An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show ... more An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random walk theory well approximates the coarse behavior of this quantity in terms of a continuous function. This theory also reproduces a full suppression of the strength of diffusion, which occurs at the dynamical transition from normal to anomalous diffusion. Similarly, the probability density function of this map exhibits a nontrivial fine structure while its coarse functional form is governed by a time fractional diffusion equation. A more detailed understanding of the irregular structure of the generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo formula establishing a relation to de Rham-type fractal functions.
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fracta... more We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.
Journal of The Acoustical Society of America, 2010
A multiple sensor array was employed to identify the spatial locations of all vocalizing male bul... more A multiple sensor array was employed to identify the spatial locations of all vocalizing male bullfrogs ͑Rana catesbeiana͒ in five natural choruses. Patterns of vocal activity collected with this array were compared with computer simulations of chorus activity. Bullfrogs were not randomly spaced within choruses, but tended to cluster into closely spaced groups of two to five vocalizing males. There were nonrandom, differing patterns of vocal interactions within clusters of closely spaced males and between different clusters. Bullfrogs located within the same cluster tended to overlap or alternate call notes with two or more other males in that cluster. These near-simultaneous calling bouts produced advertisement calls with more pronounced amplitude modulation than occurred in nonoverlapping notes or calls. Bullfrogs located in different clusters more often alternated entire calls or overlapped only small segments of their calls. They also tended to respond sequentially to calls of their farther neighbors compared to their nearer neighbors. Results of computational analyses showed that the observed patterns of vocal interactions were significantly different than expected based on random activity. The use of a multiple sensor array provides a richer view of the dynamics of choruses than available based on single microphone techniques.
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show ... more An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random walk theory well approximates the coarse behavior of this quantity in terms of a continuous function. This theory also reproduces a full suppression of the strength of diffusion, which occurs at the dynamical transition from normal to anomalous diffusion. Similarly, the probability density function of this map exhibits a nontrivial fine structure while its coarse functional form is governed by a time fractional diffusion equation. A more detailed understanding of the irregular structure of the generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo formula establishing a relation to de Rham-type fractal functions.
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fracta... more We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.
Journal of The Acoustical Society of America, 2010
A multiple sensor array was employed to identify the spatial locations of all vocalizing male bul... more A multiple sensor array was employed to identify the spatial locations of all vocalizing male bullfrogs ͑Rana catesbeiana͒ in five natural choruses. Patterns of vocal activity collected with this array were compared with computer simulations of chorus activity. Bullfrogs were not randomly spaced within choruses, but tended to cluster into closely spaced groups of two to five vocalizing males. There were nonrandom, differing patterns of vocal interactions within clusters of closely spaced males and between different clusters. Bullfrogs located within the same cluster tended to overlap or alternate call notes with two or more other males in that cluster. These near-simultaneous calling bouts produced advertisement calls with more pronounced amplitude modulation than occurred in nonoverlapping notes or calls. Bullfrogs located in different clusters more often alternated entire calls or overlapped only small segments of their calls. They also tended to respond sequentially to calls of their farther neighbors compared to their nearer neighbors. Results of computational analyses showed that the observed patterns of vocal interactions were significantly different than expected based on random activity. The use of a multiple sensor array provides a richer view of the dynamics of choruses than available based on single microphone techniques.
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Papers by Marie Gonchar