1,622 research outputs found
Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws
No full textWe study the contraction properties (up to shift) for admissible Rankine-Hugoniot discontinuities of systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in (Serre and Vasseur, J l'Ecole Polytech 1, 2014), using the spatially inhomogeneous pseudo-distance introduced in (Vasseur, Contemp Math AMS, 2013). Our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems, including the Euler system. Moreover, we introduce necessary conditions for contraction, specifically targeted for intermediate shocks. As an application, we show that intermediate shocks of the two-dimensional isentropic magnetohydrodynamics do not verify any of our contraction properties. We also investigate the contraction properties, for contact discontinuities of the Euler system, for a certain range of contraction weights. None of the results involve any smallness condition on the initial perturbation or on the size of the shock.
L-2-contraction for shock waves of scalar viscous conservation laws
No full textWe consider the L-2-contraction up to a shift for viscous shocks of scalar viscous conservation laws with strictly convex fluxes in one space dimension. In the case of a flux which is a small perturbation of the quadratic Burgers flux, we show that any viscous shock induces a contraction in L-2, up to a shift. That is, the L-2 norm of the difference of any solution of the viscous conservation law, with an appropriate shift of the shock wave, does not increase in time. If, in addition, the difference between the initial value of the solution and the shock wave is also bounded in L-1, the L-2 norm of the difference converges at the optimal rate t(-1/4). Both results do not involve any smallness condition on the initial value, nor on the size of the shock. In this context of small perturbations of the quadratic Burgers flux, the result improves the Choi and Vasseur's result in [7]. However, we show that the L-2-contraction up to a shift does not hold for every convex flux. We construct a smooth strictly convex flux, for which the L-2-contraction does not hold any more even along any Lipschitz shift.
Regularity Criterion For 3D Navier-Stokes Equations In Terms Of The Direction Of The Velocity
No full textIn this short note we give a link between the regularity of the solution u to the 3D Navier-Stokes equation and the behavior of the direction of the velocity u/|u|. It is shown that the control of div(u/vertical bar u vertical bar) in a suitable L (t/p) (L (x/q) ) norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based on very standard methods, relies on a straightforward relation between the divergence of the direction of the velocity and the growth of energy along streamlines.Mathematic
INVISCID LIMIT TO THE SHOCK WAVES FOR THE FRACTAL BURGERS EQUATION
No full textWe show the vanishing viscosity limit to entropy shocks for the fractal Burgers equation in one space dimension. More precisely, we quantify the rate of convergence of the inviscid limit in L-2 for large initial perturbations around the entropy shock on any bounded time interval. This is the first result on the inviscid limit to entropy shock for the fractal Burgers equation with the quantified convergence, for large initial perturbations.
Asymptotic analysis of Vlasov-type equations under strong local alignment regime
No full textWe consider the hydrodynamic limit of a collisionless and non-diffusive kinetic equation under strong local alignment regime. The local alignment is first considered by Karper, Mellet and Trivisa in [On strong local alignment in the kinetic Cucker-Smale model, in Hyperbolic Conservation Laws and Related Analysis with Applications, Springer Proceedings in Mathematics & Statistics, Vol. 49 (Springer, 2014), pp. 227-242], as a singular limit of an alignment force proposed by Motsch and Tadmor in [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 141 (2011) 923-947]. As the local alignment strongly dominates, a weak solution to the kinetic equation under consideration converges to the local equilibrium, which has the form of mono-kinetic distribution. We use the relative entropy method and weak compactness to rigorously justify the weak convergence of our kinetic equation to the pressureless Euler system.
Alexis Wright interview
No full textCoincidentally tonight, as governments continue to grapple with the on-going social crisis in Aboriginal communities, Indigenous author Alexis Wright has just been announced as the winner of the Miles Franklin Award, Australia's most prestigious literary prize, for her second novel Carpentaria. An Indigenous member of the Waanyi nation of Queensland's far north, and long-time activist on Aboriginal affairs, Alexis Wright's sweeping, poetic book explores the rich mythology, chequered history and present day drama of her Gulf country homeland, and was praised by judges as the standout in a highly competitive field, which included dual Booker Prize winner, Peter Carey
A brief conversation with Alexis Wright
No full textAn interview with the author Alexis Wright is presented. When asked about her interest in books, she explains that she is reading a series of natural history books. She also comments on her interest in travel and the process of writing another novel. The challenges of the writing process are also explored
Episode 35: Alexis Castellanos, Author of “Isla to Island”, and Her Panel Presentation during the Operación Pedro Pan Two-Day Event
No full textIn Part 1 of “Operación Pedro Pan: The Voices and Stories of Cuba’s Child Exodus—A Knights HistoryCast Mini-Series,” the Department of History’s Sebastian Garcia talked with Alexis Castellanos, an author, illustrator, graphic novelist, and a panelist at the esteemed, conspicuous, and powerful “Operación Pedro Pan: Honoring the Cultural, Historical Legacy of Cuba’s Child Exodus” Two-Day Program that Florida Humanities, UCF’s Department of English and Department of Modern Languages and Literatures sponsored (see https://cah.ucf.edu/pedro-pan/ for more details on sponsors and the program in general).
Sebastian structured this specific episode on Alexis Castellanos’ Isla to Island, a wordless graphic novel grounded by her personal family history and the history of Operación Pedro Pan (Operation Peter Pan). By analyzing such a historic event through the medium of fiction, Sebastian argued that this is one of the most unique Knights HistoryCast episodes of all time. Naturally, their conversation expanded to what she talked about during her panel presentation in Panel One, Day 1 of the event that featured “internationally renowned scholars that discussed the political, historical, and cultural legacy of Operación Pedro Pan (1960-1962).” (https://cah.ucf.edu/pedro-pan/)
To purchase Isla to Island (strongly recommend), check out: https://islatoisland.com/.
To find out more about Alexis and her professional work, check out her website at https://alexiscastellanos.com/https://stars.library.ucf.edu/knightshistorycast/1034/thumbnail.jp
Time-Asymptotic Stability of Generic Riemann Solutions for Compressible Navier-Stokes-Fourier Equations
No full textWe establish the time-asymptotic stability of generic Riemann solutions to the one-dimensional compressible Navier-Stokes-Fourier equations. The Riemann solution under consideration is a generic combination of a shock, a contact discontinuity, and a rarefaction wave. We prove that the perturbed solution of Navier-Stokes-Fourier converges, uniformly in space as time goes to infinity, to an ansatz composed of viscous shock with time-dependent shift, a viscous contact wave and an inviscid rarefaction wave. This is a first resolution of the time-asymptotic stability of three waves of different kinds associated with the generic Riemann solutions. Our approach relies on the method of a-contraction with shifts and relative entropy, specifically applied to both the shock wave and the contact wave. It enables the application of a global energy method for the generic combination of three waves.
THE MYSTIC ROAD : SELECTED POEMS - ALEXIS KARPOUZOS
No full text
Alexis karpouzos (born on April 09, 1967) is a philosopher, author, spiritual master and pioneer of higher consciousness. He is author of several books on philosophy, metaphysics, spirituality, modern science. His most famous books are: ‘’Universal consciousness’’, ‘’non-duality’’, ‘’An ocean of souls’’, ‘’Beyond the heaven’’. Alexis Karpouzos is also a recording artist. He has recorded two music albums and twenty-four singles songs. He has also appeared in two documentary films, television and radio productions. He is the pioneer of the post-ontology consciousness and the wisdom of universal wholeness. The global language of poetry of Alexis Karpouzos, by following the paths of wisdom, is a vehicle for transmitting human knowledge and values, history, ancient traditions, and links with nature. It transmits the human values and worldly knowledge that are essential for opening ourselves to the Other. Poetic creation, therefore, forges very strong links between humans -it transcends beyond languages, beliefs and cultures. Each poem appears in its original form, in a vibrant celebration of life, diversity, language, and the enduring power of poetry. At a time when the Humanities are under threat, this book offers a defense of poetry within the context of growing interest in mindfulness in spirituality, in consciousness, in art, in education.</p
- …
