THREE-BODY FORCE MODELS OF NONHYPERCENTRAL HARMONIC AND ANHARMONIC POTENTIALS IN THREE-DIMENSIONAL POTENTIALS

2008 ◽  
Vol 23 (40) ◽  
pp. 3411-3417 ◽  
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI
Keyword(s):  
Exact Solution ◽  
Body Force ◽  
Three Dimensional ◽  
Hyperspherical Harmonic ◽  
Three Dimensions ◽  
Systematic Analysis ◽  
Relative Coordinates ◽  
Internal Particle ◽  
Three Body ◽  
Special Case

We present a theoretical approach to the internal motion of a system based on three-body forces among particles in a special case, using three-body potentials. The three-body force models are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of the Jacobian relative coordinates ρ, λ and R. The problems related to three-body nonhypercentral potentials in three dimensions are investigated. While the difficulties that arise in the study of nonhypercentral potentials are explicitly shown, we discuss some results obtained using nonhypercentral harmonic and anharmonic and some inverse power terms; however the potential can be easily generalized in order to allow a systematic analysis, which presents an exact solution to the wave function. The method is also applied to some other types of potentials.

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

A Theory of Lubrication With Turbulent Flow and Its Application to Slider Bearings

1960 ◽  
Vol 27 (1) ◽  
pp. 1-4 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Closed Form ◽  
Governing Equation ◽  
Reynolds Equation ◽  
Three Dimensions ◽  
Slider Bearing ◽  
Numerical Example ◽  
Special Case

The governing equation of turbulent lubrication in three dimensions, equivalent to the Reynolds equation of laminar lubrication, is derived. The problem of a slider bearing with no side leakage is then analyzed. An exact solution is found in closed form. Bearing characteristics are also established. It is found that the Reynolds number is an important parameter in the problem of turbulent lubrication. Furthermore, it is shown that the laminar lubrication may be considered as the special case of the present study. A numerical example is also included.

Crystallography of quasi-crystals

1986 ◽  
Vol 42 (4) ◽  
pp. 261-271 ◽  
Author(s):  
T. Janssen
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Crystal Phase ◽  
Two Dimensional ◽  
Space Group ◽  
Quasi Crystals ◽  
Special Case

The symmetry of quasi-crystals, a class of materials that has recently aroused interest, is discussed. It is shown that a quasi-crystal is a special case of an incommensurate crystal phase and that it can be described by a space group in more than three dimensions. A number of relevant three-dimensional quasi-crystals is discussed, in particular dihedral and icosahedral structures. The symmetry considerations are also applied to the two-dimensional Penrose patterns.

THREE-BODY FORCES FROM n-BODY INVERSION

1995 ◽  
Vol 04 (02) ◽  
pp. 431-441
Author(s):  
E.J.O. GAVIN ◽  
H. FIEDELDEY ◽  
S.A. SOFIANOS
Keyword(s):  
Body Force ◽  
Order Approximation ◽  
Expansion Method ◽  
Bound State ◽  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion ◽  
Body Forces ◽  
Quark System ◽  
Three Body ◽  
Hyperspherical Harmonic Expansion Method

Within the context of the lowest order approximation to the calculation of the n-body bound state in the Hyperspherical Harmonic Expansion Method, the hypercentral potential may be determined from n-body spectral data. Previously, we showed how the two-body force can be determined exactly from the hypercentral potential in the absence of three-body forces. In this paper, we investigate to what extent the three-body force can be determined if the two-body force is assumed to be known. For this purpose, a three-quark system is considered.

scholarly journals Incidences with Curves in $\mathbb{R}^d$

10.37236/5840 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Micha Sharir ◽  
Adam Sheffer ◽  
Noam Solomon
Keyword(s):  
Recent Result ◽  
Degrees Of Freedom ◽  
Algebraic Curves ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Bounded Degree ◽  
Four Dimensions ◽  
Mild Conditions ◽  
Point Line ◽  
Special Case

We prove that the number of incidences between $m$ points and $n$ bounded-degree curves with $k$ degrees of freedom in ${\mathbb R}^d$ is\[ O\left(m^{\frac{k}{dk-d+1}+\varepsilon}n^{\frac{dk-d}{dk-d+1}}+ \sum_{j=2}^{d-1} m^{\frac{k}{jk-j+1}+\varepsilon}n^{\frac{d(j-1)(k-1)}{(d-1)(jk-j+1)}} q_j^{\frac{(d-j)(k-1)}{(d-1)(jk-j+1)}}+m+n\right),\]for any $\varepsilon>0$, where the constant of proportionality depends on $k, \varepsilon$ and $d$, provided that no $j$-dimensional surface of degree $\le c_j(k,d,\varepsilon)$, a constant parameter depending on $k$, $d$, $j$, and $\varepsilon$, contains more than $q_j$ input curves, and that the $q_j$'s satisfy certain mild conditions. This bound generalizes the well-known planar incidence bound of Pach and Sharir to $\mathbb{R}^d$. It generalizes a recent result of Sharir and Solomon concerning point-line incidences in four dimensions (where d=4 and k=2), and partly generalizes a recent result of Guth (as well as the earlier bound of Guth and Katz) in three dimensions (Guth's three-dimensional bound has a better dependency on $q_2$). It also improves a recent d-dimensional general incidence bound by Fox, Pach, Sheffer, Suk, and Zahl, in the special case of incidences with algebraic curves. Our results are also related to recent works by Dvir and Gopi and by Hablicsek and Scherr concerning rich lines in high-dimensional spaces. Our bound is not known to be tight in most cases.

On the measurement of turbulent magnetic diffusivities: the three-dimensional case

2013 ◽  
Vol 735 ◽  
pp. 457-472
Author(s):  
F. Cattaneo ◽  
S. M. Tobias
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Passive Scalar ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Turbulent Diffusivity ◽  
Dynamo Action ◽  
Thermally Driven ◽  
Special Case

AbstractIt has been shown that it is possible to measure the turbulent diffusivity of a magnetic field by a method involving oscillatory sources. So far the method has only been tried in the special case of two-dimensional fields and flows. Here we extend the method to three dimensions and consider the case where the flow is thermally driven convection in a large-aspect-ratio domain. We demonstrate that if the diffusing field is horizontal the method is successful even if the underlying flow can sustain dynamo action. We show that the resulting turbulent diffusivity is comparable with, although not exactly the same as, that of a passive scalar. We were not able to measure unambiguously the diffusivity if the diffusing field is vertical, but argue that such a measurement is possible if enough resources are utilized on the problem.

scholarly journals ON GOOD TRIANGULATIONS IN THREE DIMENSIONS

1992 ◽  
Vol 02 (01) ◽  
pp. 75-95 ◽  
Author(s):  
TAMAL KRISHNA DEY ◽  
CHANDERJIT L. BAJAJ ◽  
KOKICHI SUGIHARA
Keyword(s):  
Convex Hull ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Convex Polyhedra ◽  
Finite Precision ◽  
Robust Implementation ◽  
Guaranteed Quality ◽  
Point Set ◽  
Finite Precision Arithmetic ◽  
Special Case

In this paper, we give an algorithm that triangulates the convex hull of a three dimensional point set with guaranteed quality tetrahedra. Good triangulations of convex polyhedra are a special case of this problem. We also give a bound on the number of additional points used to achieve these guarantees and report on the techniques we use to produce a robust implementation of this algorithm under finite precision arithmetic.

scholarly journals The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1726
Author(s):  
Abdelhalim Ebaid ◽  
Weam Alharbi ◽  
Mona D. Aljoufi ◽  
Essam R. El-Zahar
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Solar System ◽  
Angular Velocity ◽  
Body Problem ◽  
Relevant Literature ◽  
Three Dimensional ◽  
Three Dimensions ◽  
System Of Differential Equations ◽  
Physical Quantities

Very recently, the system of differential equations governing the three-dimensional falling body problem (TDFBP) has been approximately solved. The previously obtained approximate solution was based on the fact that the Earth’s rotation (ER) is quite slow and hence all high order terms of ω in addition to the magnitude ω2R were neglected, where ω is the angular velocity and R is the radius of Earth. However, it is shown in this paper that the ignorance of such magnitudes leads, in many cases, to significant errors in the estimated falling time and other physical quantities. The current results are based on obtaining the exact solutions of the full TDFBP-system and performing several comparisons with the approximate ones in the relevant literature. The obtained results are of great interest and importance, especially for other planets in the Solar System or exterior planets, in which ω and/or ω2R are of considerable amounts and hence cannot be ignored. Therefore, the present analysis is valid in analyzing the TDFBP near to the surface of any spherical celestial body.

scholarly journals Comprehensive knowledge base of two- and three-dimensional activity cliffs for medicinal and computational chemistry

F1000Research ◽  
2015 ◽  
Vol 4 ◽  
pp. 168 ◽  
Author(s):  
Ye Hu ◽  
Norbert Furtmann ◽  
Dagmar Stumpfe ◽  
Jürgen Bajorath
Keyword(s):  
Knowledge Base ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Binding Modes ◽  
Activity Data ◽  
Systematic Analysis ◽  
Comprehensive Knowledge ◽  
Or Groups ◽  
2D And 3D ◽  
Activity Cliffs

Activity cliffs are formed by pairs or groups of structurally similar or analogous active compounds with large differences in potency. They can be defined in two or three dimensions by comparing graph-based molecular representations or compound binding modes, respectively. Through systematic analysis of publicly available compound activity data and ligand-target X-ray structures we have in a series of studies determined all currently available two- and three-dimensional activity cliffs (2D- and 3D-cliffs, respectively). Furthermore, we have systematically searched for 2D extensions of 3D-cliffs. Herein, we specify different categories of activity cliffs we have explored and introduce an open access data deposition in ZENODO (doi: 10.5281/zenodo.18490) that makes the entire knowledge base of current activity cliffs freely available in an organized form.

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