Lodgepole Pine Bole Wood Density and Decay Rate 1, 11, and 22 Years After Felling in Central Montana, United States

Estimates of dead and down woody material (DWM) biomass are important for nutrient cycling, wildlife habitat assessment, fire effects and climate change science. Most methods used to sample woody material initially assess volume then estimates of wood density are used to convert volume to biomass. To assess initial wood density and decomposition rate, this study examined in situ wood density of lodgepole pine logs at the Tenderfoot Creek Experimental Forest (TCEF), central Montana, United States, 1, 11, and 22 years after felling. Mean wood density decreased from 0.39 to 0.27 g cm–3 over 22 years and the single exponential decay rate was k = 0.012 yr–1 1 and 11-years post-felling and 0.022 yr–1 11 and 22 years post-felling. A common 5-category decay classification system was evaluated for estimating wood density by decay class, which identified significant difference in three of four observed classes.

Diatom Dominance Enhances Resistance of Phytoplanktonic POM to Mesopelagic Microbial Decomposition

Particulate organic matter (POM) lability is one of the key factors determining the residence time of organic carbon (OC) in the marine system. Phytoplankton community composition can influence the rate at which heterotrophic microorganisms decompose phytoplankton detrital particles and thus, it controls the fraction of OC that reaches the ocean depths, where it can be sequestered for climate-relevant spans of time. Here, we compared the degradation dynamics of POM from phytoplankton assemblages of contrasting diatom dominance in the presence of mesopelagic prokaryotic communities during a 19-day degradation experiment. We found that diatom-derived POM exhibited an exponential decay rate approximately three times lower than that derived from a community dominated by flagellated phytoplankton (mainly coccolithophores and nanoflagellates). Additionally, dissolved organic matter (DOM) released during the degradation of diatom particles accumulated over the experiment, whereas only residual increases in DOM were detected during the degradation of non-diatom materials. These results suggest that diatom-dominance enhances the efficiencies of the biological carbon pump and microbial carbon pump through the relatively reduced labilities of diatom particles and of the dissolved materials that arise from their microbial processing.

Feedback stabilization of a 3D fluid flow by shape deformations of an obstacle

We consider a fluid flow in a time dependent domain $\Omega_f(t)=\Omega \setminus \Omega_s(t)\subset {\mathbb R}^3$, surrounding a deformable obstacle $\Omega_s(t)$. We assume that the fluid flow satisfies the incompressible Navier-Stokes equations in $\Omega_f(t)$, $t>0$. We prove that, for any arbitrary exponential decay rate $\omega>0$, if the initial condition of the fluid flow is small enough in some norm, the deformation of the boundary $\partial \Omega_s(t)$ can be chosen so that the fluid flow is stabilized to rest, and the obstacle to its initial shape and its initial location, with the exponential decay rate $\omega>0$.

Large deviations for acyclic networks of queues with correlated Gaussian inputs

We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The flow of work departing from each server is split deterministically and routed to its neighbors according to a fixed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any fixed threshold, also referred to as the ‘overflow probability’. In particular, we first leverage Schilder’s sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to infinity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are nonnegatively correlated, non-short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.

Decision Theory and large deviations for dynamical hypotheses tests: The Neyman-Pearson Lemma, Min-Max and Bayesian tests

<p style='text-indent:20px;'>We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different Hölder Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is that here the two measures are singular with respect to each other. Among other objectives, we are interested in the decay rate of the wrong decisions probability, when the sample size <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> goes to infinity. We show a dynamical version of the Neyman-Pearson Lemma displaying the ideal test within a certain class of similar tests. This test becomes exponentially better, compared to other alternative tests, when the sample size goes to infinity. We are able to present the explicit exponential decay rate. We also consider both, the Min-Max and a certain type of Bayesian hypotheses tests. We shall consider these tests in the log likelihood framework by using several tools of Thermodynamic Formalism. Versions of the Stein's Lemma and Chernoff's information are also presented.</p>

Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

<p style='text-indent:20px;'>In this paper, we consider the initial boundary value problem for a mixed pseudo-parabolic Kirchhoff equation. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions with initial energy <inline-formula><tex-math id="M1">\begin{document}$ J(u_0)\leq d $\end{document}</tex-math></inline-formula>. When the initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_0)&gt;d $\end{document}</tex-math></inline-formula>, we find another criterion for the vanishing solution and blow-up solution. Our interest also lies in the discussion of the exponential decay rate of the global solution and life span of the blow-up solution.</p>

Stability of a suspension bridge with a localized structural damping

<p style='text-indent:20px;'>Strong vibrations can cause lots of damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exist evidences that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes, winds, ..., features and modifications such as dampers are used to stabilize these bridges. In this work, we use a minimum amount of dissipation to establish exponential decay- rate estimates to the following nonlocal evolution equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}(x,y,t)+\Delta^2 u(x,y,t) - \phi(u) u_{xx}- \left(\alpha(x, y) u_{xt}(x,y,t)\right)_x = 0, $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>which models the deformation of the deck of either a footbridge or a suspension bridge.</p>

Optimal Control and Simulation for Enterprise Financial Risk in Industry Environment

A technique for enterprise financial risk optimal control with exponential decay rate and simulation is developed in industry environment. The factors of industry environment risks to enterprise financial activities are considered, based on the evaluation method taking into both subjectivity and objectivity, seven kinds of industry environment risks influencing enterprise financial activities are chosen as state variables, and the enterprise financial risk dynamical system model is established for the first time. In order to reduce the risk of enterprise financial activity subjected to industry environment, an average performance index with exponential decay rate is chosen for the systems. Using the optimal control approach, an optimal vibration controller with exponential decay rate is designed. Numerical simulation results illustrate the effectiveness of the proposed technique.