Results 51 to 60 of about 53,695 (215)

Solvation Structure and Dynamics of the Thiocyanate Anion in mixed N,N‐Dimethylformamide‐Water Solvents: A Molecular Dynamics Approach

ChemPhysChem, Volume 26, Issue 6, March 15, 2025.
The solvation structure and dynamics of the SCN− anion in mixed N, N‐Dimethylformamide (DMF)‐water liquid solvents is investigated using classical molecular dynamics simulations. A preferential solvation of SCN− by the water molecules is observed in the first hydration shell, followed by a second shell consisting by both DMF and water molecules.
Ioannis Skarmoutsos, Ilias G. Karvounis
wiley   +1 more source

Study on fracture parameter calibration and failure characteristics of rock with hole and crack

Deep Underground Science and Engineering, EarlyView.
The SIF and plastic zone equations for a single hole and crack have been derived. The model's failure state leads to the identification of four types of cracks. The plastic zone increases with increased brittleness and decreased crack length. Abstract Cracks within the surrounding rock of roadways significantly affect their stability and failure ...
Shaochi Peng, Wensong Wang
wiley   +1 more source

On $hp$-Convergence of PSWFs and A New Well-Conditioned Prolate-Collocation Scheme

, 2013
The first purpose of this paper is to provide a rigorous proof for the nonconvergence of $h$-refinement in $hp$-approximation by the PSWFs, a surprising convergence property that was first observed by Boyd et al [J. Sci. Comput., 2013].
Wang, Li-Lian, Zhang, Jing, Zhang, Zhimin   +2 more
core   +1 more source

A Property of Legendre Polynomials [PDF]

Proceedings of the National Academy of Sciences, 1970
Remark I: The Legendre polynomials are the spherical functions for the symmetric space SO(3)/SO(2). A property analogous to that stated in the above theorem holds for other symmetric spaces. In this fashion we get also new properties for Gegenbauer polynomials, Bessel, and Legendre functions.
openaire   +3 more sources

The Combined Effects of Variable Viscosity and Thermal Conductivity of An Unsteady Casson Fluid Flow Along a Vertical Porous Channel With Convective Cooling Walls, Using the Bivariate Spectral Local Linearization Method

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This study examines the combined impact of different thermal conductivity and viscosity on unsteady non‐Newtonian Casson fluid flow of incompressible, electrical conductivity in a porous vertical channel with convective cooling walls, uniform magnetic field, and constant pressure gradient.
A. S. Adeyemo, Precious Sibanda, S. P. Goqo   +2 more
wiley   +1 more source

A novel improved extreme learning machine algorithm in solving ordinary differential equations by Legendre neural network methods

Advances in Difference Equations, 2018
This paper develops a Legendre neural network method (LNN) for solving linear and nonlinear ordinary differential equations (ODEs), system of ordinary differential equations (SODEs), as well as classic Emden–Fowler equations.
Yunlei Yang, Muzhou Hou, Jianshu Luo
doaj   +1 more source

Associated Legendre Functions and Spherical Harmonics of Fractional Degree and Order

, 2017
Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory.
Maier, Robert S.
core   +1 more source

A Novel Optimized Local Linearization Hybrid Block Method for Chaotic Systems: Applications to Stretch‐Twist‐Fold Flow and Bond Orbital Chaotic Attractors

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The numerical approximation of nonlinear chaotic differential systems, such as the modified stretch‐twist‐fold (STF) flow and multi‐bond chaotic attractors, presents a significant challenge due to their sensitive dependence on initial conditions and complex dynamics where analytical solutions are unattainable.
Shina Daniel Oloniiju, Anastacia Dlamini
wiley   +1 more source

Studying the Dynamics Response of Viscoelastic Orthotropic Plates Based on Fractional-Order Derivatives and Shifted Legendre Polynomials

Mathematics
This paper primarily investigates the dynamics response of viscoelastic orthotropic plates under a fractional-order derivative model, which is efficiently simulated numerically using the FKV (Fractional Kelvin–Voigt) model and the shifted Legendre ...
Qianqian Fan, Qiumei Liu, Yiming Chen, Yuhuan Cui, Jingguo Qu, Lei Wang   +5 more
doaj   +1 more source

An objective method to associate local weather extremes with characteristic circulation structures [PDF]

, 2009
In this paper we give methods to find characteristic circulation patterns which are connected to local extreme temperature anomalies. Two data reduction techniques are applied: Legendre polynomial fitting and watershedding. For polynomial fitting a clear
Marczyska, K, Szczepanska, A, Ziemer, C
core