Abstract

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
)

Abstract

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.

Abstract

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.

Abstract

We use an algebraic mehod to model the molecular collison dynamics of a ollinear tiatomic system. Beginning with a forced oscillator, we develop a mathematical framework upon which inelastic and reactive collisions are modeled. The model is considered algebraic because it takes adavantage of the properties of a Lie algebra in the derivation of a time-evolution operator. The time-evolution operator is shown to generate both phase-sapce and quanum dynamics of a forced oscillator simultaneously. The model is nconsidered semi-classical becuas eonly the molecule's internal degrees-of-freedom are quantized. the relative translaion betweent eh collidng atom and molecule in an exchange reaction (AB + C = A + BC) contains no bound states and any possible tunneling is neglected so the relative transaltion is treated classically.The purpose of this dissertaton is to develop a workign model for the quantum dynamics of acollinear reactive collision. after a reliable model is developed we apply statistical mechanics prinicples by averaging collisions wih molecules in a thermal bath. The initial Boltzmann distribution is of the oscillator energies. the relative velocities of the colliding particles is considered a thermal average. REsults are show of quantum transition probabilties aroudn the transition state that are highly dynamic due to the coupling between the translational and transverse coordinate.

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

Abstract

Abstract

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.

Abstract

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.

Abstract

Using the idea that a quantum mechanical system drops to its ground state as its temperature goes to absolute zero several operators are devised to enable the approximation of the lowest order energy eigenstate of a given symmetry; as well as an approximation to the energy eigenvalue of the same order.

Malcolm Stuart Hicken (Masters Thesis, August 2001,
Advisor: Manuel Berrondo
)

Abstract

The effects of placing hydrogen or sodium atom at the center of a spherically symmetric infinite potential are examined in this thesis. The specific properties discussed are the wave functions, energy levels, radial integrals, oscillator strengths and lifetimes. The radial part of the Schrodinger equation is solved using Numerov’s method and matching conditions on the wave function and its derivative. Using the generated wave functions and energies, the dipole approximation is used to calculate the transition matrix elements. From this the oscillator strengths and lifetimes are calculated. Energy levels are seen to rise with tighter confinement. Oscillator strengths generally increase with loose confinement. For many transitions there is a certain confinement where the dipole oscillator strengths and radials integrals vanish as the two wave functions involved in the transition become orthogonal with respect to r. Lifetimes decrease under confinement. Unconfined lifetimes increase with n whereas, with sufficient confinement, this ordering becomes inverted – lifetimes decrease with n.

Clark S Snow (Masters Thesis, August 1997,
Advisor: Manuel Berrondo
)

Abstract

The vibrational frequencies of oxidic anions of the form (TOm)-n T= Si, Ge, P, B, S, Ta, W, Mo, Hf, C, Be and where m is four or three and n is four, three, two, one or zero. The calculations were performed using the Hartree-Fock Self-Consistent Field Method implemented in the Gaussian 4 program. All calculations were carried out on a free anion. The Los Alamos National Labs Two Double Zero 9LANL2DZ) basis set which employs a relativistic pseudopotential to treat the core electrons was used on all the calculations. Many of the recently developed scintillators have an oxidic component. It is believed that high vibrational frequencies of the oxidic component cause nonradiative transitions which quench the photo luminescence. The free anion frequencies are compared to averages of experimental crystal values and a scale factor relating free anion calculations to an average crystal environment is developed. Using the scale factor several scintillating materials were analyzed, the high frequencies are approximately 1085 cm-1 for berylate, 976 cm-1 for silicate, and 750 cm-1 for germinate. Frequencies below 1500 cm-1 are less likely to cause nonradiative transitions. This criteria suggests that the berylate, silicate, and germinate compounds make good scintillators.

Eric William Gardner (PhD Dissertation, December 1995,
Advisor: Manuel Berrondo
)

Abstract

A method is introduced for computational analysis and simulation of structures that is intermediate between the atomistic view and the continuum limit. This method, labeled here the mesoscopic model, consists of a large number of mass points representing the shape of the material, each interacting with their neighbors through Hooke’s law forces (springs). The arising dynamical equations are then solved by direct integration. This same method maybe extended to use anharmonic interactions rather than the simpler Hooke’s law forces in order to model nonlinear phenomena. The model is tested by comparing to beam theory for a rectangular bar fixed at one end, a load placed at the other. The results are linear in all spatial dimensions as predicted by beam theory, and linear in load for light to intermediate loads (slight negative curvature for heavier loads). Finally, a different method for material deformation is presented, i.e., a thin film on top of the bulk material that has different elastic and thermal properties from the bulk. With this method, structures with ribs etched in the back to control the deformation are modeled.

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

Abstract