156 research outputs found
Domain wall roughening in dipolar films in the presence of disorder
We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domain
wall in a thin film with in-plane magnetization, where we consider the
contribution of the long-range dipolar interaction beyond the quadratic
approximation. We show that such a Hamiltonian is analogous to the Hamiltonian
of a one-dimensional polaron in an external random potential. We use a replica
variational method to compute the roughening exponent of the domain wall for
the case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and
references 1,2 and 12 were added to conform with the referee's repor
Normal forms and internal regularization of nonlinear differential-algebraic control systems
In this article, we propose two normal forms for nonlinear differential-algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, that is, when there exists a state feedback transforming the DACS into a differential-algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs
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