Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through a constitutive relation.

By eliminating ρ and J, using Maxwell's equations, and manipulating using the theorems of vector calculus, this form of the equation can be used to derive the Maxwell stress tensor σ, in turn this can be combined with the Poynting vector S to obtain the electromagnetic stress-energy tensor T used in general relativity.

The judging commission felt that “ the true equations of the movement were not established ,” even though “ the experiments presented ingenious results .” Lagrange was able to use Germain's work to derive an equation that was “ correct under special assumptions .”

Another way to derive Snell ’ s Law involves an application of the general boundary conditions of Maxwell equations for electromagnetic radiation.

* 1968 — Brandon Carter uses Hamilton-Jacobi theory to derive first-order equations of motion for a charged particle moving in the external fields of a Kerr-Newman black hole

The second is to use these linear equations in conjunction with known plaintext-ciphertext pairs to derive key bits.

The equations from which complex system models are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of systems of nature that are considered fundamentally complex.

* A parameter denoted as warped time used to derive the equations for homogeneous azeotropic distillation

Delambre was one of the first astronomers to derive astronomical equations from analytical formulas, was the author of Delambre's Analogies and, after the age of 70, also the author of works on the history of astronomy like the Histoire de l ' astronomie.

While not seriously advocated after Einstein's development of relativity, Newtonian gravity can be used to model the universe and non-rigorously derive the Friedmann equations that are used in the big bang universe.

The Reynolds equations can be used to derive the governing principles for the fluids.

In 1926, Erwin Schrödinger published an equation describing how this matter wave should evolve — the matter wave equivalent of Maxwell ’ s equations — and used it to derive the energy spectrum of hydrogen.

Alternatively, we may use just the last two equations given for the compositional property of the solvent in each of the preceding sections, together with the relationships given below, to derive the remainder of properties in that set:

These sets of differential equations can be used to derive a transfer function that models the behavior of the system.

Using Maxwell's equations simultaneously with the curl of Ohm's Law, one can derive what is basically the linear eigenvalue equation for magnetic fields ( B ) which can be done when assuming that the magnetic field is independent from the velocity field.

The preceding section explains how to derive Fowler-Nordheim-type equations.

Using the Navier-Stokes equations for fluids, Rott was able to derive equations specific for thermoacoustics.

In spite of this fact, scientists have not yet been able to derive the equations for nonlinear response theory from the FT.

) The general form of the metric follows from the geometric properties of homogeneity and isotropy ; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time.

Let us repeat the derivation more systematically in order to show how the Lorentz equations can be used explicitly to derive a relativistic Doppler shift equation for waves that themselves are not relativistic.

This general equation may be used to derive any continuity equation, ranging from as simple as the volume continuity equation to as complicated as the Navier – Stokes equations.

The rate equations may be solved by numerical integration to obtain a time-domain solution, or used to derive a set of steady state or small signal equations to help in further understanding the static and dynamic characteristics of semiconductor lasers.

Computational fluid dynamics dispenses with many of the simplifying assumptions used to derive classical formulas and computer software facilitates optimization.

Driven by Sir Isaac Newton's somewhat obscure assertion of " a certain most subtle spirit which pervades and lies hid in all gross bodies ", Challis was driven to attempt to derive all physical phenomena from a model of intert spherical atoms embedded in an elastic fluid ether, an enterprise described as an attempt at a " Victorian unified field theory ".

We derive the ion acoustic wave dispersion relation for a linearized fluid description of a plasma with multiple ion species.

In their classical text on fluid mechanics, Landau and Lifshitz derive an aeroacoustic equation analogous to Lighthill's ( i. e., an equation for sound generated by " turbulent " fluid motion ) but for the incompressible flow of an inviscid fluid.

These descriptions may be used in order to derive several interesting properties.

The potential is then used to derive the thermodynamic properties of the system assuming thermal equilibrium.

He then went on to apply the Laplace transform in the same way and started to derive some of its properties, beginning to appreciate its potential power.

Prescriptivism is also supported by Imperative logic, in which there are no truth values for imperatives, and by the idea of the Naturalistic fallacy: even if someone could prove the existence of an ethical property and express it in a factual statement, he could never derive any command from this statement, so the search for ethical properties is pointless.

These properties derive from ultraviolet's power to alter chemical bonds, even without having quite enough energy to ionize atoms.

These properties derive from the ultraviolet photon's power to alter chemical bonds in molecules, even without having enough energy to ionize atoms.

This equation for the chemical potential may then be used to derive other thermodynamic properties of an ideal solution.

Simple box models, i. e. box model with a small number of boxes whose properties ( e. g. their volume ) do not change with time, are often useful to derive analytical formulas describing the dynamics and steady-state abundance of a species.

Other princes derive their title not from dynastic membership as such, but from inheritance of a title named for a specific and historical territory, although the family's possession of prerogatives or properties in that territory may be long past.

In their derivation, they derive the velocity field by demanding the appropriate transformation properties given by the various symmetries that Schrödinger's equation satisfies, once the wavefunction is suitably transformed.

The same word was also used for the substance amber, probably because of the pale yellow color of certain varieties, and it is from the electrostatic properties of amber that the modern English words " electron " and " electricity " derive.

John Earman and John Norton have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the second law of thermodynamics cannot be violated by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc.

Simple box models, i. e. box model with a small number of boxes whose properties ( e. g. their volume ) do not change with time, are often useful to derive analytical formulas describing the dynamics and steady-state abundance of a species.

Given that X, Y, and Z are sets of attributes in a relation R, one can derive several properties of functional dependencies.

Spectroscopy can be used to derive many properties of distant stars and galaxies, such as their chemical composition, but also their motion by Doppler shift measurements.

Key derivation functions are also used in applications to derive keys from secret passwords or passphrases, which typically do not have the desired properties to be used directly as cryptographic keys.

While these sounds do not necessarily share any particular phonetic properties in common, most historically derive from a common source.

Nagel notes that new physical properties are discovered through explanatory inference from known physical properties ; following a similar process, mental properties would seem to derive from properties of matter not included under the label of " physical properties ", and so they must be additional properties of matter.