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The Second Law as a constraint and admitting the approximate nature of constitutive assumptions
Amit Acharya
A scheme for treating the Second Law of thermodynamics as a constraint and accounting for the approximate nature of constitutive assumptions in continuum thermomechanics is discuss…
Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants
N. Sukumar, Amit Acharya
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do…
Variational Dual Solutions of Chern-Simons Theory
Amit Acharya, Janusz Ginster, Ambar N. Sengupta
A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for…
Ideal Magnetohydrodynamics and Field Dislocation Mechanics
Amit Acharya
The fully nonlinear (geometric and material) system of Field Dislocation Mechanics is reviewed to establish an exact analogy with the equations of ideal magnetohydrodynamics (ideal…
A Hidden Convexity of Nonlinear Elasticity
Siddharth Singh, Janusz Ginster, Amit Acharya
A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notion…