Browsing by Subject "stability"
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Item Long-time dynamics of a hinged-free plate driven by a non-conservative force(EMS Press, 2022-02-25) Bonheure, Denis; Gazzola, Filippo; Lasiecka, Irena; Webster, JustinA partially hinged, partially free rectangular plate is considered, with the aim to address the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal stretching active in the span-wise direction. The wind-flow in the chord-wise direction is modeled through a piston-theoretic approximation, which provides both weak (frictional) dissipation and non-conservative forces. The long-time behavior of solutions is analyzed from various points of view. Compact global attractors, as well as fractal exponential attractors, are constructed using the recent quasi-stability theory. The non-conservative nature of the dynamics requires the direct construction of a uniformly absorbing ball, and this relies on the superlinearity of the stretching. For some parameter ranges, the non-triviality of the attractor is shown through the spectral analysis of the stationary linearized (non self-adjoint) equation and the existence of multiple unimodal solutions is shown. Several stability results, obtained through energy estimates under various smallness conditions and/or assumptions on the equilibrium set, are also provided. Finally, the existence of a finite set of determining modes for the dynamics is demonstrated, justifying the usual modal truncation in engineering for the study of the qualitative behavior of suspension bridge dynamics.Item Metacommunity theory meets restoration: isolation may mediate how ecological communities respond to stream restoration(Ecological Society of America, 2017) Swan, Christopher; Brown, BryanAn often-cited benefit of river restoration is an increase in biodiversity or shift in composition to more desirable taxa. Yet, hard manipulations of habitat structure often fail to elicit a significant response in terms of biodiversity patterns. In contrast to conventional wis- dom, the dispersal of organisms may have as large an influence on biodiversity patterns as environmental conditions. This influence of dispersal may be particularly influential in river networks that are linear branching, or dendritic, and thus constrain most dispersal to the river corridor. As such, some locations in river networks, such as isolated headwaters, are expected to respond less to environmental factors and less by dispersal than more well-connected down- stream reaches. We applied this metacommunity framework to study how restoration drives biodiversity patterns in river networks. By comparing assemblage structure in headwater vs. more well-connected mainstem sites, we learned that headwater restoration efforts supported higher biodiversity and exhibited more stable ecological communities compared with adjacent, unrestored reaches. Such differences were not evident in mainstem reaches. Consistent with theory and mounting empirical evidence, we attribute this finding to a relatively higher influ- ence of dispersal-driven factors on assemblage structure in more well-connected, higher order reaches. An implication of this work is that, if biodiversity is to be a goal of restoration activity, such local manipulations of habitat should elicit a more profound response in small, isolated streams than in larger downstream reaches. These results offer another significant finding supporting the notion that restoration activity cannot proceed in isolation of larger-scale, catchment-level degradation.Item Modeling Optical Time and Frequency Generation and Transfer Systems(2019-02-01) Menyuk, CurtisWe describe the results of a project to carry out theoretical and computational modeling of frequency comb sources in support of experimental efforts in the DARPA PULSE program. This work had two thrusts. The first was to model the SESAM fiber lasers that were used by the Newbury team at NIST to carry out free-space frequency transfer experiments. The second was to model frequency comb generation in microresonators, focusing on solitons and cnoidal waves. We developed a unique set of computational algorithms based on dynamical systems theory that allowed us to rapidly and unambiguously determine the stability and noise performance of the lasers and microresonators. We applied these tools to explain the performance limitations and optimize the performance of the SESAM lasers. We also used these tools to explain in part the difficulty in accessing solitons and to find a deterministic approach for generating large-bandwidth soliton trains, as a special limit of cnoidal waves.Item The small and large ribosomal subunits depend on each other for stability and accumulation(Life Science Alliance, 2019-03-05) Gregory, Brian; Rahman, Nusrat; Bommakanti, Ananth; Shamsuzzaman, Md; Thapa, Mamata; Lescure, Alana; Zengel, Janice M.; Lindahl, LasseThe 1:1 balance between the numbers of large and small ribosomal subunits can be disturbed by mutations that inhibit the assembly of only one of the subunits. Here, we have investigated if the cell can counteract an imbalance of the number of the two subunits. We show that abrogating 60S assembly blocks 40S subunit accumulation. In contrast, cessation of the 40S pathways does not prevent 60S accumulation, but does, however, lead to fragmentation of the 25S rRNA in 60S subunits and formation of a 55S ribosomal particle derived from the 60S. We also present evidence suggesting that these events occur post assembly and discuss the possibility that the turnover of subunits is due to vulnerability of free subunits not paired with the other subunit to form 80S ribosomes.