1,720,968 research outputs found
Singular limit of equations for linear viscoelastic fluids with periodic boundary conditions
No full textWe consider a one-parameter family of problems, governing, for any fixed parameter, the motion of a linear viscoelastic fluid in a two-dimensional domain with periodic boundary conditions. The asymptotic behavior of each problem is analyzed, by proving the existence of the global attractor. Moreover, letting the parameter go to zero, since the memory effect disappears, we obtain a limiting problem, given by the Navier–Stokes equations. For any fixed parameter, we construct an exponential attractor. The resulting family is robust, meaning that these exponential attractors converge, in an appropriate sense, to an exponential attractor of the limiting problem
Three-dimensional nonlocal models of deformable ferroelectrics: A thermodynamically consistent approach
Get PDFWithin the framework of continuum thermodynamics, the paper develops a scheme for the study of piezo-ferroelectric materials undergoing large deformations. The ferroelectric polarization is decomposed into the sum of a reversible and a residual part which is con- sidered as an independent variable. The modeling of the constitutive properties is made simpler by using referential, Euclidean invariant quantities. Constitutive functions depend on a set of variables that includes their time derivatives and gradients, and therefore must be consistent with a nonlocal statement of the second law of thermodynamics where the entropy production is represented as the sum of a non-negative supply and a flux. Both terms are also assigned by means of constitutive functions. A new and quite general model relating the residual-polarization rate and the ‘electric Gibbs free entropy’ is established. This thermodynamic potential is modeled according to the Landau-Devonshire approach and appropriate explicit expressions are proposed for anisotropic materials. Consequently, a new explicit evolution equation for the polarization vector is obtained for both high and low temperatures. In particular, the Landau-Devonshire scalar model is recovered in the isotropic case. Under the assumption of small strains and small polarization gradients, hys- teresis and electromechanical coupling are described for a simple one-dimensional model. The advantage of our original approach is that a few constitutive parameters provide a good fit of material behavior
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Convecting–radiating fins: Explicit solutions, efficiency and optimization
Get PDFWe analyze the second order, non-linear, one dimensional differential equation describing the steady conduction of heat in convecting–radiating longitudinal fins. We introduce an auxiliary dependent variable, solving a first order differential equation and related to the thickness of the fin, giving the distribution of the heat along the fin. The purely convecting case, corresponding to a linear equation, and the convecting–radiating case, corresponding to a non-linear equation, are treated separately. For the linear case, different solutions, corresponding to different shapes of the fin, are analyzed. For the non-linear case, an explicit solution in terms of the auxiliary variable is obtained. The distribution of the temperature, the efficiency of the fin and the applicability of the results are discussed
Free energies in one-dimensional models of magnetic transitions with hysteresis
No full textA one-dimensional non-isothermal model for magnetic materials is proposed. It provides a simplified description of transitions from paramagnetic to either ferro- or ferri-magnetic phase which also accounts for hysteresis loops. The temperature enters the model as a parameter leading the transition, so that the compatibility with thermodynamics is ensured by the Clausius-Duhem inequality. Above the critical temperature, the paramagnetic susceptibility is assumed to obey a proper law depending on the material: the Curie-Weiss law for ferromagnets and the Néel-Curie-Weiss law for antiferromagnets and ferrimagnets. At a temperature below the critical point, a bilinear rate-independent o.d.e. rules the evolution of magnetization versus magnetic field strength. Because of the special form of its skeleton curve, the model applies to materials whose major hysteresis loop is not rectangular-shaped. In addition, the explicit form of the minimum and maximum free energies is obtained under isothermal conditions for the paramagnetic and hysteretic regimes. This allows us to highlight the amount of work performed on the system which is stored as magnetic energy change
Free Energies and Pseudo-Elastic Transitions for Shape Memory Alloys
No full textA one-dimensional model for a shape memory alloy is proposed. It provides a simplified description of the pseudo-elastic regime, where stress-induced transitions from austenitic to oriented martensitic phases occurs. The stress-strain evolution is ruled by a bilinear rate-independent o.d.e. which also accounts for the fine structure of minor hysteresis loops and applies to the case of single crystals only. The temperature enters the model as a parameter through the yield limit. Above the critical temperature, the austenite-martensite phase transformations are described by a Ginzburg-Landau theory involving an order parameter, which is related to the anelastic deformation. As usual, the basic ingredient is the Gibbs free energy, which is a function of the order parameter, the stress and the temperature. Unlike other approaches, the expression of this thermodynamic potential is derived rather then assumed, here. The explicit expressions of the minimum and maximum free energies are obtained by exploiting the Clausius-Duhem inequality, which ensures the compatibility with thermodynamics, and the complete controllability of the system. This allows us to highlight the role of the Ginzburg-Landau equation when phase transitions in materials with hysteresis are involved
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