Minimum Distance Of Approach Research Articles

The Avoidance of Close Quarters in Clear Weather

What constitutes a minimum safe distance of approach in an overtaking or meeting situation is a problem that has engaged the interest of seamen since steam began to supplant sail. Prior to that time vessels were often obliged to steer zig-zag courses in tacking against the wind, and though they were probably no less concerned with avoiding a collision the problem was of a different order.

Particle motions in sheared suspensions: XXX. Rotations of rigid and flexible dumbbells (theoretical)

Theoretical models of dumbbells of equal-sized, rigid spheres have been formulated for the case of (i) rigid dumbbells having a fixed interparticle distance with the relative rotation of the spheres hindered by viscous damping, and (ii) flexible dumbbells having variable interparticle distance with the spheres linked by an elastic filament. The general method of calculating forces, torques, and translational and rotational velocities based on the matrix formulation of Brenner and O'Neill was used. In the case of the rigid dumbbell, the additional torque exerted on the spheres is described by a damping coefficient X. It is shown that even a small increase in λ from 0 (the value for freely rotating spheres) results in a marked decrease in the dimensionless period of rotation TG. With the flexible dumbbell it is assumed that the filament only exerts a force on the spheres when the distance between the points of attachment exceeds its resting length. The results show that no matter what the initial conditions of release, the trajectories of the spheres, characterized by an elliptical path of their centers about the mid-point of the dumbbell axis, tend to a limit cycle within a few rotations. It is therefore possible to define a period of rotation which is predicted to decrease with increasing filament stiffness, and to increase with increasing length and diameter, the latter also determining the minimum distance of approach of the sphere surfaces.

The solar corona

view Abstract Citations (8) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The solar corona. Beard, D. B. Abstract The physical behavior of interplanetary dust and electrons has been examined with a view to anticipating their spatial distribution and consequent contribution to the intensity of the solar corona. From consideration of 'local' spherical expansion of the solar wind an electron distribution with solar distance r is proposed, r to the -2 power exp (W/r), which results in an excellent fit to observations of the solar corona and electron density at 1 AU. Analysis of total coronal observations during maximum and minimum solar activity at polar and equatorial elongations yields a time-constant spatial distribution of interplanetary dust in the equatorial plane beyond a minimum distance of closest approach of the dust of 4.5 solar radii. Several significant clear-cut deductions about the origin of the solar wind may be made from the expression for the electron density. Publication: The Astrophysical Journal Pub Date: December 1979 DOI: 10.1086/157546 Bibcode: 1979ApJ...234..696B Keywords: Interplanetary Dust; Solar Corona; Solar Electrons; Electron Density (Concentration); Solar Activity; Solar Wind; Spatial Distribution; Solar Physics; Interplanetary Dust:Distribution; Interplanetary Dust:Solar Corona; Solar Corona:Electrons; Solar Corona:Models; Solar Wind:Velocities full text sources ADS |

Excitation functions for quasielastic transfer reactions induced with heavy ions in bismuth

The excitation functions for the production of $^{210}\mathrm{Bi}$, $^{210}\mathrm{Po}$, $^{207\ensuremath{-}211}\mathrm{At}$, and $^{211}\mathrm{Rn}$ through quasielastic transfer reactions induced with heavy ions in $^{209}\mathrm{Bi}$ have been measured. The corresponding reactions involved the transfer of one neutron, one proton, two charges, and three charges from projectile to target. The projectiles used were $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$, $^{19}\mathrm{F}$, $^{20}\mathrm{Ne}$, $^{40}\mathrm{Ar}$, $^{40}\mathrm{Ca}$, $^{56}\mathrm{Fe}$, and $^{63}\mathrm{Cu}$. The experimental techniques involved target irradiations and off-line $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$ activity measurements. Chemical separations were used to solve specific problems. Careful measurements of incident energies and cross sections were performed close to the reaction thresholds. All excitation functions exhibit the typical features of quasielastic transfer reactions: a sharp increase at low energy, and a constant value at high incident energy. The position of the thresholds are strongly influenced by the energetics of the reaction: High cross sections are observed under the strong interaction barrier if the energy balance at the minimum distance of approach is positive. This balance is equal to the difference between the interaction potentials in the entrance and exit channels, corrected for the mass balance. The constant cross sections observed for the high energy part of a given excitation function are consistent with the assumption that the curve $P(R)$ which represents the transfer probability versus the distance between the nucleus centers does not vary with incident energy. This assumption implies the constancy of the optimum distance of approach ${R}_{\mathrm{opt}}$, of the $R$ window $\ensuremath{\Delta}R$ for which $P(R)$ is significant, and of the magnitude of $P(R)$. Moreover the data show that the high energy cross sections for one-proton transfer are independent of the projectile, while odd-even effects of the projectile atomic number $Z$ on the two-charge transfer cross sections are observed for the lightest incident ions $^{14}\mathrm{N}$ to $^{20}\mathrm{Ne}$.NUCLEAR REACTIONS $^{209}\mathrm{Bi}(\mathrm{HI}, X)$, $^{211,210,209,208,207}\mathrm{At}$, $^{211}\mathrm{Rn}$, with HI=$^{12}\mathrm{C}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$, $^{19}\mathrm{F}$, $^{20}\mathrm{Ne}$, $^{40}\mathrm{Ar}$, $^{56}\mathrm{Fe}$, $^{63}\mathrm{Cu}$. $\frac{E}{A}\ensuremath{\simeq}4.5\ensuremath{-}10$ MeV/nucleon. Measured $\ensuremath{\sigma}(E)$.

Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids. II. Finite jumps and independent T1 processes

Hwang and Freed have previously given solutions for the relative diffusion of molecules that include the proper boundary condition (i.e., an excluded volume due to a distance of minimum approach) which has usually been neglected in spin relaxation theories. In this work their results are extended to include effects of (1) one type of spin that is rapidly relaxing, (2) diffusion by jumps of finite size, and (3) frequency-dependent diffusion coefficients in the theory of spin relaxation by intermolecular dipolar interactions. These results are mathematically simpler and sounder than those commonly employed. In particular, it is shown that for case (2) measurements of J (O), the zero-frequency spectral density cannot solely be used to determine the jump size, in constrast to the Torrey theory, which did not consider the boundary-value problem.

Interaction of electric and magnetic charges

It is shown classically that in a head-on collision between an electric and a magnetic charge a repulsive polarization force of the form ${r}^{\ensuremath{-}5}$ results (where $r$ is the distance between the charges), if one (both) charge(s) is (are) assigned a finite spherical size. This force leads to a minimum distance of approach and prevents one particle from going through the other, and thus guards against the violation of the conservation of angular momentum. This polarization force is a manifestation of the diamagnetism (diaelectricity) of extended electric (magnetic) charges.

Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids

It is shown how the equilibrium pair correlation function between spin-bearing molecules in liquids may be incorporated as an effective force in the relative diffusion expressions, and how one may solve for the resulting time correlation functions and spectral densities needed for studies of spin relaxation by translational diffusion. The use of finite difference methods permits the solution no matter how complex the form of the pair correlation function (pcf) utilized. In particular, a Percus–Yevick pcf as well as one corrected from computer dynamics, both for hard spheres, are utilized. Good agreement with the experiments of Harmon and Muller on dipolar relaxation in liquid ethane is obtained from this analysis. Effects of ionic interactions in electrolyte solutions upon dipolar relaxation are also obtained in terms of Debye–Hückel theory for the pcf. Analytic solutions are given which are appropriate for the proper boundary-value problem for the relative diffusion of molecules (i.e., a distance of minimum approach) that has usually been neglected in the spin relaxation theories. Other molecular dynamics aspects of spin relaxation by translational diffusion in liquids are briefly discussed.

On the assumption of a step function for the adsorption-layer thickness in the nonionic stabilization of dispersions

The stability of poly (styrene) glycol (PS) latex dispersions in water and in the presence of n-dodecyl glycolhexaoxyethylene monoether (C 12E 8), as investigated by Ottewill and Walker, has been interpreted quantitatively from the depth of the secondary minimum, assuming that a steep nonionic repulsion potential gives rise to a secondary minimum at a distance of separation of the particle surfaces equaling twice the experimentally determined adsorption-layer thickness. In view of Hesselink's tail and loop size distributions for the case of longchain molecules and polymers, respectively, such correlations for the PS latex-C 12E 6-water system and the AgI-poly(vinyl alcohol)-water system (as observed previously), suggest either that such distributions could be quite narrow or that any hydrodynamically measured adsorption layer thickness is a good indication of half the minimum distance of approach between two particles with adsorption layers. Consequently, the assumption of a step function for the adsorption-layer thickness seems adequate for the interpretation of the stabilization of lyophobic dispersion by nonionic additives.

Complete Fusion Nuclear Reactions Induced by Krypton Ions. Effective Threshold and Minimum Distance of Approach for the ReactionsCd116+Kr84andGe72+Kr84

Effective energy thresholds have been measured for the cross sections of complete fusion reactions induced by krypton ions on ${\mathrm{Cd}}^{116}$ and ${\mathrm{Ge}}^{72}$. They show that the minimum distance of approach for the reaction is shorter than with lighter projectiles and corresponds to a Coulomb repulsion at a distance of ${r}_{0}({{A}_{1}}^{\frac{1}{3}}+{{A}_{2}}^{\frac{1}{3}})$ fm with ${r}_{0}=1.32$ fm instead of 1.45 fm.

Orientation—dependent effects in Oort's theory of comet origin: I. Evolution of the orbital orientations and perihelion distances of long-period comets

The orbital orientations and perihelion distances of long-period comets undergo appreciable systematic evolution due to planetary perturbations over many perihelion passages, and such evolution should have a significant bearing upon Oort's theory of comet origin. Once a comet has been captured into a long-period orbit, the effects of stellar perturbations upon its orbital orientation are generally small and random, so that the orientation is well defined from one perihelion passage to the next. The direct perturbation of Jupiter dominates the planetary perturbations; the indirect perturbations are small and random, while the principal effect of the combined direct perturbations of the other planets is to increase the rate of evolution by a factor of about 1.6. A method has been developed to calculate the mean evolution of a long-period orbit over many perihelion passages; the method is applicable to orbits with perihelion distances less than or on the order of 1 a.u. This technique has been applied to the numerical calculation of the evolution of 100 orbits with initially isotropic orientations and initial perihelion distances of 0.1 a.u. The results of these calculations are summarized in Table II. In this table, n is the number of perihelion passages since the injection of each hypothetical comet into a long-period orbit; A, B, and C are direction cosines which fix the orientation of the cometary orbit with respect to the plane of Jupiter's orbit (as defined in Section III); q is the perihelion distance; and Δ m a 0 is the minimum possible distance of approach of the comet to Jupiter, in units of Jupiter's semi-major axis. The more common orbital parameters are expressed in terms of the direction cosines in Eqs. (26), (27), and (28). In these calculations, the typical time scale of evolution was on the order of 100 perihelion passages. Long-period comets with larger perihelion distances will undergo similar evolution, but the mean evolution rate will be slower by a factor of about q −1 2 . The existence of an anamalously high correlation between the observed inclinations and latitudes of perihelion of the long-period comets can be explained at least qualitatively by this evolution.

The calculation of self-broadened line widths in linear molecules

The Anderson theory of collision broadening of spectral lines as expounded by Tsao and Curnutte has been rigorously applied, by means of high-speed digital computation, to self-broadening in linear molecules. The model includes directional forces resulting from dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole attractions and a non-directional minimum distance of closest approach b min . For molecules with known dipole moments there are only two adjustable parameters, the quadrupole moment Q and b min . Results are given for the hydrogen and deuterium halides and CO. Some comparisons with experiment and a brief discussion of the limitations of the model are given.

Some dynamic aspects of the nuclear envelope.

Nuclei of frog oocytes were isolated, fixed in OsO(4) or KMnO(4), and washed. Nuclear envelopes were then dissected off, placed on grids, and air-dried for electron microscopy. Envelopes from immature oocytes at the stage of beginning yolk deposition were compared with those from mature oocytes. Envelopes from the immature stage had "pores" whose annuli contained more material and showed central globules in the center much more frequently than envelopes from mature eggs. Annuli and central globules had similar appearance and fixation properties, suggesting similar chemical composition. After fixation with KMnO(4), residual densities suggested that "pore" diaphragms are much more variable in thickness or composition in the younger stages. Envelopes of the immature oocytes had about 40 per cent more "pores" per unit area than mature envelopes. In crowding together, the "pores" tended to assume geometrical packing arrays in the young envelope, showing minimum center-to-center spacings of about 1530 A. Since the actual discontinuities in the membranes of the envelope are only about 950 A in diameter, this minimum distance of approach suggests that adjacent formations of the nuclear surface are associated with "pore" structure and perhaps set their limiting spacing distances. If this is true, then it can be deduced that "pore"-associated structures of the nuclear surface are probably circular in outline and about 1500 A in diameter. Isotopically labeled lysine was administered to intact, growing oocytes for 1 to 4 hours and the envelopes were subsequently isolated and fixed. Autoradiography of entire envelopes showed little or no incorporation of lysine into proteins, as compared with small fragments from other parts of the cell of roughly comparable mass. It was concluded that the isolated envelope, as seen in the electron micrographs, does not synthesize or turn over lysine-containing protein at a high rate.

A Relation between Internuclear Distances and Potential Barriers of Methyl Groups

An empirical relation is shown between contributions of various groups to the potential barriers of methyl groups and the minimum distance of approach of atoms of these groups to the methyl group. The use of this relation to derive barrier values for other molecules is demonstrated.