37,244 research outputs found

    Constrained Adiabatic Trajectory Method (CATM): a global integrator for explicitly time-dependent Hamiltonians

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    The Constrained Adiabatic Trajectory Method (CATM) is reexamined as an integrator for the Schr\"odinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet and the (t,t') theories is presented in detail. Two points are then more particularly analysed and illustrated by a numerical calculation describing the H2+H_2^+ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system.Comment: 15 pages, 14 figure

    Fast iterative solution of reaction-diffusion control problems arising from chemical processes

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    PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs

    VirtFogSim: A parallel toolbox for dynamic energy-delay performance testing and optimization of 5G Mobile-Fog-Cloud virtualized platforms

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    It is expected that the pervasive deployment of multi-tier 5G-supported Mobile-Fog-Cloudtechnological computing platforms will constitute an effective means to support the real-time execution of future Internet applications by resource- and energy-limited mobile devices. Increasing interest in this emerging networking-computing technology demands the optimization and performance evaluation of several parts of the underlying infrastructures. However, field trials are challenging due to their operational costs, and in every case, the obtained results could be difficult to repeat and customize. These emergingMobile-Fog-Cloud ecosystems still lack, indeed, customizable software tools for the performance simulation of their computing-networking building blocks. Motivated by these considerations, in this contribution, we present VirtFogSim. It is aMATLAB-supported software toolbox that allows the dynamic joint optimization and tracking of the energy and delay performance of Mobile-Fog-Cloud systems for the execution of applications described by general Directed Application Graphs (DAGs). In a nutshell, the main peculiar features of the proposed VirtFogSim toolbox are that: (i) it allows the joint dynamic energy-aware optimization of the placement of the application tasks and the allocation of the needed computing-networking resources under hard constraints on acceptable overall execution times, (ii) it allows the repeatable and customizable simulation of the resulting energy-delay performance of the overall system; (iii) it allows the dynamic tracking of the performed resource allocation under time-varying operational environments, as those typically featuring mobile applications; (iv) it is equipped with a user-friendly Graphic User Interface (GUI) that supports a number of graphic formats for data rendering, and (v) itsMATLAB code is optimized for running atop multi-core parallel execution platforms. To check both the actual optimization and scalability capabilities of the VirtFogSim toolbox, a number of experimental setups featuring different use cases and operational environments are simulated, and their performances are compared

    A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

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    A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes.Comment: submitted for journal publicatio
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