Related papers: Computing collinear 4-Body Problem central configu…
Solutions to the collinear three-body problem which do not end in triple collision pass through an infinite number of binary collisions. Given three masses, we show that four geometric quantities generate a finite description of itineraries…
We show that a system of four particles in a one-dimensional box with a two-particle harmonic interaction can by described by means of the symmetry point group $O_h$. Group theory proves useful for the discussion of both the small-box and…
A method for computing electron momentum densities and Compton profiles from ab initio calculations is presented. Reciprocal space is divided into optimally-shaped tetrahedra for interpolation, and the linear tetrahedron method is used to…
Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat $3$-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral…
We study kite central configurations in the Newtonian four-body problem. We present a new proof that there exists a unique convex kite central configuration for a given choice of positive masses and a particular ordering of the bodies. Our…
The four-parameter tetrahedral neutrino mass matrix introduced earlier by the author is studied in two specific limits, both having only two parameters and resulting in theta_13=0, theta_23=pi/4, and tan^2 theta_12=1/2. One limit…
In this paper, we use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions for the collinear four- body problem in both the decoupled case and the coupled case. All…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
In order to study 4-body atomic collisions such as excitation-ionization, transfer with target excitation, and double electron capture, the calculation of a nine-dimensional numerical integral is often required. This calculation can become…
Reliable and robust methods of predicting the crystal structure of a compound, based only on its chemical composition, is crucial to the study of materials and their applications. Despite considerable ongoing research efforts, crystal…
Four-dimensional mass is determined in four-dimensional pseudo-Euclidean space as a physical invariant of that space. That invariant is discussed as an invariant of electromagnetic type. Finally, equations of Maxwell type are obtained for…
This paper shows the existence of a periodic orbit with singularity in the symmetric collinear four body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision…
In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of…
The strength of chaos in large $N$ quantum systems can be quantified using $\lambda_L$, the rate of growth of certain out-of-time-order four point functions. We calculate $\lambda_L$ to leading order in a weakly coupled matrix $\Phi^4$…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is…
Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we…
A new coordinate system on the tangent space to planar configurations is introduced to simplify some calculations on central configurations and relative equilibria in the $N$-body problem with a homogeneous potential, which includes the…
We study the ordered equilibrium structures of patchy particles where the patches are located on the surface of the colloid such that they form a regular tetrahedron. Using optimization techniques based on ideas of evolutionary algorithms…