Optimal control (motion planning) of the free interface in classical two-phase Stefan problems is considered. The evolution of the free interface is modeled by a level set function. The first-order optimality system is derived on a formal basis. It provides gradient information based on the adjoint temperature and adjoint level set function. Suitable discretization schemes for the forward and a...

In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we c...

Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite differe...

We discuss the spectrum of hadrons with a heavy colour-adjoint particle-motivated by the gluino of supersymmetry. Using the lattice approach, we explore in detail the gluonic bound states-the 'glueballino' or 'gluelump'. We also make a first determination of the spectrum of the 'adjoint mesons'-which have a light quark and antiquark bound to the heavy adjoint particle. A comparison of the spect...

A new characterization of the positive self-adjoint extensions of symmetric operators, T0, is presented, which is based on the Friedrichs extension of T0, a direct sum decomposition of domain of the adjoint T ∗ 0 and the boundary mapping of T ∗ 0 . In applying this result to ordinary differential equations, we characterize all positive self-adjoint extensions of symmetric regular differential o...

Traditionally, solving the adjoint equation for unsteady problems involves solving a large, structured linear system. This paper presents a variation on this technique and uses a Monte Carlo linear solver. The Monte Carlo solver yields a forward-time algorithm for solving unsteady adjoint equations. When applied to computing the adjoint associated with Burgers’ equation, the Monte Carlo approac...

This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl asymptotics for the eigenvalues of non-self-adjoint operators with small random perturbations. In the introduction we also review the notion of pseudo-spectrum ...

Wilson loops in the adjoint representation are evaluated on cooled lattices in SU(2) lattice gauge theory. It is found that the string tension of an adjoint Wilson loop vanishes, if the loop is evaluated in a sub-ensemble of configurations in which no center vortex links the loop. This result supports our recent proposal that the adjoint string tension, in the Casimir-scaling regime, can be att...

Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear Schrödinger equations. The linear eigenvalue problem for a non-self-adjoint operator is studied with two self-adjoint matrix Schrödinger operators. Sharp bounds on the number and type of unstable eigenvalues in the spectral problem are found from the inertia law for quadrati...

This is an addendum to [1]. In this report, we initially present the derivation of the equilibrium strategies from Isaac’s conditions. Then we derive the final values of the adjoint variables on the UP. Once we have the final values of the adjoint variables, we solve the adjoint equation backward in time to construct a value function in the state-space. From those value functions, we derive the...