1,720,982 research outputs found
Minimization of a Ginzburg–Landau functional with mean curvature operator in 1-D
No full textThe aim of this paper is to investigate the minimization problem related to a Ginzburg- Landau energy functional, where in particular a nonlinear diffusion of mean curvature-type is considered, together with a classical double well potential. A careful analysis of the corresponding Euler-Lagrange equation, equipped with natural boundary conditions and mass constraint, leads to the existence of an unique Maxwell solution , namely a monotone increasing solution obtained for small diffusion and close to the so-called Maxwell point . Then, it is shown that this particular solution (and its reversal) has least energy among all the stationary points satisfying the given mass constraint. Moreover, as the viscosity parameter tends to zero, it converges to the increasing (decreasing for the reversal) single interface solution , namely the constrained minimizer of the corresponding energy without diffusion. Connections with Cahn- Hilliard models, obtained in terms of variational derivatives of the total free energy considered here, are also presented
Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity
No full textIn this paper, we investigate spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the (ρ,u), that is, density and velocity, variables. We derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of eigenvalues with non-negative real part. In addition, we present numerical computations of the Evans function in sufficiently large domain of the unstable half-plane and show numerically that its winding number is (approximately) zero, thus giving a numerical evidence of point spectrum stability
Traveling waves for quantum hydrodynamics with nonlinear viscosity
Full text linkIn this paper we study existence of traveling waves for 1-D compressible Euler system with dispersion (which models quantum effects through the Bohm potential) and nonlinear viscosity in the context of quantum hydrodynamic models for superfluidity. The existence of profiles is proved for appropriate (super– or sub– sonic) end states defining Lax shocks for the underlying Euler system formulated in terms of density and velocity without restrictions for the viscosity and dispersion parameters. On the other hand, the interplay of the dispersion and the viscosity plays a crucial role in proving the existence of oscillatory profiles, showing in this way how the dispersion plays a significant role in certain regimes. Numerical experiments are also provided to analyze the sensitivity of such profiles with respect to the viscosity/dispersion terms and with respect to the nearness to vacuum
High friction limit for Euler–Korteweg and Navier–Stokes–Korteweg models via relative entropy approach
Full text linkThe aim of this paper is to investigate the singular relaxation limits for the Euler–Korteweg and the Navier–Stokes–Korteweg system in the high friction regime. We shall prove that the viscosity term is present only in higher orders in the proposed scaling and therefore it does not affect the limiting dynamics, and the two models share the same equilibrium equation. The analysis of the limit is carried out using the relative entropy techniques in the framework of weak, finite energy solutions of the relaxation models converging toward smooth solutions of the equilibrium. The results proved here take advantage of the enlarged formulation of the models in terms of the drift velocity introduced in [6], generalizing in this way the ones proved in [15] for the Euler–Korteweg model
Numerical investigations of dispersive shocks and spectral analysis for linearized quantum hydrodynamics
No full textThe aim of this paper is to study solutions of one dimensional compressible Euler system with dissipation–dispersion terms, where the dispersive term is originated by the quantum effects described through the Bohm potential, as customary in quantum hydrodynamic models. We shall investigate numerically the sensitivity of the profiles with respect to the viscosity parameter, in particular in terms of their monotonicity properties. In addition, we shall also pinpoint numerically how the profile becomes more oscillatory as the end states approach the vacuum. The analysis of spectral properties of the linearized system around constant states is also provided, as well as the (numerical) localization of the point spectrum of the linearization along a profile. The latter investigation is carried out through the Evans function method
Dispersive shocks in quantum hydrodynamics with viscosity
No full textIn this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of quantum hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm potential; moreover we introduce a (linear) viscosity to analyze its interplay with the former while proving existence, monotonicity and stability of traveling waves connecting a Lax shock for the underlying Euler system. The existence of monotone profiles is proved for sufficiently small shocks; while the case of large shocks leads to the (global) existence for an oscillatory profile, where dispersion plays a significant role. The spectral analysis of the linearized problem about a profile is also provided. In particular, we derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of the eigenvalues in the unstable plane, using a careful analysis of the Evans function
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
Relaxation Limit from the Quantum Navier-Stokes Equations to the Quantum Drift-Diffusion Equation
Full text linkThe relaxation time limit from the quantum Navier-Stokes-Poisson system to the quantum drift-diffusion equation is performed in the framework of finite energy weak solutions. No assumptions on the limiting solution are made. The proof exploits the suitably scaled a priori bounds inferred by the energy and BD entropy estimates. Moreover, it is shown how from those estimates the Fisher entropy and free energy estimates associated to the diffusive evolution are recovered in the limit. As a byproduct, our main result also provides an alternative proof for the existence of finite energy weak solutions to the quantum drift-diffusion equation
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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