Population Growth in Space and Time

How great an effect does self-generated spatial structure have on logistic population growth? Results are described from an individual based model (IBM) with spatially localized dispersal and competition, and from a deterministic approximation to the IBM describing the dynamics of the first and spatial moments. The dynamical system incorporates a novel closure that gives a close approximation to the IBM in the presence of strong spatial structure. Population growth given by the spatial logistic equation can differ greatly from that of the non-spatial logistic model. Numerical simulations show that populations may grow more slowly or more rapidly than would be expected from the non-spatial model, and may reach their maximum rate of increase at densities other than half of the carrying capacity. Populations can achieve asymptotic densities substantially greater than or less than the carrying capacity of the non-spatial logistic model, and can even tend toward extinction. These properties of the spatial logistic equation are caused by a local dispersal and competition which effect spatial structure, which in turn affects population growth. Accounting for these spatial processes brings the theory of single-species population growth a step closer to the growth of real spatially-structured populations

Causes and Effects of Small-Scale Spatial Structure in Plant Populations

Small-scale spatial structure is important in plant ecology. Plants interact primarily with their immediate neighbors and the view of the community as seen by an individual plant can be quite different from large-scale spatial average. We describe a spatial statistic that captures the plant's-eye view and use it to illustrate the strong spatial structure present in a grassland community. Many processes affect small-scale spatial structure, including intraspecific competition, dispersal of propagules, interactions with other species and the spatial structure of the environment. Spatial structure in turn affects the the vital processes of growth, birth and death; the dynamics of plant communities thus involve a coupling of spatial structure and the vital processes. We describe recent work towards making this coupling explicit by means of individual-based models and the dynamics of spatial moments

Development and testing of a SREX flowsheet for the partitioning of strontium and lead from simulated ICPP sodium-bearing waste

Laboratory experimentation has indicated that the SREX process is effective for partitioning {sup 90}Sr from acidic radioactive waste solutions located at the Idaho Chemical Processing Plant. Previous countercurrent flowsheet testing of the SREX process with simulated waste resulted in 99.98% removal of Sr. With this previous test, however, Pb was extracted by the SREX solvent and was not back-extracted in the dilute nitric acid strip section. The Pb concentration increased in the recycled solvent and in the aqueous phase of the strip section, resulting in the formation of a Pb precipitate. Subsequently, studies were initiated to identify alternative stripping agents which will selectively strip Sr and Pb from the SREX solvent. Based on the results of these studies, a countercurrent flow sheet was developed and tested in the 5.5-cm Centrifugal Contactor Mockup using simulated waste. The flowsheet tested consisted of an extraction section (0.15 M 4{prime},4{prime}(5)-di-(tert-butyldicyclohexo)-18-crown-6 and 1.2 M TBP in Isopar-L{reg_sign}), a 0.05 M nitric acid strip section for the removal of Sr from the SREX solvent, a 0.1 M ammonium citrate strip section for the removal of Pb from the SREX solvent, and a 2.0 M nitric acid equilibration section. The behavior of Sr, Pb, Al, Ca, Hg, Na, Zr, and H{sup +} was evaluated. The described flowsheet successfully extracted and selectively stripped Sr and Pb from the SBW simulant. Removal efficiencies of 97.9% and 99.91% were obtained for Sr and Pb, respectively. Essentially all of the extracted Sr (99.998%) and 1.9% of extracted Pb exited with the 0.05 M nitric acid strip product; whereas, 0.002% of the extracted Sr and 97.9% of the extracted Pb existed with the 0.1 M ammonium citrate strip product. Also, 95% of the Hg and 63% of the Zr were extracted by the SREX solvent

Optimally squeezed spin states

We consider optimally spin-squeezed states that maximize the sensitivity of the Ramsey spectroscopy, and for which the signal to noise ratio scales as the number of particles $N$. Using the variational principle we prove that these states are eigensolutions of the Hamiltonian $H(\lambda)=\lambda S_z^2-S_x,$ and that, for large $N$, the states become equivalent to the quadrature squeezed states of the harmonic oscillator. We present numerical results that illustrate the validity of the equivalence

Statistics of level spacing of geometric resonances in random binary composites

We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing distribution $P(t)$ and level number variance $\Sigma^2(L)$ have the general features. It is also shown that the short-range fluctuation $P(t)$ and long-range spectral correlation $\Sigma^2(L)$ lie between the profiles of the Poisson ensemble and Gaussion orthogonal ensemble (GOE). At the percolation threshold $p_c$, crossover behavior of functions $P(t)$ and $$ is obtained, giving the finite size scaling of mean level spacing $\delta$ and mean level number $n$, which obey the scaling laws, $$ and $n=0.911L^{1.970}$.Comment: 11 pages, 7 figures,submitted to Phys. Rev.

On the Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations

Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier spacediagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose-Einstein condensates

Dynamics of Dark-Bright Solitons in Cigar-Shaped Bose-Einstein Condensates

We explore the stability and dynamics of dark-bright solitons in two-component elongated Bose-Einstein condensates by developing effective 1D vector equations as well as solving the corresponding 3D Gross-Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the dark-bright (DB) soliton on the atom number of its components is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom for a large occupation of the component supporting the dark soliton. Moreover, the interactions of two DB solitons are investigated with special emphasis on the importance of their relative phases. Experimental results showcasing dark-bright soliton dynamics and collisions in a BEC consisting of two hyperfine states of $^{87}$Rb confined in an elongated optical dipole trap are presented.Comment: 4 pages, 5 figure

Darkness visible: reflections on underground ecology

1 Soil science and ecology have developed independently, making it difficult for ecologists to contribute to urgent current debates on the destruction of the global soil resource and its key role in the global carbon cycle. Soils are believed to be exceptionally biodiverse parts of ecosystems, a view confirmed by recent data from the UK Soil Biodiversity Programme at Sourhope, Scotland, where high diversity was a characteristic of small organisms, but not of larger ones. Explaining this difference requires knowledge that we currently lack about the basic biology and biogeography of micro-organisms. 2 It seems inherently plausible that the high levels of biological diversity in soil play some part in determining the ability of soils to undertake ecosystem-level processes, such as carbon and mineral cycling. However, we lack conceptual models to address this issue, and debate about the role of biodiversity in ecosystem processes has centred around the concept of functional redundancy, and has consequently been largely semantic. More precise construction of our experimental questions is needed to advance understanding. 3 These issues are well illustrated by the fungi that form arbuscular mycorrhizas, the Glomeromycota. This ancient symbiosis of plants and fungi is responsible for phosphate uptake in most land plants, and the phylum is generally held to be species-poor and non-specific, with most members readily colonizing any plant species. Molecular techniques have shown both those assumptions to be unsafe, raising questions about what factors have promoted diversification in these fungi. One source of this genetic diversity may be functional diversity. 4 Specificity of the mycorrhizal interaction between plants and fungi would have important ecosystem consequences. One example would be in the control of invasiveness in introduced plant species: surprisingly, naturalized plant species in Britain are disproportionately from mycorrhizal families, suggesting that these fungi may play a role in assisting invasion. 5 What emerges from an attempt to relate biodiversity and ecosystem processes in soil is our extraordinary ignorance about the organisms involved. There are fundamental questions that are now answerable with new techniques and sufficient will, such as how biodiverse are natural soils? Do microbes have biogeography? Are there rare or even endangered microbes