481:
1344:
1234:
1230:
1206:
1075:compliance tensor
1067:elasticity tensor
895:(dimensionless):
795:Stress and strain
768:
708:
707:
392:
16:(Redirected from
7836:
7804:
7803:
7801:
7799:
7794:on 19 April 2018
7790:. Archived from
7780:
7774:
7773:
7753:
7747:
7746:
7740:
7736:
7734:
7726:
7703:
7697:
7696:
7694:
7688:. Archived from
7663:
7654:
7648:
7637:
7631:
7630:
7610:
7604:
7603:
7582:
7576:
7563:
7557:
7556:
7554:
7553:
7535:
7529:
7518:
7512:
7511:
7490:
7484:
7483:
7465:
7459:
7452:
7446:
7445:
7427:
7421:
7411:
7405:
7398:
7392:
7391:
7371:
7365:
7364:
7358:
7354:
7352:
7344:
7328:
7303:
7297:
7296:
7289:
7283:
7279:
7277:
7269:
7249:
7233:
7214:
7160:
7158:
7157:
7152:
7150:
7146:
7144:
7139:
7136:
7126:
7121:
7118:
7084:
7082:
7081:
7076:
7074:
7073:
6973:
6971:
6970:
6965:
6963:
6961:
6960:
6959:
6946:
6938:
6936:
6935:
6917:
6916:
6840:
6838:
6837:
6832:
6830:
6828:
6827:
6826:
6813:
6805:
6803:
6802:
6787:
6786:
6772:
6771:
6762:
6761:
6746:
6744:
6743:
6742:
6729:
6721:
6709:
6707:
6706:
6701:
6612:electric current
6580:
6578:
6577:
6572:
6570:
6568:
6567:
6566:
6553:
6545:
6543:
6535:
6527:
6526:
6506:of system (Paā
m)
6448:
6446:
6445:
6440:
6438:
6436:
6435:
6434:
6421:
6413:
6411:
6410:
6392:
6391:
6314:Property/effect
6311:
6275:
6273:
6272:
6267:
6265:
6263:
6262:
6259:
6250:
6234:
6232:
6231:
6226:
6224:
6223:
6185:
6183:
6182:
6177:
6175:
6173:
6172:
6163:
6158:
6153:
6152:
6149:
6135:
6133:
6132:
6127:
6125:
6124:
6087:
6085:
6084:
6079:
6077:
6069:
6036:
6034:
6033:
6028:
6026:
6018:
5985:
5983:
5982:
5977:
5972:
5971:
5950:
5949:
5937:
5936:
5894:
5892:
5891:
5886:
5884:
5879:
5871:
5838:
5836:
5835:
5830:
5828:
5820:
5777:
5763:
5761:
5760:
5755:
5753:
5748:
5740:
5735:
5727:
5690:
5688:
5687:
5682:
5680:
5678:
5667:
5634:
5632:
5631:
5626:
5624:
5622:
5614:
5609:
5539:
5537:
5536:
5531:
5520:
5519:
5514:
5510:
5508:
5500:
5492:
5437:
5435:
5434:
5429:
5421:
5420:
5405:
5404:
5384:
5382:
5381:
5376:
5365:
5363:
5355:
5347:
5297:
5295:
5294:
5289:
5238:
5221:
5219:
5218:
5213:
5211:
5210:
5198:
5197:
5176:
5175:
5133:
5131:
5130:
5125:
5123:
5120:
5119:
5110:
5109:
5100:
5096:
5091:
5090:
5071:
5058:
5042:
5040:
5039:
5034:
5032:
5023:
5019:
4986:
4984:
4983:
4978:
4976:
4974:
4973:
4964:
4963:
4954:
4949:
4948:
4869:
4867:
4866:
4861:
4859:
4857:
4856:
4847:
4846:
4837:
4832:
4829:
4828:
4827:
4818:
4817:
4807:
4799:
4798:
4793:
4788:
4787:
4778:
4736:refractive index
4729:Refractive index
4716:
4714:
4713:
4708:
4706:
4705:
4696:
4695:
4680:
4679:
4624:
4622:
4621:
4616:
4614:
4612:
4611:
4610:
4597:
4589:
4587:
4586:
4568:
4567:
4513:
4511:
4510:
4505:
4503:
4502:
4490:
4489:
4428:
4426:
4425:
4420:
4412:
4411:
4399:
4398:
4338:Property/effect
4335:
4326:
4324:
4323:
4318:
4316:
4315:
4303:
4302:
4284:
4283:
4233:
4231:
4230:
4225:
4223:
4222:
4213:
4212:
4194:
4193:
4142:
4140:
4139:
4134:
4132:
4131:
4119:
4118:
4100:
4099:
4047:
4045:
4044:
4039:
4037:
4036:
4027:
4026:
4017:
4016:
3998:
3997:
3918:Property/effect
3915:
3867:effective medium
3847:Green's function
3820:continuous media
3744:
3742:
3741:
3736:
3731:
3720:
3709:
3699:
3688:
3677:
3614:
3612:
3611:
3606:
3604:
3597:
3593:
3592:
3581:
3577:
3566:
3560:
3556:
3555:
3547:
3530:
3526:
3517:
3507:
3506:
3501:
3500:
3492:
3487:
3479:
3478:
3472:
3468:
3462:
3461:
3456:
3455:
3445:
3443:
3442:
3430:
3412:
3404:
3395:
3391:
3390:
3379:
3375:
3364:
3358:
3354:
3353:
3345:
3328:
3324:
3315:
3305:
3304:
3299:
3298:
3290:
3285:
3277:
3276:
3270:
3266:
3260:
3259:
3254:
3253:
3243:
3242:
3217:
3209:
3186:. In such cases
3147:
3145:
3144:
3139:
3134:
3133:
3124:
3123:
3110:
3098:
3097:
3084:
3083:
3074:
3073:
3060:
3048:
3047:
3028:are second-rank
2918:
2916:
2915:
2910:
2908:
2903:
2902:
2887:
2878:
2867:
2836:transport theory
2805:
2803:
2802:
2797:
2789:
2788:
2776:
2775:
2763:
2762:
2753:
2735:
2734:
2722:
2721:
2709:
2708:
2699:
2662:
2660:
2659:
2654:
2646:
2641:
2633:
2624:
2613:
2565:
2563:
2562:
2557:
2552:
2547:
2546:
2534:
2525:
2520:
2519:
2510:
2509:
2497:
2417:
2415:
2414:
2409:
2407:
2406:
2397:
2392:
2384:
2375:
2370:
2369:
2357:
2307:
2305:
2304:
2299:
2297:
2281:
2273:
2256:
2248:
2243:
2241:
2240:
2228:
2210:
2202:
2184:
2176:
2159:
2151:
2146:
2145:
2120:
2112:
2066:magnetic H-field
1946:Electromagnetism
1930:
1928:
1927:
1922:
1816:
1814:
1813:
1808:
1803:
1797:
1794:
1789:
1788:
1775:
1754:
1750:
1747:
1745:
1744:
1739:
1737:
1733:
1732:
1730:
1729:
1728:
1715:
1714:
1713:
1700:
1695:
1693:
1692:
1691:
1678:
1677:
1676:
1663:
1656:
1648:
1643:
1642:
1624:
1620:
1617:
1615:
1614:
1609:
1607:
1603:
1602:
1601:
1586:
1578:
1573:
1572:
1546:
1545:
1495:
1493:
1492:
1487:
1482:
1480:
1472:
1464:
1440:). In a uniform
1389:(dimensionless)
1387:drag coefficient
1381:
1379:
1378:
1373:
1371:
1370:
1355:
1354:
1345:
1337:
1305:on an object of
1281:
1270:
1263:
1256:
1245:
1243:
1242:
1237:
1235:
1233:
1232:
1231:
1228:
1226:
1220:
1215:
1209:
1208:
1207:
1204:
1202:
1196:
1191:
1185:
1057:
1055:
1054:
1049:
1047:
1046:
1033:
1032:
1011:
1010:
993:
992:
979:
978:
957:
956:
927:
925:
924:
919:
870:
868:
867:
862:
860:
859:
841:
840:
801:linear materials
786:
784:
783:
778:
770:
769:
766:
699:
697:
696:
691:
686:
647:
645:
644:
639:
631:
617:
574:
572:
571:
566:
558:
544:
533:
491:
489:
488:
483:
475:
461:
418:
416:
415:
410:
405:
394:
393:
390:
337:
335:
334:
329:
324:
273:
271:
270:
265:
260:
201:
153:and is known as
119:first principles
115:phenomenological
21:
7844:
7843:
7839:
7838:
7837:
7835:
7834:
7833:
7809:
7808:
7807:
7797:
7795:
7788:www.mx.iucr.org
7782:
7781:
7777:
7770:
7755:
7754:
7750:
7737:
7727:
7723:
7705:
7704:
7700:
7692:
7672:(10): 2761 ff.
7661:
7656:
7655:
7651:
7638:
7634:
7627:
7612:
7611:
7607:
7600:
7584:
7583:
7579:
7564:
7560:
7551:
7549:
7537:
7536:
7532:
7519:
7515:
7508:
7492:
7491:
7487:
7480:
7467:
7466:
7462:
7453:
7449:
7442:
7429:
7428:
7424:
7412:
7408:
7399:
7395:
7388:
7373:
7372:
7368:
7355:
7345:
7341:
7322:
7317:
7304:
7300:
7290:
7280:
7270:
7266:
7251:
7250:
7246:
7242:
7237:
7236:
7215:
7211:
7206:
7179:
7170:
7112:
7108:
7091:
7090:
7065:
7048:
7047:
7046:
7041:
7038:(dimensionless)
7027:
7018:
6951:
6947:
6939:
6924:
6908:
6903:
6902:
6899:
6818:
6814:
6806:
6791:
6778:
6763:
6750:
6734:
6730:
6722:
6715:
6714:
6713:
6683:
6682:
6681:
6676:
6651:current density
6624:of material (Ī©)
6604:in material (V)
6558:
6554:
6546:
6518:
6513:
6512:
6509:
6426:
6422:
6414:
6399:
6383:
6378:
6377:
6374:
6289:
6287:Definitive laws
6254:
6238:
6237:
6213:
6212:
6210:
6164:
6144:
6139:
6138:
6114:
6113:
6111:
6057:
6056:
6006:
6005:
5963:
5941:
5928:
5917:
5916:
5872:
5859:
5858:
5841:Ī©, Vā
A = Jā
sā
C
5808:
5807:
5741:
5715:
5714:
5706:
5671:
5655:
5654:
5615:
5594:
5593:
5590:
5501:
5493:
5487:
5486:
5481:
5480:
5477:
5440:
5409:
5393:
5388:
5387:
5356:
5348:
5341:
5340:
5334:
5271:
5270:
5233:
5228:
5199:
5180:
5164:
5159:
5158:
5140:
5111:
5101:
5082:
5077:
5076:
5070:
5060:
5057:
5047:
5007:
5006:
4996:
4965:
4955:
4937:
4932:
4931:
4922:complex numbers
4919:
4908:
4901:
4894:
4883:
4848:
4838:
4819:
4809:
4808:
4800:
4779:
4766:
4765:
4756:
4748:physical optics
4734:The (absolute)
4732:
4725:
4697:
4684:
4671:
4666:
4665:
4659:
4602:
4598:
4590:
4575:
4559:
4554:
4553:
4544:
4494:
4481:
4467:
4466:
4457:
4403:
4390:
4382:
4381:
4372:
4353:Pyroelectricity
4304:
4288:
4275:
4270:
4269:
4260:
4214:
4198:
4182:
4177:
4176:
4167:
4120:
4104:
4091:
4086:
4085:
4076:
4069:, (dielectric)
4028:
4018:
4002:
3989:
3984:
3983:
3970:
3955:current density
3903:crystallography
3899:
3792:
3786:
3668:
3667:
3644:depend on both
3630:
3602:
3601:
3585:
3572:
3571:
3567:
3540:
3521:
3512:
3508:
3489:
3480:
3463:
3449:
3434:
3422:
3397:
3396:
3383:
3370:
3369:
3365:
3338:
3319:
3310:
3306:
3287:
3278:
3261:
3247:
3234:
3227:
3196:
3195:
3176:heterostructure
3125:
3112:
3089:
3075:
3062:
3039:
3034:
3033:
2891:
2858:
2857:
2812:
2780:
2767:
2754:
2726:
2713:
2700:
2687:
2686:
2604:
2603:
2582:
2575:
2538:
2511:
2501:
2488:
2487:
2453:
2434:
2427:
2398:
2361:
2348:
2347:
2341:
2295:
2294:
2232:
2220:
2195:
2194:
2137:
2130:
2099:
2098:
2021:plasma modeling
1975:quantum physics
1967:
1953:
1948:
1898:
1897:
1866:Kronecker delta
1863:
1850:
1841:
1828:
1777:
1756:
1755:
1752:
1748:
1720:
1716:
1705:
1701:
1683:
1679:
1668:
1664:
1661:
1657:
1631:
1626:
1625:
1622:
1618:
1590:
1561:
1560:
1556:
1534:
1529:
1528:
1523:
1473:
1465:
1449:
1448:
1401:Newtonian fluid
1394:
1362:
1346:
1325:
1324:
1292:
1282:to occur ā for
1276:
1271:for completely
1265:
1258:
1250:
1221:
1210:
1197:
1186:
1173:
1172:
1159:
1152:
1140:
1083:
1035:
1015:
999:
981:
961:
945:
940:
939:
900:
899:
883:Young's modulus
851:
832:
827:
826:
809:spring constant
797:
761:
750:
749:
744:
718:
713:
668:
667:
658:Compressibility
599:
598:
512:
511:
443:
442:
429:Young's modulus
385:
380:
379:
376:
367:elastic modulus
354:
303:
302:
274:
242:
241:
226:
199:
147:
127:spring constant
80:fluid mechanics
28:
23:
22:
15:
12:
11:
5:
7842:
7840:
7832:
7831:
7826:
7821:
7811:
7810:
7806:
7805:
7775:
7768:
7748:
7721:
7698:
7695:on 2012-05-14.
7649:
7632:
7625:
7605:
7598:
7577:
7558:
7530:
7513:
7506:
7485:
7478:
7460:
7447:
7440:
7422:
7406:
7393:
7386:
7366:
7339:
7314:Noll's account
7298:
7264:
7243:
7241:
7238:
7235:
7234:
7208:
7207:
7205:
7202:
7201:
7200:
7195:
7190:
7185:
7178:
7175:
7172:
7171:
7169:
7168:
7161:
7149:
7143:
7134:
7130:
7125:
7116:
7111:
7107:
7104:
7101:
7098:
7087:
7072:
7068:
7064:
7061:
7058:
7055:
7042:
7040:
7039:
7029:
7025:
7020:
7016:
7011:
7001:
6990:
6988:
6975:
6974:
6958:
6954:
6950:
6945:
6942:
6934:
6931:
6927:
6923:
6920:
6915:
6911:
6900:
6898:
6897:
6882:
6872:
6861:
6859:
6843:
6842:
6825:
6821:
6817:
6812:
6809:
6801:
6798:
6794:
6790:
6785:
6781:
6776:
6770:
6766:
6760:
6757:
6753:
6749:
6741:
6737:
6733:
6728:
6725:
6699:
6696:
6693:
6690:
6677:
6675:
6674:
6664:
6654:
6644:
6641:electric field
6625:
6615:
6605:
6594:
6592:
6582:
6581:
6565:
6561:
6557:
6552:
6549:
6541:
6538:
6533:
6530:
6525:
6521:
6510:
6508:
6507:
6492:
6486:
6476:
6465:
6463:
6450:
6449:
6433:
6429:
6425:
6420:
6417:
6409:
6406:
6402:
6398:
6395:
6390:
6386:
6375:
6373:
6372:
6357:
6351:
6340:
6338:
6322:
6321:
6318:
6315:
6306:
6305:
6297:Flux (density)
6288:
6285:
6282:
6281:
6279:
6276:
6257:
6253:
6248:
6245:
6235:
6222:
6208:
6199:
6192:
6191:
6189:
6186:
6171:
6167:
6162:
6156:
6147:
6136:
6123:
6109:
6100:
6094:
6093:
6091:
6088:
6075:
6072:
6067:
6064:
6054:
6049:
6043:
6042:
6040:
6037:
6024:
6021:
6016:
6013:
6003:
5998:
5992:
5991:
5989:
5986:
5975:
5970:
5966:
5962:
5959:
5956:
5953:
5948:
5944:
5940:
5935:
5931:
5927:
5924:
5914:
5909:
5901:
5900:
5898:
5895:
5882:
5878:
5875:
5869:
5866:
5856:
5851:
5845:
5844:
5842:
5839:
5826:
5823:
5818:
5815:
5805:
5800:
5794:
5793:
5790:
5787:
5784:
5781:
5770:
5769:
5767:
5764:
5751:
5747:
5744:
5738:
5733:
5730:
5725:
5722:
5712:
5701:
5697:
5696:
5694:
5691:
5677:
5674:
5670:
5665:
5662:
5652:
5647:
5641:
5640:
5638:
5635:
5621:
5618:
5613:
5607:
5604:
5601:
5591:
5589:
5588:
5577:
5566:
5552:
5546:
5545:
5543:
5540:
5529:
5526:
5523:
5518:
5513:
5507:
5504:
5499:
5496:
5490:
5478:
5476:
5475:
5469:
5462:
5453:
5447:
5446:
5444:
5441:
5439:
5438:
5427:
5424:
5419:
5416:
5412:
5408:
5403:
5400:
5396:
5385:
5374:
5371:
5368:
5362:
5359:
5354:
5351:
5337:
5335:
5333:
5332:
5326:
5320:
5313:
5311:
5304:
5303:
5301:
5298:
5287:
5284:
5281:
5278:
5268:
5262:
5255:
5254:
5251:
5248:
5245:
5242:
5232:
5229:
5227:
5224:
5223:
5222:
5209:
5206:
5202:
5196:
5193:
5190:
5187:
5183:
5179:
5174:
5171:
5167:
5139:
5136:
5135:
5134:
5118:
5114:
5108:
5104:
5099:
5094:
5089:
5085:
5068:
5055:
5044:
5043:
5029:
5026:
5022:
5017:
5014:
5000:speed of light
4995:
4992:Speed of light
4989:
4988:
4987:
4972:
4968:
4962:
4958:
4952:
4947:
4944:
4940:
4917:
4909:. In general,
4906:
4899:
4892:
4881:
4871:
4870:
4855:
4851:
4845:
4841:
4835:
4826:
4822:
4816:
4812:
4806:
4803:
4796:
4791:
4786:
4782:
4776:
4773:
4754:
4731:
4726:
4724:
4721:
4718:
4717:
4704:
4700:
4694:
4691:
4687:
4683:
4678:
4674:
4663:
4660:
4658:
4657:
4647:
4641:
4634:
4632:
4630:Peltier effect
4626:
4625:
4609:
4605:
4601:
4596:
4593:
4585:
4582:
4578:
4574:
4571:
4566:
4562:
4551:
4545:
4543:
4542:
4536:
4530:
4523:
4521:
4519:Seebeck effect
4515:
4514:
4501:
4497:
4493:
4488:
4484:
4480:
4477:
4474:
4464:
4458:
4456:
4455:
4449:
4438:
4436:
4430:
4429:
4418:
4415:
4410:
4406:
4402:
4397:
4393:
4389:
4379:
4373:
4371:
4370:
4364:
4357:
4355:
4349:
4348:
4345:
4342:
4339:
4328:
4327:
4314:
4311:
4307:
4301:
4298:
4295:
4291:
4287:
4282:
4278:
4267:
4261:
4259:
4258:
4248:
4241:
4239:
4235:
4234:
4221:
4217:
4211:
4208:
4205:
4201:
4197:
4192:
4189:
4185:
4174:
4168:
4166:
4165:
4159:
4152:
4150:
4144:
4143:
4130:
4127:
4123:
4117:
4114:
4111:
4107:
4103:
4098:
4094:
4083:
4077:
4075:
4074:
4064:
4057:
4055:
4049:
4048:
4035:
4031:
4025:
4021:
4015:
4012:
4009:
4005:
4001:
3996:
3992:
3981:
3971:
3969:
3968:
3958:
3948:
3937:
3935:
3929:
3928:
3925:
3922:
3919:
3898:
3895:
3833:as applied to
3785:
3782:
3763:perfect metals
3746:
3745:
3734:
3730:
3726:
3723:
3719:
3715:
3712:
3708:
3703:
3698:
3694:
3691:
3687:
3683:
3680:
3676:
3629:
3628:
3600:
3596:
3591:
3588:
3584:
3580:
3576:
3570:
3565:
3559:
3554:
3550:
3546:
3543:
3539:
3536:
3533:
3529:
3525:
3520:
3516:
3511:
3505:
3498:
3495:
3486:
3483:
3477:
3471:
3467:
3460:
3454:
3448:
3441:
3437:
3433:
3428:
3425:
3423:
3421:
3418:
3415:
3411:
3407:
3403:
3399:
3398:
3394:
3389:
3386:
3382:
3378:
3374:
3368:
3363:
3357:
3352:
3348:
3344:
3341:
3337:
3334:
3331:
3327:
3323:
3318:
3314:
3309:
3303:
3296:
3293:
3284:
3281:
3275:
3269:
3265:
3258:
3252:
3246:
3241:
3237:
3233:
3230:
3228:
3226:
3223:
3220:
3216:
3212:
3208:
3204:
3203:
3180:liquid crystal
3150:Dependence of
3148:
3137:
3132:
3128:
3122:
3119:
3115:
3109:
3105:
3101:
3096:
3092:
3087:
3082:
3078:
3072:
3069:
3065:
3059:
3055:
3051:
3046:
3042:
3001:
2977:
2940:
2920:
2919:
2907:
2901:
2898:
2894:
2890:
2886:
2881:
2877:
2873:
2870:
2866:
2811:
2808:
2807:
2806:
2795:
2792:
2787:
2783:
2779:
2774:
2770:
2766:
2761:
2757:
2752:
2748:
2744:
2741:
2738:
2733:
2729:
2725:
2720:
2716:
2712:
2707:
2703:
2698:
2694:
2664:
2663:
2652:
2649:
2645:
2640:
2636:
2632:
2627:
2623:
2619:
2616:
2612:
2580:
2573:
2567:
2566:
2555:
2551:
2545:
2541:
2537:
2533:
2528:
2524:
2518:
2514:
2508:
2504:
2500:
2496:
2452:
2449:
2432:
2425:
2419:
2418:
2405:
2401:
2396:
2391:
2387:
2383:
2378:
2374:
2368:
2364:
2360:
2356:
2340:
2337:
2309:
2308:
2293:
2290:
2287:
2284:
2280:
2276:
2272:
2268:
2265:
2262:
2259:
2255:
2251:
2247:
2239:
2235:
2231:
2226:
2223:
2221:
2219:
2216:
2213:
2209:
2205:
2201:
2197:
2196:
2193:
2190:
2187:
2183:
2179:
2175:
2171:
2168:
2165:
2162:
2158:
2154:
2150:
2144:
2140:
2136:
2133:
2131:
2129:
2126:
2123:
2119:
2115:
2111:
2107:
2106:
2050:and so forth.
2048:conductivities
2044:permeabilities
2040:permittivities
2009:fluid dynamics
1952:
1949:
1947:
1944:
1932:
1931:
1920:
1917:
1914:
1911:
1908:
1905:
1859:
1846:
1837:
1824:
1818:
1817:
1806:
1802:
1792:
1787:
1784:
1780:
1774:
1770:
1766:
1763:
1736:
1727:
1723:
1719:
1712:
1708:
1704:
1698:
1690:
1686:
1682:
1675:
1671:
1667:
1660:
1654:
1651:
1646:
1641:
1638:
1634:
1606:
1600:
1597:
1593:
1589:
1584:
1581:
1576:
1571:
1568:
1564:
1559:
1555:
1552:
1549:
1544:
1541:
1537:
1519:
1497:
1496:
1485:
1479:
1476:
1471:
1468:
1462:
1459:
1456:
1392:
1383:
1382:
1369:
1365:
1361:
1358:
1353:
1349:
1343:
1340:
1335:
1332:
1291:
1288:
1247:
1246:
1225:
1219:
1214:
1201:
1195:
1190:
1183:
1180:
1157:
1150:
1146:of separation
1144:relative speed
1139:
1136:
1135:
1134:
1133:
1132:
1125:
1120:
1116:
1111:
1108:
1100:
1095:
1092:
1082:
1079:
1059:
1058:
1045:
1042:
1038:
1031:
1028:
1025:
1022:
1018:
1014:
1009:
1006:
1002:
997:
991:
988:
984:
977:
974:
971:
968:
964:
960:
955:
952:
948:
929:
928:
917:
913:
910:
907:
872:
871:
858:
854:
850:
847:
844:
839:
835:
796:
793:
788:
787:
776:
773:
764:
760:
757:
742:
733:reaction force
717:
714:
712:
709:
706:
705:
703:
700:
689:
685:
681:
678:
675:
665:
660:
654:
653:
651:
648:
637:
634:
630:
626:
623:
620:
616:
612:
609:
606:
596:
587:
581:
580:
578:
575:
564:
561:
557:
553:
550:
547:
543:
539:
536:
532:
528:
525:
522:
519:
509:
504:
498:
497:
495:
492:
481:
478:
474:
470:
467:
464:
460:
456:
453:
450:
440:
431:
425:
424:
422:
419:
408:
404:
400:
397:
388:
377:
374:
369:
362:
361:
360:Dimensionless
358:
355:
353:
352:
345:
338:
327:
323:
319:
316:
313:
310:
300:
295:
288:
287:
285:
282:
263:
259:
255:
252:
249:
239:
230:
218:
217:
214:
211:
208:
205:
198:
195:
146:
143:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7841:
7830:
7827:
7825:
7822:
7820:
7817:
7816:
7814:
7793:
7789:
7785:
7779:
7776:
7771:
7769:0-12-544422-2
7765:
7761:
7760:
7752:
7749:
7744:
7739:|author=
7732:
7724:
7722:981-02-4094-5
7718:
7714:
7713:
7708:
7702:
7699:
7691:
7687:
7683:
7679:
7675:
7671:
7667:
7660:
7653:
7650:
7646:
7642:
7636:
7633:
7628:
7626:0-7506-6321-9
7622:
7618:
7617:
7609:
7606:
7601:
7599:0-8218-3968-3
7595:
7591:
7590:
7581:
7578:
7574:
7571:
7567:
7562:
7559:
7548:on 2010-10-13
7547:
7543:
7542:
7534:
7531:
7527:
7523:
7517:
7514:
7509:
7507:0-471-30932-X
7503:
7499:
7495:
7489:
7486:
7481:
7475:
7471:
7464:
7461:
7457:
7451:
7448:
7443:
7441:9780521316248
7437:
7433:
7426:
7423:
7420:
7419:0 7195 3382 1
7416:
7410:
7407:
7403:
7397:
7394:
7389:
7383:
7379:
7378:
7370:
7367:
7362:
7357:|author=
7350:
7342:
7340:3-540-02779-3
7336:
7332:
7326:
7321:
7315:
7311:
7308:
7302:
7299:
7294:
7287:
7282:|author=
7275:
7267:
7265:3-540-02779-3
7261:
7257:
7256:
7248:
7245:
7239:
7231:
7227:
7223:
7222:Lorentz force
7219:
7213:
7210:
7203:
7199:
7196:
7194:
7191:
7189:
7186:
7184:
7181:
7180:
7176:
7166:
7162:
7147:
7141:
7132:
7128:
7123:
7114:
7109:
7105:
7102:
7099:
7096:
7089:
7088:
7085:
7070:
7066:
7062:
7059:
7056:
7053:
7043:
7037:
7033:
7030:
7024:
7021:
7015:
7012:
7009:
7005:
7002:
6999:
6995:
6992:
6991:
6989:
6987:
6983:
6981:
6977:
6976:
6956:
6952:
6943:
6932:
6929:
6925:
6921:
6918:
6913:
6909:
6901:
6895:
6891:
6887:
6883:
6880:
6876:
6873:
6870:
6866:
6863:
6862:
6860:
6858:
6855:
6851:
6849:
6848:Fourier's law
6845:
6844:
6841:
6823:
6819:
6810:
6799:
6796:
6792:
6788:
6783:
6779:
6768:
6764:
6758:
6755:
6751:
6747:
6739:
6735:
6726:
6710:
6697:
6694:
6691:
6688:
6678:
6672:
6669:, electrical
6668:
6665:
6662:
6658:
6655:
6652:
6648:
6645:
6642:
6638:
6634:
6630:
6626:
6623:
6619:
6616:
6613:
6609:
6606:
6603:
6599:
6596:
6595:
6593:
6590:
6588:
6584:
6583:
6563:
6559:
6550:
6539:
6536:
6531:
6528:
6523:
6519:
6511:
6505:
6501:
6497:
6493:
6490:
6487:
6484:
6480:
6477:
6475:of medium (m)
6474:
6470:
6467:
6466:
6464:
6462:
6458:
6456:
6452:
6451:
6431:
6427:
6418:
6407:
6404:
6400:
6396:
6393:
6388:
6384:
6376:
6370:
6369:concentration
6366:
6362:
6358:
6355:
6352:
6349:
6345:
6342:
6341:
6339:
6337:
6333:
6332:
6328:
6324:
6323:
6317:Nomenclature
6312:
6309:
6304:
6302:
6298:
6294:
6293:
6292:
6286:
6280:
6277:
6255:
6251:
6246:
6236:
6207:
6203:
6200:
6198:
6194:
6193:
6190:
6187:
6169:
6154:
6145:
6137:
6108:
6104:
6101:
6099:
6096:
6095:
6092:
6089:
6073:
6070:
6065:
6062:
6055:
6053:
6050:
6048:
6045:
6044:
6041:
6038:
6022:
6019:
6014:
6011:
6004:
6002:
5999:
5997:
5994:
5993:
5990:
5987:
5968:
5964:
5960:
5957:
5951:
5946:
5942:
5938:
5933:
5929:
5925:
5922:
5915:
5913:
5910:
5907:
5903:
5902:
5899:
5896:
5880:
5876:
5873:
5867:
5864:
5857:
5855:
5852:
5850:
5847:
5846:
5843:
5840:
5824:
5821:
5816:
5813:
5806:
5804:
5801:
5799:
5796:
5795:
5778:
5768:
5765:
5749:
5745:
5736:
5731:
5728:
5723:
5720:
5713:
5710:
5705:
5702:
5699:
5698:
5695:
5692:
5675:
5672:
5668:
5663:
5660:
5653:
5651:
5648:
5646:
5643:
5642:
5639:
5636:
5619:
5605:
5602:
5599:
5592:
5586:
5582:
5578:
5575:
5571:
5568:
5567:
5564:
5560:
5556:
5553:
5551:
5548:
5547:
5544:
5541:
5527:
5524:
5521:
5516:
5511:
5505:
5497:
5488:
5479:
5473:
5470:
5467:
5464:
5463:
5461:
5457:
5454:
5452:
5449:
5448:
5445:
5442:
5425:
5417:
5414:
5410:
5406:
5401:
5398:
5394:
5386:
5372:
5369:
5366:
5360:
5352:
5339:
5338:
5336:
5330:
5327:
5324:
5321:
5318:
5315:
5314:
5312:
5310:
5306:
5305:
5302:
5299:
5285:
5282:
5279:
5276:
5269:
5266:
5263:
5261:
5260:heat capacity
5257:
5256:
5239:
5230:
5225:
5207:
5204:
5200:
5194:
5191:
5188:
5185:
5177:
5172:
5169:
5165:
5157:
5156:
5155:
5153:
5149:
5145:
5137:
5116:
5112:
5106:
5102:
5097:
5092:
5087:
5083:
5075:
5074:
5073:
5067:
5063:
5054:
5050:
5027:
5024:
5020:
5015:
5012:
5005:
5004:
5003:
5002:in matter is
5001:
4993:
4990:
4970:
4966:
4960:
4956:
4950:
4945:
4942:
4938:
4930:
4929:
4928:
4925:
4923:
4916:
4912:
4905:
4898:
4891:
4887:
4880:
4876:
4853:
4849:
4843:
4839:
4833:
4824:
4820:
4814:
4810:
4804:
4801:
4794:
4789:
4784:
4780:
4774:
4771:
4764:
4763:
4762:
4760:
4753:
4749:
4745:
4741:
4737:
4730:
4727:
4722:
4702:
4698:
4692:
4689:
4681:
4676:
4672:
4664:
4661:
4655:
4651:
4648:
4645:
4642:
4639:
4636:
4635:
4633:
4631:
4628:
4627:
4607:
4603:
4594:
4583:
4580:
4576:
4572:
4569:
4564:
4560:
4552:
4549:
4546:
4540:
4537:
4534:
4531:
4528:
4525:
4524:
4522:
4520:
4517:
4516:
4499:
4495:
4486:
4482:
4478:
4475:
4465:
4462:
4459:
4453:
4450:
4447:
4443:
4440:
4439:
4437:
4435:
4432:
4431:
4416:
4408:
4404:
4400:
4395:
4391:
4380:
4377:
4374:
4368:
4365:
4362:
4359:
4358:
4356:
4354:
4351:
4350:
4336:
4312:
4309:
4305:
4299:
4296:
4293:
4289:
4285:
4280:
4276:
4268:
4265:
4262:
4256:
4255:magnetization
4252:
4249:
4247:, Stress (Pa)
4246:
4243:
4242:
4240:
4237:
4236:
4219:
4215:
4209:
4206:
4203:
4199:
4195:
4190:
4187:
4183:
4175:
4172:
4169:
4163:
4160:
4157:
4154:
4153:
4151:
4149:
4146:
4145:
4128:
4125:
4121:
4115:
4112:
4109:
4105:
4101:
4096:
4092:
4084:
4081:
4078:
4072:
4068:
4065:
4063:, Stress (Pa)
4062:
4059:
4058:
4056:
4054:
4051:
4050:
4033:
4029:
4023:
4019:
4013:
4010:
4007:
4003:
3999:
3994:
3990:
3982:
3979:
3976:, electrical
3975:
3972:
3966:
3962:
3959:
3956:
3952:
3949:
3946:
3942:
3939:
3938:
3936:
3934:
3931:
3930:
3916:
3910:
3908:
3905:, a field of
3904:
3896:
3894:
3892:
3888:
3884:
3880:
3875:
3873:
3869:
3868:
3863:
3859:
3858:conglomerates
3855:
3850:
3848:
3844:
3840:
3836:
3832:
3828:
3823:
3821:
3815:
3813:
3809:
3805:
3804:Lorentz force
3801:
3797:
3791:
3783:
3781:
3779:
3775:
3774:metamaterials
3770:
3768:
3764:
3760:
3756:
3752:
3732:
3724:
3721:
3713:
3710:
3701:
3692:
3689:
3681:
3678:
3666:
3665:
3664:
3662:
3658:
3655:
3651:
3647:
3643:
3639:
3635:
3634:bianisotropic
3626:
3622:
3618:
3598:
3594:
3589:
3586:
3582:
3578:
3568:
3557:
3548:
3544:
3541:
3537:
3534:
3531:
3527:
3518:
3509:
3503:
3493:
3484:
3481:
3469:
3458:
3446:
3439:
3435:
3431:
3426:
3424:
3416:
3413:
3392:
3387:
3384:
3380:
3376:
3366:
3355:
3346:
3342:
3339:
3335:
3332:
3329:
3325:
3316:
3307:
3301:
3291:
3282:
3279:
3267:
3256:
3244:
3239:
3235:
3231:
3229:
3221:
3218:
3193:
3189:
3185:
3181:
3177:
3173:
3169:
3165:
3161:
3157:
3153:
3149:
3135:
3130:
3126:
3120:
3117:
3113:
3107:
3103:
3099:
3094:
3090:
3085:
3080:
3076:
3070:
3067:
3063:
3057:
3053:
3049:
3044:
3040:
3031:
3027:
3023:
3019:
3018:
3013:
3012:
3011:birefringence
3007:
3006:
3002:
2999:
2995:
2991:
2987:
2983:
2982:
2978:
2975:
2971:
2967:
2963:
2959:
2955:
2951:
2950:
2946:
2942:
2941:
2939:
2937:
2933:
2929:
2925:
2899:
2896:
2892:
2888:
2879:
2871:
2868:
2856:
2855:
2854:
2851:
2849:
2845:
2841:
2837:
2833:
2829:
2825:
2821:
2817:
2809:
2793:
2790:
2785:
2781:
2777:
2772:
2768:
2764:
2759:
2755:
2750:
2746:
2742:
2739:
2736:
2731:
2727:
2723:
2718:
2714:
2710:
2705:
2701:
2696:
2692:
2685:
2684:
2683:
2681:
2677:
2673:
2669:
2650:
2647:
2643:
2634:
2625:
2617:
2614:
2602:
2601:
2600:
2598:
2594:
2590:
2586:
2579:
2572:
2553:
2543:
2539:
2535:
2526:
2516:
2512:
2506:
2502:
2498:
2486:
2485:
2484:
2482:
2478:
2474:
2470:
2466:
2462:
2458:
2450:
2448:
2446:
2442:
2438:
2431:
2424:
2403:
2399:
2394:
2385:
2376:
2366:
2362:
2358:
2346:
2345:
2344:
2338:
2336:
2334:
2330:
2326:
2325:magnetization
2322:
2318:
2314:
2291:
2285:
2282:
2266:
2260:
2257:
2237:
2233:
2229:
2224:
2222:
2214:
2211:
2188:
2185:
2169:
2163:
2160:
2142:
2138:
2134:
2132:
2124:
2121:
2097:
2096:
2095:
2093:
2089:
2085:
2081:
2076:
2074:
2070:
2067:
2063:
2059:
2056:
2051:
2049:
2045:
2041:
2036:
2034:
2030:
2026:
2022:
2018:
2014:
2010:
2006:
2002:
1998:
1994:
1989:
1987:
1983:
1980:
1976:
1972:
1966:
1962:
1958:
1950:
1945:
1943:
1941:
1937:
1918:
1915:
1912:
1909:
1906:
1903:
1896:
1895:
1894:
1892:
1888:
1884:
1880:
1876:
1875:
1874:ideal gas law
1869:
1867:
1862:
1858:
1854:
1849:
1845:
1840:
1836:
1832:
1831:flow velocity
1827:
1823:
1804:
1790:
1785:
1782:
1778:
1772:
1768:
1764:
1734:
1725:
1721:
1710:
1706:
1696:
1688:
1684:
1673:
1669:
1658:
1652:
1649:
1644:
1639:
1636:
1632:
1604:
1598:
1595:
1591:
1582:
1579:
1574:
1569:
1566:
1562:
1557:
1553:
1550:
1547:
1542:
1539:
1535:
1527:
1526:
1525:
1522:
1518:
1514:
1510:
1506:
1502:
1483:
1477:
1469:
1460:
1457:
1454:
1447:
1446:
1445:
1443:
1439:
1435:
1431:
1427:
1424:
1423:flow velocity
1420:
1416:
1413:
1409:
1406:
1402:
1397:
1395:
1388:
1367:
1363:
1359:
1356:
1351:
1347:
1341:
1338:
1333:
1330:
1323:
1322:
1321:
1319:
1315:
1311:
1308:
1304:
1301:
1297:
1296:drag equation
1289:
1287:
1285:
1279:
1274:
1268:
1261:
1254:
1181:
1178:
1171:
1170:
1169:
1167:
1164:, defined by
1163:
1156:
1149:
1145:
1137:
1130:
1126:
1124:
1121:
1117:
1115:
1112:
1109:
1107:
1104:
1103:
1101:
1099:
1096:
1093:
1091:
1088:
1087:
1086:
1080:
1078:
1076:
1072:
1068:
1064:
1043:
1040:
1036:
1029:
1026:
1023:
1020:
1016:
1012:
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1004:
1000:
989:
986:
982:
975:
972:
969:
966:
962:
958:
953:
950:
946:
938:
937:
936:
934:
933:stress tensor
915:
911:
908:
905:
898:
897:
896:
894:
891:
887:
884:
880:
877:
856:
852:
848:
845:
842:
837:
833:
825:
824:
823:
821:
818:
814:
810:
806:
802:
794:
792:
774:
771:
762:
758:
755:
748:
747:
746:
741:
737:
734:
730:
726:
722:
715:
710:
704:
701:
687:
683:
679:
676:
673:
666:
664:
661:
659:
656:
655:
652:
649:
632:
628:
624:
614:
610:
607:
604:
597:
595:
591:
588:
586:
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582:
579:
576:
559:
555:
551:
541:
534:
530:
526:
520:
517:
510:
508:
505:
503:
502:Shear modulus
500:
499:
496:
493:
476:
472:
468:
458:
454:
451:
448:
441:
439:
435:
432:
430:
427:
426:
423:
420:
406:
402:
398:
395:
386:
378:
373:
370:
368:
364:
363:
359:
356:
350:
346:
343:
340:
339:
325:
321:
317:
311:
308:
301:
299:
296:
294:
290:
289:
286:
283:
281:
277:
261:
257:
253:
250:
247:
240:
238:
234:
231:
229:
224:
220:
219:
202:
196:
194:
192:
188:
184:
179:
177:
173:
169:
164:
160:
156:
152:
144:
142:
140:
136:
132:
128:
124:
120:
116:
111:
109:
105:
101:
97:
93:
89:
85:
81:
77:
76:physical laws
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
19:
7796:. Retrieved
7792:the original
7787:
7778:
7758:
7751:
7711:
7701:
7690:the original
7669:
7665:
7652:
7644:
7640:
7635:
7615:
7608:
7587:
7580:
7572:
7570:Am. J. Phys.
7569:
7566:Aspnes, D.E.
7561:
7550:. Retrieved
7546:the original
7540:
7533:
7525:
7521:
7516:
7497:
7488:
7469:
7463:
7450:
7431:
7425:
7409:
7396:
7376:
7369:
7330:
7324:
7309:
7301:
7254:
7247:
7229:
7225:
7217:
7212:
7164:
7044:
7031:
7022:
7013:
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6993:
6985:
6978:
6889:
6885:
6874:
6864:
6856:
6846:
6711:
6679:
6666:
6661:conductivity
6656:
6646:
6632:
6628:
6617:
6607:
6597:
6585:
6499:
6495:
6488:
6478:
6473:permeability
6468:
6460:
6453:
6364:
6360:
6353:
6343:
6335:
6325:
6307:
6300:
6296:
6295:
6290:
6205:
6201:
6106:
6102:
6051:
6000:
5911:
5904:Resistivity
5853:
5802:
5708:
5703:
5649:
5580:
5569:
5562:
5558:
5554:
5471:
5465:
5459:
5455:
5328:
5322:
5316:
5264:
5151:
5147:
5141:
5065:
5061:
5052:
5048:
5045:
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4926:
4914:
4910:
4903:
4896:
4889:
4885:
4878:
4874:
4872:
4758:
4751:
4739:
4738:of a medium
4733:
4649:
4643:
4637:
4547:
4538:
4532:
4526:
4460:
4451:
4441:
4375:
4366:
4360:
4263:
4250:
4244:
4170:
4161:
4155:
4079:
4071:polarization
4066:
4060:
3973:
3960:
3950:
3940:
3900:
3891:ellipsometry
3886:
3878:
3876:
3865:
3853:
3851:
3824:
3816:
3811:
3807:
3793:
3771:
3747:
3660:
3656:
3653:
3649:
3645:
3641:
3637:
3631:
3191:
3187:
3167:
3163:
3159:
3155:
3151:
3025:
3021:
3015:
3009:
3003:
2997:
2993:
2989:
2985:
2981:Nonlinearity
2979:
2969:
2965:
2957:
2953:
2943:
2935:
2931:
2927:
2923:
2921:
2852:
2827:
2823:
2819:
2815:
2813:
2810:General case
2680:permeability
2676:permittivity
2671:
2667:
2665:
2596:
2592:
2577:
2570:
2568:
2480:
2476:
2472:
2468:
2464:
2460:
2454:
2445:permeability
2437:permittivity
2429:
2422:
2420:
2342:
2332:
2328:
2320:
2317:polarization
2312:
2310:
2091:
2087:
2083:
2079:
2077:
2072:
2068:
2061:
2057:
2052:
2037:
1990:
1968:
1957:Permittivity
1940:gas constant
1935:
1933:
1890:
1886:
1882:
1878:
1872:
1870:
1860:
1856:
1847:
1843:
1838:
1834:
1825:
1821:
1819:
1520:
1516:
1512:
1508:
1504:
1500:
1498:
1437:
1433:
1429:
1421:(transverse
1414:
1412:shear stress
1407:
1398:
1390:
1384:
1317:
1316:at velocity
1313:
1309:
1302:
1293:
1284:superelastic
1277:
1266:
1259:
1252:
1248:
1154:
1147:
1141:
1123:Hyperelastic
1106:Viscoelastic
1084:
1070:
1062:
1060:
930:
892:
885:
878:
873:
819:
817:displacement
812:
798:
789:
739:
735:
728:
719:
662:
593:
589:
585:Bulk modulus
506:
437:
433:
371:
348:
341:
297:
279:
275:
236:
232:
180:
167:
151:Robert Hooke
148:
112:
108:deformations
50:(especially
43:
39:
29:
7458:quantities.
7402:R.G. Lerner
7312:. See also
6671:resistivity
6659:, electric
6649:, electric
6455:Darcy's law
5849:Resistivity
5231:Definitions
3978:resistivity
3953:, electric
3933:Hall effect
3872:wavelengths
2848:microscopic
2844:macroscopic
1942:(Jā
Kā
mol).
1881:and volume
1419:strain rate
1257:, in which
805:Hooke's law
197:Definitions
172:Walter Noll
163:Walter Noll
155:Hooke's law
36:engineering
7813:Categories
7707:AC Gilbert
7552:2012-05-22
7240:References
7036:emissivity
6852:, defines
6622:resistance
6327:Fick's law
5792:Dimension
5253:Dimension
3788:See also:
3767:skin depth
3184:hysteresis
3005:Anisotropy
2949:absorption
2945:Dispersion
2483:they are:
2441:free space
2319:field and
2064:, and the
1955:See also:
1442:shear flow
1385:where the
1300:drag force
1298:gives the
1205:separation
1151:separation
1138:Collisions
216:Dimension
181:In modern
135:non-linear
7731:cite book
7349:cite book
7320:"Preface"
7307:Truesdell
7274:cite book
7129:−
7106:σ
7103:ε
7063:σ
7060:ε
6949:∂
6941:∂
6926:λ
6922:−
6879:heat flux
6816:∂
6808:∂
6793:σ
6775:⇌
6752:ρ
6732:∂
6724:∂
6587:Ohm's law
6556:∂
6548:∂
6540:μ
6537:κ
6532:−
6483:viscosity
6424:∂
6416:∂
6397:−
6331:diffusion
6320:Equation
6278:Wbā
A = H
6244:Λ
6197:permeance
6195:Magnetic
6188:Aā
Wb = H
6166:Φ
6074:ρ
6063:σ
5961:−
5952:α
5943:ρ
5930:ρ
5926:−
5923:ρ
5865:ρ
5789:SI units
5750:λ
5743:Δ
5673:δ
5669:λ
5617:∇
5606:−
5600:λ
5574:heat flux
5525:γ
5503:∂
5495:∂
5423:Δ
5411:α
5395:ε
5370:α
5358:∂
5350:∂
5250:SI units
5201:σ
5182:Π
5113:μ
5103:ε
5028:μ
5025:ε
4994:in matter
4850:μ
4840:ε
4821:μ
4811:ε
4805:μ
4802:ε
4744:geometric
4723:Photonics
4686:Π
4654:heat flux
4600:∂
4592:∂
4577:β
4573:−
4492:Δ
4473:Δ
4414:Δ
4388:Δ
4347:Equation
4306:σ
4184:ε
4122:σ
4004:ρ
3927:Equation
3862:laminates
3759:microwave
3751:bandwidth
3725:ζ
3714:μ
3693:ξ
3682:ε
3497:^
3494:χ
3447:∫
3436:μ
3295:^
3292:χ
3245:∫
3236:ε
3114:μ
3104:∑
3064:ε
3054:∑
3017:dichroism
3008:(such as
2897:−
2893:μ
2872:ε
2782:χ
2769:μ
2756:μ
2747:μ
2728:χ
2715:ε
2702:ε
2693:ε
2648:μ
2618:ε
2540:χ
2513:χ
2503:ε
2457:isotropic
2400:μ
2363:ε
2267:−
2234:μ
2139:ε
1971:classical
1769:∑
1762:Δ
1718:∂
1703:∂
1681:∂
1666:∂
1592:δ
1588:Δ
1575:−
1554:μ
1536:τ
1475:∂
1467:∂
1461:μ
1455:τ
1405:viscosity
1357:ρ
1114:Anelastic
1037:σ
1001:ε
996:⇌
983:ε
947:σ
916:ε
906:σ
846:−
763:μ
702:Pa = mā
N
650:Pa = Nā
m
622:Δ
577:Pa = Nā
m
549:Δ
494:Pa = Nā
m
466:Δ
455:σ
421:Pa = Nā
m
407:ε
399:σ
315:Δ
309:ε
284:Pa = Nā
m
248:σ
213:SI units
60:substance
56:kinematic
7798:19 April
7496:(1999).
7327:in 1965)
7198:Rheology
7177:See also
6481:, fluid
6301:gradient
5258:General
3621:magnetic
3617:electric
3590:′
3579:′
3545:′
3528:′
3485:′
3470:′
3388:′
3377:′
3343:′
3326:′
3283:′
3268:′
2589:magnetic
2585:electric
2583:are the
2086:and the
1969:In both
1893:of gas:
1426:gradient
1229:approach
1158:approach
725:friction
721:Friction
716:Friction
365:General
291:General
228:pressure
221:General
96:stresses
7674:Bibcode
7010:(Wā
mā
K)
6502:, (1d)
6346:, mass
5307:linear
4446:entropy
3030:tensors
2974:complex
2455:In an (
2323:is the
2315:is the
1999:or the
1995:or the
1979:coupled
1938:is the
1864:is the
1436:(units
1160:by the
1098:Elastic
1090:Plastic
1073:is the
1065:is the
104:strains
52:kinetic
32:physics
7766:
7719:
7623:
7596:
7504:
7476:
7456:tensor
7438:
7417:
7384:
7337:
7262:
6485:(Paā
s)
6367:, (1d)
6039:S = Ī©
5766:mā
Kā
W
5693:Wā
mā
K
5637:Wā
mā
K
4920:) are
4913:(also
4873:where
3980:(Ī©ā
m)
3885:, and
3755:metals
3636:where
2984:where
2972:being
2952:where
2666:where
2569:where
2467:, and
2421:where
2311:where
1963:, and
1934:where
1820:where
1753:
1749:
1623:
1619:
1410:, the
1399:For a
1061:where
890:strain
888:, and
876:stress
727:force
293:strain
223:stress
131:tensor
72:forces
68:fields
7693:(PDF)
7662:(PDF)
7589:Korea
7226:bound
7204:Notes
7000:(Wā
m)
6350:(mā
s)
6211:, Ī,
4656:(Wā
m)
4448:(Jā
K)
4257:(Aā
m)
4073:(Cā
m)
3967:(Aā
m)
3957:(Aā
m)
3947:(Nā
C)
3178:or a
1621:with
1499:with
125:or a
100:loads
86:, in
64:field
7800:2018
7764:ISBN
7743:help
7717:ISBN
7621:ISBN
7594:ISBN
7502:ISBN
7474:ISBN
7436:ISBN
7415:ISBN
7382:ISBN
7361:help
7335:ISBN
7293:link
7286:help
7260:ISBN
7218:free
7216:The
7163:0 ā¤
6090:Ī©ā
m
5897:Ī©ā
m
5300:Jā
K
5142:The
5059:and
4746:and
3860:and
3845:and
3810:and
3798:and
3776:and
3659:and
3648:and
3640:and
3619:and
3190:and
3162:and
3154:and
3024:and
2996:and
2988:and
2968:and
2956:and
2947:and
2926:and
2922:but
2826:and
2818:and
2678:and
2670:and
2595:and
2587:and
2576:and
2443:and
2428:and
2331:and
2090:and
2082:and
2071:and
2060:and
2031:and
1973:and
1871:The
1751:and
1294:The
1251:0 ā¤
1142:The
1069:and
189:and
178:.
82:the
38:, a
34:and
7682:doi
7137:sys
7119:ext
7026:ext
7017:sys
6329:of
3158:on
3014:or
2846:or
2439:of
1795:div
1428:) ā
1403:of
1280:ā„ 1
1269:= 0
1262:= 1
1255:ā¤ 1
391:mod
375:mod
106:or
102:to
98:or
70:or
62:or
42:or
30:In
7815::
7786:.
7735::
7733:}}
7729:{{
7680:.
7670:51
7668:.
7664:.
7573:50
7353::
7351:}}
7347:{{
7329:.
7278::
7276:}}
7272:{{
7230:no
7034:,
7006:,
6996:,
6892:,
6888:/ā
6877:,
6867:,
6635:,
6631:/ā
6620:,
6610:,
6600:,
6498:/ā
6471:,
6363:/ā
6204:,
6112:,
6105:,
5988:K
5583:,
5572:,
5565:,
5561:,
5557:,
5542:K
5458:,
5443:K
5072:,
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5051:=
4924:.
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3909:.
3893:.
3849:.
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3032:,
2934:,
2834:,
2046:,
2042:,
2035:.
2027:,
2019:,
2015:,
2011:,
2007:,
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7684::
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7057:=
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6986:Īµ
6957:j
6953:x
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6919:=
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6865:Ī»
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6789:=
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6748:=
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6736:x
6727:V
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6692:=
6689:V
6667:Ļ
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6639:(
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6627:ā
6618:R
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6529:=
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6500:x
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6494:ā
6489:q
6479:Ī¼
6469:Īŗ
6461:Īŗ
6432:j
6428:x
6419:C
6408:j
6405:i
6401:D
6394:=
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6385:J
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6359:ā
6354:J
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6336:D
6260:m
6256:R
6252:1
6247:=
6221:P
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6206:P
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6161:M
6155:=
6150:m
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6122:R
6110:m
6107:R
6103:R
6071:1
6066:=
6052:Ļ
6023:R
6020:1
6015:=
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6001:G
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5939:=
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5868:=
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5817:=
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5737:=
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5724:=
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5664:=
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5603:=
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5555:Īŗ
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5498:V
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5367:=
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5280:=
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5178:=
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5093:=
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5069:0
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5062:Ī¼
5056:0
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5049:Īµ
5021:1
5016:=
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4971:B
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4957:n
4951:=
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4875:Īµ
4854:r
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4834:=
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4815:0
4795:=
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4775:=
4772:n
4759:c
4755:0
4752:c
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4703:i
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4682:=
4677:j
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4650:q
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4570:=
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4533:T
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4479:=
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4401:=
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4300:k
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4286:=
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4000:=
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3879:Īµ
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3100:=
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2932:E
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2869:=
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2828:B
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2820:M
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2794:1
2791:+
2786:m
2778:=
2773:r
2765:=
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2711:=
2706:0
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2578:Ļ
2574:e
2571:Ļ
2554:,
2550:H
2544:m
2536:=
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2527:,
2523:E
2517:e
2507:0
2499:=
2495:P
2481:M
2477:P
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2469:M
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2426:0
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2395:/
2390:B
2386:=
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2359:=
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2329:M
2321:M
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2271:M
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2135:=
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2110:D
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1936:R
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1913:n
1910:=
1907:V
1904:p
1891:n
1887:T
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1844:e
1839:i
1835:x
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1596:i
1583:3
1580:1
1570:j
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1558:(
1551:2
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1513:y
1509:u
1505:y
1503:(
1501:u
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1458:=
1438:s
1434:y
1430:u
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1408:Ī¼
1393:d
1391:c
1368:2
1364:v
1360:A
1352:d
1348:c
1342:2
1339:1
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1267:e
1260:e
1253:e
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1200:|
1194:v
1189:|
1182:=
1179:e
1155:v
1148:v
1131:.
1071:S
1063:C
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1041:k
1030:l
1027:k
1024:j
1021:i
1017:S
1013:=
1008:j
1005:i
990:l
987:k
976:l
973:k
970:j
967:i
963:C
959:=
954:j
951:i
912:E
909:=
893:Īµ
886:E
879:Ļ
857:i
853:x
849:k
843:=
838:i
834:F
820:x
813:k
775:.
772:R
767:f
759:=
756:F
743:f
740:Ī¼
736:R
729:F
688:B
684:/
680:1
677:=
674:C
663:C
636:)
633:V
629:/
625:V
619:(
615:/
611:P
608:=
605:B
594:B
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546:(
542:/
538:)
535:A
531:/
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524:(
521:=
518:G
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403:/
396:=
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349:D
347:Ī
342:D
326:D
322:/
318:D
312:=
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280:A
276:F
262:A
258:/
254:F
251:=
237:Ļ
233:P
20:)
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