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Variational Continuation for Double Pendulum Periodic Orbits
Researchers introduce a Hessian-based, integrator-free method using automatic differentiation to continue periodic orbits in the double pendulum, uncovering previously unreported orbit families.
A new arXiv paper presents a variational, Hessian-based framework for numerically continuing periodic orbits in dynamical systems, parametrizing candidate loops as Fourier series and minimizing deviation from the governing differential equations. Automatic differentiation replaces hand-derived Jacobians, and flat directions of the loss landscape guide the continuation search. The method is demonstrated on the double pendulum, mapping bifurcations along orbit families, including periodic orbits where neither pendulum mass is ever simultaneously at rest.
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Besxar is building an orbital semiconductor factory, one SpaceX rocket at a time
Besxar, founded by a former OpenAI staffer, raised ~$14M to prototype semiconductor manufacturing in orbit using SpaceX Falcon 9 booster flights.
Besxar, founded by former OpenAI staffer Ashley Pilipiszyn, raised almost $14 million, including a $9 million seed led by Dauntless Ventures and Overture VC, to build orbital semiconductor fabrication. Its first two "fabship" canisters flew on a July Starlink mission and returned wafer samples cleaner than comparable terrestrial wafers. The company plans to iterate over two years with a dozen Falcon 9 booster flights before flying larger fabs on Starship, targeting wafers for power-regulation chips used in data centers, robots, and electric vehicles.
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Hierarchical NeRF with JAX3D for Volumetric Rendering, Novel-View Synthesis, and 3D Reconstruction
MarkTechPost tutorial implements a hierarchical NeRF in JAX using jax3d volume-rendering primitives for novel-view synthesis and 3D reconstruction.
The tutorial builds an end-to-end hierarchical Neural Radiance Field using JAX, Flax, Optax, and jax3d's volume-rendering functions (sample_along_rays, volume_rendering, sample_piecewise_constant_pdf). It implements positional encoding, skip connections, separate coarse and fine networks, and view-direction conditioning with hierarchical importance sampling. Training uses JAX JIT compilation, Adam optimization, exponential learning-rate decay, and gradient clipping. Evaluation covers PSNR, depth and opacity visualization, 360-degree rendering, and marching-cubes geometry extraction.
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