An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation Adjoint method (ISP-Adjoint, [33]). Its performance in a full 4-D VAR setup with a limited area is assessed by comparing with the adjoint model derived by the automatic differentiation approach, where it is used for optimising the initial conditions. It is shown that ISP-Adj...

We study the phase diagram of 5-dimensional $SU(2)$ Yang-Mills theory on lattice. consider two extensions fundamental plaquette Wilson action in search for continuous transition suggested by $4+\epsilon$ expansion. The correspond to new terms action: i) a unit size adjoint representation or ii) two-unit sided square representation. use Monte Carlo sample first and second derivative entropy near...

We study the eigenspace decomposition of a basic classical Lie superalgebra under adjoint action toral subalgebra, thus extending results Kostant. In recognition Kostant's contribution we refer to eigenfunctions appearing in as Kostant roots. then prove that root systems inherit main properties systems. Our approach is combinatorial nature and utilizes certain graphs naturally associated with p...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

A detailed study is made of four dimensional SU(2) gauge theory with static adjoint “quarks” in the context of string breaking. A tadpole-improved action is used to do simulations on lattices with coarse spatial spacings as, allowing the static potential to be probed at large separations at a dramatically reduced computational cost. Highly anisotropic lattices are used, with fine temporal spaci...

The functional Schrödinger equation (FSE) for QCD gives a unique perspective on generation of a gluon mass m, as required for center vortices. The FSE, which yields a special d=3 gauge action, combined with lattice calculations strictly in d=3 give a value for the dimensionless ratio of d=3 coupling to mass g2 3/m. From this we infer a reasonably accurate value for the d=4 running coupling g2(0...

An action ∗ : V × A−→ A of a monoidal category V on a category A corresponds to a strong monoidal functor F : V−→ [A,A] into the monoidal category of endofunctors of A. In many practical cases, the ordinary functor f : V−→ [A,A] underlying the monoidal F has a right adjoint g; and when this is so, F itself has a right adjoint G as a monoidal functor—so that, passing to the categories of monoids...

Pauli’s well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamiltonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate t...

Generalized adjoint with modified discretization and generalized coarse-grain adjoint are derived for a vector system of equations that contains parameterized on/off switches. With vector examples, it is shown that the conventional adjoint minimization may have a convergence problem in multidimensional space. The problem can be solved by the generalized adjoint with modified discretization or b...

The behavior of analytic and numerical adjoint solutions is examined for the quasi-1D Euler equations. For shocked ow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock and that an internal adjoint boundary condition is required at the shock. A Green's function approach is used to derive the analytic adjoint solutions corresp...