24 papers · ranked by Valyu relevance
Petro Kolosov
| 1. | Introduction | 1 | | --- | --- | --- | | 2. | Definitions for discrete distribution | 3 | | 3. | Difference and derivative of power function | 4 | | 4. | Difference of polynomials | 6 | | 5. | Relation with Partial derivatives | 8 | | 6. | Relations between finite differences | 10 | | 7. | The error of…
Deena Roller, Andrew M. Rappe, Leeor Kronik, Olle Hellman
Interpolation for Reduction of Grid-Related Errors in Real-Space Pseudopotential Density Functional Theory Authors: ['Deena Roller' 'Andrew M. Rappe' 'Leeor Kronik' 'Olle Hellman'] The real-space pseudopotential approach is a well-known method for large-scale density functional theory (DFT) calculations. One of its…
Muhammad Adeel Ajaib
We discuss physical implications of the explicit method in numerical analysis. Numerical methods have there own condition for causality, known as the Courant-Friedrichs-Lewy condition. It is proposed that numerical causality merges with physical causality as the grid interval size approaches zero. We discuss the…
A. Aguayo-Ortiz, S. Mendoza, D. Olvera, Iratxe Puebla
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the…
Ewelina Kubacka, Piotr Ostrowski, Alexander Yu Churyumov, Giovanni Garcea
'Giovanni Garcea'] Among composites, we can distinguish periodic structures, biperiodic structures, and structures with a functional gradation of material properties made of two or more materials. The selection of the composite’s constituent materials and the way they are distributed affects the weight of the…
Frank Uhlig
Zhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer from low truncation error orders. This paper develops a constructive method to find convergent look-ahead finite difference schemes of…
Hao-Jun Michael Shi, Yuchen Xie, Melody Qiming Xuan, Jorge Nocedal
A common approach for minimizing a smooth nonlinear function is to employ finitedifference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is noisy, the optimal choice requires information about the noise level and…
André Nachbin
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of convergence is not fixed and improves with the function's regularity. For example…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics, Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC), which aim to quantify structural intricacies in pattern formation, enhancing…
Dmitri Finkelshtein, Yuri Kondratiev, Eugene Lytvynov, Maria Joao Oliveira
'Maria Joao Oliveira'] The paper describes known and new results about finite difference calculus on configuration spaces. We describe finite difference geometry on configuration spaces, connect finite difference operators with cannonical commutation relations, find explicit form for certain finite difference Markov…
Sheng-Feng Wang, Ting-Zhu Huang, Xian-Ming Gu, Wei-Hua Luo
In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the Toeplitz structure and the fast Toeplitz matrix-vector product can…
Fauzia Jabeen, Silvana Ilie
Biochemical reaction systems in a cell exhibit a stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some reacting species have…
Alexander Pikovski, Dennis Salahub
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue…
Nicolas Castel, François-Xavier Coudert
Mechanical properties of amorphous phases of metal-organic frameworks, such as MOF glasses, are difficult to determine experimentally. Moreover, computational characterization is limited by the level of theory chosen for the description of interatomic interactions and is often computationally expensive. In this work…
P. K. Pandey
In this article, we present a novel second order numerical method for solving third order boundary value problems using the quartic polynomial splines. We establish the convergence of the method. We present numerical experiments to demonstrate the efficiency of the method and validity of our second order method, which…
Authors not listed
Chemical hardness is one of the fundamental concepts in chemical reactivity theory, rigorously defined within the framework of Conceptual Density Functional Theory (CDFT). The associated maximum hardness principle (MHP), which postulates that, a favorable direction of reaction is towards the state of maximum hardness…
Johannes G. Borgqvist, Philip Gerlee, Carl Lundholm
The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit…
Sukanta Nayak, Snehashish Chakraverty
This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently developed method. Here the concepts of fuzzy numbers are combined with Finite…
Nicolas Castel, François-Xavier Coudert
Mechanical properties of amorphous phases of metal-organic frameworks (MOF), such as MOF glasses, are difficult to determine experimentally. Moreover, computational characterization is limited by the level of theory chosen for the description of interatomic interactions and is often computationally expensive. In this…
Sergio Cobo-López, Matthew Witt, Lucas J. Carbajal, Forest L. Rohwer + 1 more
All dynamical systems are transient. The dynamics of our world at biogeochemical, ecological, and astronomical scales exist in a transient state because the Earth, Sun, and universe are evolving toward thermodynamic equilibrium. However, predicting the tipping points associated with major dynamical shifts in these…
Ming Yang, Louis Z. Yang
What values of relative numerical tolerance should be chosen in simulation of a deterministic model of a biochemical reaction is unclear, which impairs the modeling effort since the simulation outcomes of a model may depend on the relative numerical tolerance values. In an attempt to provide a guideline to selecting…
Nils Edvin Richard Zimmermann, Gabriela Guevara-Carrion, Jadran Vrabec, Niels Hansen
The thermodiffusion behavior of binary Lennard-Jones mixtures in the liquid state was investigated by combining the individual strengths of non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) simulations. On the one hand, boundarydriven NEMD simulations are useful to quickly predict Soret…
Christoph Jacob, Johannes Neugebauer
The past years since the publication of our review on subsystem density-functional theory (sDFT) [WIREs Comput. Mol. Sci. 2014, 4:325--362] have witnessed a rapid development and diversification of quantum mechanical fragmentation and embedding approaches related to sDFT and frozen-density embedding (FDE). In this…
Noor Jamal, Muhammad Sarwar, Parveen Agarwal, Nabil Mlaiki + 1 more
'Ahmad Aloqaily'] In this article, we present an algorithm for computing analytical solutions of linear fuzzy advection-diffusion equations and one-dimensional fuzzy heat equations involving an external source. The fuzzy problems can be solved by using the natural transform and Adomian decomposition method. The results…