Repulsive Potential Function Research Articles

Spatial data analysis by epidermal Langerhans cells reveals an elegant system

Langerhans cells are dendritic cells situated in the mammalian epidermis. In human epidermis, the concentration is between 460 and 1000 mm −2. Langerhans cells fulfill an essential role in skin immune responses. Numerous scientific reports on Langerhans cells have appeared, but with no systematic research on the pattern of the spatial distributions. On the contrary, in certain fields, a spatial distribution is an important theme, and spatial data analysis has a long history. We hypothesized that epidermal Langerhans cells were set in the best formation for their immuno-surveillance by a sophisticated mechanism. To prove this hypothesis, we have imported spatial data analysis into the study of epidermal Langerhans cells. Here, we show that the distribution is completely regular; the pattern of Voronoi divisions fits the territories; the random packing model simulates their bone marrow derivation; a repulsive interaction is demonstrated and a repulsive potential function is estimated. Spatial data analysis-based computer simulation will be a new method of Langerhans cell study. In addition, this procedure shows promise for future distribution research of certain cells.

New potential functions for mobile robot path planning

The paper first describes the problem of goals unreachable with obstacles nearby when using potential field methods for mobile robot path planning. Then, new repulsive potential functions are presented by taking the relative distance between the robot and the goal into consideration, which ensures that the goal position is the global minimum of the total potential.

Continuum resonance Raman scattering in 127I79 Br1

Abstract We have simulated high resolution continuum resonance Stokes- and anti-Stokes-Raman spectra of isotopically pure 127 I 79 Br using second order perturbation theory in the time independent and time dependent approach. By use of extensive fitting procedures of argon ion laser excited spectra potential function parameters for the repulsive branches of the excited states 1 Π 1u and 3 Π 0+u are determined. The high sensitivity of resonance Raman band shapes to small changes of excited state repulsive potential functions and to the strength of transition moments is shown. A symmetry principle of Stokes versus anti-Stokes Raman spectra is also shown and discussed as well as a reflection principle and scattering delay times for this diatomic molecule.

Continuum resonance Raman scattering in isotopically pure127I35Cl

High-resolution polarized and depolarized continuum resonance Raman spectra of isotopically pure 127I35Cl for fundamental and overtone transitions Δν = 1-4 with excitation from the green to the blue spectral region have been used to determine the repulsive part of the potential function 3Π0+ as well as the pure repulsive potential function 1Π1. The latter is responsible for the predissociation of the 3Π0+ state. The continuum resonance Raman spectra are highly sensitive to the position and shape of the excited state potential functions and hence allow an accurate determination of these functions. The experimental spectra were simulated applying time dependent as well as time independent second-order perturbation theory.

Thermal and elastic behaviour of mixed alkali halide crystals within the framework of compressible ion theory

The Narayan and Ramaseshan (NR) short-range repulsive potential function, extended up to second neighbours was used to study the mixed systems of NaBr x Cl (1 − x) , KBr x Cl (1 − x) , KI x Br (1 − x) , crystallizing into the rock salt structure. The cohesive energy E, isothermal bulk modulus ( B t ), the first and second order pressure derivatives ( dB t dp and d 2B t dp 2 ) of the isothermal bulk modulus of these mixed systems were evaluated using the NR potential. The computations were also extended to calculate the Grüneisen parameter (γ) and mode Grüneisen parameter ( q) using Slater, Dugdale and McDonald, and free volume theories. The results are discussed with the interpolated experimental data.

Semiclassical calculation for collision induced dissociation. II. Morse oscillator model

A recently developed semiclassical procedure for calculating collision induced dissociation probabilities Pdiss is applied to the collinear collision between a particle and a Morse oscillator diatomic. The particle–diatom interaction is described with a repulsive exponential potential function. Pdiss is reported for a system of three identical particles, as a function of collision energy Et and initial vibrational state of the diatomic n1. The results are compared with the previously reported values for the collision between a particle and a truncated harmonic oscillator. The two studies show similar features, namely: (a) there is an oscillatory structure in the Pdiss energy profiles, which is directly related to n1; (b) Pdiss becomes noticeable (≳10−3) for Et values appreciably higher than the energetic threshold; (c) vibrational enhancement (inhibition) of collision induced dissociation persists at low (high) energies; and (d) good agreement between the classical and semiclassical results is found above the classical dynamic threshold. Finally, the convergence of Pdiss for increasing box length is shown to be rapid and satisfactory.

Experimental measurement of dissociative molecular potential functions from continuum resonance raman spectra

We present a novel method for accurately determining repulsive potential functions of diatomic molecules. The method utilizes an analysis of the continuum resonance Raman spectra observed from such molecular vapors. We report the results of applying this method to determine the repulsive 1Π 1u state potential function of I 2.

Inversion of total cross sections for repulsive ion-atom scattering in the classical regime

With the use of the momentum approximation of classical scattering theory we derive an inversion formula for incomplete total scattering cross sections measured by ion-atom scattering experiments as a function of ion energy. The formula allows direct determination of repulsive interatomic potential functions without the use of trial functions for the potential and, in addition, an estimate of the absolute error as a function of interatomic distance. Analysis of the K +Ar cross sections of Amdur and coworkers shows that for the inversion to be only moderately accurate, the experimental data must cover an energy range of more than an order of magnitude.

Applicability of exponentially attractive and repulsive interactomic potential functions in the description of cubic crystals

The well-known Morse function φ(r) = D {exp [−2α(r−r0)] −2 exp [−α(r−r0)]} can be considered to be a particular case of the general family of potential functions with exponential attraction and exponential repulsion, viz., φm(r) = [D/(m−1)] {exp[−mα(r−r0)] −m × exp[−α(r−r0)]}. This study examines the suitability of applying the functions φm (r) to the description of mechanical properties of cubic crystals. For bcc lattices, the ratio C11/C12 for the theoretical model of the crystal made up of atoms with φm (r) interatomic interactions is shown to be too small to provide a realistic description of bcc metals; also, the bcc crystals are found to be inherently unstable for larger values of αa0, where a0 is the lattice parameter of the crystal. For fcc lattices, however, the theoretical model of the crystal is found to be mechanically stable for arbitrary (i.e., m>1) exponentially attractive and repulsive interactions and the elastic moduli C11 and C12 of the theoretical fcc crystals are found to be capable of conforming to the respective experimental values of fcc metals. The results are in agreement with Born's analyses of lattice stability. Numerical values of D, α, and r0 are calculated for several different values of the parameter m for fcc Ni using experimental values of C11, C12, and lattice parameter. The element Ni is selected because, among the fcc metals, Ni most closely obeys the Cauchy condition C12 = C44. The functions φm are then used to calculate theoretical pressure versus volume (P-V) behavior (at pressures large enough to produce considerable anharmonicity) and the results are compared with experiment; good agreement is found between the calculated and experimental P-V relations.

Flame photometric determinations of diffusion coefficients. Part 3.—Results for nitric oxide

The point-source technique for measuring gas-phase diffusion coefficients has been tested using trace quantities of nitric oxide diffusing in the burnt gases of atmospheric pressure flames of H2+ O2+ N2. The air afterglow emission was used to monitor concentrations of nitric oxide. The results validate quantitatively the technique, and diffusion coefficients for nitric oxide have been measured over the temperature range 1920–2520 K. These data can be accounted for with either a Lennard-Jones (12: 6) potential or a purely repulsive inverse power potential function to describe interactions of a nitric oxide molecule with those of the principal flame species. A slight preference for the second potential function is indicated. With the Lennard-Jones function it is not possible to arrive at one unique pair of force constants for NO. However, either σ= 3.60 × 10–10 m and (Iµ/k)= 85 K or σ= 3.58 × 10–10 m and (Iµ/k)= 91 K can be used to calculate diffusion coefficients with reasonable accuracy. For the other potential function, repulsive forces varying inversely with separation to the 12th power fit the measured diffusion coefficients best. Values of the corresponding force constants are given.

Analytical theory of fluctuations in the predissociation linewidth

Analytical expressions for the predissociation linewidth as a function of vibrational and rotational state are obtained by a semiclassical (WKB) method. It is then shown how the classical turning points for the curve contained between the upper parts of the repulsive and attractive potential functions may be deduced for an experimental pattern of linewidths. The theory is successfully applied to data for the A 2Σ+ state of OD.

Classical perturbation theory of the thermal accommodation coefficient in n dimensions

The theory of the thermal accommodation coefficient is studied using a classical perturbation theory, in which the solid is represented by various n-dimensional models. A general formula is found for the effective thermal accommodation coefficient of a single gas atom in terms of a summation over the normal modes of vibration of the model; this formula applies to any classical harmonic model of the solid. From this formula are derived expansions in closed form for the effective thermal accommodation coefficient which are valid in the regimes of high and low incident gas atom speed; attempts are made to define the conditions under which these expansions are valid. The theory restricts all motion to the direction normal to the solid surface, and all gas atom-surface atom collisions are head-on. A modified exponential repulsive gas-solid interaction potential function which includes realistically a long-range gas-solid attraction is used; a consequence of the form of this potential function is that the perturbation theory is not restricted in general to small accommodation coefficients. In the low-speed regime the theory is not restricted in general to small gas atomic mass, but this restriction applies in the high-speed regime. The theory is applied in turn to the following models of the solid: the n-dimensional lattice with different central and non-central spring force constants; the one-dimensional lattice with a surface impurity; the n-dimensional lattice with various types of surface impurity; the n-dimensional continuum. Where appropriate, the physical significance of the results of these models is considered, and relations among the results are studied; in this way, for example, the role of the three-dimensional continuum theory of Landau is clarified. It is shown that great care must be taken in using such perturbation theory expansions, as they apply only to a very limited group of experimental systems. It is concluded that, in fact, no satisfactory comparison with experimental data is possible at present, and the need is stressed for a more general theory. That the much-used one-dimensional model is not useful in any regime for realistic studies of gas-surface interactions is conclusively established in various ways; similar remarks will apply also to one-dimensional quantum-mechanical models.

Computer Simulation of Sputtering

Present computers have neither enough memory capacity nor computation speed to completely simulate the sputtering process. The conclusions reported here were obtained with purely repulsive potential functions. Surface binding energies were included artificially. The simulations produce excellent spot patterns, but only approximately correct sputtering ratios. The Ar+–Cu system has been studied in detail and a few trials have been made on the Xe+–Cu system. The three Gibson potentials and the Anderson-Sigmund potential were used for the Cu–Cu interaction. Changing these functions produces quantitatively, but not qualitatively, different results; so a majority of the investigation was conducted with the Gibson II potential. The Ar–Cu and Xe–Cu potentials were those obtained locally from secondary electron emission studies. Variation of parameters in these functions had little effect on the spot patterns. Sputtering ratios change appreciably as the parameters of the potentials are varied, but the unexplained systematic difference between simulation and experiment cannot be removed by parametric variation within a Born-Mayer potential function model. The simulations indicate that sputtering is caused by two mechanisms: (a) In the more common situation the incoming ion strikes two lattice atoms almost simultaneously. The lower energy of these two primary knock-on atoms then initiates the sputtering of several of its neighbors. The higher-energy primary knock-on may also cause some sputtering, but it usually is less efficient because a large fraction of its momentum is directed into the surface. (2) In a relatively small number of events the ion, after having made one or more collisions, is reflected from the second or third layer of the crystal. It then can initiate sputtering as it returns toward the surface. The second mechanism has never been seen when the ion is heavier than the lattice atoms. Primary knock-on ions rarely sputter. Occasionally (after making several collisions) one escapes accidently. Almost every incident ion sputters at least one atom, even those which enter a (110) channel. Ions which hit the end of a (110) chain with zero impact parameter, or ions which penetrate normally into the absolute center of the trigonal lens of the (111) surface or the square lens of the (100) surface do not cause sputtering. Surface dynamics dominate the sputtering process. The probability of focuson sputtering appears to be vanishingly small. The relationships between the surface dynamics, transparency, and channeling models are discussed.

Calculation of the Energy of Activation for Some Simple Reactions. I. Ortho-Para Hydrogen Reaction

A model is proposed from which energies of activation and potential energy surfaces of three atom reactions may be calculated. The method makes use of internuclear attractive and repulsive potential functions which have been derived from a quantum mechanical delta-function model. The energy of activation of the ortho-para hydrogen reaction was calculated and found to have a value of 8.5 kcal in agreement with the experimental value. The model predicts the presence of a slightly stable H3 complex. This complex, however, is asymmetric, located at a minimum in the potential curve just before the barrier, and is stable by an energy of about 1 kcal. The method may be classified as semiempirical. However, all parameters used are obtained theoretically from the proposed model. One advantage of the method is that the main points of interest on the potential energy surface may be calculated without calculating a complete potential energy surface.