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Third-order smoothness metric to characterize progressive addition lenses.
J Opt Soc Am A Opt Image Sci Vis
August 2024
Although second-order surface analyses, mainly mean power and cylinder maps, are commonly used to characterize the progressive addition lens (PAL) surface, recently it has been suggested that third-order variations may also have relevancy in PAL optical and visual performance. This paper proposes a third-order smoothness metric, and its associated Riemannian distance, to further characterize PAL's surface optical performance. These metrics can provide a complementary scoring tool to those classical ones, particularly, to analyze the transition zones between far, near, intermediate, and blending zones.
View Article and Find Full Text PDFSelecting Initial Conditions for Trajectory-Based Nonadiabatic Simulations.
Acc Chem Res
January 2025
Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom.
ConspectusPhotochemical reactions have always been the source of a great deal of mystery. While classified as a type of chemical reaction, no doubts are allowed that the general tenets of ground-state chemistry do not directly apply to photochemical reactions. For a typical chemical reaction, understanding the critical points of the ground-state potential (free) energy surface and embedding them in a thermodynamics framework is often enough to infer reaction yields or characteristic time scales.
View Article and Find Full Text PDFPair approximating the action for molecular rotations in path integral Monte Carlo.
J Chem Phys
January 2025
Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair discrete variable representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed helium, is naturally well-suited for systems interacting with a pairwise potential.
View Article and Find Full Text PDFh-CMD: An efficient hybrid fast centroid and quasi-centroid molecular dynamics method for the simulation of vibrational spectra.
J Chem Phys
January 2025
Division of Energy, Matter and Systems, School of Science and Engineering, University of Missouri-Kansas City, Kansas City, Missouri 64110, USA.
Developing efficient path integral (PI) methods for atomistic simulations of vibrational spectra in heterogeneous condensed phases and interfaces has long been a challenging task. Here, we present the h-CMD method, short for hybrid centroid molecular dynamics, which combines the recently introduced fast quasi-CMD (f-QCMD) method with fast CMD (f-CMD). In this scheme, molecules that are believed to suffer more seriously from the curvature problem of CMD, e.
View Article and Find Full Text PDFModel predictive path integral for decentralized multi-agent collision avoidance.
PeerJ Comput Sci
August 2024
HSE University, Moscow, Russia.
Collision avoidance is a crucial component of any decentralized multi-agent navigation system. Currently, most of the existing multi-agent collision-avoidance methods either do not take into account the kinematic constraints of the agents (., they assume that an agent might change the direction of movement instantaneously) or are tailored to specific kinematic motion models (.
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