Department Library


Christian Lambert (Senior Thesis, February 2019, Advisor: Manuel Berrondo )


Emergent behavior - behavior exhibited by groups that is not seen in individuals - is a critical part of our world and is difficult to model well. We present a dynamic model where a flock of simulated birds (boids) exists in two dimensions. Each boid has a constant speed and a fixed randomly determined number of neighbors, defined as those boids that influence the direction of its motion (consensus). Modifications of the boids’ flight following a specific algorithm (frustration) during the simulation results in emergent behavior. The flock of boids is mapped to a directed graph. Changing the boids’ neighbors also modifies the graph. Rigorously defined sub-flocks are identified using graph theory. Using a new method of frustration, α turns, we can enhance the emergent behavior exhibited. Analyzing this emergent behavior is done through order parameters that help us understand how ordered the flock or sub-groups of the flock are. Analyzing the mapping of the graph to the flock can expand our understanding of how and when dynamic emergence occurs in this flocking model. This is done by showing how physical the model is in whether the flock splits like we see real flocks of birds doing. Using α turns and the nearest neighbor consensus method we find we have emergent behavior within a specific range of the model parameters.

Eric Lenhart (Senior Thesis, August 2019, Advisor: Manuel Berrondo )


In the interest of drawing conclusions about Aeolian environments based on remote imaging, we investigated how air flow forms self-organizing patterns, such as ripples, across loose particulate surfaces. Specifically, we analyzed various models of sand transport, particularly Nishimori’s model, to note the effects of altering various parameters, including wind direction, saltation length, diffusion, and a saltation proportionality constant. As a measure of the frustration of the emergent patterns, Y-junctions were counted at various values of the parameters. A strong correlation with the saltation proportionality constant and no correlation with the saltation height were found. As an additional use of the model, terrestrial gravel ripples in the Lut Desert, Iran were measured, with an average length of 50.0 m and a right-skewed distribution found. For these gravel ripples, particle movement has a larger dependence on initial height than for smaller, more common sand ripples.


Garett Brown (Senior Thesis, April 2017, Advisor: Manuel Berrondo )


The complexity and pattern found in animal aggregations, such as starling murmurations, reveals emergent phenomena which arise from the simple, individual interactions of its members. Simulated in a two-dimensional algorithmic model, self-driven particles (boids) group together and display emergent flocking characteristics. The model is based on the ideas of consensus and frustration, where consensus is a nonlinear topological averaging that drives the boids toward one of three unique phases, and frustration is a perturbation that pushes the boids beyond these simple phases and toward disordered behavior. The nonlinearity merged with the perturbation produces characteristics which go beyond the dynamic interplay of global and local phase transitions. The emergent results are interpreted in terms of global and local order parameters, and correlation functions. The results also strongly agree with observational data and empirical analysis.


Ty Beus (Senior Thesis, August 2013, Advisor: Manuel Berrondo )


Soyoung Jung (Senior Thesis, December 2013, Advisor: Manuel Berrondo )


We study the dynamics of multi-spin systems with energy dissipation with the Heisenberg model for anti-/ferromagnetism. Individual two-spin short-range interactions of magnetic dipoles give rise to coherent long-range behavior on a lattice structure. The spins are free to rotate and can arrange themselves in a parallel configuration in the ordered state. The local magnetic field acting on each spin arises as the result of the addition of nearest neighbor spins. Additional dissipative effects allow us to study the onset of ordered states as dynamical process. We include anisotropy to simulate the layered structure of the experimental samples and a long range interaction as an opposing force. As a result, we have been able to observe properties of magnetism in simulated 2D anti-/ferromagnetic lattice including the formation of domains, domain walls, spin waves, and magnetic pattern formation, which correlates well with experimental observations in thin magnetic films. We discuss how these results can sharpen the understanding of anti-/ferromagnetism and the dynamics of complex system by comparing the result with other complex system.


Wesley Krueger (Senior Thesis, September 2010, Advisor: Manuel Berrondo )


The emergence of self-organized behavior is characteristic of multi-particle systems in which individual motion is governed by the application of simple rules of interaction. The resulting dynamic order cannot be understood in terms of individual particles, but can be elucidated by formulating the system in terms of an abstract notion of dimensional coupling. We define this notion and consider two such systems in which the coupling rules are drawn from classical Newtonian mechanics. First we develop a deterministic flocking model based on the principles of consensus and frustration and demonstrate that both rules are required to elicit complex, flock-like behavior from the system. We then employ a quasi-stationary checkerboard lattice to develop a discretized damped Heisenberg model and demonstrate the spontaneous onset of magnetic domains. Finally, we discuss the importance of antagonistic interaction rules in the onset of complex, coherent dynamics away from equilibrium.


William Henstrom (Senior Thesis, April 1995, Advisor: Manuel Berrondo )