Lattice field theory with the sign problem and the maximum entropy method.
Mathematical and Computational Models in Tumor Immunology
The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...
Phase field model for mode III crack growth in two dimensional elasticity
A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.
Vorticity dynamics and turbulence models for large-Eddy simulations
We consider in this paper the problem of finding appropriate models for Large Eddy Simulations of turbulent incompressible flows from a mathematical point of view. The Smagorinsky model is analyzed and the vorticity formulation of the Navier–Stokes equations is used to explore more efficient subgrid-scale models as minimal regularizations of these equations. Two classes of variants of the Smagorinsky model emerge from this approach: a model based on anisotropic turbulent viscosity and a selective...
Vorticity dynamics and turbulence models for Large-Eddy Simulations
We consider in this paper the problem of finding appropriate models for Large Eddy Simulations of turbulent incompressible flows from a mathematical point of view. The Smagorinsky model is analyzed and the vorticity formulation of the Navier–Stokes equations is used to explore more efficient subgrid-scale models as minimal regularizations of these equations. Two classes of variants of the Smagorinsky model emerge from this approach: a model based on anisotropic turbulent viscosity and...