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ModConFlexInterested in doing a <a href="https://mastodon.social/tags/PhD" class="mention hashtag" rel="nofollow noopener" target="_blank">#PhD</a> in <a href="https://mastodon.social/tags/engineering" class="mention hashtag" rel="nofollow noopener" target="_blank">#engineering</a>? Open Position:➡️ <a href="https://euraxess.ec.europa.eu/jobs/371136" rel="nofollow noopener" translate="no" target="_blank">https://euraxess.ec.europa.eu/jobs/371136</a>👩‍🎓 <a href="https://mastodon.social/tags/ControlTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#ControlTheory</a> <a href="https://mastodon.social/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.social/tags/ElectricalEngineering" class="mention hashtag" rel="nofollow noopener" target="_blank">#ElectricalEngineering</a> The intention is to investigate the grid integration of renewable energy. In particular, the researcher will work on oscillation reduction in floating wind turbines and on the stabilization of power grids using virtual synchronous machines. <a href="https://mastodon.social/tags/HorizonEU" class="mention hashtag" rel="nofollow noopener" target="_blank">#HorizonEU</a>

Scientific WorldAn Applied Mathematics degree is more than just numbers on a page—it’s a passport to solving real‑world problems with precision, creativity, and impact. Explore whether an applied mathematics degree is worth. <a href="https://mastodon.social/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.social/tags/MathCareers" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathCareers</a> <a href="https://mastodon.social/tags/STEMEducation" class="mention hashtag" rel="nofollow noopener" target="_blank">#STEMEducation</a> <a href="https://www.scientificworldinfo.com/2025/08/is-applied-mathematics-degree-worth-it.html" rel="nofollow noopener" translate="no" target="_blank">https://www.scientificworldinfo.com/2025/08/is-applied-mathematics-degree-worth-it.html</a>

Academic EuropeJob Alert 📢PhD Candidate (m/f/d): Analysis of Microscopic BIOMedical Images (AMBIOM)Deadline: 2025-07-31 Location: Germany, Dortmund, Nordrhein Westfalen<a href="https://www.academiceurope.com/ads/phd-candidate-m-f-d-analysis-of-microscopic-biomedical-images-ambiom/" rel="nofollow noopener" translate="no" target="_blank">https://www.academiceurope.com/ads/phd-candidate-m-f-d-analysis-of-microscopic-biomedical-images-ambiom/</a><a href="https://mstdn.business/tags/hiring" class="mention hashtag" rel="nofollow noopener" target="_blank">#hiring</a> <a href="https://mstdn.business/tags/PhD" class="mention hashtag" rel="nofollow noopener" target="_blank">#PhD</a> <a href="https://mstdn.business/tags/IT" class="mention hashtag" rel="nofollow noopener" target="_blank">#IT</a> <a href="https://mstdn.business/tags/computerscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#computerscience</a> <a href="https://mstdn.business/tags/statistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#statistics</a> <a href="https://mstdn.business/tags/appliedmathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#appliedmathematics</a> <a href="https://mstdn.business/tags/datascience" class="mention hashtag" rel="nofollow noopener" target="_blank">#datascience</a> <a href="https://mstdn.business/tags/biomedicalengineering" class="mention hashtag" rel="nofollow noopener" target="_blank">#biomedicalengineering</a>

Sólo YoUna alternativa para detectar patrones en señales contaminadas con ruido y otras señales en la misma banda espectral que la deseada, es por medio de un cambio de base en la ventana móvil del espectrograma.<a href="https://doi.org/10.29057/icbi.v12iEspecial4.13171" rel="nofollow noopener" translate="no" target="_blank">https://doi.org/10.29057/icbi.v12iEspecial4.13171</a><a href="https://mastodon.social/tags/appliedmathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#appliedmathematics</a> <a href="https://mastodon.social/tags/physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#physics</a> <a href="https://mastodon.social/tags/signalprocessing" class="mention hashtag" rel="nofollow noopener" target="_blank">#signalprocessing</a>

Sólo YoUn interesante método para recuperar la información de archivos corruptos cuando se tiene una base de datos previa.<a href="https://www.mdpi.com/2079-3197/13/4/95" rel="nofollow noopener" translate="no" target="_blank">https://www.mdpi.com/2079-3197/13/4/95</a><a href="https://mastodon.social/tags/computerscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#computerscience</a> <a href="https://mastodon.social/tags/imageeditor" class="mention hashtag" rel="nofollow noopener" target="_blank">#imageeditor</a> <a href="https://mastodon.social/tags/appliedmathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#appliedmathematics</a>

UK<a href="https://www.europesays.com/uk/190760/" rel="nofollow noopener" translate="no" target="_blank">https://www.europesays.com/uk/190760/</a> Optical solitons, bifurcation, and chaos in the nonlinear conformable Schrödinger equation with group velocity dispersion coefficients and second-order spatiotemporal terms <a href="https://pubeurope.com/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://pubeurope.com/tags/Bifurcation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Bifurcation</a> <a href="https://pubeurope.com/tags/ConformableDerivative" class="mention hashtag" rel="nofollow noopener" target="_blank">#ConformableDerivative</a> <a href="https://pubeurope.com/tags/HumanitiesAndSocialSciences" class="mention hashtag" rel="nofollow noopener" target="_blank">#HumanitiesAndSocialSciences</a> <a href="https://pubeurope.com/tags/MathematicalModel" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathematicalModel</a> <a href="https://pubeurope.com/tags/multidisciplinary" class="mention hashtag" rel="nofollow noopener" target="_blank">#multidisciplinary</a> <a href="https://pubeurope.com/tags/NewDirectMappingMethod" class="mention hashtag" rel="nofollow noopener" target="_blank">#NewDirectMappingMethod</a> <a href="https://pubeurope.com/tags/NonlinearConformableSchr%C3%B6dingerEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#NonlinearConformableSchrödingerEquation</a> <a href="https://pubeurope.com/tags/NonlinearOptics" class="mention hashtag" rel="nofollow noopener" target="_blank">#NonlinearOptics</a> <a href="https://pubeurope.com/tags/OpticalSolitonSolutions" class="mention hashtag" rel="nofollow noopener" target="_blank">#OpticalSolitonSolutions</a> <a href="https://pubeurope.com/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://pubeurope.com/tags/Science" class="mention hashtag" rel="nofollow noopener" target="_blank">#Science</a> <a href="https://pubeurope.com/tags/Solitons" class="mention hashtag" rel="nofollow noopener" target="_blank">#Solitons</a> <a href="https://pubeurope.com/tags/UK" class="mention hashtag" rel="nofollow noopener" target="_blank">#UK</a> <a href="https://pubeurope.com/tags/UnitedKingdom" class="mention hashtag" rel="nofollow noopener" target="_blank">#UnitedKingdom</a>

Khurram Wadee ✅A few days back, I posted some <a href="https://mastodon.org.uk/tags/AnimatedGifs" class="mention hashtag" rel="nofollow noopener" target="_blank">#AnimatedGifs</a> of the exact solution for a large-amplitude undamped, unforced <a href="https://mastodon.org.uk/tags/Pendulum" class="mention hashtag" rel="nofollow noopener" target="_blank">#Pendulum</a>. I then thought to complete the study to include the case when it has been fed enough <a href="https://mastodon.org.uk/tags/energy" class="mention hashtag" rel="nofollow noopener" target="_blank">#energy</a> to allow it just to undergo <a href="https://mastodon.org.uk/tags/FullRotations" class="mention hashtag" rel="nofollow noopener" target="_blank">#FullRotations</a>, rather than just <a href="https://mastodon.org.uk/tags/oscillations" class="mention hashtag" rel="nofollow noopener" target="_blank">#oscillations</a>. Well, it turns out that it is “a bit more complicated than I first expected” but I finally managed it.<a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/SpecialFunctions" class="mention hashtag" rel="nofollow noopener" target="_blank">#SpecialFunctions</a> <a href="https://mastodon.org.uk/tags/DynamicalSystems" class="mention hashtag" rel="nofollow noopener" target="_blank">#DynamicalSystems</a> <a href="https://mastodon.org.uk/tags/NonlinearPhenomena" class="mention hashtag" rel="nofollow noopener" target="_blank">#NonlinearPhenomena</a>

Khurram Wadee ✅Here we see three identical pendulums, oscillating independently. The red and purple ones are vibrating with small amplitudes and so their periods are nearly the same. But the blue one is undergoing what would be considered to be very large amplitude oscillations and has a significantly longer period. In fact, as the amplitude approaches π radians, the period increases without bound and approaches infinity.<a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener" target="_blank">#MyWork</a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#CCBYSA</a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/ClassicalMechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ClassicalMechanics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://mastodon.org.uk/tags/Animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Animation</a>

Khurram Wadee ✅The above is only strictly true for “small” amplitudes. If the <a href="https://mastodon.org.uk/tags/pendulum" class="mention hashtag" rel="nofollow noopener" target="_blank">#pendulum</a> is subject to large amplitudes, it is no longer governed by the simple linear differential equations alluded to above. Given that the rod remains rigid and no energy is dissipated, the pendulum <a href="https://mastodon.org.uk/tags/equations" class="mention hashtag" rel="nofollow noopener" target="_blank">#equations</a> may still be solved exactly, though they are now <a href="https://mastodon.org.uk/tags/nonlinear" class="mention hashtag" rel="nofollow noopener" target="_blank">#nonlinear</a>.<a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener" target="_blank">#MyWork</a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#CCBYSA</a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/ClassicalMechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ClassicalMechanics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://mastodon.org.uk/tags/Animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Animation</a>

Khurram Wadee ✅In elementary <a href="https://mastodon.org.uk/tags/mechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mechanics</a> we are taught about the <a href="https://mastodon.org.uk/tags/SimplePendulum" class="mention hashtag" rel="nofollow noopener" target="_blank">#SimplePendulum</a>, which is modelled as a point <a href="https://mastodon.org.uk/tags/mass" class="mention hashtag" rel="nofollow noopener" target="_blank">#mass</a> hanging via a rigid <a href="https://mastodon.org.uk/tags/rod" class="mention hashtag" rel="nofollow noopener" target="_blank">#rod</a> or <a href="https://mastodon.org.uk/tags/string" class="mention hashtag" rel="nofollow noopener" target="_blank">#string</a> of a given length, under uniform <a href="https://mastodon.org.uk/tags/gravity" class="mention hashtag" rel="nofollow noopener" target="_blank">#gravity</a>. This simple model is also useful in introducing <a href="https://mastodon.org.uk/tags/OrdinaryDifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#OrdinaryDifferentialEquations</a> and helps us to understand <a href="https://mastodon.org.uk/tags/SimpleHarmonicMotion" class="mention hashtag" rel="nofollow noopener" target="_blank">#SimpleHarmonicMotion</a>.<a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener" target="_blank">#MyWork</a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#CCBYSA</a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/ClassicalMechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ClassicalMechanics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://mastodon.org.uk/tags/Animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Animation</a>

Academic EuropeJob Alert 🌱🎓 Tandem Professur (W1 LBesO) Sichere Software SystemeDeadline: 2025-05-26Location: Germany, Zweibrücken, Rheinland Pfalz🔗 <a href="https://www.academiceurope.com/job/?id=7612" rel="nofollow noopener" translate="no" target="_blank">https://www.academiceurope.com/job/?id=7612</a><a href="https://mstdn.business/tags/hiring" class="mention hashtag" rel="nofollow noopener" target="_blank">#hiring</a> <a href="https://mstdn.business/tags/Professor" class="mention hashtag" rel="nofollow noopener" target="_blank">#Professor</a> <a href="https://mstdn.business/tags/ITSecurity" class="mention hashtag" rel="nofollow noopener" target="_blank">#ITSecurity</a> <a href="https://mstdn.business/tags/SoftwareEngineering" class="mention hashtag" rel="nofollow noopener" target="_blank">#SoftwareEngineering</a> <a href="https://mstdn.business/tags/AI" class="mention hashtag" rel="nofollow noopener" target="_blank">#AI</a> <a href="https://mstdn.business/tags/TandemProfessur" class="mention hashtag" rel="nofollow noopener" target="_blank">#TandemProfessur</a> <a href="https://mstdn.business/tags/informatics" class="mention hashtag" rel="nofollow noopener" target="_blank">#informatics</a> <a href="https://mstdn.business/tags/appliedphysics" class="mention hashtag" rel="nofollow noopener" target="_blank">#appliedphysics</a> <a href="https://mstdn.business/tags/appliedmathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#appliedmathematics</a>

Bytes EuropeThe analysis of artificial intelligence knowledge graphs for online music learning platform under deep learning <a href="https://www.byteseu.com/1004938/" rel="nofollow noopener" translate="no" target="_blank">https://www.byteseu.com/1004938/</a> <a href="https://pubeurope.com/tags/AI" class="mention hashtag" rel="nofollow noopener" target="_blank">#AI</a> <a href="https://pubeurope.com/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://pubeurope.com/tags/ArtificialIntelligence" class="mention hashtag" rel="nofollow noopener" target="_blank">#ArtificialIntelligence</a> <a href="https://pubeurope.com/tags/ComputationalScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputationalScience</a> <a href="https://pubeurope.com/tags/ComputerScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputerScience</a> <a href="https://pubeurope.com/tags/DataSparsity" class="mention hashtag" rel="nofollow noopener" target="_blank">#DataSparsity</a> <a href="https://pubeurope.com/tags/FeatureFusion" class="mention hashtag" rel="nofollow noopener" target="_blank">#FeatureFusion</a> <a href="https://pubeurope.com/tags/HumanitiesAndSocialSciences" class="mention hashtag" rel="nofollow noopener" target="_blank">#HumanitiesAndSocialSciences</a> <a href="https://pubeurope.com/tags/InformationTechnology" class="mention hashtag" rel="nofollow noopener" target="_blank">#InformationTechnology</a> <a href="https://pubeurope.com/tags/KnowledgeGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#KnowledgeGraphs</a> <a href="https://pubeurope.com/tags/MathematicsAndComputing" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathematicsAndComputing</a> <a href="https://pubeurope.com/tags/multidisciplinary" class="mention hashtag" rel="nofollow noopener" target="_blank">#multidisciplinary</a> <a href="https://pubeurope.com/tags/MusicRecommendationSystem" class="mention hashtag" rel="nofollow noopener" target="_blank">#MusicRecommendationSystem</a> <a href="https://pubeurope.com/tags/PureMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#PureMathematics</a> <a href="https://pubeurope.com/tags/Science" class="mention hashtag" rel="nofollow noopener" target="_blank">#Science</a> <a href="https://pubeurope.com/tags/ScientificData" class="mention hashtag" rel="nofollow noopener" target="_blank">#ScientificData</a> <a href="https://pubeurope.com/tags/software" class="mention hashtag" rel="nofollow noopener" target="_blank">#software</a> <a href="https://pubeurope.com/tags/statistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#statistics</a>

Academic EuropeJob - Alert 🌱🌎 <a href="https://mstdn.business/tags/PhD" class="mention hashtag" rel="nofollow noopener" target="_blank">#PhD</a> Position (f_m_x) – Uncertainty Analysis of Coupled Reactive Transport ModelsDeadline: 2025-05-27Location: Germany, Potsdam, Brandenburg <a href="https://www.academiceurope.com/job/?id=7517" rel="nofollow noopener" translate="no" target="_blank">https://www.academiceurope.com/job/?id=7517</a> 🌎<a href="https://mstdn.business/tags/hiring" class="mention hashtag" rel="nofollow noopener" target="_blank">#hiring</a> <a href="https://mstdn.business/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mstdn.business/tags/ComputerSciences" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputerSciences</a> <a href="https://mstdn.business/tags/geochemistry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geochemistry</a> <a href="https://mstdn.business/tags/GeoScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#GeoScience</a> <a href="https://mstdn.business/tags/Programming" class="mention hashtag" rel="nofollow noopener" target="_blank">#Programming</a> <a href="https://mstdn.business/tags/Statistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Statistics</a>

david jon furbishI cannot think of an applied mathematics that is more beautiful and far-reaching, or philosophically wilder, than probability. No, nonlinear dynamics and chaos people, it’s not even close 🤣<a href="https://mastodon.online/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#probability</a> <a href="https://mastodon.online/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mastodon.online/tags/appliedmathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#appliedmathematics</a> <a href="https://mastodon.online/tags/philosophy" class="mention hashtag" rel="nofollow noopener" target="_blank">#philosophy</a> <a href="https://mastodon.online/tags/philosophyofscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#philosophyofscience</a> <a href="https://newsmast.community/@philosophy" class="u-url mention" rel="nofollow noopener" target="_blank">@philosophy@newsmast.community</a> <a href="https://a.gup.pe/u/philosophy" class="u-url mention" rel="nofollow noopener" target="_blank">@philosophy@a.gup.pe</a>

Khurram Wadee ✅We’re having a <a href="https://mastodon.org.uk/tags/Soliton" class="mention hashtag" rel="nofollow noopener" target="_blank">#Soliton</a> sale over here! Get yours quick! Seriously, though, this is a quick <a href="https://mastodon.org.uk/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#animation</a> of the <a href="https://mastodon.org.uk/tags/SolitonInteraction" class="mention hashtag" rel="nofollow noopener" target="_blank">#SolitonInteraction</a> surface – the solution of the <a href="https://mastodon.org.uk/tags/Korteweg" class="mention hashtag" rel="nofollow noopener" target="_blank">#Korteweg</a>-deVries <a href="https://mastodon.org.uk/tags/Eauation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Eauation</a> showing (x,t,u(x,t)) giving you an all-round view.<a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener" target="_blank">#MyWork</a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#CCBYSA</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Mathematic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematic</a> <a href="https://mastodon.org.uk/tags/Phyiscs" class="mention hashtag" rel="nofollow noopener" target="_blank">#Phyiscs</a> <a href="https://mastodon.org.uk/tags/KdV" class="mention hashtag" rel="nofollow noopener" target="_blank">#KdV</a> <a href="https://mastodon.org.uk/tags/KdVEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#KdVEquation</a> <a href="https://mastodon.org.uk/tags/FreeSoftware" class="mention hashtag" rel="nofollow noopener" target="_blank">#FreeSoftware</a> <a href="https://mastodon.org.uk/tags/WxMaxima" class="mention hashtag" rel="nofollow noopener" target="_blank">#WxMaxima</a>

Khurram Wadee ✅I posted on <a href="https://mastodon.org.uk/tags/Soliton" class="mention hashtag" rel="nofollow noopener" target="_blank">#Soliton</a> interactions in the <a href="https://mastodon.org.uk/tags/Korteweg" class="mention hashtag" rel="nofollow noopener" target="_blank">#Korteweg</a>-deVries <a href="https://mastodon.org.uk/tags/Equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Equation</a> yesterday with an <a href="https://mastodon.org.uk/tags/Animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Animation</a> of how two <a href="https://mastodon.org.uk/tags/SolitaryWaves" class="mention hashtag" rel="nofollow noopener" target="_blank">#SolitaryWaves</a> interact. The <a href="https://mastodon.org.uk/tags/PhaseShift" class="mention hashtag" rel="nofollow noopener" target="_blank">#PhaseShift</a> experienced by both can also be seen in a static <a href="https://mastodon.org.uk/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> plot with time, t, plotted on one axis. You should be able to see a “dog-leg” in the trajectory of each wave after it interacts with the other.<a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener" target="_blank">#MyWork</a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#CCBYSA</a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://mastodon.org.uk/tags/FreeSoftware" class="mention hashtag" rel="nofollow noopener" target="_blank">#FreeSoftware</a> <a href="https://mastodon.org.uk/tags/WxMaxima" class="mention hashtag" rel="nofollow noopener" target="_blank">#WxMaxima</a>

Khurram Wadee ✅A subtlety probably difficult to spot in the animation is that the interaction of the two waves leaves them phase shifted, with the taller wave gaining position, while the shorter one loses it. This further animation shows the interactions again (purple) but I’ve also shown what would happen if each wave moved without interaction with the other (red and blue).<a href="https://mastodon.org.uk/tags/Animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Animation</a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://mastodon.org.uk/tags/WxMaxima" class="mention hashtag" rel="nofollow noopener" target="_blank">#WxMaxima</a> <a href="https://mastodon.org.uk/tags/FreeSoftware" class="mention hashtag" rel="nofollow noopener" target="_blank">#FreeSoftware</a>

Khurram Wadee ✅Here is an example taken from Solitons: an introduction by Drazin & Johnson, where taller wave overtakes a shorter one moving in the same direction.4/4<a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a>

Khurram Wadee ✅When you start looking at <a href="https://mastodon.org.uk/tags/NonlinearWaves" class="mention hashtag" rel="nofollow noopener" target="_blank">#NonlinearWaves</a>, some of these principles no longer apply. For example, in the Korteweg-de Vries equation, which has <a href="https://mastodon.org.uk/tags/Soliton" class="mention hashtag" rel="nofollow noopener" target="_blank">#Soliton</a> or solutions, you can no longer simply add two solutions together as the resulting function would not be a solution of the governing equation. Waves of different heights travel at different velocities, with the taller waves moving faster than the shorter ones. Instead, they interact <a href="https://mastodon.org.uk/tags/nonlinearly" class="mention hashtag" rel="nofollow noopener" target="_blank">#nonlinearly</a>.3/4<a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a>

Khurram Wadee ✅Also, waves of different heights travel at different velocities, with the taller waves moving faster than the shorter ones.2/4<a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mastodon.org.uk/tags/AppliedMathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedMathematics</a> <a href="https://mastodon.org.uk/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a>

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