No abstract

For the three-dimensional case under hypotheses related to bounded curvature of the boundaries, see C. de la Vall6e Poussin, Propriitis des fonctions harmoniques dans un domaine ouvert limite par des surfaces d courbure bornee,

Parameter identification determines the essential system parameters required to build real-world dynamical systems by fusing crucial physical relationships and experimental data. However, the data-driven approach faces main difficulties, such as a lack of observational data, discontinuous or inconsistent time trajectories, and noisy measurements. The ill-posedness of the inverse problem comes from the chaotic divergence of the forward dynamics. Motivated by the challenges, we shift from the Lagrangian particle perspective to the state space flow field's Eulerian description. Instead of using pure time trajectories as the inference data, we treat statistics accumulated from the Direct Numerical Simulation (DNS) as the observable, whose continuous analog is the steady-state probability density function (PDF) of the corresponding Fokker-Planck equation (FPE). We reformulate the original parameter identification problem as a data-fitting, PDE-constrained optimization problem. An upwind scheme based on the finite-volume method that enforces mass conservation and positivity preserving is used to discretize the forward problem. We present theoretical regularity analysis for evaluating gradients of optimal transport costs and introduce three different formulations for efficient gradient calculation. Numerical results using the quadratic Wasserstein metric from optimal transport demonstrate this novel approach's robustness for chaotic dynamical system parameter identification.

The night-time atmospheric chemistry of the biogenic volatile organic compounds (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol, has been studied at room temperature. Rate coefficients for reactions of the nitrate radical (NO(3)) with these stress-induced plant emissions were measured using the discharge-flow technique. We employed off-axis continuous-wave cavity-enhanced absorption spectroscopy (CEAS) for the detection of NO(3), which enabled us to work in excess of the hexenol compounds over NO(3). The rate coefficients determined were (2.93 +/- 0.58) x 10(-13) cm(3) molecule(-1) s(-1), (2.67 +/- 0.42) x 10(-13) cm(3) molecule(-1) s(-1), (4.43 +/- 0.91) x 10(-13) cm(3) molecule(-1) s(-1), (1.56 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1), and (1.30 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1) for (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol, (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol. The rate coefficient for the reaction of NO(3) with (Z)-hex-3-en-1-ol agrees with the single published determination of the rate coefficient using a relative method. The other rate coefficients have not been measured before and are compared to estimated values. Relative-rate studies were also performed, but required modification of the standard technique because N(2)O(5) (used as the source of NO(3)) itself reacts with the hexenols. We used varying excesses of NO(2) to determine simultaneously rate coefficients for reactions of NO(3) and N(2)O(5) with (E)-hex-3-en-1-ol of (5.2 +/- 1.8) x 10(-13) cm(3) molecule(-1) s(-1) and (3.1 +/- 2.3) x 10(-18) cm(3) molecule(-1) s(-1). Our new determinations suggest atmospheric lifetimes with respect to NO(3)-initiated oxidation of roughly 1-4 h for the hexenols, comparable with lifetimes estimated for the atmospheric degradation by OH and shorter lifetimes than for attack by O(3). Recent measurements of [N(2)O(5)] suggest that the gas-phase reactions of N(2)O(5) with unsaturated alcohols will not be of importance under usual atmospheric conditions, but they certainly can be in laboratory systems when determining rate coefficients.

Rate coefficients for reactions of nitrate radicals (NO3) with (Z)-pent-2-ene, (E)-pent-2-ene, (Z)-hex-2-ene, (E)-hex-2-ene, (Z)-hex-3-ene, (E)-hex-3-ene and (E)-3-methylpent-2-ene were determined to be (6.55 +/- 0.78)x 10(-13) cm3 molecule(-1) s(-1), (3.78 +/- 0.45)x 10(-13) cm3 molecule(-1) s(-1), (5.30 +/- 0.73)x 10(-13) cm(3) molecule(-1) s(-1), (3.83 +/- 0.47)x 10(-13) cm(3) molecule(-1) s(-1), (4.37 +/- 0.49)x 10(-13) cm(3) molecule(-1) s(-1), (3.61 +/- 0.40)x 10(-13) cm3 molecule(-1) s(-1) and (8.9 +/- 1.5)x 10(-12) cm3 molecule(-1) s(-1), respectively. We performed kinetic experiments at room temperature and atmospheric pressure using a relative-rate technique with GC-FID analysis. The experimental results demonstrate a surprisingly large cis-trans(Z-E) effect, particularly in the case of the pent-2-enes, where the ratio of rate coefficients is ca. 1.7. Rate coefficients are discussed in terms of electronic and steric influences, and our results give some insight into the effects of chain length and position of the double bond on the reaction of NO3 with unsaturated hydrocarbons. Atmospheric lifetimes were calculated with respect to important oxidants in the troposphere for the alkenes studied, and NO3-initiated oxidation is found to be the dominant degradation route for (Z)-pent-2-ene, (Z)-hex-3-ene and (E)-3-methylpent-2-ene.