We present a theory of dynamical control by modulation for optimal decoherence reduction. The theory is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.

We study the contact between nonlinearly elastic bodies by variational methods. After the formulation of the mechanical problem we provide existence results based on polyconvexity and on quasiconvexity. Then we derive the Euler-Lagrange equation as a necessary condition for minimizers. Here Clarke’s generalized gradients are the essential tool to treat the nonsmooth obstacle condition.

where g : R 7→ R strictly monotone increasing and differentiable, Ω open set with compact closure in R , and D convex closed subset of R. Under the assumption that ∇ū ∈ D a.e. in Ω, there is a unique solution u to (1.1) and we can actually give an explicit representation of u is terms of a Lax-type formula. The solution is clearly Lipschitz continuous because ∇u ∈ ∂D a.e. in Ω. The Euler-Lagran...

This papers studies discrete nonholonomic mechanical systems whose configuration space is a Lie group G Assuming that the discrete Lagrangian and constraints are left-invariant, the discrete Euler–Lagrange equations are reduced to the discrete Euler–Poincaré–Suslov equations. The dynamics associated with the discrete Euler–Poincaré–Suslov equations is shown to evolve on a subvariety of the Lie ...

Method: The presented EL method uses the open access software OpenFOAM to solve bubble dynamics with bubble interactions computed via Monte Carlo methods. The estimated bubble size distribution and the predicted hold-up are compared with experimental data and other simulative EE work with a reasonable consensus for both. Benchmarks with state of the art EE simulations shows that the EL approach...

Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivatives over faces of the polytope or its dilations. There are two kinds of Euler Maclaurin formulas: exact formulas, which apply to exponential or polynomial functions, and formulas with remainder, which apply to arbitrary...

The equilibrium position of an Euler-Bernoulli beam is investigated. Using the discrete Euler-Lagrange and Lagrange-d’Alembert principles, the behavior of the beam is simulated using variational integrators and, in particular, AVIs (Asynchronous Variational Integrators). Special emphasis is placed on the discrete mechanics and geometric structure underlying stress resultant beam models.

Non-rigid registration of landmarked datasets is an important problem that finds many applications in medical image analysis. In this paper, we present a method for interpolating a sequence of landmarks. The sequence of landmarks may be a model of growth, where anatomical object boundaries are parametrized by landmarks and the growth processes generate a landmarked sequence in time. In a variat...

We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and verifying that it leads to the correct solution to the Euler-Lagrange equations. email: [email protected] email: [email protected]

We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler–Lagrange equation. AMS (MOS) Subject Classification. 39A0, 49K20.