Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1405.7404

Computer algebra in spacetime embedding

Waldir L. Roque·Renato P. dos Santos
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper we describe an algorithm to determine the vectors normal to a space-time V4 embedded in a pseudo-Euclidean manifold M4+n. An application of this algorithm is given considering the Schwarzchild space-time geometry embedded in a 6 dimensional pseudo-Euclidean manifold, using the algebraic computing system REDUCE.

Explore related subjects

physics.comp-phgr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Waldir L. Roque, Renato P. dos Santos. 2014-05-28. Computer algebra in spacetime embedding. https://doi.org/10.1016/s0747-7171(08)80156-3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bi-Hamiltonian in Semiflexible Polymers built upon Overdamping Process

Quantifying the interaction between a system of interest and its ambient conditions, the memory effect links the states of two distinct Hamiltonians: one for the target system and one for the environment. In this paper, we propose the diffusion process derived from the Smoluchowski equation that can derive the evolution process described by the memory effect integration in a non Markovian regime. The Smoluchowski picture, within the framework of stochastic thermodynamics, justifies a diffusion process incorporated into the equations of motion, and the result of the derivation enables a coarse-grained molecular dynamics simulation with the modified equation of motion to reproduce attenuation from collisions between single walled carbon nanotubes (SWCNTs) under far from equilibrium conditions. The results of the numerical experiments on the collision confirm that heat diffusion compensates for the correlated momentum arising from the memory effect between the two Hamiltonians in both equilibrium and far from equilibrium states.

physics.comp-ph↗
arXiv2026

Translation of transient acoustic fields

A method is presented for the translation of acoustic field data from a source to a target region. Field data are represented as spherical harmonic expansions on spheres surrounding the source and target regions respectively and expansions are translated using a ``point and shoot'' method using the Kirchhoff--Helmholtz integral to carry out an axial translation from one sphere to the other. The principal motivation for the method is its use in a time-domain Fast Multipole Method, and test cases reflective of this application are presented. The method converges to six digits for appropriate values of parameters and for the values of $N$ considered here computational effort scales approximately as $N^{2}$ where $N$ is the order of spherical harmonic expansion for the field data. The method is causal and thus avoids artifacts generated in methods which are not based on intrinsically causal formulations.

physics.comp-ph↗
arXiv2026

Learning continuous reaction paths for transition-state prediction

Transition states are defined by reaction pathways, yet most machine-learning methods predict them as isolated geometries. We introduce MARC-TS, a two-stage framework that learns a continuous, endpoint-conditioned path, queries it at any resolution and uses local path context to refine a transition-state candidate. We construct T1x-IRC-8K, a dataset of 8,209 reactions and 1,088,725 path-resolved geometries. On held-out reactions, the path model reduced complete-path error by 48.4% relative to endpoint interpolation, and the localizer achieved a mean aligned structural error of 0.127 Å. Quantum-chemical optimization and vibrational analysis yielded 405 frequency-confirmed first-order saddle-point candidates from 410 predictions. In a 100-reaction nudged elastic band comparison, learned-path initialization reached a joint geometry-and-force target for 66% of reactions, compared with 12% for geometric interpolation after 100 optimizer steps. By treating the path as a reusable representation rather than an auxiliary output, MARC-TS connects transition-state prediction, mechanistic interpretation and quantum-chemical refinement.

physics.comp-ph↗