Alapfogalmak
Granular kinetic equations exhibit complex behavior with potential blow-up phenomena.
Kivonat
The content delves into the behavior of granular kinetic equations, focusing on potential blow-up scenarios. It discusses numerical investigations and heuristic arguments to understand singularity formation in velocity direction. The article explores finite-time blow-up infinite mass solutions and their implications. Various initial conditions are analyzed to validate the numerical solver's capability in predicting blow-up times accurately.
Abstract:
- Simplified kinetic description of rapid granular media.
- Nonlocal Vlasov-type equation with convolution integral operator.
- Singular behavior analysis in nonlinear continuity equations.
- Study on singularity enhancement or mitigation due to shear in phase space.
Introduction:
- Granular flows omnipresent in nature.
- Distinct features of granular particles due to inelastic collisions.
- Derivation of kinetic equations from statistical mechanics.
- Successes and challenges in computing transport coefficients for hydrodynamic descriptions.
Data Extraction:
- "We present a preliminary study through a meticulous numerical investigation and heuristic arguments."
- "We have numerically developed a structure-preserving method with adaptive mesh refinement."
Quotations:
- "Will the singularity formed in v-direction be enhanced or mitigated by the shear?"
- "Despite that numerical analysis has its own theory and tools, it is undoubtedly that PDE analysis is the stepping stone for the development of the numerical analysis of PDEs."
Statisztikák
"We present a preliminary study through a meticulous numerical investigation and heuristic arguments."
"We have numerically developed a structure-preserving method with adaptive mesh refinement."
Idézetek
"Will the singularity formed in v-direction be enhanced or mitigated by the shear?"
"Despite that numerical analysis has its own theory and tools, it is undoubtedly that PDE analysis is the stepping stone for the development of the numerical analysis of PDEs."