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Elemental Weapon Ball Territory War 93 (☀️v🦇v🪨v✨) #elements #weaponball #animation #physics #fantasy
93,995 Aufrufe • vor 8 Tagen •via X (Twitter)
8 Kommentare
Spaceman SpiffyNnemonicvor 6 Tagen
What a fucking comeback from Vampire though
Jeepers!vor 4 Tagen
I KNEW VAMPIRE WOULDWIN I KNEW IT I KNEW IT
Just a Random Stickfigure (Spli!t)vor 4 Tagen
ALWAYS bet on Vampire.
Ryvor 3 Tagen
Vampire the fucking goat
Motivos Para A Minha Alegriavor 5 Tagen
Manoooooo, que virada insana!!
Wishvor 3 Tagen
Poop sword
KidHFigaro (Vagabundo digital)vor 3 Tagen
Noooo Earth!
Mydo(🟢)vor 3 Tagen
Sempre confiei no mano vampiro
![#UnityTips: 🔥 Fluid 'simulation' trail shader. 🫧 Inspired by a #b3d node animation. [U]V gradient masks control the colour/alpha/width over trail. ✨ ('fluid' is 100% rendered in the shader) #unity3d #gamedev #indiedev #madewithunity #gameart #vfx #realtimevfx #proceduralart](https://image.24vids.com/tw-1638136059027488768/ext_tw_video_thumb/1637950484349591553/pu/img/w9Zj456v9XJP0CWA.jpg)
![🇹🇭 ช่วงเวลาที่แฟน ๆ ชาวไทย don’t wanna wake from fantasy~⋆.˚🦋༘⋆ 📸 SM True ขอพาไปสัมผัสภาพบรรยากาศเบื้องหลังการถ่ายทำ MV เพลง 💙 ‘You Give Me Butterflies’ 💜 ที่ทุกความรู้สึกล้วน feeling’s so beautiful จนแฟน ๆ ไม่อาจละสายตาได้~✨ [Official MV] ‘You Give Me Butterflies’ - BLUE PONGTIWAT feat. TEN 📹 รับฟังเพลง ‘You Give Me Butterflies’ - BLUE PONGTIWAT feat. TEN 🎧 #TEN #李永钦 #텐 #BLUEPONGTIWAT Bluepongtiwat #BLUExTENYouGiveMeButterflies #NCT NCT #WayV #威神V WayV #LOVEiSENTERTAINMENT LOVEiS](https://image.24vids.com/tw-2037107290088820917/amplify_video_thumb/2037070491886956544/img/1V0KPcLjtDSMtV9B.jpg)
![Quantum Mechanics Series Lecture 4 Lecture 1 established that ρ(x,t) = |ψ(x,t)|² behaves like a conserved probability density. Lecture 2 showed what drives that flow. We also saw that writing ψ = r exp(iθ) makes the probability current proportional to the phase gradient, making it clear that phase geometry literally steers the motion. Lecture 3 then showed that the centroid of that flow can move almost classically when the packet is tight and the external potential is smooth. However, that raises yet another question. If the centroid can look classical, why does the full wave still spread, bend, split, and interfere in ways no classical particle cloud would? This is because the wave is not driven only by the external potential. It is also driven by its own curvature. Write ψ(x,t) = r(x,t) exp(iθ(x,t)) with ρ = r². Then Schrödinger’s equation gives two coupled real equations. One is the continuity equation you already know. The other looks like a Hamilton-Jacobi equation, but with one extra term: Q = −(1/2m) ∇²r / r This is the so-called Quantum Potential. It depends entirely on how the amplitude bends across space. So, the wave is being shaped not only by V(x,t), but also by the geometry of its own envelope. In the animation, the upper surface is still |ψ| and its skin is still colored by arg(ψ). The glowing threads still trace the probability current. But now a second membrane hangs underneath. That lower membrane encodes the quantum potential Q itself. The porcelain bead marks the quantum centroid. The amber bead follows a classical centroid under the same external V. When those paths separate, the lower membrane tells you why. The difference is not magic but the extra term classical mechanics does not have. The math breakdown: Start from Schrödinger evolution in units with ħ = 1: i ∂ψ/∂t = [ −(1/2m) ∇² + V(x,t) ] ψ Write the state in polar form: ψ = r exp(iθ) Then ρ = |ψ|² = r² From the imaginary part, you recover probability conservation: ∂ρ/∂t + ∇·j = 0 with j = (1/m) Im(ψ* ∇ψ) = (ρ/m) ∇θ So the local velocity field is v = j / ρ = ∇θ / m Now take the real part of Schrödinger’s equation. That gives ∂θ/∂t + |∇θ|² / (2m) + V + Q = 0 where Q = −(1/2m) ∇²r / r This is the classical Hamilton-Jacobi equation with one extra term. That extra term is what makes quantum motion locally different from classical motion. Take a gradient of that phase equation and use v = ∇θ / m. Then the flow obeys an Euler-like equation: ∂v/∂t + (v·∇)v = −(1/m) ∇(V + Q) In other words, there are really two forces in the problem. One comes from the external potential V. The other comes from the wave’s own curvature through Q. That is why Ehrenfest is only approximate. The centroid can still satisfy d⟨x⟩/dt = ⟨p⟩/m d⟨p⟩/dt = −⟨∇V⟩ but the internal shape of the packet evolves under the combined influence of V and Q. When the packet stays broad and smooth, Q is gentle and the motion looks more classical. When the packet develops sharp curvature or interference structure, Q becomes strong and the classical picture breaks down. That is what this scene is designed to show live. #QuantumMechanics #Wavefunction #SchrodingerEquation #BornRule #ProbabilityCurrent #ContinuityEquation #Phase #EhrenfestTheorem #QuantumPotential #Madelung #HamiltonJacobi #MathematicalPhysics #Mathematics #Physics](https://image.24vids.com/tw-2044118124148973661/amplify_video_thumb/2044117901251072000/img/IXBMEKzfYfpY_xGi.jpg)
