1,721,070 research outputs found
A kinetic flocking model with diffusion
No full textWe study the stability of the equilibrium states and the rate of convergence of solutions towards them for the continuous kinetic version of the Cucker-Smale flocking in presence of diffusion whose strength depends on the density. This kinetic equation describes the collective behavior of an ensemble of organisms, animals or devices which are forced to adapt their velocities according to a certain rule implying a final configuration in which the ensemble flies at the mean velocity of the initial configuration. Our analysis takes advantage both from the fact that the global equilibrium is a Maxwellian distribution function, and, on the contrary to what happens in the Cucker-Smale model, the interaction potential is an integrable function. Precise conditions which guarantee polynomial rates of convergence towards the global equilibrium are found
Sparse Approximation for Blind Source Separation and Magnetoencephalography Applications
No full textFluid dynamic description of flocking via Povzner–Boltzmann equation
Full text linkWe introduce and discuss the possible dynamics of groups of indistinguishable agents, which are interacting according to their relative positions, with the aim of deriving hydrodynamic equations. These models are developed to mimic the collective motion of groups of species such as bird flocks, fish schools, herds of quadrupeds or bacteria colonies. Our starting model for these interactions is the Povzner equation, which describes a dilute gas in which binary collisions of elastic spheres depend of their relative positions. Following the Cucker and Smale model, we will consider binary interactions between agents that are dissipative collisions in which the coefficient of restitution depends on their relative distance. Under the assumption of weak dissipation, it is shown that the Povzner equation is modified through a correction in the form of a nonlinear friction type operator. Using this correction we formally obtain from the Povzner equation in a direct way a fluid dynamic description of a system of weakly interacting agents interacting in a dissipative way, with a coefficient of restitution that depends on their relative distance
A Relaxed Kaanov iteration for the p-poisson problem
No full textDiening L, Fornasier M, Tomasi R, Wank M. A Relaxed Kaanov iteration for the p-poisson problem. Numerische Mathematik. 2020;145:1-34.In this paper we introduce and analyze an iteratively re-weighted algorithm, that allows to approximate the weak solution of the p-Poisson problem for 1<p2 by iteratively solving a sequence of linear elliptic problems. The algorithm can be interpreted as a relaxed Kaanov iteration, as so-called in the specific literature of the numerical solution of quasi-linear equations. The main contribution of the paper is proving that the algorithm converges at least with an algebraic rate
The role of the Italian courts in the effective implementation of the European Convention on Human Rights. Introductory remarks
No full textGoing 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
Linearly constrained evolutions of critical points and an application to cohesive fractures
No full textAsymptotic flocking dynamics for the kinetic Cucker-Smale model
No full textWe analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale, which describes the collective behavior of an ensemble of organisms, animals or devices. The kinetic version is here obtained starting from a Boltzmann-type equation.
The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. It is proven that the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution
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