2,725 research outputs found
Flows of singular vector fields and applications to fluid and kinetic equations
No full textSeveral physical phenomena arising in fluid dynamics and kinetic equations can be modeled by nonlinear transport PDE. Such quantities are the vorticity of a fluid, or the density of a collection of particles advected by a velocity field which is highly irregular. The theory of characteristics provides a link between this PDE and the ODE dX/dt=b(t,X(t,x)), where b is the velocity field. When b has Sobolev or BV regularity and bounded divergence, the theory of DiPerna-Lions and Ambrosio gives a good notion of solution to the ordinary differential equation using the concept of regular Lagrangian flow. Extending the results of Crippa-DeLellis, and more recently Bouchut-Crippa, we study Lagrangian flows associated to velocity fields with anisotropic regularity: those with gradient given by the singular integral of an L^1 function in some directions, and the singular integral of a measure in others. We exploit an anisotropic version of the previous arguments and estimate the difference quotients in this context, thereby gaining quantitative estimates in terms of the given regularity bounds. One then recovers well-posedness for the ordinary differential equation. This answers positively the question of existence of Lagrangian solutions to the Vlasov Poisson and Euler equations with L^1 data
Charged pion production from Au + Au collisions at GeV in the Relativistic Vlasov-Uehling-Uhlenbeck model
No full textUsing the isospin-dependent relativistic Vlasov-Uehling-Uhlenbeck (RVUU)
model, we study charged pion () production in Au+Au collisions at
2.4 GeV. By fitting the density dependence of the
resonance production cross section in nuclear medium to reproduce the
experimental multiplicities measured by the HADES Collaboration, we
obtain a good description of the rapidity distributions and transverse momentum
spectra of in collisions at various centralities. Some shortcomings
in the description of production may indicate the need for
including the strong potential on in RVUU, which is at present
absent. We also calculate the proton rapidity distribution in the most central
collisions and compare with the coalescence invariant proton rapidity
distribution extracted from preliminary HADES data.Comment: 7 pages, 5 figures, version to appear in PL
Application of the Galerkin-Vlasov method to the flexural analysis of simply supported rectangular Kirchhoff plates under uniform loads
No full textPlates are important structural elements used to model bridge decks, retaining walls, floor slabs, spacecraft panels, aerospace structures, and ship hulls amongst. Plates have been modelled using three dimensional elasticity theory, Reissner’s theory, Kirchhoff theory, Shimpi’s theory, Von Karman’s theory, etc. The resulting plate equations have also been solved using classical and numerical techniques.In this research, the Galerkin-Vlasov variational method was used to present a general formulation of the Kirchhoff plate problem with simply supported edges and under distributed loads. The problem was then solved to obtain the displacements, and the bending moments in a Kirchhoff plate with simply supported edges and under uniform load. Maximum values of the displacement and the bending moments were found to occur at the plate center. The Galerkin Vlasov solutions for a rectangular simply supported Kirchhoff plate carrying uniform load was found to be exactly identical with the Navier double trigonometric series solution. http://dx.doi.org/10.4314/njt.v35i4.
On a selection principle for multivalued semiclassical flows
No full textWe study the semiclassical behaviour of solutions of a Schr ̈odinger equation with a scalar po- tential displaying a conical singularity. When a pure state interacts strongly with the singularity of the flow, there are several possible classical evolutions, and it is not known whether the semiclassical limit cor- responds to one of them. Based on recent results, we propose that one of the classical evolutions captures the semiclassical dynamics; moreover, we propose a selection principle for the straightforward calculation of the regularized semiclassical asymptotics. We proceed to investigate numerically the validity of the proposed scheme, by employing a solver based on a posteriori error control for the Schr ̈odinger equation. Thus, for the problems we study, we generate rigorous upper bounds for the error in our asymptotic approximation. For 1-dimensional problems without interference, we obtain compelling agreement between the regularized asymptotics and the full solution. In problems with interference, there is a quantum effect that seems to survive in the classical limit. We discuss the scope of applicability of the proposed regularization approach, and formulate a precise conjecture
Vlasov-Uehling-Uhlenbeck theory of medium energy heavy ion reactions: role of mean field dynamics and two body collisions
No full textThe role of nonequilibrium and quantal effects in fast nucleus-nucleus collisions is studied via the Vlasov-Uehling-Uhlenbeck theory which includes the nuclear mean field dynamics, two-body collisions, and Pauli blocking. The intranuclear cascade model, where the dynamics is governed by independent NN collisions, and the Vlasov equation, where the nuclear mean field determines the collision dynamics, are also studied as reference cases. The Vlasov equation (no collision term) yields single particle distribution functions which–after the reaction–are only slightly modified in momentum space; even in central collisions, transparency is predicted. This is in agreement with the predictions of the quantal time-dependent Hartree-Fock method. In contrast, large momentum transfer is obtained when the Uehling-Uhlenbeck collision term is incorporated; then the final momentum distribution is nearly spherically symmetric in the center of mass and a well-equilibrated nuclear system is formed: the nuclei stop each other; the translational kinetic energy is transformed into randomized microscopic motion. The Vlasov-Uehling-Uhlenbeck theory is supplemented with a phase space coalescence model of fragment formation. Calculated proton spectra compare well with recent data for Ar(42, 92, and 137 MeV/nucleon) + Ca. Also the total yields of medium mass fragments are well reproduced in the present approach. The mean field dynamics without two-body collisions, on the other hand, exhibits forward peaked proton distributions, in contrast to the data. The cascade approach underpredicts the yields of low energy protons by more than an order of magnitude
Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs
No full textWe extend the concept of self-consistency for the Fokker-Planck equation
(FPE) to the more general McKean-Vlasov equation (MVE). While FPE describes the
macroscopic behavior of particles under drift and diffusion, MVE accounts for
the additional inter-particle interactions, which are often highly singular in
physical systems. Two important examples considered in this paper are the MVE
with Coulomb interactions and the vorticity formulation of the 2D Navier-Stokes
equation. We show that a generalized self-consistency potential controls the
KL-divergence between a hypothesis solution to the ground truth, through
entropy dissipation. Built on this result, we propose to solve the MVEs by
minimizing this potential function, while utilizing the neural networks for
function approximation. We validate the empirical performance of our approach
by comparing with state-of-the-art NN-based PDE solvers on several example
problems.Comment: Accepted to NeurIPS 202
Scalable k-NN graph construction for visual descriptors
No full textThe k-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct k-NN graphs remains a challenge, especially for large-scale high-dimensional data. In this paper, we propose a new approach to construct approximate k-NN graphs with emphasis in: efficiency and accuracy. We hierarchically and randomly divide the data points into subsets and build an exact neighborhood graph over each subset, achieving a base approximate neighborhood graph; we then repeat this process for several times to generate multiple neighborhood graphs, which are combined to yield a more accurate approximate neighborhood graph. Furthermore, we propose a neighborhood propagation scheme to further enhance the accuracy. We show both theoretical and empirical accuracy and efficiency of our approach to k-NN graph construction and demonstrate significant speed-up in dealing with large scale visual data.Computer Science, Artificial IntelligenceComputer Science, Interdisciplinary ApplicationsEngineering, Electrical & ElectronicEICPCI-S(ISTP)1
Energy flux in isotropic turbulence under large variations of external forcing
No full textWe investigate the response of energy flux in isotropic turbulence to step-function like perturbation in external forcing at large length scales. From both physical experiments and direct numerical simulations, we measured the evolution of the Eulerian velocity structure functions, such as , , before and after the perturbation in forcing. In both cases, we observed the cascade of the energy excess at large scales cascade through scales to the dissipative range, which can be used to study the dynamics of the cascade, and in particular, to estimate the relevant time scales
Racism Detection by Analyzing Differential Opinions Through Sentiment Analysis of Tweets Using Stacked Ensemble GCR-NN Model
No full textWith social media's dominating role in the socio-political landscape, several existing and new forms of racism took place on social media. Racism has emerged on social media in different forms, both hidden and open, hidden with the use of memes and open as the racist remarks using fake identities to incite hatred, violence, and social instability. Although often associated with ethnicity, racism is now thriving based on color, origin, language, cultures, and most importantly religion. Social media opinions and remarks provocating racial differences have been regarded as a serious threat to social, political, and cultural stability and have threatened the peace of different countries. Consequently, social media being the leading source of racist opinions dissemination should be monitored and racism remarks should be detected and blocked timely. This study aims at detecting Tweets that contain racist text by performing the sentiment analysis of Tweets. Owing to the superior performance of deep learning, a stacked ensemble deep learning model is assembled by combining gated recurrent unit (GRU), convolutional neural networks (CNN), and recurrent neural networks RNN, called, Gated Convolutional Recurrent- Neural Networks (GCR-NN). GRU is on the top in the GCR-NN model to extract the suitable and prominent features from raw text, CNN extracts important features for RNN to make accurate predictions. Obviously, several experiments are conducted to investigate and analyze the performance of the proposed GCR-NN within the scope of machine learning and deep learning models indicating the superior performance of GCR-NN with increased 0.98 accuracy. The proposed GCR-NN model can detect 97% of the tweets that contain racist comments
Book launch and discussion
No full textBook launch event for Nick Drake: Dreaming England (Reaktion 2013) at the NN Cafe, Number 9 Guildhall Road, Northampton, NN1 1DP, Thursday 3rd October 2013.
Author Nathan Wiseman-Trowse talked about and read from his book on the musician Nick Drake. Music was provided by Gregg Cave and Ant Savage and the book's photographer Paul Hillery DJd. The event was publically promoted and around sixty attended
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