Action-angle coordinates
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General formulation of vibronic spectroscopy in internal coordinates Open
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended …
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New algorithms to obtain analytical solutions of Einstein’s equations in isotropic coordinates Open
The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein’s Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method, w…
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Dynamic Analysis of Planar Rigid Multibody Systems modeled using Natural Absolute Coordinates Open
This paper deals with the dynamic simulation of rigid multibody systems described with the use of two-dimensional natural absolute coordinates. The computational methodology discussed in this investigation is referred to as planar Natural …
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The multi-dimensional generalized Langevin equation for conformational motion of proteins Open
Using the generalized Langevin equation (GLE) is a promising approach to build coarse-grained (CG) models of molecular systems since the GLE model often leads to more accurate thermodynamic and kinetic predictions than Brownian dynamics or…
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Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules Open
A new procedure is presented for building a general kinetic energy operator expressed as a polynomial series expansion of symmetry-adapted curvilinear coordinates for semirigid polyatomic molecules. As a starting point, the normal-mode Wat…
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Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator Open
We present the first use of curvilinear vibrational coordinates, specifically polyspherical coordinates, in combination with vibrational coupled cluster theory. The polyspherical coordinates are used in the context of both the adaptive den…
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Determining internal coordinate sets for optimal representation of molecular vibration Open
Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational …
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The action–angle dual of an integrable Hamiltonian system of Ruijsenaars–Schneider–van Diejen type Open
Integrable deformations of the hyperbolic and trigonometric ${\mathrm{BC}}_n$ Sutherland models were recently derived via Hamiltonian reduction of certain free systems on the Heisenberg doubles of ${\mathrm{SU}}(n,n)$ and ${\mathrm{SU}}(2n…
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Explicit Equations to Transform from Cartesian to Elliptic Coordinates Open
Explicit equations are obtained to convert Cartesian coordinates to elliptic coordinates, based on which a function in elliptic coordinates can be readily mapped in physical space. Application to Kirchhoff vortex shows that its elliptical …
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Lattice Boltzmann model in curvilinear coordinates for the study of the vibrational modes of a trumpet Open
Since its origins, lattice-Boltzmann methods have been restricted to rectangular coordinates, a fact which jeopardises the applications to problems with cylindrical or spherical symmetries and complicates the implementations with complex g…
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Variational Barycentric Coordinates Open
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in pract…
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Maximum Likelihood Coordinates Open
Any point inside a d‐dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycent…
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The extended Lissajous–Levi-Civita transformation Open
Action-angle variables for the Levi-Civita regularized planar Kepler problem were introduced independently first by Chenciner and then by Deprit and Williams. The latter used explicitly the so-called Lissajous variables. When applied to th…
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Determination of the principal coordinates in solving the problem of the vertical dynamics of the vehicle using the method of mathematical modeling Open
Attention to the theory of rolling stock oscillations is due primarily to the fact that oscillatory processes, which inevitably arise as a result of driving along a usually uneven road, degrade almost all the basic properties of rolling st…
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Electrostatic potential of a uniformly charged triangle in barycentric coordinates Open
We compute the electrostatic potential of a uniformly charged triangle. Barycentric coordinates are employed to express the field point, the parametrization of the surface integral, and the gradient operator. The resultant analytic express…
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Stochastic Computation of Barycentric Coordinates Open
This paper presents a practical and general approach for computing barycentric coordinates through stochastic sampling. Our key insight is a reformulation of the kernel integral defining barycentric coordinates into a weighted least-square…
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Symmetry Analysis of the Two-Dimensional Stationary Gas Dynamics Equations in Lagrangian Coordinates Open
This article analyzes the symmetry of two-dimensional stationary gas dynamics equations in Lagrangian coordinates, including the search for equivalence transformations, the group classification of equations, the derivation of group foliati…
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Extracting dynamical frequencies from invariants of motion in finite-dimensional nonlinear integrable systems Open
Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with n degrees of freedom possesses n nontrivial integrals of motion, and can be solved,…
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Biharmonic Coordinates and their Derivatives for Triangular 3D Cages Open
As a natural extension to the harmonic coordinates, the biharmonic coordinates have been found superior for planar shape and image manipulation with an enriched deformation space. However, the 3D biharmonic coordinates and their derivative…
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Efficient object location determination and error analysis based on barycentric coordinates Open
In this paper, we propose an efficient computational method for converting local coordinates to world coordinates using specially structured coordinate data. The problem in question is the computation of world coordinates of an object thro…
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N-Dimensional Quasipolar Coordinates - Theory and Application Open
In this thesis, various generalizations to the n-dimension of the polar coordinates and spherical coordinates are introduced and compared with each other and the existent ones in the literature. The proof of the Jacobian of these coordinat…
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Are Orthogonal Separable Coordinates Really Classified? Open
We prove that the set of orthogonal separable coordinates on an arbitrary\n(pseudo-)Riemannian manifold carries a natural structure of a projective\nvariety, equipped with an action of the isometry group. This leads us to\npropose a new, a…
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Collective coordinate fix in the path integral Open
Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parametrize a manifold of zero modes and more broadl…
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On construction of a field of forces along given trajectories in the presence of random perturbations Open
In this paper, a force field is constructed along a given integral manifold in the presence of random perturbing forces. In this case, two types of integral manifolds are considered separately: 1) trajectories that depend on generalized co…
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Canonical Coordinates with Tame Estimates for the Defocusing NLS Equation on the Circle Open
In a case study for integrable PDEs, we construct real analytic, canonical coordinates for the defocusing NLS equation on the circle, specifically tailored to the needs in perturbation theory. They are defined in neighbourhoods of families…
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Redundant configuration coordinates and nonholonomic velocity coordinates in analytical mechanics Open
Several established concepts of analytical mechanics are reviewed and extended to include redundant configuration coordinates and nonholonomic velocity coordinates. The main motivation for redundant coordinates is that the resulting formul…
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A quartic force field coordinate substitution scheme using hyperbolic sine coordinates Open
Quartic force fields (QFF) are currently the most cost‐effective method for the approximation of potential energy surfaces for the calculation of anharmonic vibrational energies. It is known, although, that its performance can be less than…
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Coordinates for the Universal Moduli Space of Holomorphic Vector Bundles Open
In this paper we provide two ways of constructing complex coordinates on the moduli space of pairs of a Riemann surface and a stable holomorphic vector bundle centred around any such pair. We compute the transformation between the coordina…
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On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes Open
It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twis…
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Sasaki–Ricci Flow and Deformations of Contact Action–Angle Coordinates on Spaces T1,1 and Yp,q Open
In this paper, we are concerned with completely integrable Hamiltonian systems and generalized action–angle coordinates in the setting of contact geometry. We investigate the deformations of the Sasaki–Einstein structures, keeping the Reeb…