1,721,011 research outputs found
Limiting models in condensed matter Physics and gradient flows of 1-homogeneous functionals
No full textWe survey some recent results of the authors on variational and evolution problems concerning a certain class of convex 1-homogeneous functionals for vector-valued maps related to models in phase transitions (Hele-Shaw), superconductivity (Ginzburg-Landau) and superfluidity (Gross-Pitaevskii). Minimizers and gradient flows of such functionals may be characterized as solutions of suitable non-local vectorial generalization of the classical obstacle problem
Long-Time Behavior of the Mean Curvature Flow with Periodic Forcing
Full text linkWe consider the long-time behavior of the mean curvature flow in heterogeneous media with periodic fibrations, modeled as an additive driving force. Under appropriate assumptions on the forcing term, we show existence of generalized traveling waves with maximal speed of propagation, and we prove the convergence of solutions to the forced mean curvature flow to these generalized waves
The geometry of mesoscopic phase transition interfaces
No full textWe consider a mesoscopic model of phase transitions and investigate the geometric properties of the interfaces of the associated minimal solutions. We provide density estimates for level sets and, in the periodic setting, we construct minimal interfaces at a universal distance from any given hyperplane
Closed curves of prescribed curvature and a pinning effect
Full text linkWe prove that for any H : R(2) -> R which is Z(2)-periodic, there exists H(epsilon), which is smooth, epsilon-close to H in L(1), with L(infinity)-norm controlled by the one of H, and with the same average of H, for which there exists a smooth closed curve gamma(epsilon) whose curvature is H(epsilon). A pinning phenomenon for curvature driven flow with a periodic forcing term then follows. Namely, curves in fine periodic media may be moved only by small amounts, of the order of the period
One-dimensional symmetry for semilinear equations with unbounded drift
Full text linkWe consider semilinear equations with unbounded drift in the whole of Rn and we show that monotone solutions with nite energy are one-dimensional
On the gradient flow of a one-homogeneous functional
No full textWe consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of a Hele–Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele–Shaw problem. As a consequence we get existence and uniqueness of a weak solution to the Hele–Shaw flow. We also obtain an explicit representation for the Total Variation flow in dimension 1, and easily deduce basic qualitative properties,
concerning in particular the “staircasing effect”
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
Geometric strong segmentation theory for compositionally asymmetric diblock copolymer melts
No full textVariations 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
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