#appliedmathematics — Public Fediverse posts

V. Ocqueteau (University of Bordeaux) and his supervisor M. Tucsnak have a new publication in the Journal of Mathematical Fluid Mechanics:

They study the small vertical motion of a floating cylinder. Coupling the water wave equations with the body's equation of motion, they prove the well-posedness of the system by analyzing a Dirichlet-to-Neumann map.

https://link.springer.com/article/10.1007/s00021-026-01047-0

https://arxiv.org/abs/2504.20523

#AppliedMathematics #FluidMechanics #MathematicalPhysics #WellPosedness

#MSCA #EUhorizon

Physics-informed neural networks (PINNs) are artificial intelligence models pre-programmed with fundamental physical laws to accurately predict how quickly controlled-release materials will dispense therapeutic agents.
#ArtificialIntelligence #ComputationalPharmaceutics #AppliedMathematics #MaterialsEngineering #sflorg
https://www.sflorg.com/2026/07/ai07062601.html

Frenet–Serret Formula ✍️

It explains how a curve reveals its hidden geometry by tracking the way it bends and twists through space. Imagine tracing the path of a roller coaster, a winding river, or the spiral of a DNA strand. At every point along the path, the curve is constantly changing direction, and the Frenet–Serret formulas provide a precise way to describe that change.

They do this by attaching a moving frame of three special directions to each point on the curve. The first points forward along the path, showing where the curve is heading. The second points inward, toward the direction of bending. The third stands perpendicular to both, capturing how the curve twists out of its plane. Together, they form a local coordinate system that travels with the curve itself.

As you move along the curve, these three directions rotate and evolve. The formulas measure this evolution using two key quantities: curvature and torsion. Curvature tells how sharply the path bends, while torsion tells how strongly it twists into three dimensions. If curvature vanishes, the path becomes straight; if torsion vanishes, the curve lies flat in a plane.

Mathematicians and physicists use the Frenet–Serret formulas to study motion, design smooth paths in engineering, understand particle trajectories, and analyze natural shapes. They transform a simple line into a rich geometric story, revealing exactly how space is being navigated at every step.

#FrenetSerretFormula #DifferentialGeometry #Geometry #Mathematics #Math #PureMathematics #AppliedMathematics #MathematicalPhysics #Physics #STEM #ScienceEducation #MathEducation #Curvature #Torsion #SpaceCurves #VectorCalculus #Calculus #LinearAlgebra #GeometricAnalysis

💼 #Job #opportunities

3 x #ResearchFellow roles to work on #ESRCfunded Connecting #Generations projects, based at the #UniversityofStAndrews

📨 Apply by 29 June. More info: https://www.cpc.ac.uk/news/vacancies/

#jobs #researchjobs #jobsearch #demography #statistics #computerscience #appliedmathematics #phd #Geography #socialscience #longitudinaldata #dataanalysis #qualitativedata #eventhistoryanalysis #population #intergenerational #family #fertility #socialsciences #migration #community

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithsUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

In elementary #mechanics we are taught about the #SimplePendulum, which is modelled as a point #mass hanging via a rigid #rod or #string of a given length, under uniform #gravity. This simple model is also useful in introducing #OrdinaryDifferentialEquations and helps us to understand #SimpleHarmonicMotion.

#MyWork #CCBYSA #Mathematics #ClassicalMechanics #AppliedMathematics #Physics #Animation

Forgive the recent apparent obsession (I’d call it a fascination) with the #cycloid but I’ve just discovered something I’d not heard of before. It is also called a #TautochroneCurve or #Isochrone curve, which means that a particle starting from any location on the curve will get to the #MinimumPoint at precisely the same time as a particle starting at any other point.

#Dynamics #Kinematics #Mathematics #AppliedMathematics #Mechanics #ClassicalMecanics #WxMaxima #FreeSoftware #MyWork #CCBYSA

Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.

#Mathematics #Geometry #Maths #AppliedMathematics #Mechanics #Kinematics #Dynamics #Physics

Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic #curve with #period over the #circle's circumference and has #cusps whenever the point is in contact with the surface (the two sides of the curve are tangentially vertical at that point).

#Mathematics #Geometry #Maths #AppliedMathematics #Mechanics #Kinematics #Dynamics #Physics #MyWork #CCBYSA #WxMaxima