The Hidden Math of Ocean Waves

https://fed.brid.gy/r/https://www.wired.com/story/the-hidden-math-of-ocean-waves-crashes-into-view/

Postdoc Fellow in Bhamla Lab
Bhamla Lab at Georgia Institute of Technology

See the full job description on jobRxiv: https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/

#biologicalphysics #biomechanics #frugalscience #mathematicalphysics #Raman #ScienceJobs #hiring #research
https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/?fsp_sid=5072

The ‘10 Martini’ Proof Connects Quantum Mechanics With Infinitely Intricate Mathematical Structures

https://fed.brid.gy/r/https://www.wired.com/story/the-10-martini-proof-connects-quantum-mechanics-with-infinitely-intricate-mathematical-structures/

Postdoc Fellow in Bhamla Lab
Bhamla Lab at Georgia Institute of Technology

See the full job description on jobRxiv: https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/

#biologicalphysics #biomechanics #frugalscience #mathematicalphysics #Raman #ScienceJobs #hiring #research
https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/?fsp_sid=3231

#physics #mathematicalphysics

Postdoc Fellow in Bhamla Lab
Bhamla Lab at Georgia Institute of Technology

See the full job description on jobRxiv: https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/

#biologicalphysics #biomechanics #frugalscience #mathematicalphysics #Raman #ScienceJobs #hiring #research
https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/?fsp_sid=1047

Postdoc Fellow in Bhamla Lab
Bhamla Lab at Georgia Institute of Technology

See the full job description on jobRxiv: https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/

#biologicalphysics #biomechanics #frugalscience #mathematicalphysics #Raman #ScienceJobs #hiring #research
https://jobrxiv.org/job/bhamla-lab-at-georgia-institute-of-technology-27778-postdoc-fellow-in-bhamla-lab/?fsp_sid=319

Categorical Symmetries in Quantum Field Theory (Conference and School)
(August 27 – September 8, 2023)

The SwissMAP Research Station (SRS)

https://swissmaprs.ch/videos/categorical-symmetries-in-quantum-field-theory-conference-and-school/

#HigherCategory #CategoricalSymmetry #MathematicalPhysics

Some of you might have noticed that for quite a number of years I got frequently distracted from my hacking by a side project that I was working on. 😂

Happily, this is now finally completely published: 🎉

https://tuprints.ulb.tu-darmstadt.de/22028/

In my thesis I present a mathematical theory to describe the inherently probabilistic dynamics of quantum systems in terms of their possible trajectories inspired by classical coding theory. 🤓

#mathematicalPhysics #quantumStochastics
#operatorAlgebras

how interesting to come across an effusive article about W K Clifford (1845-1879) that does NOT mention Clifford Algebras https://heritage.humanists.uk/william-kingdon-clifford/ #humanism #mathematicalphysics

This book aims to equip readers with the mathematical physics skills necessary to solve problems in mechanics, heat conduction, and electromagnetism. It covers a wide range of topics, from basic to advanced, and is intended for both students and researchers. The book provides hints for solving problems and includes detailed solutions to selected ones. Readers should have a solid background in applied mathematics to fully benefit from the book, but most problems in the earlier chapters are accessible to those with a basic understanding of mathematical physics methods.

Translated from the Russian by Richard A. Silverman.

Get the book here.

Contents

PART 1

CONTENTS

PROBLEMS, Page 1

DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS, Page 3

1. Mechanics, 3
2. Heat Conduction, 9
3. Electricity and Magnetism, 11

SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS, Page 19

1. Hyperbolic Equations, 19
2. Elliptic Equations: The Green’s Function Method, 27
3. Elliptic Equations: The Method of Conformal Mapping, 33

STEADY-STATE HARMONIC OSCILLATIONS, Page 42

1. Elastic Bodies: Free Oscillations, 43
2. Elastic Bodies: Forced Oscillations, 46
3. Electromagnetic Oscillations, 49

THE FOURIER METHOD, Page 55

1. Mechanics: Vibrating Systems, Acoustics, 60
2. Mechanics: Statics of Deformable Media, Fluid Dynamics, 73
3. Heat Conduction: Nonstationary Problems, 77
4. Heat Conduction: Stationary Problems, 83
5. Electricity and Magnetism, 91

THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS, Page 103

1. Mechanics: Vibrating Systems, 107
2. Mechanics: Statics of Deformable Media, 114
3. Heat Conduction: Nonstationary Problems, 119
4. Heat Conduction: Stationary Problems, 124
5. Electricity and Magnetism, 131

INTEGRAL TRANSFORMS, Page 143

1. The Fourier Transform, 146
2. The Hankel Transform, 160
3. The Laplace Transform, 169
4. The Mellin Transform, 189
5. Integral Transforms Involving Cylinder Functions of Imaginary Order, 194

CURVILINEAR COORDINATES, Page 203

1. Elliptic Coordinates, 204
2. Parabolic Coordinates, 210
3. Two-Dimensional Bipolar Coordinates, 212
4. Spheroidal Coordinates, 219
5. Paraboloidal Coordinates, 231
6. Toroidal Coordinates, 233
7. Three-Dimensional Bipolar Coordinates, 242
8. Some General Problems on Separation of Variables, 247

INTEGRAL EQUATIONS, Page 253

1. Diffraction Theory, 254
2. Electrostatics, 259

PART 2 SOLUTIONS, Page 273

MATHEMATICAL APPENDIX, Page 381

1. Special Functions Appearing in the Text, 381
2. Expansions in Series of Orthogonal Functions, 384
3. Some Definite Integrals Frequently Encountered in the Applications, 386
4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates, 388

Supplement: VARIATIONAL AND RELATED METHODS, Page 391

1. Variational Methods, 392
   1.1 Formulation of Variational Problems, 392
   1.2 The Ritz Method, 396
   1.3 Kantorovich’s Method, 401
2. Related Methods, 404
   2.1 Galerkin’s Method, 404
   2.2 Collocation, 407
   2.3 Least Squares, 411

References, 412

BIBLIOGRAPHY, Page 415

NAME INDEX, Page 423

SUBJECT INDEX, Page 427

https://mirtitles.org/2024/10/09/worked-problems-in-applied-mathematics-by-n-n-lebedev-i-p-skalskaya-y-s-uflyand/

#curvilinearCoordinates #eigenfunctionMethod #ellipticEquations #FluidDynamics #fourierMethod #harmonicOscillations #heatTransfer #hyperbolicEquations #integralEquations #mathematicalPhysics #mathematics #mechanics #physics #problemsAndSolutions #variationalMethods

🚨 New #preprint !

We study a stochastic PDE whose solutions want to be close to constant -1 or +1. But because it’s stochastic, the solutions occasionally jump between those two optima. How often, on average?

In technical terms, we study a certain nonlinear wave equation whose invariant measure is the \( \phi^4 \) #QuantumFieldTheory. The average transition time is called an Eyring–Kramers law, asymptotic in the low-temperature limit. It has already been derived for 2D stochastic heat equation and 1D wave; we extend it to 2D and 3D wave equations.

Joint work with my PhD advisor Nikolay Barashkov. #MathematicalPhysics #MathPhys

https://arxiv.org/abs/2410.03495

Wir freuen uns diese Woche auf sehr spannende Vorträge in der zweiten #WiMGo #Konferenz zu "Developments in Modern Mathematics" bei uns im Mathematischen Institut, sowie die #Ausstellung "Women of Mathematics from around the World" in unserer historischen Sammlung!

https://academiccloud.social/@rtg2491/112796072564262365

#Göttingen #Mathematik #MathematicalPhysics #Mathematics #conference #UniGoettingen #womenInSTEM #GenderStudies

Wir freuen uns u.a. folgende Sprecher*innen begrüßen zu dürfen:

#MathematicalPhysics
* Patrizia Vitale (University of Neaples)
* Raimar Wulkenhaar (University of Münster)
* Giovanni Landi (University of Trieste)

#OperatorTheory
* Magdalena Musat (University of Copenhagen)
* Sara Azzali (University of Bari)
* Runlian Xia (University of Glasgow)

Anmeldungen sind nun möglich für
"Developments in Modern #Mathematics:
the 2nd #WiMGo #conference" in #Göttingen vom 02.-05.09.2024

Schwerpunkt der Vorträge werden sein:
* #MathematicalPhysics
* #OperatorTheory
* #HigherStructures
* #Geometry
* #Topology
* #NumberTheory
* #GenderStudies

https://www.uni-goettingen.de/en/688539.html

How Is Science Even Possible?
https://www.quantamagazine.org/how-is-science-even-possible-20240620/ #podcast #transcript #ArtificialIntelligence #Biology #Complexity #Emergence #MathematicalBiology #MathematicalPhysics #Mathematics #Physics #Proofs #TheJoyOfWhy

There's singularities and singularities.

Mathematicians Attempt to Glimpse Past the Big Bang | Quanta Magazine https://www.quantamagazine.org/mathematicians-attempt-to-glimpse-past-the-big-bang-20240531/

#cosmology #MathematicalPhysics #GeneralRelativity

Removals firm hopefully not too chaotic #hamiltonian #mathematicalphysics #physics #mechanics #chaos

Lecture notes on General Relativity by Sean Carroll https://arxiv.org/abs/gr-qc/9712019 #generalrelativity #mathematicalphysics

It's a pleasure to announce that a new article has just been published by our recent research fellows Prof Sako and Prof Grosse as an outcome of their Research in Teams Project at @ESIVienna. 📑

🔵 Harald Grosse, Akifumi Sako: #Integrability of Φ
4 Matrix Model
as N-body Harmonic Oscillator System 🔵

Check out the article on https://arxiv.org/pdf/2308.11523.pdf

(Permission is given by the authors for using their figure from the paper for this post)

#MathematicalPhysics #HighEnergyPhysics
@univienna