1,721,210 research outputs found
Naples et Pompeii nell'Encyclopédie
No full textThe entries “Naples”, “Herculanum”, “Pompeii” in the Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers
(1751-1772) are of different lengths and depths. These are entries that on the one hand report some of the effects of the archeolo gical
discoveries which amaze Europe during those years, while on the other they impose themselves as testimonies of some explanatory
techniques (and of some imperfections) which are typical of the ripest “encyclopedism”. Their author De Jaucourt carries out a d edicated
and significant work of construction and divulgation and he brings to the attention of the subscribers of the Encyclopédie the treasures
at the core of the Vesuvius land
Implementation of the PaperRank and AuthorRank indices in the Scopus database
Full text linkWe implement the PaperRank and AuthorRank indices introduced in [Amodio & Brugnano, 2014] in the Scopus database, in order to highlight quantitative and qualitative information that the bare number of citations and/or the h-index of an author are unable to provide. In addition to this, the new indices can be cheaply updated in Scopus, since this has a cost comparable to that of updating the number of citations. Some examples are reported to provide insight in their potentialities, as well as possible extensions
“High Order Generalized Upwind Schemes and the Numerical Solution of Singular Perturbation Problems”
No full textAddendum: Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics (2021 Eur. J. Phys. 42 065405)
No full textWe describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also derive and discuss the analytical expressions of the external forces acting on the punctiform charge and associated with the boundaries of the one-dimensional box in the presence of the electric field
Arbitrarily high-order energy-conserving methods for Poisson problems
Full text linkIn this paper, we are concerned with energy-conserving methods for Poisson problems, which are effectively solved by defining a suitable generalization of HBVMs, a class of energy-conserving methods for Hamiltonian problems. The actual implementation of the methods is fully discussed, with a particular emphasis on the conservation of Casimirs. Some numerical tests are reported, in order to assess the theoretical findings
Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems
No full textRecently, the numerical solution of stiffly/highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods in time. While a theoretical analysis of this spectral approach has been only partially addressed, there is enough numerical evidence that it turns out to be very effective even when applied to a wider range of problems. Here, we fill this gap by providing a thorough convergence analysis of the methods and confirm the theoretical results with the aid of a few numerical tests
A didactically motivated reexamination of a particle’s quantum mechanics with square-well potentials
No full textWe address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of the standard a priori omission of the potential’s vertical segments in the analysis of the eigenvalue problem is licit. The detour we follow to find out the answer considers a trapezoidal potential, includes the solution, analytical and numerical, of the corresponding eigenvalue problem and then analyzes the behavior of that solution in the limit when the slope of the trapezoidal potential’s ramps becomes vertical. The second question, obviously linked to the first one, pertains whether or not eigenfunction’s and its first derivative’s continuity at the potential’s jump points is justified as a priori assumption to kick-off the solution process, as it is standardly accepted in textbook approaches to the potential’s eigenvalue problem. We show that, by following the indicated detour, the irrelevance of the potential’s vertical segments and the continuity of eigenfunctions and their first derivatives at the potential’s jump points turn out to be proven results instead of initial assumptions
(Spectral) Chebyshev collocation methods for solving differential equations
No full textRecently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of the vector field along the Legendre orthonormal basis. Interestingly, this approach can be extended to cope with other orthonormal bases and, in particular, we here consider the case of the Chebyshev polynomial basis. The corresponding Runge-Kutta methods were previously obtained by Costabile and Napoli (Numer. Algo., 27, 119–130 2021). In this paper, the use of a different framework allows us to carry out a novel analysis of the methods also when they are used as spectral formulae in time, along with some generalizations of the methods
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