Using chaotic forcing to detect damage in a structure

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure.     

Testing whether two chaotic one dimensional processes are dynamically identical

Consider the situation where two individuals observe the same chaotic physical process but through time series of different measured variables (e.g., one individual measures a temperature and the other measures a voltage). If the two individuals now use their data to reconstruct (e.g., via delay coordinates) a map, the maps they obtain may appear quite different. In the case where the resulting maps appear one dimensional, we introduce a method to test consistency with the hypothesis that they represent the same physical process. We illustrate this method using experimental data from an electric circuit.     

MECHANISMS OF QUENCHING OF THE FLUORESCENCE OF A BENZO[a]PYRENE TETRAOL METABOLITE MODEL COMPOUND BY 2'-DEOXYNUCLEOSIDES

Abstract— The hydrophobic interactions of bulky polycyclic aromatic hydrocarbons with nucleic acid bases and the formation of noncovalent complexes with DNA are important in the expressions of the mutagenic and carcinogenic potentials of this class of compounds. The fluorescence of the polycyclic aromatic residues can be employed as a probe of these interactions. In this work, the interactions of the (+)-trans stereoisomer of the tetraol 7,8,9,10-tetrahydroxytetrahydrobenzo[a]pyrene (BPT), a hydrolysis product of a highly mutagenic and carcinogenic diol epoxide derivative of benzo[a]pyrene, were studied with 2′-deoxynucleosides in aqueous solution by fluorescence and UV spectroscopic techniques. Ground-state complexes between BPT and the purine derivatives 2′-deoxyguanosine (dG), 2′-deoxyadenosine (dA), and 2′-deoxyinosine (dI) are formed with association constants in the range of ～40–130 M^?1 Complex formation with the pyrimidine derivatives 2′-deoxythymidine (dT), 2′-deoxycytidine (dC), and 2′-deoxyuridine (dU) is significantly weaker. Whereas dG is a strong quencher of the fluorescence of BPT by both static and dynamic mechanisms (dynamic quenching rate constant k_dyn= [2.5 ± 0.41 × 10⁹M¹ s ¹, which is close to the estimated diffusion-controlled value of ～ 5 × 10⁹M^{? 1} s^?1), both dA and dI are weak quenchers and form fluorescenceemitting complexes with BPT. The pyrimidine derivatives dC, dU, and dT are efficient dynamic fluorescence quenchers (K_dyn～ [1.5–3.0] × 10⁹M^?1 s^?1), with a small static quenching component due to complex formation evident only in the case of dT. None of the four nucleosidcs dG, dA, dC and dT are dynamic quenchers of BPT in the triplet excited state; the observed lower yields of triplets are attributed to the quenching of single excited states of BPT by 2′-deoxynucleosides without passing through the triplet manifold of BPT. Possible fluorescence quenching mechanisms involving photoinduced electron transfer are discussed. The strong quenching of the fluorescence of BPT by dG, dC and dT accounts for the low fluorescence yields of BPT-native DNA and of pyrene-DNA complexes.     

Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data

We show that one can use recently introduced statistics for continuity and differentiability to show the effect of filters of infinite extent in time on a chaotic time series. The statistics point to a discontinuous or nondifferentiable function between the unfiltered attractor and the filtered attractor as the origin of attractor dimension increase when the filtering is severe. The density of discontinuities as a function of resolution follows a scaling relation. We present direct visualization of this effect in the filtered Henon attractor where the origin of dimension increase becomes obvious.     

High-performance liquid chromatography and capillary electrophoresis: methodological challenges for the determination of biologically relevant low-aliphatic aldehydes in human saliva

Tobacco smoke is involved in the pathogenesis of cardiovascular and respiratory diseases and also has a local toxic effect in the oral cavity. Low-aliphatic aldehydes, such as formaldehyde, acetaldehyde and acrolein, are among the main components of mainstream cigarette smoke and their local noxious and carcinogenic effects in the oral cavity and upper gastrointestinal tract are well-known. Although various studies have been performed so far to determine their content in cigarette smoke, none has included the direct measurement of these compounds in the saliva of smoking and nonsmoking subjects. Thus, in an attempt to verify whether typical chromatographic (high-performance liquid chromatography, HPLC) and/or electrophoretic (capillary electrophoresis, CE) techniques could be reliable methods for determining the levels of these analytes in human saliva, we submitted specimens obtained from a selected population of heavy, moderate, and nonsmoking subjects to HPLC and CE analyses. Both methods showed good reproducibility in terms of migration times and peak height and/or areas and had comparable linearity. Quantitative analyses performed on the specimens investigated evidenced a 3.5-fold increase of low-aliphatic aldehydes in saliva of nonsmoking subjects after they have smoked a single cigarette and a further 2-fold increase of these compounds in saliva of smokers with a daily consumption of 10 or more cigarettes.     

A unified approach to attractor reconstruction

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e., attractor reconstruction. The process has focused primarily on intuitive, heuristic, and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approach has left several longstanding, but common problems unresolved in which the standard approaches produce inferior results or give no guidance at all. We view the current reconstruction process as unnecessarily broken into separate problems. We propose an alternative approach that views the problem of choosing all embedding parameters as being one and the same problem addressable using a single statistical test formulated directly from the reconstruction theorems. This allows for varying time delays appropriate to the data and simultaneously helps decide on embedding dimension. A second new statistic, undersampling, acts as a check against overly long time delays and overly large embedding dimension. Our approach is more flexible than those currently used, but is more directly connected with the mathematical requirements of embedding. In addition, the statistics developed guide the user by allowing optimization and warning when embedding parameters are chosen beyond what the data can support. We demonstrate our approach on uni- and multivariate data, data possessing multiple time scales, and chaotic data. This unified approach resolves all the main issues in attractor reconstruction.     

Centred TVD schemes for hyperbolic conservation laws

New first- and high-order centred methods for conservation lawsare presented. Convenient TVD conditions for constructing centredTVD schemes are then formulated and some useful results areproved. Two families of centred TVD schemes are constructedand extended to nonlinear systems. Some numerical results arealso presented.