Browsing by Subject "ANOMALOUS DIFFUSION"

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  • Niu, Pingping; Helin, Tapio; Zhang, Zhidong (2020)
    In this work the authors consider an inverse source problem the stochastic fractional diffusion equation. The interested inverse problem is to reconstruct the unknown spatial functions f and g (the latter up to the sign) in the source by the statistics of the final time data u(x, T). Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then a reconstruction scheme for f and g up to the sign is given. To tackle the ill-posedness, Tikhonov regularization is adopted and some numerical results are displayed.
  • PHENIX Collaboration; Adare, A.; Kim, D. J.; Krizek, F.; Novitzky, N.; Rak, J. (2018)
    We present a detailed measurement of charged two-pion correlation functions in 0-30% centrality root= 200 GeV Au+Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from Levy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter lambda, the Levy index of stability alpha, and the Levy length scale parameter R as a function of average transverse mass of the parr m(T). We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same Levy-stable source functions. The lambda(m(T)) measurements indicate a decrease of the strength of the correlations at low m(T). The Levy length scale parameter R(m(T)) decreases with increasing m(T), following a hydrodynamically predicted type of scaling behavior. The values of the Levy index of stability a are found to be significantly lower than the Gaussian case of alpha = 2, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.
  • Koponen, Ismo (2021)
    Associative knowledge networks are often explored by using the so-called spreading activation model to find their key items and their rankings. The spreading activation model is based on the idea of diffusion- or random walk -like spreading of activation in the network. Here, we propose a generalisation, which relaxes an assumption of simple Brownian-like random walk (or equally, ordinary diffusion process) and takes into account nonlocal jump processes, typical for superdiffusive processes, by using fractional graph Laplacian. In addition, the model allows a nonlinearity of the diffusion process. These generalizations provide a dynamic equation that is analogous to fractional porous medium diffusion equation in a continuum case. A solution of the generalized equation is obtained in the form of a recently proposed q-generalized matrix transformation, the so-called q-adjacency kernel, which can be adopted as a systemic state describing spreading activation. Based on the systemic state, a new centrality measure called activity centrality is introduced for ranking the importance of items (nodes) in spreading activation. To demonstrate the viability of analysis based on systemic states, we use empirical data from a recently reported case of a university students' associative knowledge network about the history of science. It is shown that, while a choice of model does not alter rankings of the items with the highest rank, rankings of nodes with lower ranks depend essentially on the diffusion model.