Applied Physical Mathematics

• Theory and methods that are order preserving (monotonicity), invertible, symmetric and optimal (principle of stationary action).
• Reduction of many-body problems to one-body problems that respects the dynamic or statistical order not solely reliant on mean-field assumptions.
• Noise and statistical modeling, in particular non-Gaussian distributions. Higher order and non-linear treatment of noise processes using mathematical and physics-based approaches for noise reduction or disambiguation in complex environments.
• Generalized mathematical inversion methods for large complex problems or systems.
• Mathematics that govern fundamental physical dynamics that allow for invertible, nonlinear transformations, and full vector solution of constituent equations without the use of linear encoding methods.
• New theory based in calculus of variations.

• Models and methods that make use of Langrangian frameworks to preserve and simplify geometrical order in transport problems.
• Hydrodynamic analogs, gravito-electromagnetism and methods to unify different theories or provide new insight and understanding through local realist approaches to physical theories.
• Methods, theory and experiments that provide the ability to understand how a material, fluid, particle(s) or system acts on or with its environment through transport of mass, heat, energy, and momentum.
• Physical theory, methods and experiments that use conservation laws and symmetries to gain new insight or break previous assumptions in hydrodynamics, materials, quantum/classical mechanics, electronic and chemical processes.
• Active matter, non-equilibrium systems and collective system dynamics.

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