#Hamiltonian modeling of systems www.linkedin.com/posts/eric-d...

Physicists often say that if y...

New #physics #classicalmechanics video - solving the simple harmonic oscillator with #hamiltonian mechanics. #python and phase space diagram included #iteachphysics

https://youtu.be/DoahMcolKHk

'Learnability of Linear Port-Hamiltonian Systems', by Juan-Pablo Ortega, Daiying Yin.

http://jmlr.org/papers/v25/23-0450.html

#hamiltonian #manifold #learnability

🌘 基本的 Hamiltonian 表述 of the Navier–Stokes 問題 | 流體力學期刊 | 劍橋核心
➤ 一個對 Navier-Stokes 問題的 Hamiltonian 表述
✤ https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/canonical-hamiltonian-formulation-of-the-navierstokes-problem/B3EB9389AE700867A6A3EA63A45E69C6
本文提出了基於最小作用原理導出的最小平方法的漂移 Navier-Stokes 問題的新穎 Hamiltonian 表述。這個表述使用速度 $𝑢_{𝑖}(𝑥_{𝑗},𝑡)$ 和壓力 $𝑝(𝑥_{𝑗},𝑡)$ 作為需要變動的場量，以及從分析中得出的正則共軛動量。從這些場量構造出一個滿足 Hamilton 正則方程的守恆 Hamiltonian 泛函 $H^{*}$，並為壓縮
#流體力學 #Hamiltonian 表述 #Navier-Stokes 問題

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

'Microcanonical Hamiltonian Monte Carlo', by Jakob Robnik, G. Bruno De Luca, Eva Silverstein, Uroš Seljak.

http://jmlr.org/papers/v24/22-1450.html

#microcanonical #langevin #hamiltonian

Derp. I confused an #Eulearian walk with a #Hamiltonian one. But, I’m on holiday, and what really is the difference anyway.

While other visitors to #Dublin may be preparing for a #Bloomsday walk, I will be heading out to Brooms Bridge. I will be sure to take a different path there than back, so that my route will be properly #Hamiltonian.

I will refrain from scratching anything into the bridge.

New #physics video - solving projectile motion in polar coordinates with #Hamiltonian mechanics. Why would I make a simple problem so difficult? Because it's fun. #ClassicalMechanics

https://youtu.be/ibweVaJFeQQ

Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes

Magnus Ross, Markus Heinonen

https://openreview.net/forum?id=DHEZuKStzH

#hamiltonian #trajectories #gaussian

This blog post describing #Hamiltonian #MonteCarlo for #statistics is pretty good!

https://bjlkeng.github.io/posts/hamiltonian-monte-carlo/#hamiltonian-mechanics

I studied a bit about #MCMC in grad school, but I never quite got far enough to see Hamiltonian Monte Carlo methods. But I do know enough about Hamiltonian mechanics that this explanation made a lot of sense to me.

It's a bit long, but I definitely recommend this post

Hamiltonian field equations:
\[\boxed{\boxed{\dot\phi_i=+\dfrac{\delta\mathcal{H}}{\delta\pi_i},\ \dot\pi_i=-\dfrac{\delta\mathcal{H}}{\delta\phi_i}}}\]
The field analogue of the Hamiltonian formulation of classical mechanics!
#Hamiltonian #classicalmechanics #field #quantumfield #fieldequations #functional #theoreticalphysics #differentialequations

#arxivfeed :

"A thermodynamical model of non-deterministic computation in cortical neural networks"
https://www.biorxiv.org/content/10.1101/2022.12.03.518978v1

#Neuroscience #Neuro #Brain #ComputationalNeuroscience #Computations #ProbabilisticCoding #Thermodynamic #Hamiltonian

Verlet integrator family, increases E over very long t scales, though error ~ constant. These do not reproduce actual #Hamiltonian mechanics of system; instead, they reproduce a closely related "shadow" Hamiltonian whose value they conserve many orders of magnitude > closely

2 permissible #quantum ops to manipulate composite system:
- an observation, which irreversibly collapses system -> #eigenstate of an observable, corrupting the information contained #qubit(s). Bad
Or control #Hamiltonian of combined system, time-evolution operator.

But #topological #Hilbert space seem to be a thing , as you note states of matter as #Hamiltonian

#Painlevé equations can all be represented as #Hamiltonian systems

Ehrenfest's theorem -> Liouville's theorem of #Hamiltonian mechanics, which involves #Poisson bracket instead of a commutator. #Dirac's rule of thumb : statements S in qm w commutator -> S classical mechanics where commutator is supplanted by a Poisson bracket multiplied by iħ.

basic point is replacement of set of second order equations by another first order set of equations. We may get this second set of equations by #Hamiltonian formulation in an easy way

basic point is replacement of set of second order equations by another first order set of equations. We may get this second set of equations by #Hamiltonian formulation in an easy way