Different Regions Of Space Research Articles

The asymptotic theory of rapidly rotating sound fields

A rapidly rotating sound field, such as that produced by a supersonic propeller, may contain several types of diffraction pattern, each in a different region of space. This paper determines these patterns and their locations for the field around a propeller of simple type ; the method used is stationary phase analysis of a certain double integral, and leads to asymptotic formulae valid when the number of blades is not too small or the high harmonics are being investigated. Physically, the results describe propagation along rays : each stationary phase point is a ‘ loud spot ’, producing a ray which points directly at the observer; most of the noise comes from these loud spots, because extensive cancellation takes place everywhere else. At most two interior and two boundary stationary points may be present: the number and type depend on the position of the observer in relation to a cusped torus and two hyperboloids of one sheet. As these surfaces are crossed, the acoustic field changes in character. For example, when two stationary points coalesce and annihilate each other, as they do at a caustic, an Airy function describes the transition from a loud zone of rapid oscillation to a quiet zone of exponential decay; and when an interior stationary point crosses the boundary of the disc the transition region is described either by a Fresnel integral or by a generalized Airy function. Separate analyses are given for regions close to and well away from the transition surfaces, and inner and outer limits are calculated for use in the method of matched asymptotic expansions. In all cases, an overlap region is found in which the leading term s agree. The results of the paper determine completely the geometry of the acoustic field, because the different regions have boundaries at known positions and cover the whole of space.

On the use of different basis functions for different regions of space

A new approach to the use of different basis functions for different regions of space in quantum-chemical calculations is presented and illustrated with a simple example.

Nonadiabatic dynamics of excited excess electrons in simple fluids

We present a surface hopping trajectory method for studying nonadiabatic excess electronic relaxation in condensed systems. This approach is used to explore the nonadiabatic relaxation after photoexciting an equilibrated excess electron in dense fluid helium. We survey the different types of nonadiabatic phenomena which are important in excess electronic relaxation. Very rapid diabatic processes are common when the nuclear dynamics provides only weak couplings between the adiabatic states. This is generally the case when the states are localized in different regions of space. We find that the nuclear dynamics provides a mechanism for strong coupling between s- and p-like states localized in the same solvent cavity. These strong nonadiabatic interactions can persist over a wide range of nuclear configurations and for many hundreds of femtoseconds.

Different regions of space or different spaces altogether: What are the dorsal/ventral systems processing?

Different regions of space or different spaces altogether: What are the dorsal/ventral systems processing?

Localization and other common features of degenerate perturbations.

Diverse problems lead to groups of states with wave functions localized into different regions of space. This result is shown to be characteristic of a large number of problems in physics (atomic and nuclear examples are given) where states of highly degenerate manifolds are mixed by an interaction, which may be one or two particle in nature. Common analytical structures are derived and their origin traced. Random distributions and statistical arguments have often been used for the form of the localization which we derive, however, as a consequence of specific structures in the interaction Hamiltonians.

Stresses in mixture theory

The foundations of mixture theory are formulated using a geometrical approach. In order to model diffusion, configurations of mixtures are allowed in which the various constituents may occupy different regions in space in addition to the usual relaxation of the impenetrability axiom. Forces on a mixture are defined as continuous linear functional on the space of virtual displacements of the mixture. This implies the existence of partial stresses without any further assumptions. The notions of the total force and the total stress are critically reviewed and introduced through the definition of a simple body model of a mixture. Some examples of such models are given.

Perception, Thought, and Reality

In (Daniels, 1976) I sketched out a problem that not only continues to puzzle me, but has since led me to this study. It is often thought there is such a thing as purely perceptual knowledge or belief, knowledge or belief that is not infected by inference or memory. Suppose so. Suppose I know that my coffee is both black and tepid. Can I know this on a purely perceptual basis? I think not. Leaving aside the matter of how I know that what I'm sensing is coffee, let me just consider my knowledge that at least something here is black and tepid. While I may know that something here's black by my sense of sight alone, I do not know that something here's both black and tepid by my sense of sight alone because I do not know that something here is tepid by my sense of sight alone. Also, of course, while I may know that something here is tepid by my sense of touch alone, I do not know that something here is both black and tepid by my sense of touch alone because I do not know that something here is black by my sense of touch alone. Grant, for the moment, that I can know that something here is black by my sense of sight alone and that I can know that something here is tepid by my sense of touch alone. That something here's black and something here's tepid doesn't entail that something here's black and tepid. To know the thing that's black is the thing that's tepid I cannot do by sight, alone or touch alone, or just by sight and touch actingjointly, since the case in which the thing that's black is not the thing that's tepid is perceptually indistinguishable from the case in which it is. I make this claim because of the possibility, albeit a weak conceptual possibility, that the body with which I see may be in a different region of space from the body with which I feel. I claim fur-

Electron correlation in momentum space: the ground state of Li(2S)

Electron correlation is examined in momentum space for the individual intra- and inter-shell electron pairs in the ground state of Li(2S). It is established that the radial and angular components of the correlation have opposing influences on the inter-particle momentum distributions f(p12) and g(p12;p1), where p12= mod p1-p2 mod and p1= mod p1 mod . By examining the Coulomb shifts Delta f(p12) and, in particular, the partial Coulomb shifts Delta g(p12;P1) for each electron pair, such a feature enables one to identify the major component of correlation in different regions of momentum space. This represents a distinct advantage over the more traditional position space approach. For K alpha K beta , not only was it found that intra-shell correlation effects were influenced by the occupation of the 2s orbital but, more interestingly, the nature of the influence was seen to change markedly throughout different regions of space. For the K alpha L alpha and K beta L alpha inter-shells, the importance of angular correlation was highlighted and, for K alpha L alpha , the consequence of the Fermi effect was observed. Comparisons were made with a previous, and complementary, position-based study of Li(2S) and with the correlation effects found in momentum space for closed shell Li+(1S) and Be(1S).

Simultaneous observation of upstream waves with ISEE and AMPTE

Measurements obtained by ISEE-2 and the UKS spacecraft upstream of the Earth's bow shock are examined. simultaneous observations show that upstream waves are excited over a broad frequency range. Even when peaked spectra occur the peaks can occur at different frequencies in different regions of space. Generally the spectra seen at the two locations are most similar at high frequencies and least similar at low frequencies. The position dependent nature of the upstream waves indicates that comparisons between ground-based measurements and in situ observations must be undertaken with some caution.

The gradient expansions of the kinetic energy and the mean momentum for light diatomic molecules

For eleven neutral diatomic systems and one positive ion we have numerically evaluated the three terms in the gradient expansion of the molecular kinetic energy T=T0+T2+T4. Hartree–Fock–Roothaan molecular densities were used throughout. For the molecules studied T2/T0 ∼0.1, T4/T2 ∼0.2. The contributions to these integrals from different regions of space were examined. We have also estimated the values of the two terms in the gradient expansion of the mean momentum P=P0+P2 and find P2/P0 ∼0.5. Lastly we make contact with earlier work of Mucci and March. D/N2 is found to correlate grossly with T2, where D is the dissociation energy and N the total number of electrons in the molecule.

Collisions of Rydberg atoms in an electric field: Calculations using hydrogenic wave functions in parabolic coordinates

The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms ($n=10, 15, \mathrm{and} 20$) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number $m$. The origin of this tendency is discussed.

ChemInform Abstract: MOLECULAR STRUCTURES OF 2,4‐DIAMINOPYRIMIDINE ANTIFOLATES WITH ANTINEOPLASTIC ACTIVITY

2,4-Diamino-5-(1-adamantyl)-6-methylpyrimidine (DAMP) and its ethanesulfonate salt (DAMP-ES) are potent inhibitors of mammalian dihydrofolate reductase and also inhibit the growth of cultured cells as effectively as the drug methotrexate (MTX). DAMP is currently in phase I clinical studies. An analogue of DAMP having 5-(1-naphthyl) in place of the adamantyl group (DNMP) possesses little cytotoxic as well as enzyme inhibitory activity. The crystal and molecular structures of DAMPM-ES and DNMP were determined in order to elucidate the conformational aspects of drug specificity. The molecular conformation of DAMP-ES shows that the C8--C7 bond of the adamantyl ring is nearly coplanar with the pyrimidine ring (C8--C7--C5--C6 = 7.5 degrees) instead of staggered as expected from steric considerations. As a result, the pyrimidine ring and its 4,6-substituents are severely distorted from coplanarity. In DNMP, the 1-naphthalene ring is perpendicular to the pyrimidine ring (C8--C7--C5--C6 = -87.0 degrees) which is itself planar. N1 is protonated in DAMP-ES but not in DNMP. When the two structures are compared, the 5-substituents occupy different regions of space, with the outer ring of the naphthalene group outside of the volume occupied by the adamantyl ring. Therefore, the reduced effectiveness of DNMP may be caused by the inability of the naphthalene to fit the binding site in dihydrofolate reductase. This is the situation when DNMP is placed in the methotrexate binding site of Lactobacillus casei crystal structure.

Molecular structures of 2,4-diaminopyrimidine antifolates with antineoplastic activity.

2,4-Diamino-5-(1-adamantyl)-6-methylpyrimidine (DAMP) and its ethanesulfonate salt (DAMP-ES) are potent inhibitors of mammalian dihydrofolate reductase and also inhibit the growth of cultured cells as effectively as the drug methotrexate (MTX). DAMP is currently in phase I clinical studies. An analogue of DAMP having 5-(1-naphthyl) in place of the adamantyl group (DNMP) possesses little cytotoxic as well as enzyme inhibitory activity. The crystal and molecular structures of DAMPM-ES and DNMP were determined in order to elucidate the conformational aspects of drug specificity. The molecular conformation of DAMP-ES shows that the C8--C7 bond of the adamantyl ring is nearly coplanar with the pyrimidine ring (C8--C7--C5--C6 = 7.5 degrees) instead of staggered as expected from steric considerations. As a result, the pyrimidine ring and its 4,6-substituents are severely distorted from coplanarity. In DNMP, the 1-naphthalene ring is perpendicular to the pyrimidine ring (C8--C7--C5--C6 = -87.0 degrees) which is itself planar. N1 is protonated in DAMP-ES but not in DNMP. When the two structures are compared, the 5-substituents occupy different regions of space, with the outer ring of the naphthalene group outside of the volume occupied by the adamantyl ring. Therefore, the reduced effectiveness of DNMP may be caused by the inability of the naphthalene to fit the binding site in dihydrofolate reductase. This is the situation when DNMP is placed in the methotrexate binding site of Lactobacillus casei crystal structure.

Coulomb correlation in the 21S, 23S, 21P and 23P states of He

Electron correlation has been examined in detail for the 21S, 23S, 21P and 23P states of He and comparisons are made with the ground state. The correlated and Hartree-Fock descriptions of these (1s, nl) excited states are provided by the wavefunctions of Tweed (1973) and Davidson (1965), respectively. Coulomb holes, various partial Coulomb holes and several one- and two-particle expectation values are presented. The concept of partial Coulomb holes and their collective presentation has surfaces as been demonstrated to be particularly informative. These surfaces enabled us to interpret correlation effects in different regions of space and so provide a rationalisation of the correlation mechanisms in each state. For all four states, correlation caused a significant inward shift of density from the outer regions due to a reduction in nuclear shielding. However, in the inner regions around the nucleus, the influence of correlation was more complicated and depended not only on the multiplicity of the state but also on its symmetry.

Diamagnetic contributions to the nuclear spin–spin coupling constants of several small molecules. An application of Monte Carlo integration methods to molecular one-electron properties

A numerical Monte Carlo integration procedure has been developed for calculation of J1a, the diamagnetic contribution to the nuclear spin–spin coupling constant from an arbitrary molecular charge density. The method is applied first to the HD molecule where several previous values of JHD1a are refined and corrected. A test of Brillouin’s theorem for this unusual sum of one-electron operators is made and the extensive cancellations from different regions of space are examined in detail. Values of J1a are then given for HF, BF, CO, and HCN. It appears that J1a may be the one-electron property most sensitive to the quality of the wavefunction which has been considered to date. Monte Carlo integration may be employed for the calculation of one-electron properties when alternatives to analytic integral evaluation are sought.

Equivalent width of interstellar molecular lines

We have made an analysis of the observed equivalent widths of the lines of Lyman and Werner bands by Smith. The H2 column densities of 3×1019 to 1020 and the excitation temperature of 80 to 150 K satisfy the observations. This temperature refers to the kinetic temperature. We have also discussed the importance of getting the excitation temperature from lines of H2 and other heteronuclear diatomic molecules for the same star and from different regions of space.

THE SECOND-ORDER TERM IN THE REDSHIFT-MAGNITUDE RELATION

The recent discussion by Humason, Mayall, and Sandage has suggested the possibility of a second-order term in the redshiftmagnitude relation for extragalactic nebulae.1 This possibility raises some interesting points. The present brief review discusses the meaning of a second-order term and indicates a few of the properties of the universe which can be obtained, in principle, from the observations. The cosmological framework to which the observations are to be fitted is well known (Einstein,2 Robertson,3 Bondi,4 Couderc,5 McCrea,6 and others). The relevant theoretical concepts have been recently reviewed by Robertson.7 Common to all cosmologies is the so-called cosmological postulate. This postulate is a type of generalized Copernican hypothesis and states that observers in different regions of space must obtain the same description for the nonrandom characteristics of the universe. Provided there is no rigid-body rotation of the whole universe, the only systematic large-scale motion compatible with this principle is a linear relation between the distances to objects and their observed redshifts. We therefore expect that, at any given cosmic time, a relation exists of the form eΔλ/λ = ΗΌ. Here c is the velocity of light, Δλ/λ the redshift, Η the Hubble redshift parameter, and D an appropriately defined distance. If Η is a function of time (which is admissible in certain theories), then we must expect deviations from linearity in the observed velocity-distance relation. This is because the speed of light is finite and therefore as we look out into space we also look back in time. If the expansion rate was different at an earlier epoch of the universe, this earlier rate will be observed in the distant nebulae. The observations, as it were, can be made to sample the universe to determine Η at various times in the past. It is there-