Differential Equations as a Projection of Implicit Functions Using Spatio-Temporal Taylor Expansion and Critical Points Properties

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43976634" target="_blank" >RIV/49777513:23520/24:43976634 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1063/5.0210444" target="_blank" >https://doi.org/10.1063/5.0210444</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0210444" target="_blank" >10.1063/5.0210444</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Differential Equations as a Projection of Implicit Functions Using Spatio-Temporal Taylor Expansion and Critical Points Properties

Popis výsledku v původním jazyce

This contribution introduces a novel method for formulating differential equations. This method relies on expanding an implicit function that varies with time (denoted as &quot;t&quot;) in the space-time domain using Taylor series. This formulation encompasses both ordinary differential equations (ODEs) and partial differential equations (PDEs).In the context of visualizing vector fields, such as fluid flow and electromagnetic fields, the critical points of ODEs play a crucial role in understanding physical phenomena behavior. This paper outlines a general approach for formulating ODEs and PDEs by treating them as time-varying scalar functions using the Taylor expansion. Furthermore, a new condition for identifying critical points is derived and specified specifically for cases where the function is invariant with respect to time (referred to as &quot;t-invariant&quot;). This newly derived formula enhances the detection of critical points, particularly in the context of acquiring and analyzing large 3D fluid flow data. This advancement enables efficient compression of 3D vector data and their representation through radial basis functions (RBFs).

Název v anglickém jazyce

Differential Equations as a Projection of Implicit Functions Using Spatio-Temporal Taylor Expansion and Critical Points Properties

Popis výsledku anglicky

This contribution introduces a novel method for formulating differential equations. This method relies on expanding an implicit function that varies with time (denoted as &quot;t&quot;) in the space-time domain using Taylor series. This formulation encompasses both ordinary differential equations (ODEs) and partial differential equations (PDEs).In the context of visualizing vector fields, such as fluid flow and electromagnetic fields, the critical points of ODEs play a crucial role in understanding physical phenomena behavior. This paper outlines a general approach for formulating ODEs and PDEs by treating them as time-varying scalar functions using the Taylor expansion. Furthermore, a new condition for identifying critical points is derived and specified specifically for cases where the function is invariant with respect to time (referred to as &quot;t-invariant&quot;). This newly derived formula enhances the detection of critical points, particularly in the context of acquiring and analyzing large 3D fluid flow data. This advancement enables efficient compression of 3D vector data and their representation through radial basis functions (RBFs).

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

AIP Conference Proceedings

ISBN

978-0-7354-4954-1

ISSN

0094-243X

e-ISSN

1551-7616

Počet stran výsledku

4

Strana od-do

1-4

Název nakladatele

AIP Publishing

Místo vydání

Heraklion

Místo konání akce

Heraklion

Datum konání akce

19. 9. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001244923000099