1,720,976 research outputs found
Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves
No full textExistence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a Helfrich type contribution, a Frank type contribution and a coupling term between the orientation of the surfactants and the curvature of the interface. Analytical results are proven in a one–dimensional situation for curves
Semisoft elasticity and director reorientation in stretched sheets of nematic elastomers
No full textA two-dimensional effective model for the semisoft elastic behavior of nematic elastomers is derived in the thin film limit. The model is used to investigate numerically the force-stretch curves and the deformed shape, and to resolve the local patterns in the director orientation in a stretching experiment. From the force-stretch curves we recover the two critical stretches which mark the transition from hard to soft and back to hard response. We present an analytical model for their dependence on the aspect ratio of the sample, and compare it with numerical results
Soft elastic response of stretched sheets of nematic elastomers: a numerical study
No full textStretching experiments on sheets of nematic elastomers have revealed soft deformation modes and formation of microstructure in parts of the sample. Both phenomena are manifestations of the existence of a symmetry-breaking phase transformation from a random, isotropic phase to an aligned, nematic phase. The microscopic energy proposed by Bladon et al. (Phys. Rev. E 47 (1993), R 3838) to model this transition delivers a continuum of symmetry-related zero-energy states, which can be combined in different ways to achieve a variety of zero-energy macroscopic deformations. We replace the microscopic energy with a macroscopic effective energy, the so-called quasiconvexification. This procedure yields a coarse-grained description of the physics of the system, with (energetically optimal) fine-scale oscillations of the state variables correctly accounted for in the energetics, but averaged out in the kinematics. Knowledge of the quasiconvexified energy enables us to compute efficiently with finite elements, and to simulate numerically stretching experiments on sheets of nematic elastomers. Our numerical experiments show that up to a critical, geometry-dependent stretch, no reaction force arises. At larger stretches, a force is transmitted through parts of the sheet and, although fine phase mixtures disappear from most of the sample, microstructures survive in some pockets. We reconstruct from the computed deformation gradients a possible composition of the microstructure, thereby resolving the local orientation of the nematic director
Macroscopic response of nematic elastomers via relaxation of a class of SO(3)-invariant energies
No full textWe obtain an explicit formula for the relaxation of the free-energy density for nematic elastomers proposed by Bladon, Terentjev&Warner (Phys. Rev. E 47 (1993), 3838–3840). The proof is based on a characterization of the level sets of the relaxed energy. In particular, the construction uses only laminates within laminates and it identifies those deformations that correspond to simple laminates
Effects of toroidal inhomogeneities on the effective properties of a composite
Full text linkThe present work focuses on the problem of rigid inhomogeneity of toroidal shape embedded in an elastic matrix. Inhomogeneities of this kind occur both in natural and man-made materials. Analytical modeling of materials with such microstructure has not been well developed. In the homogenization schemes, the inhomogeneities are usually assumed to be of ellipsoidal shape. This unrealistic assumption is largely responsible for insuffcient linkage between methods of micromechanics and materials science applications. While for 2-D non-elliptical inhomogeneities many analytical and numerical results have been obtained, only a limited number of numerical results and approximate estimates are available for non-ellipsoidal 3-D shapes. Most of them are related to pores and cracks. The problem of the effective conductivity (thermal or electric) of a material containing toroidal insulating inhomogeneities has been addressed in a pèrevious work, where an analytic solution is presented for the steady-state temperature distribution in an infinite conductive medium containing an insulated toroidal inclusion, under uniform heat flux in an arbitrary direction. The temperature flux on the torus surface is then determined as a function of torus parameters. This result is then used to determine resistivity contribution tensor for the toroidal inhomogeneity and for calculation of effective conductive
properties of a material containing multiple inhomogeneities of this shape.
A general analytical solution is developed here for the problem of an infinite elastic medium containing a rigid toroidal inhomogeneity, under remotely applied uniform strain. The traction vector on the torus surface is determined as a function of torus parameters and remote strain components. The results are utilized to calculate the components of the fourth-rank stiffness contribution tensor of the rigid toroidal inhomogeneity that are required for calculation of the overall elastic properties of a material containing multiple toroidal inhomogeneities. The analytical results are verified by comparison with FEM calculations
Material instabilities in nematic elastomers
No full textSoft deformation paths and domain patterns in nematic elastomers are analyzed through the minimization of a nonconvex free-energy recently proposed in the literature. The free-energy density has multiple wells, and is not restricted to small deformations. The problems of calculating the quasiconvex hull of the energy wells and the quasiconvex envelope of the free-energy density are formulated and solved (the latter only in two spatial dimensions). This leads to a complete characterization of the set of soft deformations paths available to a given material, and of its effective macroscopic energy
Stripe--domains in nematic elastomers: old and new
No full textDesimone, Antonio; Dolzmann, Georg. (2005). Stripe--domains in nematic elastomers: old and new. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4125
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
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