Search results for "Equations"
showing 10 items of 955 documents
Une quête d'exactitude : machines, algèbre et géométrie pour la construction traditionnelle des équations différentielles
2015
In La Géométrie, Descartes proposed a “balance” between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In particular, Cartesian tools were polynomial algebra (analysis) and a class of diagrammatic constructions (synthesis). This setting provided a classification of curves, according to which only the algebraic ones were considered “purely geometrical.” This limit was overcome with a general method by Newton and Leibniz introducing the infinity in the analytical part, whereas the synthetic perspective gradually lost importance with respect to the analytical one—geometry became a mean of visualization, no longer of construction. Descartes’s…
Experimental characterization and comparison of TLIM performances with different primary winding connections
2017
Abstract This paper presents an experimental characterization and comparison of the performances achieved by a Tubular Linear Induction Motor (TLIM) prototype with different typologies of primary winding connections. More in detail, three different configurations have been considered, analyzed and discussed: full-pitch star, 5/6 shortened pitch star and 5/6 shortened pitch double star. For this purpose, an experimental test bench at the Sustainable Development and Energy Saving Laboratory (SDESLab), University of Palermo, Italy, has been set-up. The obtained results have allowed the identification of the best winding configuration for different applications intended for the motor. Moreover,…
Numerical stochastic perturbation theory in the Schrödinger functional
2013
The Schr\"odinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Dirac equation as a quantum walk over the honeycomb and triangular lattices
2018
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in $(2+1)$--dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.
Nonlinear quantum Langevin equations for bosonic modes in solid-state systems
2017
Based on the experimental evidence that impurities contribute to the dissipation properties of solid-state open quantum systems, we provide here a description in terms of nonlinear quantum Langevin equations of the role played by two-level systems in the dynamics of a bosonic degree of freedom. Our starting point is represented by the description of the system/environment coupling in terms of coupling to two separate reservoirs, modelling the interaction with external bosonic modes and two level systems, respectively. Furthermore, we show how this model represents a specific example of a class of open quantum systems that can be described by nonlinear quantum Langevin equations. Our analysi…
A fully adaptive wavelet algorithm for parabolic partial differential equations
2001
We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.
Theoretical investigations of different excitation modes for Penning trap mass spectrometry
2013
Abstract In Penning trap mass spectrometry the motion of trapped ions is manipulated by external radio-frequency fields. This paper describes a general theoretical framework to classify the various types of excitation of the ion's motional modes, to identify the resonance frequencies, and to find the effective interaction Hamiltonians which are valid in the vicinity of the resonances. Instead of Cartesian or cylindrical coordinates and momenta our theoretical approach uses the complex oscillator amplitudes of the cyclotron, magnetron, and axial oscillators as its basic dynamical variables. Equations of motion are set up, which can be simplified in the vicinity of resonances by the resonatin…
Fluid–structure interaction of downwind sails: a new computational method
2018
The spreading of high computational resources at very low costs led, over the years, to develop new numerical approaches to simulate the fluid surrounding a sail and to investigate the fluidâstructure interaction. Most methods have concentrated on upwind sails, due to the difficulty of implementing downwind sailing configurations that present, usually, the problem of massive flow separation and large displacements of the sail under wind load. For these reasons, the problem of simulating the fluidâstructure interaction (FSI) on downwind sails is still subject of intensive investigation. In this paper, a new weak coupled procedure between a RANS solver and a FEM one has been implemented t…
Simulation of mid-IR amplification in Er3+-doped chalcogenide microstructured optical fiber
2009
International audience; This paper deals with the design of an erbium doped microstructured optical fiber (MOF) amplifier operating in the mid-infrared (mid-IR) wavelength range, more precisely around 4.5 µm wavelength. A homemade numerical code which solves the rate equations and the power propagation equations has been ad hoc developed to theoretically investigate the feasibility of mid-IR MOF amplifier. On the basis of the measured energy level transition parameters of a Er3+-doped Ga5Ge20Sb10S65 chalcogenide glass, the amplifier feasibility is demonstrated exhibiting high gain and low noise figure.
Control of hysteretic instability in rotating machinery by elastic suspension systems subject to dry and viscous friction
2010
Abstract Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-…