The measurement of phytoplankton distributions in ocean ecosystems provides the basis for elucidating the influences of physical processes on plankton dynamics. Technological advances allow for measurement of phytoplankton data to greater resolution, displaying high spatial variability. In conventional mathematical models, the mean value of the measured variable is approximated to compare with the model output, which may misinterpret the reality of planktonic ecosystems, especially at the microscale level. To consider intermittency of variables, in this work, a new modelling approach to the planktonic ecosystem is applied, called the closure approach. Using this approach for a simple nutrient-phytoplankton model, we have shown how consideration of the fluctuating parts of model variables can affect system dynamics. Also, we have found a critical value of variance of overall fluctuating terms below which the conventional non-closure model and the mean value from the closure model exhibit the same result. This analysis gives an idea about the importance of the fluctuating parts of model variables and about when to use the closure approach. Comparisons of plot of mean versus standard deviation of phytoplankton at different depths, obtained using this new approach with real observations, give this approach good conformity.

We study the two-dimensional affine Toda field equations for affine Lie algebra $\hat{\mathfrak{g}}$ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra $\hat{\mathfrak{g}}$, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra $\mathfrak{g}$, which were found by Dorey et al. in study of the ODE/IM correspondence.Comment: 29 pages; added references and note, fixed typos, minor rewritin

We study the linear problem associated with modified affine Toda field equation for the Langlands dual $\hat{\mathfrak{g}}^\vee$, where $\hat{\mathfrak{g}}$ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the $Q$-functions for $\mathfrak{g}$-type quantum integrable models. The $\psi$-system for the solutions associated with the fundamental representations of $\mathfrak{g}$ leads to Bethe ansatz equations associated with the affine Lie algebra $\hat{\mathfrak{g}}$. We also study the $A^{(2)}_{2r}$ affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T-Q relations.Comment: 22 page

The TORUS algorithm is able to automatically generate trajectories having improved plan quality and delivery time over standard IMRT and VMAT treatments. TORUS offers an exciting and promising avenue forward toward increasing dynamic capabilities in radiation delivery.

This paper discusses a turbulent intermittency model introduced in 1990, the B-model. It was found that the original manuscript which introduced the B-model contained a couple arithmetic errors in the equations. This work goes over corrections to the original equations, and explains where problems arose in the derivations. These corrections cause the results to differ from those in the original manuscript, and these differences are discussed. A generalization of this B-model is then introduced to explore the range of behaviors this style of model provides. To distinguish between the different intermittency models discussed in this paper requires structure function power exponents of order greater than 12. As a source of comparison, data from a flume experiment is introduced, and, with the corrections introduced, this data seems to imply that an intermittency coefficient between 0.17 and 0.2 gives good agreement. Higher quality future measurements of high order moments could help with distinguishing the different intermittency models.