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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2009

Random walks

Articles 1 - 3 of 3

Full-Text Articles in Physical Sciences and Mathematics

Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell Oct 2009

Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell

Mathematics and Statistics Faculty Publications

Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project de-signed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a 2-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp …

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Transitional Probabilities For The Four-State Random Walk On A Lattice In The Presence Of Partially Reflecting Boundaries, Ramakrishna Janaswamy Mar 2009

Transitional Probabilities For The Four-State Random Walk On A Lattice In The Presence Of Partially Reflecting Boundaries, Ramakrishna Janaswamy

Ramakrishna Janaswamy

The four-state random walk (4RW) model, wherein the particle is endowed with two states of spin and two states of directional motion in each space coordinate, permits a stochastic solution of the Schrödinger equation (or the equivalent parabolic equation) without resorting to the usual analytical continuation in complex space of the particle trajectories. Analytical expressions are derived here for the various transitional probabilities in a 4RW by employing generating functions and eigenfunction expansions when the particle moves on a 1+1 space-time lattice with two-point boundary conditions. The most general case of dissimilar boundaries with partially reflecting boundary conditions is treated …

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Node Isolation Model And Age-Based Neighbor Selection In Unstructured P2p Networks, Zhongmei Yao, Derek Leonard, Dmitri Loguinov Feb 2009

Node Isolation Model And Age-Based Neighbor Selection In Unstructured P2p Networks, Zhongmei Yao, Derek Leonard, Dmitri Loguinov

Computer Science Faculty Publications

Previous analytical studies of unstructured P2P resilience have assumed exponential user lifetimes and only considered age-independent neighbor replacement. In this paper, we overcome these limitations by introducing a general node-isolation model for heavy-tailed user lifetimes and arbitrary neighbor-selection algorithms. Using this model, we analyze two age-biased neighbor-selection strategies and show that they significantly improve the residual lifetimes of chosen users, which dramatically reduces the probability of user isolation and graph partitioning compared with uniform selection of neighbors. In fact, the second strategy based on random walks on age-proportional graphs demonstrates that, for lifetimes with infinite variance, the system monotonically increases …

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