Applications of adenine nucleotide measurements in oceanography

The methodology involved in nucleotide measurements is outlined, along with data to support the premise that ATP concentrations in microbial cells can be extrapolated to biomass parameters. ATP concentrations in microorganisms and nucleotide analyses are studied

Wave Structures and Nonlinear Balances in a Family of 1+1 Evolutionary PDEs

We study the following family of evolutionary 1+1 PDEs that describe the balance between convection and stretching for small viscosity in the dynamics of 1D nonlinear waves in fluids: m_t + \underbrace{um_x \} _{(-2mm)\hbox{convection}(-2mm)} + \underbrace{b u_xm \} _{(-2mm)\hbox{stretching}(-2mm)} = \underbrace{\nu m_{xx}\ }_{(-2mm)\hbox{viscosity}}, \quad\hbox{with}\quad u=g*m . Here $u=g*m$ denotes $u(x)=\int_{-\infty}^\infty g(x-y)m(y) dy .$ We study exchanges of stability in the dynamics of solitons, peakons, ramps/cliffs, leftons, stationary solutions and other solitary wave solutions associated with this equation under changes in the nonlinear balance parameter $b$.Comment: 69 pages, 26 figure

The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles

The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity \bdB = \bnabla q\times \bnabla\theta for the three-dimensional incompressible rotating Euler equations evolves according to the same stretching equation as for \bom the vorticity and \bB, the magnetic field in magnetohydrodynamics (MHD). The \bdB-vector therefore acts like the vorticity \bom in Euler's equations and the \bB-field in MHD. For example, it allows various analogies, such as stretching dynamics, helicity, superhelicity and cross helicity. In addition, using quaternionic analysis, the dynamics of the \bdB-vector naturally allow the construction of an orthonormal frame attached to fluid particles\,; this is designated as a quaternion frame. The alignment dynamics of this frame are particularly relevant to the three-axis rotations that particles undergo as they traverse regions of a flow when the PV gradient \bnabla q is large.Comment: Dedicated to Raymond Hide on the occasion of his 80th birthda

The Influence of Corn Removal Date on Corn Rootworm Oviposition, Resultant Larval Populations and Damage

The objective of this research was to determine the effect of corn removal for silage on rootworm oviposition and on the resulting populations and damage the following years. If the corn is removed before oviposition occurs, and if the beetles go elsewhere to lay their eggs, damage to the corn roots the following spring should be prevented. This would save farmers insecticide costs the following year. To determine how adult populations present in the corn field in late summer and fall affect damage to the corn the following spring, corn vegetation was removed on different dates encompassing the time oviposition was taking place. The damage to the corn from the resulting rootworm populations was correlated to the corn removal dates as affected by fall and spring plowing

Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction

In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic functions of the first kind.Comment: 17 page

GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc