On a Multi-Species Kinetic Model of Plasma, Theory and Numerics
Explore a new multi-species kinetic model for plasma, examining its theoretical properties and numerical solutions in the context of inertial confinement fusion.
Vlasov-Maxwell-Boltzmann System
Explore the Vlasov-Maxwell-Boltzmann system and its convergence to the Navier-Stokes-Fourier-Maxwell system with Ohm's law, including uniform estimates and classical solution analysis.
Vlasov Poisson Boltzmann Equation in Bounded Domains
Explore the Vlasov-Poisson-Boltzmann system for charged particles in bounded domains, focusing on boundary effects, solution construction, and convergence to global Maxwellian distribution.
Kinetic Theory of Social Phenomena I
Explore statistical mechanics of multi-agent systems to explain distributions in human activities, focusing on skewed distributions in economics and social sciences.
Swarming Models with Local Alignment Effects
Explores phase transitions in kinetic equations for swarming models, focusing on noise-driven transitions and their applications in mathematical physics and interacting particle systems.
Scaling Limits and Effective Equations in Kinetic Theory I
Explores scaling limits and effective equations in kinetic theory, focusing on Boltzmann and Landau equations for rarefied gases and weakly interacting plasmas, discussing mathematical challenges in rigorous derivation.
Reversed Hardy Littlewood Sobolev Inequalities
Exploration of reverse Hardy-Littlewood-Sobolev inequalities, examining parameter ranges, optimal functions, and potential concentration, with connections to free energy functionals and nonlinear diffusion equations.
Quantitative Uniform Propagation of Chaos for Maxwell Molecules
Explores propagation of chaos in Kac's N-particle system for Maxwell molecules, using probabilistic coupling techniques and recent stabilization results to establish uniform-in-time estimates.
Mean Field Limit by Gamma Convergence
Explores mean-field limit for λ-convex potentials using variational methods, focusing on gradient flows and Γ-convergence in interacting particle systems.
Indirect Diffusion Effect and Convergence to Equilibrium
Explores indirect diffusion in reaction-diffusion systems, showing how non-diffusing species can still reach equilibrium through interactions with diffusing species and reversible reactions.
Renormalization and Energy Conservation for the Axisymmetric Euler Equation
Explore axisymmetric Euler equations, discussing well-posedness, qualitative properties, and renormalization results for vanishing viscosity solutions. Examine energy conservation in ideal fluid dynamics.
On the Muskat Problem with Different Mobilities and the Vortex Sheet Problem with Non-Fixed Sign
Explores recent findings on unstable Muskat problem in porous media and vortex sheet problem in Euler equations, discussing h-principle, convex integration, and globally dissipative weak solutions.
Monte Carlo and Machine Learning Approaches in Quantum Mechanics - IPAM at UCLA
Explore Monte Carlo and machine learning techniques in quantum mechanics with Andrea Tirelli, covering advanced computational methods for solving complex quantum systems.
Quantum Monte Carlo and Machine Learning Simulations of Dense Hydrogen
Explore advanced quantum simulations of dense hydrogen using Quantum Monte Carlo and machine learning techniques, focusing on electronic energies, proton distributions, and novel solid structures.
Estimate Transport Coefficients From Short Equilibrium Molecular-Dynamic Simulation
Discover optimal methods for estimating transport coefficients in molecular dynamics simulations, enhancing efficiency and accuracy in quantum mechanics research.
Convergent Orthogonality Preserving Approximations of the Kohn-Sham Orbitals
Explore convergent numerical approximations in electronic structure calculations, focusing on an extended gradient flow Kohn-Sham DFT model that preserves orbital orthogonality without additional operations.
Acceleration of Quantum Mechanical Systems by Exploiting Similarity - IPAM at UCLA
Explore innovative approaches to accelerate quantum mechanical simulations by leveraging solution similarities, focusing on extended Lagrangian Born-Oppenheimer dynamics and reduced basis methods for quantum-spin systems.
Electronic Structure Calculations of Chiral Matter - IPAM at UCLA
Explore electronic structure calculations for chiral materials, focusing on quasi-1D nanostructures. Learn about helical Bloch waves, Kohn-Sham DFT, and machine learning techniques for predicting electronic fields.
Basis-Set Correction Based on Density-Functional Theory - IPAM at UCLA
Rigorous framework for basis-set correction in quantum mechanics using density-functional theory, explored through a one-dimensional model with delta-potential interactions for systematic analysis.
Model Reduction Using Localized Bases and DMRG - IPAM at UCLA
Explore model reduction techniques in quantum mechanics using localized bases and DMRG, focusing on sliced basis sets for hydrogen chains and gausslet bases for fully diagonal Hamiltonians.
Beyond Density Functional Approximations by Lessons From Density Functional Theory
Exploring alternatives to density functional approximations in quantum mechanics, focusing on extrapolating model families and generalizing Kato's cusp condition for improved accuracy in electronic systems.