1,721,047 research outputs found
Multi-degenerate hill-top bifurcation of Fermi–Pasta–Ulam softening chains: Exact and asymptotic solutions
No full textA one-dimensional nonlinear elastic chain, known as Fermi–Pasta–Ulam system, is analyzed in the static field. The chain is made of elements admitting a quartic potential, with softening nonlinear behavior. When the chain is subject to pure tension, it exhibits a multi-degenerate hill-top bifurcation, from which several softening branches bifurcate. On each path, the springs either behave softening or hardening, in all the possible combinations, making the response non-unique. Both exact and asymptotic solutions are pursued, and the multitude of the bifurcated paths is illustrated by bifurcation diagrams. A proof of their instability is given. The role of the imperfections is commented, either in modifying the equilibrium paths and in unfolding the degenerate bifurcation
Static bifurcations of short FPU softening chains with second-order interaction: The non-degenerate case
Full text linkFermi–Pasta–Ulam chains, made of n=2,3,4 masses, taut by an end force, are considered in the static field. Each mass has a second-order interaction with the surrounding masses. Springs are of cubic type, with softening behavior. The equilibrium equations are derived by the total potential energy theorem. The fundamental nonlinear path of each chain, exhibiting a limit point, is evaluated. Then, by controlling the loading process by a displacement, instead of the force, a bifurcation analysis is carried out, to investigate both the ascending and descending branches of the fundamental path. The analysis allows evaluating the exact bifurcation points along this path, which manifest in number of n−1. The study also highlights the existence of a degenerate case in which all the bifurcation points coalesce at the limit point, an occurrence which is excluded here by assuming that all the bifurcation points are well-separated. The n−1 primary bifurcated paths are parametrically described in asymptotic form. Then, a post-bifurcation analysis is carried out along each of them, aimed at discovering further bifurcation points. Stability of all the branches found (first bifurcated and secondary bifurcated branches) is characterized from application of Lagrange–Dirichlet theorem. We show, for the present discrete nonlinear elastic systems, that for some parameters of interest, the first bifurcated branch may be stable, even if it loses stability in a secondary bifurcation scenario. The complex bifurcation scenario is depicted by 3D and 2D bifurcation diagrams, and asymptotic results validated by numerical analyses
Exact bifurcation analysis of the static response of a Fermi–Pasta–Ulam softening chain with short and long-range interactions
Full text linkThis paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with p=2 nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this n-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in (n−1) unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (Int J Non-Linear Mech 156(104509): 1-11, 2023) in the case p=1 interaction. We also numerically highlight the possibility for such a generalized FPU system to possess possible imperfection sensitivity. Numerical results support the fact that the structural boundary of the hill-top bifurcation coincides with the transition between imperfection sensitive to imperfection insensitive systems
Discrete and continuous models of linear elasticity: history and connections
Full text linkThis paper tracks the development of lattice models that aim to describe linear elasticity of solids and the field equations of which converge asymptotically toward those of isotropic continua, thus showing the connection between discrete and continuum. In 1759, Lagrange used lattice strings/rod dynamics to show the link between the mixed differential-difference equation of a one-dimensional (1D) lattice and the partial differential equation of the associated continuum. A consistent three-dimensional (3D) generalization of this model was given much later: Poincaré and Voigt reconciled the molecular and the continuum approaches at the end of the nineteenth century, but only in 1912 Born and von Kármán presented the mixed differential- difference equations of discrete isotropic elasticity. Their model is a 3D generalization of Lagrange’s 1D lattice and considers longitudinal, diagonal and shear elastic springs among particles, so the associated continuum is characterized by three elastic constants. Born and von Kármán proved that the lattice equations converge to Navier’s partial differential ones asymptotically, thus being a formulation of continuous elasticity in terms of spatial finite differences, as for Lagrange’s 1D lattice. Neglecting shear springs in Born–Kármán’s lattice equals to Navier’s assumption of pure central forces among molecules: in the limit, the lattice behaves as a one-parameter isotropic solid (“rari-constant” theory: equal Lamé parameters, or, equivalently, Poisson’s ratio υ = 1/4). Hrennikoff and McHenry revisited the lattice approach with pure central interactions using a plane truss; the equivalent Born–Kármán’s lattice in plane stress in the limit tends to a continuum with Poisson’s ratio υ = 1/3. Contrary to McHenry–Hrennikoff’s truss, Born–Kármán’s lattice leads to a “free” Poisson’s ratio bounded by its “limit’ bound (υ = 1/4 for plane strain or 3D elasticity; υ = 1/3 for plane stress elasticity). Unfortunately, Born–Kármán’s lattice model does not comply with rotational invariance principle, for non-central forces. The consistent generalization of Lagrange’s lattice in 3D was achieved only by Gazis et al. considering an elastic energy that depends on changes in both lengths and angles of the lattice. An alternative consistent three-parameter elastic lattice is the Hrennikoff’s, with additional structure in the cell. We also discuss the capability of nonlocal continuous models to bridge the gap between continuum isotropic elasticity at low frequencies and lattice anisotropic elasticity at high frequencies
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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