Fast neural oscillations known as beta (12-30Hz) and gamma (30-100Hz) rhythms are recorded across several brain areas of various species. They have been linked to diverse functions like perception, attention, cognition, or interareal brain communication. The majority of the tasks performed by the brain involves communication between brain areas. To efficiently perform communication, mathematical models of brain activity require representing neural oscillations as sustained and coherent rhythms. However, some recordings show that fast oscillations are not sustained or coherent. Rather they are noisy and appear as short and random epochs of sustained activity called bursts. Therefore, modeling such noisy oscillations and investigating their ability to show interareal coherence and phase synchronization are important questions that need to be addressed. In this thesis, we propose theoretical models of noisy oscillations in the gamma and beta bands with the same properties as those observed in in \textit{vivo}. Such models should exhibit dynamic and statistical features of the data and support dynamic phase synchronization. We consider networks composed of excitatory and inhibitory populations. Noise is the result of the finite size effect of the system or the synaptic inputs. The associated dynamics of the Local Field Potentials (LFPs) are modeled as linear equations, sustained by additive and/or multiplicative noises. Such oscillatory LFPs are also known as noise-induced or quasi-cycles oscillations. The LFPs are better described using the envelope-phase representation. In this framework, a burst is defined as an epoch during which the envelope magnitude exceeds a given threshold. Fortunately, to the lowest order, the envelope dynamics are uncoupled from the phase dynamics for both additive and multiplicative noises. For additive noise, we derive the mean burst duration via a mean first passage time approach and uncover an optimal range of parameters for healthy rhythms. Multiplicative noise is shown theoretically to further synchronize neural activities and better explain pathologies with an excess of neural synchronization. We used the stochastic averaging method (SAM) as a theoretical tool to derive the envelope-phase equations. The SAM is extended to extract the envelope-phase equations of two coupled brain areas. The goal is to tackle the question of phase synchronization of noise-induced oscillations with application to interareal brain communication. The results show that noise and propagation delay are essential ingredients for dynamic phase synchronization of quasi-cycles. This suggests that the noisy oscillations recorded in \textit{vivo} and modeled here as quasi-cycles are good candidates for such neural communication. We further extend the use of the SAM to describe several coupled networks subject to white and colored noises across the Hopf bifurcation ie in both quasi-cycle and limit cycle regimes. This allows the description of multiple brain areas in the envelope-phase framework. The SAM constitutes an appropriate and flexible theoretical tool to describe a large class of stochastic oscillatory phenomena through the envelope-phase framework.

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Using computational deterministic and Monte Carlo methods, I present an analysis of the gamma and neutron signatures emitted from special nuclear material (SNM) in weapons stockpile storage scenarios. My efforts are focused on 1 year old, 25 year old, 50 year old, and 75 year old highly enriched uranium (HEU), and 1 year old, 22.5 year old, and 50 year old weapons grade plutonium (WGPu). HEU gammas are easily shielded, and when reasonably shielded, do not produce a definable signature at low energies; however, using new methods applied in this work that involve analyzing the higher energy, penetrating gammas from HEU, it can be shown that not only the presence of the HEU can be verified, but also the age since separation of the material can be discerned. Through computational modeling, I am able to verify that the novel methods investigated are both unique and effective for HEU detection. In addition, I also present my investigation of similar methods applied to the detection of WGPu. From this work I determined that WGPu age discrimination is more challenging compared to that of HEU (in spite of more radiation per unit mass) due to the high rate of induced gammas from n-gamma interactions taking place within the Pu metal and container; however, I believe that by combining neutron detection with gamma signature verification of WGPu, the approach identified can be successful. I present the neutron signature of the WGPu and how it would be observed in the detector used for material verification. I calculated the detector response for a pre-determined neutron detector design using adjoint calculations in order to determine whether the detector will perform as designed. In addition to developing a new protocol for WGPu detection, I present in this work, a comprehensive source book as a product of this research, detailing the gamma and neutron signatures for both solid and shell configurations of HEU and WGPu. This can serve as a very beneficial guide for anyone interested in modeling SNM, since the many steps needed to obtain this radiation leakage data will save a significant amount of researcher time. The results from my work have contributed to a collaborative effort supporting funded US department of State research towards designing a mobile detection system that can rapidly validate and verify the presence of SNM in weapons pit containers.

published_or_final_version / abstract / toc / Physics / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

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