Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0411015

Numerical Evaluation of Cuspoid and Bessoid Oscillating Integrals for Applications in Chemical Physics

J. N. L. Connor·C. A. Hobbs
View original source ↗Read source document ↗Export metadata ↓

Abstract

Oscillating integrals often arise in the theoretical description of phenomena in chemical physics, in particular in atomic and molecular collisions, and in spectroscopy. A computer code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their first-order partial derivatives is described. The code uses a novel adaptive contour algorithm, which chooses a contour in the complex plane that avoids the violent oscillatory and exponential natures of the integrand and modifies its choice as necessary. Applications are made to the swallowtail canonical integral and to a bessoid integral.

Explore related subjects

physics.chem-phphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. N. L. Connor, C. A. Hobbs. 2004-11-01. Numerical Evaluation of Cuspoid and Bessoid Oscillating Integrals for Applications in Chemical Physics. https://arxiv.org/abs/physics/0411015

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

KEEP EXPLORING

Related papers

arXiv2026

Intrinsic Matching Frustration in Fluctuating Finite Systems

We formulate intrinsic matching frustration (IMF), a fluctuation-induced, kinetics-independent reduction in the mean capacity permitted by a prescribed matching rule. For complementary one-to-one matching, the instantaneous capacity is set by the minority population, so fluctuations produce a nonzero mean deficit even when the two populations are balanced on average. At finite size, this deficit depends on the full distribution of the population difference and is determined by its variance alone only in the Gaussian limit. Compartmentalization hides matching capacity by preventing cancellation between local imbalances of opposite sign. Fusion releases this hidden capacity monotonically under coarse graining, producing a measurable recovery of product yield following local reaction to completion.

physics.chem-ph↗
arXiv2026

Phonon chirality as an additive control of CISS: a symmetry-protected law

Chirality-induced spin selectivity (CISS) is usually associated with molecular handedness. The possible contribution of chiral phonons is less established. We study a helical tight-binding model in which local phonon angular momentum modulates spin-dependent nearest-neighbor hopping. Fewest-switches surface hopping calculations give the transmitted spin polarization $\mathrm{SP}=aC+b\mathrm{PH}$. Here $C$ is the molecular chirality and $\mathrm{PH}$ is the phonon chirality. A mirror symmetry reverses $C$, $\mathrm{PH}$, and $\mathrm{SP}$ simultaneously. This symmetry excludes both a chirality-independent offset and a $C\cdot\mathrm{PH}$ term. The phonon contribution can therefore enhance, cancel, or reverse the molecular CISS signal.

physics.chem-ph↗
arXiv2026

A fast physics-based matrix model for the impedance of a PEM fuel cell: Incorporating functionally graded catalyst layer and channel impedances

We extend a recent physics-based matrix model for calculating PEM fuel cell impedance (doi:10.1149/2754-2734/ad6ce8) to cases of low air flow stoichiometry and functionally graded cathode catalyst layers (CCLs). We demonstrate that the matrix model produces accurate spectra and is almost three orders of magnitude faster than a model based on the standard boundary-value problem solver. The physics-based matrix model can compete with equivalent circuit models for fitting experimental EIS spectra, particularly those measured from cells with functionally graded CCL.

physics.chem-ph↗