Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity ana...

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, wh...

Adjoint triples are an interesting generalization of t-norms and their residuated implications, since they increase the flexibility in the framework where they are used. Following the same motivation of adjoint triples, in order to reduce the mathematical requirements for the computation, extended-order algebras are studied. Extended-order algebras are implicative algebras that generalize the i...

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...

In this study, we investigate the method for adjoint-based optimal control of linear and non-linear equations. In particular, we are interested in the formulation of the unsteady adjoint method based on the high-order spectral difference method. For the linear equation, we consider the simple 1D advection equation. For the non-linear equation, we consider the 1D viscous Burger’s equation. In bo...

We propose to induce QCD by fermions in the adjoint representation of the gauge group SU(Nc) on the lattice. We consider various types of lattice fermions: chiral, Kogut–Susskind and Wilson ones. Using the mean field method we show that a first order large-N phase transition occurs with decreasing fermion mass. We conclude, therefore, that adjoint fermions induce QCD. We draw the same conclusio...

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator Q for the Lie algebra cohomology induced by BRST generator Q. We also po...

SUMMARY The objective of the paper is to construct adjoint consistent formulations of the Helmholtz 'slip' model for the simulation of electroosmotic flows. The motivation is to apply adjoint-based methods for the development of adaptive finite element tools and parameter sensitivity analyses to microfluidic problems. Issues in the current formulation of the 'slip' model lie in the fact that it...

We present a method for estimating spatial and temporal numerical errors in scalar outputs of unsteady fluid dynamics simulations using a continuous-in-time adjoint solution and general time-integration methods. A continuous formulation decouples the primal and adjoint temporal discretizations and allows the use of standard time-integration schemes for the adjoint. For non-variational methods, ...