Dynamics of Irreducible Endomorphisms of FnF_n

We consider the class non-surjective irreducible endomorphisms of the free group $F_n$. We show that such an endomorphism $\phi$ is topologically represented by a simplicial immersion $f:G \rightarrow G$ of a marked graph $G$; along the way we classify the dynamics of $\partial \phi$ acting on $\partial F_n$: there are at most $2n$ fixed points, all of which are attracting. After imposing a necessary additional hypothesis on $\phi$, we consider the action of $\phi$ on the closure $\bar{CV}_n$ of the Culler-Vogtmann Outer space. We show that $\phi$ acts on $\bar{CV}_n$ with "sink" dynamics: there is a unique fixed point $[T_{\phi}]$, which is attracting; for any compact neighborhood $N$ of $[T_{\phi}]$, there is $K=K(N)$, such that $\bar{CV}_n\phi^{K(N)} \subseteq N$. The proof uses certian projections of trees coming from invariant length measures. These ideas are extended to show how to decompose a tree $T$ in the boundary of Outer space by considering the space of invariant length measures on $T$; this gives a decomposition that generalizes the decomposition of geometric trees coming from Imanishi's theorem.Comment: v3, 46 pages, corrected gap in decomposition resul

Investigation of the growth potential and ecosystem impact of intensively farmed Atlantic salmon fed on experimental diets.

There are increasing concerns regarding the environmental impacts and sustainability of intensive fish farming. In particular, criticism has centred on the use of fish meal and fish oil in the diets of farmed carnivorous fish species such as Atlantic salmon. If the industry is to continue to expand, reduction in the levels of fish meal and fish oil incorporated into diets and/or the use of alternative terrestrial sources of protein and oil must occur. The present study assesses several diet types containing different inclusion levels and /or sources of protein and oil in terms of growth and performance as well as assessing the diets in terms of sustainability and their potential to impact on the marine environment. In two nutritional studies, Atlantic salmon fed a low protein (LP) diet achieved similar growth and performance compared to fish fed a normal commercial diet (control diet) in both studies. Growth rates of fish fed a diet containing partial replacement of fishmeal with corn gluten and fish oil with rapeseed oil (SUS) were better than those of fish fed the control and LP diet and were similar to those of fish fed a high energy; nutrient dense (ND) diet. The amount of wild fish required to produce 1 Kg farmed salmon based on fish meal and fish oil inclusion levels were lowest for fish fed the SUS diet (1.3 kg) whilst fish fed LP diets had a lower conversion value compared to both the ND and control diets based on fish meal inclusion levels only. These results suggest there is potential for aquaculture to be more environmentally sustainable by reducing the amounts of marine fishmeal and oil used in diets fed to intensively farmed Atlantic salmon. In terms of dissolved wastes, fish fed a nutrient dense diet had higher feedrelated concentration peaks of ammonia detected which occurred earlier compared to fish fed other diet types. In contrast, fish introduced to low protein diets at different sizes throughout the marine phase of production had consistently lower concentration peaks of ammonia detected compared to fish fed a standard commercial ration. All groups fed a low protein diet had between 17 and 28 % less ammonia detected as a feed related concentration peak compared to the control group. The area under each concentration peak of ammonia ranged from 43.6 to 88.8 % ± 60 min of total ammonia detected over time for all diets. These results show that feeding fish diets containing lower inclusion levels of fish meal resulted in lower feed related concentration peaks of ammonia being detected. However most of the ammonia was excreted over a short time period and its potential to impact on the marine environment was assessed using mesocosm studies. In the first of two studies, mesocosms were fertilised with NH4CI based on ammonia concentration peaks from either 500 or 1000 T rainbow trout production (LN and HN enclosures respectively). These enclosures had consistently more phytoplankton present than the control enclosures. There was evidence of rapid uptake of excess nutrients with the HN enclosures having more cells present than the LN enclosures. In the second experiment, enclosures were fertilised based on ammonia concentration peaks detected from Atlantic salmon fed a low protein (LP enclosures) or a nutrient dense diet (ND enclosures). Both had consistently more cells present than the control enclosures.. These results suggest that increases in phytoplankton communities may occur as a result of a single pulsed release of ammonia simulating discharge from intensively farmed fish. The predicted rate of dissolved nitrogen production was calculated from fish introduced to low protein diets throughout a complete marine production phase using a mass balance model. Fish introduced to low protein diets at 330, 800 and 1600 g had lower dissolved N discharge rates (22.51, 22.02 and 21.07 Kg'1 NT'1 Production respectively) compared to fish fed a standard commercial ration (23.32 Kg-1 NT-1 Production). These results show that there is potential to maximise use of low protein diets, which would result in less ammonia excretion and reduce the potential risk to impact on the marine environment. In an attempt to accurately quantify waste outputs from intensively farmed Atlantic salmon a custom-made tarpaulin was designed. Initial studies have shown that there is potential to collect data on waste outputs from fish reared in the marine environment whilst taking in to account seasonal and daily fluctuations in water temperature and salinity. The system can be used to directly compare different feed types and feeding strategies. It has been shown that changing the macronutrient inclusion level and sources results in differences in the physical characteristics of extruded feeds. High energy diets and substitution diets have similar settling velocities compared to a standard commercial diet but produce lower environmental impacts when modelled for solid waste impacts. Low protein pellets have slower sinking rates but generate more waste due to a higher FCR. The data from these results should be used in conjunction with other data for a range of feeds and environmental conditions to employ a “look-up table” approach to differentiate between diets when modelling waste dispersion

Simulational studies of epitaxial semiconductor superlattices: Quantum dynamical phenomena in ac and dc electric fields

Using high-accuracy numerical methods we investigate the dynamics of independent electrons in both ideal and realistic superlattices subject to arbitrary ac and/or dc electric fields. For a variety of superlattice potentials, optically excited initial wave packets, and combinations of ac and dc electric fields, we numerically solve the time-dependent Schrodinger equation. In the case of ideal periodic superlattice potentials, we investigate a long list of dynamical phenomena involving multiple miniband transitions and time-dependent electric fields. These include acceleration effects associated with interminiband transitions in strong fields, Zener resonances between minibands, dynamic localization with ac fields, increased single-miniband transport with an auxiliary resonant ac field, and enhanced or suppressed interminiband probability exchange using an auxiliary ac field. For all of the cases studied, the resulting time-dependent wave function is analyzed by projecting the data onto convenient orthonormal bases. This allows a detailed comparison with approximate analytic treatments;In an effort to explain the rapid decay of experimentally measured Bloch oscillation (BO) signals we incorporate a one-dimensional representation of interface roughness (IR) into our superlattice potential. We show that as a result of IR, the electron dynamics can be characterized in terms of many discrete, incommensurate frequencies near the Bloch frequency. The interference effects associated with these frequencies cause a substantial decrease in amplitude of the signal after several Bloch periods. We suggest that this is an important source of coherence loss in BO signals at low temperature and low carrier density. We also propose an experimental method that should significantly reduce the effects of IR by exciting electrons to only a single layer of the superlattice. This is accomplished by doping the central GaAs layer with a very small amount (\u3c1%) of In, thus reducing the energy gap for this layer. Thus, a laser excitation pulse tuned somewhat below the nominal electron-hole excitation energy, will only excite a few Wannier-Stark eigenstates associated with this In-doped layer. Our numerical simulations show that the THz signal from electrons optically excited using this novel procedure is nearly free from all inhomogeneous broadening associated with IR

One Small Step: An Analysis of International Space Law and How it Effects Historic Preservation

From 1969 to 1972 NASA\u27s Apollo Program successfully completed six separate manned lunar landings. Since 1972 there has been no human presence on the Moon. The lunar landing sites of Apollo\u27s 11, 12, 14, 15, 16, and 17 have sat in situ for forty years in the absolute zero vacuum of outer space. As the next phase of lunar exploration draws closer, it is important to protect the Apollo Lunar Landing Sites from exploration and damage because of their importance to human cultural heritage. This thesis assesses the international treaties that govern outer space, the Moon, and other celestial bodies and interprets whether they allow for the legal protection of human archeological sites in extraterrestrial settings. This thesis explains that is it not impossible, however extremely complicated to protect the Apollo Lunar Landing Sites because of these international laws. However, preservation on a national level is legally possible and explained in detail