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We consider a model system in which anomalous diffusion is generated bysuperposition of underlying linear modes with a broad range of relaxationtimes. In the language of Gaussian polymers, our model corresponds to Rouse(Fourier) modes whose friction coefficients scale as wavenumber to the power$2-z$. A single (tagged) monomer then executes subdiffusion over a broad rangeof time scales, and its mean square displacement increases as $t^\alpha$ with$\alpha=1/z$. To demonstrate non-trivial aspects of the model, we numericallystudy the absorption of the tagged particle in one dimension near an absorbingboundary or in the interval between two such boundaries. We obtain absorptionprobability densities as a function of time, as well as the position-dependentdistribution for unabsorbed particles, at several values of $\alpha$. Each ofthese properties has features characterized by exponents that depend on$\alpha$. Characteristic distributions found for different values of $\alpha$have similar qualitative features, but are not simply related quantitatively.Comparison of the motion of translocation coordinate of a polymer movingthrough a pore in a membrane with the diffusing tagged monomer with identical$\alpha$ also reveals quantitative differences.

First Passage Distributions in a Collective Model of Anomalous Diffusion with Tunable Exponent