25 papers · ranked by Valyu relevance
Desmond J. Higham
I give a brief, non-technical, historical perspective on numerical analysis and optimization. I also touch on emerging trends and future challenges. This content is based on the short presentation that I made at the opening ceremony of The International Conference on Numerical Analysis and Optimization, which was held…
Ronald F. Boisvert, Michael J. Donahue, Daniel W. Lozier, Robert McMichael + 1 more
'Robert McMichael' 'Bert W. Rust'] In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of…
Fergus R. Cooper, Ruth E. Baker, Alexander G. Fletcher
Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behaviour, models that consider cells as individual objects are becoming a common tool to study how…
R. Corban Harwood
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but this can be misleading if the method is not developed and operated carefully due…
Nikolaos P. Bakas
In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or…
R. Corban Harwood, Mitch Main
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations can create infeasible results. Since oscillation-free behavior is not ensured by…
Byakatonda Denis
| ABSTRACT | iii | | --- | --- | | ORGANIZATION OF THE STUDY | iv | | LIST OF ABBREVIATIONS | v | | LIST OF SYMBOLS | vi | | LIST OF FIGURES | vii | | LIST OF TABLES | viii | | CHAPTER ONE 1 | | | INTRODUCTION 1 | | | 1.0 Introduction 1 | | | 1.1 Background of the study 1 | | | 1.2 Preliminaries 3 | | | 1.4 Statement…
Philipp Städter, Yannik Schälte, Leonard Schmiester, Jan Hasenauer + 1 more
Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when…
В. В. Аристов, А. В. Строганов
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic operations in the ordinary computing device, we attempt to go to the analytical…
Authors not listed
The present study investigates the transient 3D numerical prediction of the significance of passive control techniques, using triangular and rectangular span-wise pimples, placed at cambered section at the location 32% chord length from of the nose of the hydrofoil, and combined with a modified finite trailing edge…
Wojciech Wawrzynski
Each Duffing equation has an unstable solution area with a boundary, which is also a line of bifurcation. Generally, in a system that can be modeled by the Duffing equation, bifurcations can occur at frequencies lower than the origin point frequency of the unstable solution area for a softening system and at higher…
Nikolaos Bakas
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is demonstrated, by utilizing partial sums of Taylor series in high arithmetic precision. In…
Alireza Karami, Elisa Castaldi, Evelyn Eger, Martin Hebart + 1 more
Humans can estimate the number of objects in a scene within a fraction of a second, suggesting that numerosity is encoded rapidly and directly by the visual system. Yet how this encoding unfolds over time and interacts with other visual features remains unclear. Here, we combined magnetoencephalography (MEG) with…
Dmitry Kobylkov, Uwe Mayer, Mirko Zanon, Giorgio Vallortigara
Numerical cognition is ubiquitous in the animal kingdom. Domestic chicks are a widely used developmental model for studying numerical cognition. Soon after hatching, chicks can perform sophisticated numerical tasks. Nevertheless, the neural basis of their numerical abilities has remained unknown. Here, we describe for…
Fernando Chueca-Díez, Alfonso M. Gañán‐Calvo
A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica and Matlab) do not offer a solution, is to find all the real solutions of a system of N nonlinear equations in a certain finite domain of the N-dimensional space of variables. We present an algorithm of…
Shahanaz Parvin, Siti Suzilliana Putri Mohamed Isa, Fuad S. Al- Duais, Syed M. Hussain + 4 more
'Syed M. Hussain' 'Wasim Jamshed' 'Rabia Safdar' 'Mohamed R. Eid' 'Oluwole Daniel Makinde'] A mathematical model of 2D-double diffusive layer flow model of boundary in MHD Maxwell fluid created by a sloping slope surface is constructed in this paper. The numerical findings of non-Newtonian fluid are important to the…
Authors not listed
Moving bed reactors (MBRs) are widely used in various industrial processes, making the development of mathematical models crucial for their design, optimization, and control. This study presents a semi-analytical solution (SAS) for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order…
Majeed A. Yousif, Faraidun K. Hamasalh, Ahmad Zeeshan, Mohamed Abdelwahed + 1 more
'Mohamed Abdelwahed' 'Muhammad Mubashir Bhatti'] This research presents a novel conformable-Caputo fractional non-polynomial spline method for solving the time-fractional Korteweg-de Vries (KdV) equation. Emphasizing numerical analysis and algorithm development, the method offers enhanced precision and modeling…
Authors not listed
As a prove of concept for experimental geochemistry, an advanced 3D numerical framework, here and after called Digital Twin (DT), of a diffusion experiment conducted at a synchrotron beamline, has been implemented using in-situ measurements data, physics-based modelling, a machine learning (ML) model, and parameter…
Jaroslav Rojíček, Jakub Cienciala, Martin Fusek
This article explores the structural identifiability of parameters within non-linear physical models, focussing specifically on the Anand material model. The proposed procedure is structured in two key steps: first, a local analysis identifies the most suitable parameters for testing. Subsequently, these selected…
Alireza Karami, Elisa Castaldi, Evelyn Eger, Manuela Piazza
Visual numerosity, a feature of visual sets traditionally associated with the parietal cortex, has recently been suggested to be encoded in a broader range of cortical regions, including early visual and associative cortices of both streams. However, a clear picture of how numerosity information is represented…
Marc Blétry
Buffer solutions are pervasive in chemistry, biochemistry, analytical chemistry, etc. A better understanding of buffer properties and what controls them is susceptible to be of interest in many scientific and technological fields. For instance, linear pH gradients are commonly used in electrophoresis and their…
Vicente Alejandro Aguilera González, Gizem Cetin, Stephanie Zika, Antonia Schulz + 3 more
The visual number form areas (here referred to as ITG-math) have gained recent attention as a neural substrate of mathematical cognition. Yet, the function of these regions remains debated with some research suggesting selectivity for digits and others suggesting a visual stimulus-independent role in mathematical…
Tobias Seidel, Lena-Marie Ränger, Thomas Grützner, Michael Bortz
In this work we present a new approach that we use to simulate and optimize multiple dividing wall columns at the same time. Instead of considering all model equations as constraints and all process variables as optimization variables in a large and highly nonlinear optimization problem we only incorporate a subset of…
Oliver Lee, Malte Gather, Eli Zysman-Colman
We describe a new tool for the efficient management of computational chemistry. Digichem is a program that automates and simplifies nearly the entire computational pipeline, including large-scale batch submission of calculations, analysis and results parsing, the generation of 3D density plots and 2D graphs of…