An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations

Multiple Front Propagation Into Unstable States

The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable periodic pattern. It is found by a numerical solution of a model of the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of decay of such periodic unstable states is the propagation of a second front which replaces the unstable pattern by a another unstable periodic state with larger wavelength. The speed of this second front and the periodicity of the new state are analytically calculated with a generalization of the marginal stability formalism suited to the study of front propagation into periodic unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page

On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation

We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently localized initial conditions evolve in time into a monotonic front which propagates with speed $c^*$ such that $2 \sqrt{f'(0)} \leq c^* < 2 \sqrt{\sup(f(u)/u)}$. The lower value $c_L = 2 \sqrt{f'(0)}$ is that predicted by the linear marginal stability speed selection mechanism. We derive a new lower bound on the the speed of the selected front, this bound depends on $f$ and thus enables us to assess the extent to which the linear marginal selection mechanism is valid.Comment: 9 pages, REVTE

Modelling the economic efficiency of using different strategies to control Porcine Reproductive & Respiratory Syndrome at herd level

PRRS is among the diseases with the highest economic impact in pig production worldwide. Different strategies have been developed and applied to combat PRRS at farm level. The broad variety of available intervention strategies makes it difficult to decide on the most cost-efficient strategy for a given farm situation, as it depends on many farm-individual factors like disease severity, prices or farm structure. Aim of this study was to create a simulation tool to estimate the cost-efficiency of different control strategies at individual farm level. Baseline is a model that estimates the costs of PRRS, based on changes in health and productivity, in a specific farm setting (e.g. farm type, herd size, type of batch farrowing). The model evaluates different intervention scenarios: depopulation/repopulation (D/R), close & roll-over (C&R), mass vaccination of sows (MS), mass vaccination of sows and vaccination of piglets (MS + piglets), improvements in internal biosecurity (BSM), and combinations of vaccinations with BSM. Data on improvement in health and productivity parameters for each intervention were obtained through literature review and from expert opinions. The economic efficiency of the different strategies was assessed over 5 years through investment appraisals: the resulting expected value (EV) indicated the most cost-effective strategy. Calculations were performed for 5 example scenarios with varying farm type (farrow-to-finish – breeding herd), disease severity (slightly – moderately – severely affected) and PRRSV detection (yes – no). The assumed herd size was 1000 sows with farm and price structure as commonly found in Germany. In a moderately affected (moderate deviations in health and productivity parameters from what could be expected in an average negative herd), unstable farrow-to-finish herd, the most cost-efficient strategies according to their median EV were C&R (€1′126′807) and MS + piglets (€ 1′114′649). In a slightly affected farrow-to-finish herd, no virus detected, the highest median EV was for MS + piglets (€ 721′745) and MS (€ 664′111). Results indicate that the expected benefits of interventions and the most efficient strategy depend on the individual farm situation, e.g. disease severity. The model provides new insights regarding the cost-efficiency of various PRRSV intervention strategies at farm level. It is a valuable tool for farmers and veterinarians to estimate expected economic consequences of an intervention for a specific farm setting and thus enables a better informed decision

Population regulation in Magellanic penguins: what determines changes in colony size?

Seabirds are often studied at individual colonies, but the confounding effects of emigration and mortality processes in open populations may lead to inappropriate conclusions on the mechanisms underlying population changes. Magellanic penguin (Spheniscus magellanicus) colonies of variable population sizes are distributed along the Argentine coastline. In recent decades, several population and distributional changes have occurred, with some colonies declining and others newly established or increasing. We integrated data of eight colonies scattered along ~600 km in Northern Patagonia (from 41°26´S, 65°01´W to 45°11´S, 66°30´W, Rio Negro and Chubut provinces) and conducted analysis in terms of their growth rates, production of young and of the dependence of those vital rates on colony age, size, and location. We contrasted population trends estimated from abundance data with those derived from population modeling to understand if observed growth rates were attainable under closed population scenarios. Population trends were inversely related to colony size, suggesting a density dependent growth pattern. All colonies located in the north — which were established during the last decades — increased at high rates, with the smallest, recently established colonies growing at the fastest rate. In central-southern Chubut, where colonies are the oldest, the largest breeding aggregations declined, but smaller colonies remained relatively stable. Results provided strong evidence that dispersal played a major role in driving local trends. Breeding success was higher in northern colonies, likely mediated by favorable oceanographic conditions. However, mean foraging distance and body condition of chicks at fledging were influenced by colony size. Recruitment of penguins in the northern area may have been triggered by a combination of density dependence, likely exacerbated by less favorable oceanographic conditions in the southern sector. Our results reaffirm the idea that individual colony trends do not provide confident indicators of population health, highlighting the need to redefine the scale for the study of population changes.Fil: Pozzi, Luciana Melina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Garcia Borboroglu, Jorge Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina. Global Penguin Society. Washington; Estados Unidos. University of Washington; Estados UnidosFil: Boersma, P. Dee. Global Penguin Society. Washington; Estados Unidos. University of Washington; Estados UnidosFil: Pascual, Miguel Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina. Universidad Nacional de la Patagonia; Argentin

Renormalization Group Theory And Variational Calculations For Propagating Fronts

We study the propagation of uniformly translating fronts into a linearly unstable state, both analytically and numerically. We introduce a perturbative renormalization group (RG) approach to compute the change in the propagation speed when the fronts are perturbed by structural modification of their governing equations. This approach is successful when the fronts are structurally stable, and allows us to select uniquely the (numerical) experimentally observable propagation speed. For convenience and completeness, the structural stability argument is also briefly described. We point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the assumption of physical renormalizability. We also implement a variational principle, due to Hadeler and Rothe, which provides a very good upper bound and, in some cases, even exact results on the propagation speeds, and which identifies the transition from ` linear'- to ` nonlinear-marginal-stability' as parameters in the governing equation are varied.Comment: 34 pages, plain tex with uiucmac.tex. Also available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/front_RG.tex (or .ps.Z