Maxwell’s theory

This point was taken up by Reynolds in a letter addressed to G. G. Stokes, in the latter s capacity as Secretary of the Royal Society [83]. Reynolds pointed out that Maxwell s theory evaluated the effects of thermal transpiration only in circumstances where they were too small to be measured, and complained that Maxwell had misrepresented his own theoretical treat ment of the phenomenon. However, this incipient controversy never developed... 

Under the same conditions. Maxwell s theory of radiation shows that the refractive index and the relative dielectric constant are simply related by... 

The connection between the molar polarization Pm and the molar refraction Rm is through Maxwell s theory of electromagnetism, according to which e = (at low-frequency fields). This is the basis for considering the molar refraction a measure of polarizability. 

The earliest hint that physics and information might be more than just casually related actually dates back at least as far as 1871 and the publication of James Clerk Maxwell s Theory of Heat, in which Maxwell introduced what has become known as the paradox of Maxwell s Demon. Maxwell postulated the existence of a hypothetical demon that positions himself by a hole separating two vessels, say A and B. While the vessels start out being at the same temperature, the demon selectively opens the hole only to either pass faster molecules from A to B or to pass slower molecules from B to A. Since this results in a systematic increase in B s temperature and a lowering of A s, it appears as though Maxwell s demon s actions violate the second law of thermodynamics the total entropy of any physical system can only increase, or, for totally reversible processes, remain the same it can never decrease. Maxwell was thus the first to recognize a connection between the thermodynamical properties of a gas (temperature, entropy, etc.) and the statistical properties of its constituent molecules. 

Ochoa-Tapia, JA Stroeve, P Whitaker, S, Diffusive Transport in Two-Phase Media Spatially Periodic Modles and Maxwell s Theory for Isotropic and Anisotropic Systems, Chemical Engineering Science 49, 709, 1994. 

Maxwell s theory of the electromagnetic field represents the reduction of several apparently disparate aspects of physics, to a common basis. It shows... 

Bartlett and Corle [46] proposed modification of Maxwell s equations in the vacuum by assigning a small nonzero electric condictivity to the formalism. As pointed out by Harmuth [47], there was never a satisfactory concept of propagation velocity of signals within the framework of Maxwell s theory. Thus, the equations of the latter fail for waves with nonnegligible relative frequency bandwidth when propagating in a dissipative medium. To resolve this problem, a nonzero electric conductivity ct and a corresponding current density... 

A. Fick, Ann. Phys. (Leipzig) 170, 50 (1855). He actually set up his two laws for the temporal spreading of the concentration of a tracer substance, not for the probability. The first evolution equation for a probability was the Boltzmann equation [L. Boltzmann Vorlesungen tiber Gastheorie I (J. A. Barth, Leipzig, 1896)], following Maxwell s theory of gas kinetics. 

B. The Case of Maxwell s Theory in Vacuum Electromagnetic Helicity... 

The local equivalence that we have just proved implies that the predictive contents of the Maxwell s theory and of this topological model are exactly the same when referred to local experiments, as most of them are. Accordingly, it is not possible to discern between the two by viewing locally. This is the operative meaning of local equivalence. 

This shows that there is still some linearity. In particular, there is a subset of knots that form a vector space and is therefore a linear sector of the model. It is the set of the knots with zero helicity or with unlinked lines. Note also that the theory is fully linear from the local point of view, as a consequence of the local equivalence with Maxwell s theory shown in Section V.A. By this we mean that the set of the electromagentic knots contains all the linear combinations of standard solutions around any point. 

It is locally equivalent to Maxwell s standard theory in empty space (but globally disequivalent). This means that it cannot enter in conflict with Maxwell s theory in experiments of local nature. 

One of the most important requirements for an axiomatic theory is to determine the validity-round of the laws, and to verify of the self-consistency in the theory. The M-M experiment proved that the prediction of the classical physics was not valid for light propagation, or rather, for Maxwell s theory of electromagnetism. This is an applicability limit of Newtonian physics. Beyond this limit, Newtonian physics becomes incomplete. 

In a strict sense, the classical Newtonian mechanics and the Maxwell s theory of electromagnetism are not compatible. The M-M-type experiments refuted the geometric optics completed by classical mechanics. In classical mechanics the inertial system was a basic concept, and the equation of motion must be invariant to the Galilean transformation Eq. (1). After the M-M experiments, Eq. (1) and so any equations of motion became invalid. Einstein realized that only the Maxwell equations are invariant for the Lorentz transformation. Therefore he believed that they are the authentic equations of motion, and so he created new concepts for the space, time, inertia, and so on. Within... 

In Maxwell s theory, this dispersion of energy is considered to be negligible, and no damping occurs during the propagation of an electromagnetic wave. Let us consider the plane waves propagating in the z direction ... 

T. W. Barrett, in Lakhtakia (Ed.), Essays on the Formal Aspects of Maxwell s Theory, World Scientific, Singapore, 1993, pp. 6-86. 

The droplet current / calculated by nucleation models represents a limit of initial new phase production. The initiation of condensed phase takes place rapidly once a critical supersaturation is achieved in a vapor. The phase change occurs in seconds or less, normally limited only by vapor diffusion to the surface. In many circumstances, we are concerned with the evolution of the particle size distribution well after the formation of new particles or the addition of new condensate to nuclei. When the growth or evaporation of particles is limited by vapor diffusion or molecular transport, the growth law is expressed in terms of vapor flux equation, given by Maxwell s theory, or... 

Gibbs also wrote an influential book on statistical mechanics, which developed a molecular theory of thermodynamic properties from first principles, with a treatment that was general enough to accommodate quantum mechanics, a theory that had not even been imagined yet. He championed the now standard use of vector notation over William Rowan Hamilton s quaternion algebra and wrote several seminal papers on electromagnetism in the 1880s that supported Maxwell s theory, see also Equilibrium Maxwell, James Clerk Thermodynamics. 

Comparing the classical force Q, given above, the spatial components of X, are X = yQ. verifying the historical fact that Maxwell s theory is covariant under Lorentz transformations. 

A first rather comprehensive theoretical treatment of TIR, based on Maxwell s theory, was published by Schaefer (9) in 1932. In this treatment a displacement of the incoming and the totally reflected ray, as shown in Figure 1, was predicted. But it was... 

A TREATISE ON ELECTRICITY AND MAGNETISM, James Clerk Maxwell. Important foundation work ol modern physics. Brings to final form Maxwell s theory of electromagnetism and rigorously derives his general equations of field theory. 1,084pp. 5b x 8b. 60636-8, 60637-6 Pa., Two-vol. set 19.00... 

In general, the refractive index decreases with the increment of the fluorine content in a polymer because of the small polarizability of fluorine. Column 6 in Table 1 shows refractive indexes of S-type fluorides. As the reaction temperature increases, the refractive index tends to decrease. This tendency is in good agreement with that of F/C atomic ratio. On the basis of the Maxwell s theory of electro-magnetism, the dielectric constant, e is equal to the square of refractive index, n under a fixed frequency. The dielectric constants of the S-type fluoride calculated based on the relation are also shown in Table 1, Column 7. The dielectric constant slightly decreased with increasing the fluorination temperature. 

Boltzmann generalized Maxwell s theory and found that the probability p that a molecule will be found in a state with an energy E is given by Equations 10-15,... 

On the basis of Maxwell s theory, the reflected and the refracted waves are explicitely stated by Fresnel s equations. The coefficient r correlates the amplitude E of the reflected wave with the amplitude Eq of the incident one (Bom, 1933 Bom and Wolf, 1980 Bennett and Bennett, 1978) ... 

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