1,721,174 research outputs found
Gaussian process emulation for rapid in-plane mechanical homogenization of periodic masonry
No full textSelf-similarity and probability density function of the transient response of fractional compound motion
No full textIn recent years, there has been an increasing use of fractional differential equations due to their ability to effectively represent various engineering phenomena, including viscoelasticity, heat transport, non-local continuum, and others. These equations take into account certain effects that cannot be accurately predicted using classical differential equations. This paper provides a comprehensive analysis of the fractional compound motion, specifically focusing on the response of a one-term fractional differential equation that is excited by a Poissonian white noise process. The present study introduces a straightforward equation for the probability density function of fractional compound motion. The validity of this equation is subsequently confirmed by the execution of various numerical simulations. Furthermore, a comprehensive analysis is conducted on the self-similarity of fractional compound motion, demonstrating that the phenomenon can be regarded as self-similar in weak sense. This characteristic can be effectively employed to mitigate the loss of Markovianity in fractional differential equations
Maximum entropy principle handled by using complex fractional moments
No full textA novel Maximum Entropy Principle method constrained by Complex Fractional Moments is proposed in this paper, which can be applied for reconstructing of approximate probability distribution equations with few complex fractional moments. By introducing complex fractional moments with different imaginary parameters into the entropy functional, an extended entropy functional with unknown Lagrange multipliers is constructed, which is utilized for deriving the approximate probability density function. The new method is extended to obtaining probability density function in stochastic dynamic systems based on the complex fractional moment equations which is derived from Fokker–Planck-Kolmogorov equation. Numerical simulations verified the effectiveness of the approach
Markovian approximation of linear systems with fractional viscoelastic term
No full textIt is well known that the response of a linear system enforced by a Gaussian white noise is Markovian. The order of Markovianity is n-1 being n the maximum order of the derivative of the equation ruling the evolution of the system. However when a fractional operator appears, the order of Markovianity of the system becomes infinite. Then the main aim developed in the proposed paper, consists of rewriting the system with fractional term of order r with an "equivalent" one, in which the fractional operator is substituted by two classical differential terms with integer order of derivative int(r) and int(r + 1) (for a real r). In this way the fractional differential equation reverts into a classical differential equation and then the Markovianity of the system is restored. The proposed technique for evaluating the equivalent coefficient of two terms involving the derivatives of order int(r) and int(r + 1) are evaluated by means of the classical stochastic linearisation technique, that is by performing the minimisation of the error made in passing for the original system with fractional order derivative into equivalent linear system with classical derivative terms. Since the original system is linear (fractional operators are linear) the response to a Gaussian input is Gaussian too as for the response of the equivalent one
A discrete mechanical model of fractional hereditary materials
Full text linkFractional hereditary materials are characterized for the presence, in the stress-strain relations, of fractional-order operators with order beta a[0,1]. In Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) exact mechanical models of such materials have been extensively discussed obtaining two intervals for beta: (i) Elasto-Viscous (EV) materials for 0a parts per thousand currency sign beta a parts per thousand currency sign1/2; (ii) Visco-Elastic (VE) materials for 1/2a parts per thousand currency sign beta a parts per thousand currency sign1. These two ranges correspond to different continuous mechanical models.
In this paper a discretization scheme based upon the continuous models proposed in Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) useful to obtain a mechanical description of fractional derivative is presented. It is shown that the discretized models are ruled by a set of coupled first order differential equations involving symmetric and positive definite matrices. Modal analysis shows that fractional order operators have a mechanical counterpart that is ruled by a set of Kelvin-Voigt units and each of them provides a proper contribution to the overall response. The robustness of the proposed discretization scheme is assessed in the paper for different classes of external loads and for different values of beta a[0, 1]
Piecewise power law approximation of the interlayer relaxation curve for the long term viscoelastic fractional modeling of laminated glass
No full textLaminated glass is composed of glass layers coupled by thin polymeric films which, being highly viscoelastic, influence the bending response over time. Here, an approximation of the polymer relaxation curve is proposed by means of continuously-connected power law branches. In the bi-logarithmic stress-time plane, this corresponds to a piecewise trilinear path, which well reproduces the experimental tests on most commercial polymers. A power law is naturally suited to be modeled via fractional calculus, as the Boltzmann convolution integral coincides with the definition of fractional derivative. However, the piecewise characterization through multiple power laws requires to properly extend the Grunwald-Letnikov integration scheme for fractional differential equations. For the paradigmatic case of a simply supported three-layer laminated beam, numerical results show an excellent correspondence with experiments under long duration loads. The comparison with the classic Prony series approach highlights, on the one hand, how calibration of material parameters is simplified; on the other hand, how the fractional approach is computationally more efficient and stable, even when the integration time step is wide enough to follow long term phenomena
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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