Showing papers on "Field (physics) published in 1970"

Classical Aspects of Energy Transfer in Molecular Systems

Abstract: The decay time of the luminescence of a molecule S in front of a metal mirror depends markedly on its distance from the mirror. This phenomenon is quantitatively explained by considering the radiation field of this dipole, given by Hertz classical equation. This field arrives at the molecule, after being reflected at the mirror, with a retardation of the order of 10−15 sec. The decay time of the luminescence depends on the phase shift produced by this retardation, and thus on the ratio of the distance of the oscillator from the mirror, and the wavelength of the emitted light. By measuring the distance dependence of the decay time of the luminescence this retardation effect can be studied. In quantum‐mechanical terms the phenomenon can be described as being due to a stimulation or inhibition of the emission of the light quantum. In contrast to the known cases of stimulated emission, the stimulating field is the radiation field of the emitter quantum itself. The energy transfer from an excited molecule S to an acceptor A can be treated in a similar manner by considering the phenomenon as a retardation effect. In classical terms the field of S induces A to oscillate, and the induced field of A arriving at S slows down this oscillator. Simple equations are given for the energy transfer from an excited dipole or quadrupole, and for a row of many dipoles, oscillating in phase, to a weakly absorbing acceptor layer. The latter case is considered as a model for a J‐aggregating dye and by comparison with experimental data conclusions concerning the size of a J aggregate are drawn.

Field and particle equations for the classical Yang-Mills field and particles with isotopic spin

Abstract: A complete system of equations describing the interaction between the Yang-Mills field and isotopic-spin-carrying particles in the classical limit is extracted from the equations of motion for the quantum fields. Some simple consequences are derived. The consistency of the equations is investigated.

Structure of Temperature Field in Turbulent Flow

Abstract: : The mean square of the temperature difference at two points is used as the characteristic parameter of the temperature field. The dependence of this quantity on the distance between the points of observation is determined experimentally. The order of magnitude of the characteristic parameters of the field of temperature fluctuations in the atmosphere is evaluated.

Uniformly accelerating charged mass in general relativity.

Abstract: We discuss a type-{22} solution of the Einstein-Maxwell equations which represents the field of a uniformly accelerating charged point mass. It contains three arbitrary parameters $m$, $e$, and $A$, representing mass, charge, and acceleration, respectively. The solution is a direct generalization of the Reissner-Nordstrom solution of general relativity and the Born solution of classical electrodynamics. The external "mechanical" force necessary to produce the acceleration appears in the form of a timelike nodal two-surface extending from the particle's world line to infinity. This does not prevent us from regarding the solution as asymptotically flat and calculating the radiation pattern of its electromagnetic and gravitational waves. We find as well a maximal analytic extension of the solution and discuss its properties. Except for an extra "outer" Killing horizon due to the accelerated motion, the horizon structure closely resembles the Reissner-Nordstrom case.

Effects of Magnetic Fields on the Mutual Annihilation of Triplet Excitons in Anthracene Crystals

Abstract: Detailed measurements of the magnetic field dependence of the rate of mutual annihilation of triplet excitons in anthracene crystals at room temperature are presented. The field dependence consists of an increase at low fields, with a maximum at ca. 350 Oe, followed by a decrease at higher fields to less than the zero-field annihilation rate. For most field directions, a second maximum occurs at ca. 600 Oe. The amplitude of the field dependence is highly anisotropic. For fields g2000 Oe, resonances in the annihilation rate are found at +76\ifmmode^\circ\else\textdegree\fi{} and -17\ifmmode^\circ\else\textdegree\fi{} with respect to the $a$ axis for fields in the $\mathrm{ac}$ plane and at \ifmmode\pm\else\textpm\fi{}23.5\ifmmode^\circ\else\textdegree\fi{} with respect to the $b$ axis in the $\mathrm{ab}$ plane. For fields 500 Oe, a second set of resonances occurs at directions bisecting the high-field resonances and at intermediate fields the two sets coexist. These results are discussed in terms of a density-matrix description of the spin states of the interacting triplet pair and of the annihilation process. The field dependence is accounted for on the basis of the field dependence of the pair spin states together with the postulate that annihilation is spin-allowed. The observed resonances result from level crossings among the pair spin states. All of the structure in the field dependence and anisotropy data is satisfactorily reproduced by calculations based on the model, although complete quantitative agreement is not achieved.

Magnetic-field re-connexion in a highly conducting incompressible fluid

Abstract: A theoretical model is proposed for the process of re-connexion of frozen-in magnetic-field lines at an X-type null point in the field. The model involves a diffusion region, immediately adjacent to the null point and an outer wave- dominated region. For the latter an exact solution to the magneto-hydrodynamic equations is obtained; for the former an approximate relationship is derived between the field-re-connexion rate, measured by the Alfven number of the incident flow, and the magnetic Reynolds number, based on the width of the diffusion region. The maximum field-re-connexion rate is determined entirely by conditions near the null point and may under suitable conditions become large. A condition for maximum conversion of magnetic energy is derived.

Nonlinear Electrodynamics: Lagrangians and Equations of Motion

Abstract: After a brief discussion of well‐known classical fields we formulate two principles: When the field equations are hyperbolic, particles move along rays like disturbances of the field; the waves associated with stable particles are exceptional. This means that these waves will not transform into shock waves. Both principles are applied to nonlinear electrodynamics. The starting point of the theory is a Lagrangian which is an arbitrary nonlinear function of the two electromagnetic invariants. We obtain the laws of propagation of photons and of charged particles, along with an anisotropic propagation of the wavefronts. The general ``exceptional'' Lagrangian is found. It reduces to the Lagrangian of Born and Infeld when some constant (probably simply connected with the Planck constant) vanishes. A nonsymmetric tensor is introduced in analogy to the Born‐Infeld theory, and finally, electromagnetic waves are compared with those of Einstein‐Schrodinger theory.

Latitude Dependence of the Angular Dispersion of the Geomagnetic Field

Abstract: Summary Changes in the direction of the Earth's magnetic field at a given site are produced in part by wobble of the main geomagnetic dipole, in part by fluctuations in the intensity and direction of the non-dipole field, and in part by changes in the intensity of the main dipole field. These three processes combine to produce an angular variance that is strongly latitude dependent. A method is presented for isolating the contribution due to variation with latitude of the average intensity of the non-dipole field. The aspect of geomagnetic secular variation most accessible to palaeomagnetic measurement is the angular dispersion of the field over long periods of time. The amount of the angular dispersion is determined by two factors. One is the angular wobble of the main geomagnetic field. The other is the time average of the ratio flF of the non-dipole field to the dipole field. This time average is of general geophysical interest because it provides a measure of the time average of the magnetohydrodynamic processes in the region of the Earth's core beneath the site where the palaeomagnetic samples were collected. The time average of the nondipole field may exhibit a longitude dependence and a latitude (or zonal) dependence. Existence of the former implies that lateral differences exist in the boundary conditions at the core-mantle interface. Lateral temperature variations (Cox & Doell 1964) or lateral differences in relief along the core-mantle interface (Hide 1966) may lead to longitudinal differences in the operation of the geomagnetic dynamo and hence to longitudinal differences in the time average of the non-dipole field. Even if the core-mantle boundary conditions were completely uniform, however, the angular dispersion of the geomagnetic field would still vary with latitude for two reasons. The first is that the Coriolis forces of the geomagnetic dynamo vary with latitude, hence it is reasonable that the nondipole field may also vary. The second is that because of the geometry of the vector addition of dipole and nondipole fields on a sphere, the geomagnetic angular dispersion will vary with latitude even if the non-dipole field is the same at all latitudes. The objective of the present study is to develop models that describe the latitude dependence of geomagnetic

Wannier Exciton in an Electric Field. I. Optical Absorption by Bound and Continuum States

Abstract: A comprehensive study of electric field effects on optical absorption by Wannier excitons is presented, showing field effects on both bound and continuum states. The calculations and results have been simplified by defining appropriate dimensionless parameters such that the eigenvalues are independent of field when expressed in terms of these parameters. A general normalization procedure for wave functions with continuous eigenvalues is outlined. The effect of the electron-hole interaction on the electric-field-induced oscillations is demonstrated, with the result that the electron-hole interaction enhances these oscillations near an ${M}_{0}$-type edge (positive effective masses) and quenches these oscillations near an ${M}_{3}$-type edge (negative effective masses). This effect would inhibit the observation of ${M}_{3}$-type edges in electroreflectance.

Theory of a three-level gas laser amplifier

Abstract: A laser amplifier to be treated in this work consists of an ensemble of atoms three energy levels of which form two coupled transitions of arbitrary frequencies. Two classical monochromatic travelling light waves are to be close to resonance with the transitions. The gain profile (or spontaneous emission) on the transition corresponding to the weak “probe” wave, modified by the perturbing field on the other transition, is calculated via a susceptibility. Within this framework, the atoms are described by an ensemble-averaged density matrix with full account of level degeneracies, light polarizations, and inelastic and dephasing collisions; an extension to elastic collisions and disorientation is straightforward. An integration over the thermal velocity distribution gives results applicable to gas discharges: directionally anisotropic narrow structures superimposed on the Doppler-broadened probe-gain profile due to non-linear interference effects in addition to saturation. At alower probe frequency, a peculiar non-Lorentzian signal appears even with transparency on the perturbing transition. At low intensities a distinction is reasonable of frequency correlations due to generalized two-quantum processes, and of a dynamic Stark splitting. These effects permit an information on the linewidth of the third forbidden transition. The connection with numerous related approaches is pointed out.

Source of the kerr metric

Abstract: Assuming that the Kerr-Newman metric is the field of a layer of mass and charge distributed over the equatorial disk spanning the ring singularity, the source distribution on the disk is computed explicitly. In the uncharged case, this interpretation automatically excises the noncausal parts of the manifold, so that one obtains the unique source of the causally maximal extension of the vacuum metric. A Newtonian field which gives the same source distribution is exhibited, and shown to be closely analogous to the relativistic case. In particular, the Newtonian particle orbits show the same avoidance of the ring singularity that is such a remarkable feature of geodesics in the Kerr geometry. In the charged case, we examine how the gyromagnetic moment (which is equal to that of the Dirac electron) is reflected in the character of the source distribution.

Turbulent dynamo action at low magnetic Reynolds number

Abstract: The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

Classical, Stable, Nonlinear Spinor Field with Positive Rest Energy

Abstract: The influence of nonlinear (fourth-order) terms in the Lagrangians of some classical relativistic field theories is investigated, independently of the mass and coupling-constant parameters. In the spinor case, stable localized configurations with a lowest energy state are shown to exist always for positive values of the coupling constant.

Spatially periodic dynamos

Abstract: It is established analytically that, in a precisely defined sense, almost all steady spatially periodic motions of a homogeneous conducting fluid will give dynamo action at almost all values of the conductivity. The same result is obtained for motions periodic in space-time. The asymptotic form of the growing field, for an arbitrary initial field of finite energy, is also presented. Dynamo action is first shown to require that for some real vector there is a magnetic field solution of the form B= H exp (pt+ij. x), where H is a complex function of position (or of position and time) with the same periodicity as the motion, and p has positive real part, indicating growth. This number p is an eigenvalue of a linear differential operator on the space of admissible functions H. The first term of a power series in j for the eigenvalues/) which vanish to zero order is studied. It is thus proved sufficient for dynamo action that the determinant of the symmetric part of a certain 3 x 3 tensor, a function of the motion and conductivity, is non-zero. Finally, it is shown that this determinant is an analytic function of the conductivity, and is non-zero in a small conductivity limit for nearly all motions. This proves the stated result.

Group-theoretical analysis of elementary particles in an external electromagnetic field II.—The nonrelativistic particle in a constant and uniform field

Abstract: Two subgroups of the Galilei group are shown to play a particular role in the case of charged systems in an external electro-magnetic field which is constant and uniform. Projective representations of these subgroups involve the electric charge and mass as generators of phase factors. Additivity and superselection rules for charge and mass appear as direct consequences. A comparison is made with the relativistic case investigated in the first part of this article.

Optimum Geometry of Saddle Shaped Coils for Generating a Uniform Magnetic Field

Abstract: Saddle shaped coils for generating a field perpendicular to the axis of a cylindrical shell to which the coils are confined can be designed in a compact and easily constructed form. The central magnetic field of such a system and its second derivatives with respect to displacements from the center are given as functions of the coil dimensions, and conditions for minimizing these derivatives are discussed. A coil pair with a length‐to‐diameter ratio of 2 and circular arcs of 120° will have no second order central field derivatives in any direction.

Theory of a probe in a strong magnetic field.

Abstract: An asymptotic analysis of the Langmuir‐probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C‐V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented. The theory, which fails beyond certain positive voltage, yields useful results for weak fields, too.

Ising Model with a Transverse Field

Abstract: The phase transition in the Ising model has been studied as a function of an applied transverse field, by Green's function and series-expansion methods. The critical indices are probably independent of the applied field except at $T=0$ where they appear to be related to those of the Ising model in one higher dimension.

Statistics; the essentials for research

Abstract: Published in 1986, Statistics is a valubale contribution to the field of Research Methods/Stats.

Slow motion of two spheres in a shear field

Abstract: The exact solution of the Stokes equations for the creeping motion of two spheres of arbitrary size and arbitrarily oriented with respect to a shear field is obtained by use of spherical bipolar co-ordinates. Numerical results are given for two special cases: (1) the free motion of two equal-sized spheres in simple shear flow and (2) the free motion of a sphere near a wall in the rotational shear field between two parallel disks rotating at different rates. The sphere trajectories calculated for the first of these problems are found to agree fairly well with those observed experimentally.

Quantum electrodynamics of spinless particles between conducting plates

Abstract: The energy of any system containing charged particles arises partly from its coupling to the quantized electromagnetic field; it changes on inserting the system between conducting plates, because these alter the normal modes of the field relative to free space. We calculate to order e2 such energy shifts for a free electron and for a hydrogen atom, neglecting spin, but allowing in full for electrostatic and retardation corrections as well as for changes in the Lamb shift proper. The potential between a particle and a single plate follows as a limiting case. An appendix details the distinction between classical and quantum effects.

Dipole‐Exchange Spin Waves in Ferromagnetic Films

Abstract: The effects of exchange on the magnetostatic surface and bulk spin waves of a ferromagnetic film in the regime where the dipole and exchange fields are both important are determined from the solutions of a sixth‐order differential equation. The eigenstates are admixtures of bulk and surface waves. With an applied magnetic field parallel to the film surface and for small values of the wave vector parallel to the surface, k, the Damon and Eshbach surface state is split into segments which join adjacent bulk branches. No sharp cutoff of the surface branch occurs as the angle between k and the applied field is increased, instead the character of the branch changes continuously from surface‐like to bulk‐like. For values of | k |≳104 a number of branches have significant surface character so that no single branch can be identified with the Damon‐Eshbach surface state. When the applied field is perpendicular to the surface a new type of surface spin wave occurs below the bulk manifold and is characterized by a c...

Electrohydrodynamic stability: fluid cylinders in longitudinal electric fields.

Abstract: The stability of a fluid cylinder, stressed by an axial electric field, has heretofore been studied assuming that the cylinder and its surroundings behave as perfect dielectrics and viscous effects are ignored. With many fluids this is unrealistic since the existence of even a small conductivity implies that the deformed interface carries an electric charge. Upon deformation of the interface the charge interacts with the field to produce an electrical shearing stress. Thus, to avoid singular behavior viscous shear must be considered from the outset. The analysis is applicable to situations where the relaxation time for free charges is short compared with the time scale for fluid motion. It is found that electrical shearing forces can, under some conditions, completely stabilize the cylindrical interface to axisymmetric deformations. On the other hand, the conditions under which these same forces produce instability are delineated. In instances where both fluids have low viscosities a boundary layer effect produces additional damping and, in the presence of an axial electric field, electrical shearing stresses in this boundary layer may render an otherwise stable oscillation unstable.

Spin diffusion and spin echoes in liquid 3He at low temperature

Abstract: Spin diffusion in a degenerate Fermi liquid is studied, taking into account the effects of the 'molecular field' resulting from the interactions between quasiparticles. It is shown that even in the hydrodynamic limit no equation of the conventional form delta M/ delta t=Dgrad2M exists in general; the true equation is nonlinear and depends on the strength of the interactions. Substantial new effects are therefore predicted when lambda Omega 0 tau D> approximately 1, where Omega 0 is the Larmor frequency, tau D the spin diffusion lifetime and lambda a dimensionless parameter which measures the strength of the molecular field. Specifically, it is predicted that the spin-echo attenuation in a ' phi -180-180' experiment will in general not be exponential and will depend on the external field and the initial pulse angle phi . The new effects should lie in the experimentally accessible region both for pure 3He and for mixtures.