Finite Volume Method for Diffusion Equation - Discretization of 1D Diffusion Equation
Explore discretization of 1D steady diffusion equation and solve heat conduction problems using the Finite Volume Method.
Finite Volume Method for Diffusion Equation - Boundary Conditions for 2D Diffusion Equation
Explore boundary conditions for 2D diffusion equations, including Dirichlet, Neumann, and mixed conditions in finite volume methods.
Discretization of 3D Diffusion Equation with Mixed Boundary Conditions
Explore 3D diffusion equation discretization and mixed boundary conditions using the Finite Volume Method. Learn to calculate diffusion coefficients on cell faces.
Finite Volume Method for Diffusion Equation: Steady Diffusion in Unstructured Meshes - Part 1
Explore discretization techniques for steady diffusion equations in non-orthogonal unstructured meshes using the Finite Volume Method.
Finite Volume Method for Diffusion Equation - Tri-Diagonal Matrix Algorithm
Explore diffusion coefficients, solve linear algebraic equations, and master the TDMA algorithm for finite volume methods in diffusion equations.
A Fluid-Based Model for Single-Cell Migration
Explore a deterministic model of single-cell migration using fluid dynamics and molecular interactions. Analyze static and motile behaviors through mathematical and numerical approaches.
Microtubules as a Key Target in Oncology: Mathematical Modeling of Anti-MT Agents on Cell Migration
Explore mathematical modeling of microtubule-targeted agents in cancer cell migration. Gain insights into anti-migratory effects and potential therapeutic applications through fluid-based simulations.
Spontaneous Stochasticity in Multi-Scale Dynamics
Explore spontaneous stochasticity in multi-scale dynamics, focusing on turbulence models and the formalization of stochastic solutions using renormalization-group operator attractors.
Construction of Invariant Measures for 2D Euler and Slow Growth of Sobolev Norms
Explore the growth of Sobolev norms in 2D Euler equations, examining invariant measures and their impact on solution behavior in highly regular spaces.
The Formulation of the Navier-Stokes Equations on Riemannian Manifolds
Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.
An Introduction to Super Critical Singularities - Lecture 4: Stability of Implosion
Explore advanced concepts in non-linear PDE singularities, focusing on defocusing problems and their connection to fluid mechanics. Gain insights into key results, open problems, and proof techniques.
An Introduction to Super Critical Singularities - Lecture 3: On Self Similar Solutions for Compressible Euler
Explore self-similar solutions for compressible Euler equations and their role in singularity formation for non-linear PDEs, with connections to fluid mechanics.
An Introduction to Super Critical Singularities - Lecture 2: Front Singularities
Explore front singularities in non-linear PDEs, focusing on defocusing problems and their connection to fluid mechanics. Gain insights into key results, open problems, and proof techniques.
An Introduction to Super Critical Singularities - Lecture 1: Energy Super Critical Singularity Formation
Explore energy super critical singularity formation in non-linear PDEs, focusing on recent discoveries in defocusing problems and their connection to fluid mechanics.
Ergodic Theory of the Stochastic Burgers Equation
Explorez la théorie ergodique de l'équation de Burgers stochastique, en examinant les distributions stationnaires et les propriétés à long terme des minimiseurs d'action lagrangienne aléatoires.
Mathematics and Machines: Navigating New Frontiers
Explore the intersection of mathematics and machine learning, examining how computers transform mathematical research and their potential future impact on the field.
Hyperbolic and Mixed-Type Problems in Gas Dynamics and Geometry
Explore hyperbolic and mixed-type PDEs in gas dynamics and geometry, focusing on transonic flows and isometric embedding.
Partial Differential Equations and Convexity
Explore elliptic PDEs, convexity preservation, and surprising cases of convexity breaking in evolution equations like porous medium and Stefan problem.
Particle and Game Theoretic Methods for Multi-scale and High Dimensional Problems
Explore Lagrangian and game theoretic approaches for solving complex PDEs, including front speed computation, high-dimensional entropy production, and turbulent combustion analysis.
MAgNet: Mesh Agnostic Neural PDE Solver
Explore innovative neural PDE solver for accurate, scalable climate predictions. Learn about mesh-agnostic architecture combining Implicit Neural Representations and Graph Neural Networks.
Blender Tutorial - Realistic Fluid Simulation
Discover optimal settings for creating realistic water simulations in Blender. Learn setup, fluid dynamics, baking, and post-processing techniques for stunning visual results.