A Lipschitz stable reconstruction formula for the inverse problem for the wave equation

We consider the problem to reconstruct a wave speed c ∈ C∞(M) in a domain M ⊂ R n from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map Λ. We introduce a reconstruction formula for c that is based on the Boundary Control method and incorporates features also from the complex geometric optics solutions approach. Moreover, we show that the reconstruction formula is locally Lipschitz stable for a low frequency component of c −2 under the assumption that the Riemannian manifold (M, c−2dx2 ) has a strictly convex function with no critical points. That is, we show that for all bounded C 2 neighborhoods U of c, there is a C 1 neighborhood V of c and constants C, R > 0 such that |F ec −2 − c −2 � (ξ)| ≤ Ce2R|ξ| Λe − Λ ∗ , ξ ∈ R n , for all ec ∈ U ∩ V , where Λ is the Dirichlet-to-Neumann map corre- e sponding to the wave speed ec and k·k∗ is a norm capturing certain regularity properties of the Dirichlet-to-Neumann maps

Hyperbolic inverse problem with data on disjoint sets

We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and the Neumann traces are restricted on another subset. We show that the restricted Dirichlet-to-Neumann map determines the geometry and the lower order terms in the wave equation, up the natural gauge invariances, along a convex foliation of the manifold. The main novelty is the recovery of the lower order terms when the supports of the Dirichlet traces are disjoint from the set on which the Neumann traces are restricted. We allow the lower order terms to be non-self-adjoint, and in particular, the corresponding physical system may have dissipation of energy

Simulations on the Accuracy of Laser-Flash Data Analysis Methods

The Laser-Flash thermal diffusivity measurement method can be considered one of the most succesful applications of photothermal techniques. This due to the phenomenological and experimental simplicity and ease of reaching better than 1% accuracy over a wide temperature range. The method is based on observing the temperature rise of the sample back face resulting from the absorption of a laser pulse at the other face. There are various approaches for the data reduction and, especially for high temperature measurements where heat loss effects need to be accounted for, they are based on approximations. This is because the inverse function relating thermal properties and heat exchange conditions with the temperature rise temporal shape is not available in closed form. Therefore, detailed error propagation calculations analyses that would take into account all the steps of the data analysis procedures have not in general been performed for data. In this work, simulations of the noise sensitivity and accuracy of selected data reduction schemes were studied using synthetic data. The work was done in connection with the design of a high temperature laser-flash instrument for the measurement of ceramic composites for fusion reactor applications

Decomposition of coarse woody debris in a long-term litter manipulation experiment: A focus on nutrient availability

The majority of above-ground carbon in tropical forests is stored in wood, which is returned to the atmosphere during decomposition of coarse woody debris. However, the factors controlling wood decomposition have not been experimentally manipulated over time scales comparable to the length of this process.We hypothesized that wood decomposition is limited by nutrient availability and tested this hypothesis in a long-term litter addition and removal experiment in a lowland tropical forest in Panama. Specifically, we quantified decomposition using a 15-year chronosequence of decaying boles, and measured respiration rates and nutrient limitation of wood decomposer communities.The long-term probability that a dead tree completely decomposed was decreased in plots where litter was removed, but did not differ between litter addition and control treatments. Similarly, respiration rates of wood decomposer communities were greater in control treatments relative to litter removal plots; litter addition treatments did not differ from either of the other treatments. Respiration rates increased in response to nutrient addition (nitrogen, phosphorus, and potassium) in the litter removal and addition treatments, but not in the controls.Established decreases in concentrations of soil nutrients in litter removal plots and increased respiration rates in response to nutrient addition suggest that reduced rates of wood decomposition after litter removal were caused by decreased nutrient availability. The effects of litter manipulations differed directionally from a previous short-term decomposition study in the same plots, and reduced rates of bole decomposition in litter removal plots did not emerge until after more than 6 years of decomposition. These differences suggest that litter-mediated effects on nutrient dynamics have complex interactions with decomposition over time