Search results for "Bounded function"
showing 10 items of 508 documents
Impulse-based hybrid motion control
2017
The impulse-based discrete feedback control has been proposed in previous work for the second-order motion systems with damping uncertainties. The sate-dependent discrete impulse action takes place at zero crossing of one of both states, either relative position or velocity. In this paper, the proposed control method is extended to a general hybrid motion control form. We are using the paradigm of hybrid system modeling while explicitly specifying the state trajectories each time the continuous system state hits the guards that triggers impulsive control actions. The conditions for a stable convergence to zero equilibrium are derived in relation to the control parameters, while requiring on…
Time-optimal control of spin-1/2 particles with dissipative and generalized radiation-damping effects
2013
We analyze the time-optimal control of spin-1/2 particles with bounded field amplitudes in the presence of dissipative and radiation damping effects. Using tools of geometric optimal control theory, we determine different optimal syntheses for specific values of the system parameters. We show the nontrivial role of the effective radiation damping effect on the optimal control law.
Existence of global weak solutions to the kinetic Peterlin model
2018
Abstract We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an incompressible viscous Newtonian fluid confined to a bounded domain in two or three space dimensions. The unsteady motion of the solvent is described by the incompressible Navier–Stokes equations with the elastic extra stress tensor appearing as a forcing term in the momentum equation. The elastic stress tensor is defined by Kramer’s expression through the probability density function that satisfies the corresponding Fokker–Planck equation. In thi…
Singular Extremals for the Time-Optimal Control of Dissipative Spin 1/2 Particles
2010
We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.
Dynamics of Confined Crowd Modelled Using Fermionic Operators
2014
An operatorial method based on fermionic operators is used to describe the dynamics of a crowd made of different kind of populations mutually interacting and moving in a two–dimensional bounded closed region. The densities of the populations are recovered through the Heisenberg equation and the diffusion process is driven by the Hamiltonian operator defined by requiring that the populations move along optimal paths. We apply the model obtained in a concrete situation and we discuss the effect of the interaction between the populations during their motion.
The band structure of double excited states for a linear chain
2000
Abstract The energy band structure in the case of double excited states of finite spin systems (s= 1 2 ) has been investigated. A geometrical construction based on the Bethe Ansatz method for determining eigenstates has been proposed. The formula for energy spectrum in the center and at the border of Brillouin zone has been obtained. Classification of energy bands has been elaborated on and approximated dispersion law for bounded states given. Some problems with application of the Bethe Ansatz in the case of finite system has been pointed out.
Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
2017
Let \begin{document}$A∈{\rm{Sym}}(n× n)$\end{document} be an elliptic 2-tensor. Consider the anisotropic fractional Schrodinger operator \begin{document}$\mathscr{L}_A^s+q$\end{document} , where \begin{document}$\mathscr{L}_A^s: = (-\nabla·(A(x)\nabla))^s$\end{document} , \begin{document}$s∈ (0, 1)$\end{document} and \begin{document}$q∈ L^∞$\end{document} . We are concerned with the simultaneous recovery of \begin{document}$q$\end{document} and possibly embedded soft or hard obstacles inside \begin{document}$q$\end{document} by the exterior Dirichlet-to-Neumann (DtN) map outside a bounded domain \begin{document}$Ω$\end{document} associated with \begin{document}$\mathscr{L}_A^s+q$\end{docume…
Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions
2006
We study the questions of existence and uniqueness of weak and entropy solutions for equations of type -div a(x, Du)+γ(u) ∋ φ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x, Du)·η+β(u) ∋ ψ. The nonlinear elliptic operator div a(x, Du) is modeled on the p-Laplacian operator Δp(u) = div (|Du|p−2Du), with p > 1, γ and β are maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) and 0 ∈ β(0), and the data φ ∈ L1 (Ω) and ψ ∈ L1 (∂Ω). We also study existence and uniqueness of weak solutions for a general degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Particular instances of this problem appear in various phenomena with c…
Notice of Removal: Stochastic generation of the phononic band structure of lossy and infinite crystals
2017
The concept of the band structure is central to the field of phononic crystals. Indeed, capturing the dispersion of Bloch waves — the eigenmodes of propagation in periodic media — gives invaluable information on allowed propagation modes, their phase and group velocities, local resonances, and band gaps. Band structures are usually obtained by solving an eigenvalue problem defined on a closed and bounded domain, which results in a discrete spectrum. There are at least two cases, however, that cannot be reduced to a simple eigenvalue problem: first, when materials showing dispersive loss are present and second, when the unit-cell extends beyond any bound, as in the case of phononic crystal o…
Neutrinos confronting large extra dimensions
2001
We study neutrino physics in a model with one large extra dimension. We assume the existence of two four-dimensional branes in the five-dimensional space-time, one for the ordinary particles and the other one for mirror particles, and we investigate neutrino masses and mixings in this scheme. Comparison of experimental neutrino data with the predictions of the model leads to various restrictions on the parameters of the model. For instance, the size of the extra dimension, R, turns out to be bounded from below. Cosmological considerations seem to favor a large R. The usual mixing schemes proposed as solutions to the solar and atmospheric neutrino anomalies are compatible with our model.