Abstract: The equilibrium structure of two-dimensional magnetic current sheets is investigated for systems in which the plasma pressure dominates the bulk flow energy, as appears appropriate for the quiet time plasmasheet in the geomagnetic tail. A simple model is studied in which the field is contained between plane parallel boundaries and varies exponentially along the system, while the plasma pressure is anisotropic, the anisotropy being arbitrary but constant along the centre plane. When the field is highly inflated by the plasma current it is found that adiabatic solutions exist only when the plasma pressure is close to isotropic. For the case P ∥ > P ⊥ it is argued that a thin, non-adiabatic current layer will in general form at the sheet centre, usually embedded within a much broader adiabatic current distribution. When P ⊥ > P ∥ , a broad region of very depressed fields develops about the centre of the current sheet, terminated at its outer boundary by a spike in the current density. This central region becomes unstable to the mirror mode well before the limiting adiabatic solution is reached.

Abstract: The characteristics of entrainment in and below 12 developing cumulus congestus clouds in the north-eastern Colorado area were investigated using measurements obtained with the NCAR/NOAA sailplane, supporting aircraft and rawinsondes. A region of moist adiabatic ascent was found in eight of the most vigorous clouds sampled. A gradual increase was noted in the equivalent potential temperature and the ratio of the liquid water content to the adiabatic value from the edge of the updraft region inward to the moist adiabatic core. Previous measurements and conceptual and theoretical models of entrainment are discussed in the context of the present set of measurements. The moist adiabatic core was positioned off-center with respect to the boundaries of the updraft region. The measurements supported previous conceptual cloud models in which the updraft acts as an obstacle to the horizontal wind thereby causing the environmental air to flow around the upshear portion of the cell, protecting that region f...

Abstract: It is shown that the method of adiabatic regularization, proposed by Parker & Fulling for the removal of divergences in the vacuum expectation value of the stress tensor of a quantized field propagating in a Robertson-Walker background, is well suited to calculations of cosmological interest. After verifying the equivalence of the adiabatic and point-splitting regularization schemes, both analytical and numerical examples of the use of the former method are given.

Abstract: A model system consisting of two electronic manifolds coupled through a nontotally symmetric mode of vibration is solved exactly and self‐consistently by the method described in Paper I [J. Chem. Phys. 65, 2071 (1976)]. As in I, the model is defined in terms of harmonic diabatic potentials, but the restriction to harmonic adiabatic potentials, applied in I, is lifted here. As a result, the adiabatic coupling operator which has the same analytical form as in I, can assume a much wider range of values. It leads to adiabatic potentials which in general are anharmonic and may exhibit a double minimum. The coupling is taken to be an odd function of the vibrational coordinate so that it describes the (pseudo‐) Jahn–Teller effect. Absorption and emission spectra are calculated for selected combinations of four spectroscopic parameters: (1) the electronic energy gap; (2) the diabatic harmonic frequency difference; (3) a linear adiabatic coupling parameter; and (4) a nonlinear (quasiquadratic) adiabatic coupling parameter. In the appropriate limits, the results are shown to reduce to analytical weak‐ and strong‐coupling results, but the model is shown to differ from the molecular dimer model which also permits exact numerical solution for arbitrary coupling. The calculated spectra are interpreted in terms of a number of basic characteristics. Recognition of these characteristic spectral patterns may be helpful in the analysis of vibronically contaminated spectra. For certain combinations of parameter values, the model predicts strong and possibly anomalous solvent and isotope effects. As an example, the vibrational structure of the lowest singlet absorption band of pyrazine is analyzed and shown to indicate evidence for nonlinear vibronic coupling.

Abstract: The steady one-dimensional isobaric combustion of a gaseous premixture of fuel and oxidant under a direct one-step irreversible Arrhenius-type exothermic chemical reaction is studied analytically for constant, but general, Lewis-Semenov number. Limit-process expansions are used to obtain solutions in the physically interesting limit of activation temperature large relative to the hot-boundary temperature. The eigenvalue or critical flow speed for an adiabatic system is established as a function of departure from stoichiometry. It is emphasized that, for relatively small departures from stoichiometry, the bimolecular system behaves as a monopropellant decomposition, to lowest order of approximation, because the richer reactant is effectively undepleted. The porous-disk-type flameholder for a flat-flame burner is modeled as a (nonadiabatic) heat source (supercritical flow speed) or heat sink (subcritical flow speed). The flame stand-off distance and the amount of departure of the hot-boundary tempe...

Abstract: A theory of vibrational circular dichroism is developed along the lines of the theory of intensity borrowing by forbidden electronic transitions. The vibrational transition exhibiting circular dichroism is a one-quantum jump in a mode capable of mixing different electronic states. The degree of mixing is different for the initial and final states of the vibrational transition; this is shown to be a source of circular dichroism. The theory is developed on the basis of the adiabatic and crude adiabatic approximations; expressions for rotatory strengths are given. Within the crude adiabatic picture, effects due to any change in the equilibrium configuration on electronic excitation are examined. Vibrational effects in electronic circular dichroism are also analysed.

Abstract: The proton-hydrogen-atom collision is described in terms of an impact parameter perturbed-stationary-states treatment. Spurious long-range couplings are avoided and Galilean invariance is enforced by the inclusion of momentum translation factors which are determined variationally by using an Euler-Lagrange formalism. The correct physical behaviour is obtained in both the separated-atoms and united-atoms limit. The effective electronic translational kinetic energy, averaged over all internuclear separations is shown to have less influence on the phase of the close-capture probability than has hitherto been thought the case. The locations of all seven turning points in the curve of capture probability against energy, for a scattering angle of 3 degrees, are in excellent agreement with experiment and compare more than favourably with previous extremely elaborate calculations. The adiabatic representation is thus shown to be remarkably adaptable even at energies as high as 25 keV.

Abstract: The evolution of adiabatic and nonisentropic density perturbations during the hydrogen recombination era in the universe and the temperature fluctuations of the microwave background radiation generated at that period have been calculated numerically. The results support the principal estimates and conclusions given in a 1970 analysis of the problem.

Abstract: We consider a very simple approximation, in which the splitting of the energy of a $P$ state in a united atom into $\ensuremath{\Sigma}$ and $\ensuremath{\Pi}$ quasimolecular terms for small internuclear distances $R$ depends quadratically on $R$, and the colliding atoms pass one another along a straight or a hyperbolic trajectory. In this case the transition probability for a given scattering angle or impact parameter depends on only one parameter---the Massey parameter. This probability is computed numerically along with the elastic scattering phase shifts. Approximate formulas are obtained for both the adiabatic limit (in which the parameter is large and the flight is slow) and the sudden-perturbation limit for which the parameter is small, the flight is fast, and the process reduces to a sudden rotation of the internuclear axis. We also obtain, in the adiabatic case, the first term in the expansion of the factor in front of the exponential. In the intermediate range of the parameter, simple analytic approximations, ensuring transition to the limiting cases, are proposed. Analytic expressions for the total transition cross sections are obtained in the limits of large and small collision velocities. The results of the calculations are applicable to $\ensuremath{\Sigma}\ensuremath{-}\ensuremath{\Pi}$ transitions of electrons and holes in both outer and inner shells for close collisions in a broad energy range, where, owing to a scale transformation, all cases reduce to one. Reasonable agreement is found with other more complicated calculations for the collisions of specific atoms.

Abstract: A projected valence bond method is used to obtain adiabatic and diabatic states for the study of the H++Cs collisional system. By freezing an adjusted Hartree Fock type Cs+ core the electronic problem is reduced to that of treating the outer electron of the (H-Cs)+ quasimolecule. The present treatment is designed to correct some serious defects of previous theoretical approaches. The calculated well in the adiabatic potential energy curve correlated with H++Cs satisfactorily accounts for the rainbow structures observed recently by Scheidt and colleagues (1977, 1978) in the measured elastic differential cross sections at low energy.

Abstract: Particle measurements from the geostationary ATS 6 satellite reveal striking equatorial pitch-angle anisotropies. A study of seven days of data shows a diurnal variation in anisotropy with the particle flux at a pitch angle of 40 deg greater than that at 90 deg during times of low magnetic-field intensity on the nightside and vice versa during times of high magnetic-field intensity on the dayside. Six representative anisotropy events are studied in finer detail. The 32- to 51-keV electron anisotropies increase and decrease with the total magnetic-field intensity. The proton and higher-energy electron anisotropies do not show as much variation. The particle anisotropies are studied in light of adiabatic and cyclotron resonance theory; the results indicate that adiabatic effects are the dominant modulation mechanism of particle pitch-angle distributions in the outer radiation belt

Abstract: The diabatic heating Q is the ultimate driving force of the general circulation and climate. We present seasonal and zonal mean estimates of Q (order of magnitude 10−5 K s−1) for the atmosphere from 15°S-90°N and from 50–1000 mb. Q comprises radiation, condensation, conduction, dissipation and diffusion; the first two terms are large, the last three are small. We compile Q indirectly by specifying (from the synoptic general circulation statistics of the MIT Library) sensible heat advective and storage terms, including the adiabatic heating, which together balance Q in the First Law of thermodynamics. An important component of the advective terms is subsynoptic-scale advection. We show that it is not restricted to boundary layer heating but also has convective-scale components of potential significance and seems to be active even in the stratosphere. However, we are not able to specify the total subsynoptic-scale advection since it is subject to considerable compensation. This causes a systematic ...

Abstract: A three-dimensional finite difference numerical methodology has been developed for self-gravitating, rotating gaseous systems. The fully nonlinear equations for time-varying fluid dynamics are solved by high-speed computer in a cylindrical coordinate system rotating with an instantaneous angular velocity. The time-dependent adiabatic collapse of gravitationally bound, rotating, protostellar clouds is studied for specified uniform and nonuniform initial conditions. Uniform clouds can form axisymmetric, rotating toroidal configurations. If the thermal pressure is high, nonuniform clouds can also collapse to axisymmetric ellipsoids. For low thermal pressures, however, the collapsing cloud is unstable to perturbations. The resulting fragmentation of unstable protostellar clouds is investigated by studying the response of rotating, self-gravitating, equilibrium toroids to nonaxisymmetric perturbations. The detailed evolution of the fragmentation toroid depends upon a nondimensional function of the initial entropy, the total mass in the toroid, the angular velocity of rotation, and the number of perturbation wave-lengths around the circumference of the toroid. For low and intermediate entropies, the configuration develops into corotating components with spiral streamers. In the spiral regions retrograde vortices are observed in some examples. For high levels of entropy, barred spirals can exist as intermediate states of the fragmentation.

Abstract: For pt.I see ibid., vol.11, p.1761 (1978). The specific heat of s-triazine has been measured using an adiabatic calorimeter in the temperature range 100-335K. A rapid rise in the specific heat, followed by a small latent heat discontinuity was observed at around 198K and this is identified with the quasi-continuous structural phase transition observed in previous X-ray diffraction studies. A mean-field model is shown to account for the main part of the anomaly, but significant features remain which are attributed to fluctuation effects. A further specific heat anomaly was observed around 268K and this is briefly discussed.

Abstract: The accelerating rate calorimeter disclosed herein is an instrument designed for accurately determining the adiabatic thermal runaway characteristics of reactive chemicals. The mode of operation involves measuring the adiabatic self-heat rate of exothermic chemical reactions to determine the acceleration of the reaction rate as a function of temperature. The basic instrument includes a sample vessel which is positioned inside a reaction chamber. The environment surrounding the sample vessel is a gas, such as air, or an inert gas, or it can be a vacuum environment. Separate heater means are provided for heating the reaction chamber and the sample vessel. During the exothermic reaction of the chemical in the sample vessel, the temperature of the reaction chamber and the sample vessel are continuously monitored by separate temperature sensing means. Electronic controls sense any temperature differential between the sample vessel and the reaction chamber and adjust the temperature to maintain the desired adiabatic condition for the sample vessel. The data regarding time, temperature, and self-heat rate is automatically recorded by a computer system as the reaction proceeds. This data can be used to determine the adiabatic kinetics describing the reaction. In addition, by relating the experimental time to maximum rate, as a function of temperature, the thermal runaway potential of the reactive chemical can be determined at any temperature point in the experimental range, or, by extrapolation, at any lower temperature.

Abstract: The Born–Oppenheimer method or adiabatic perturbation theory has long provided a formal basis for separation of the electronic and nuclear motions in molecules. According to it solutions of the mol...

Abstract: The object of the present invention is the preparation of ethene in the presence of catalysts using adiabatic reactors at high temperature Such adiabatic reactors may be used in parallel or be disposed in series or arranged in parallel series assemblies or only a single reactor may be used The process of the invention allows the use of ethyl alcohol diluted with a sensible heat carrying fluid as feeding material Said sensible heat carrying fluid is introduced into the reactor simultaneously with the feed, supplying the heat necessary for the performance of the reaction

Abstract: In the present paper approximate solutions for the fluid and thermal boundary layers in an incompressible laminar plane wall jet with isothermal and adiabatic walls have been studied respectively, and comparisons with the known exact solutions have been made wherever possible. It is found that the present method is simple and straightforward, and gives results being in good agreement with the exact solutions. For moderate values of the Prandtl number the method may be used for calculating the heat transfer from an isothermal wall and temperature recovery factor for an adiabatic wall respectively.

Abstract: The inclusion of a pressure ionization term in the Saha equation violates the thermodynamic Maxwell identities if corresponding changes are not made to the expressions for entropy and pressure. It is demonstrated that the usual application of the Rouse and Stewart-Pyatt modesl suffers from this limitation. Negative values of the adiabatic gradient in the degenerate dwarf models of Boehm and Straka are explained in terms of this thermodynamic inconsistency.

Abstract: For the angular dependence of quasimolecular X-ray emission in heavy ion colliding systems we present a semiclassical adiabatic model taking into account spontaneous dipole radiation. Using the most characteristic levels from a DFS-correlation diagram we are able to explain the behaviour of the observed anisotropy.