Lagrangian coherent structures are associated with fluctuations in airborne microbial populations

Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.     

A set oriented definition of finite-time Lyapunov exponents and coherent sets

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron–Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron–Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.     

Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh

Nonlinear Dynamics - In this paper, we investigate the behavior of an underactuated mixed-dynamic nonholonomic system, a Chaplygin sleigh, subjected to viscous dissipation and sinusoidal forcing....     

Photoisomerization of cis,cis-1,4-diphenyl-1,3-butadiene in the solid state: the bicycle-pedal mechanism

The cis-trans photoisomerization of crystalline or powdered cis,cis-1,4-diphenyl-1,3-butadiene (cc-DPB) was studied at room temperature. The progress of the reaction was monitored by fluorescence spectroscopy, powder X-ray diffraction, 1H NMR and HPLC. High conversions (up to 90%) to the trans,trans isomer were observed in a crystal to crystal reaction. Formation of the cis,trans isomer, the sole product obtained in solution and in very viscous glassy media at 77 K is entirely suppressed in the solid state. The observed two-bond photoisomerization is explained by Warshel's bicycle-pedal photoisomerization mechanism (BP). The results are consistent with X-ray diffraction measurements, which have revealed that cc-DPB molecules exist in crystals in edge to face alternating arrays of two conformer structures whose phenyl rings deviate significantly from the plane of the central diene moiety ( approximately 40 degrees ). One of the conformers has the two phenyls in parallel planes and the other in roughly perpendicular planes. Least motion considerations suggest that the former should undergo the two-bond photoisomerization more easily, in agreement with observations that indicate that the reaction proceeds in discrete stages. Recently reported cis,cis- to trans,trans-muconate photoisomerizations in the solid state are proposed to also proceed via the BP mechanism. The reactions are consistent with the X-ray crystal structures of the cis,cis-muconate isomers.     

Resolution of conformer-specific all-trans-1,6-diphenyl-1,3,5-hexatriene UV absorption spectra

All-trans-1,6-diphenyl-1,3,5-hexatriene (ttt-DPH) exists in solution as a mixture of s-trans,s-trans and s-cis,s-trans conformers. The latter is higher in energy, and its contribution increases with increasing temperature. ttt-DPH UV absorption spectra broaden with increasing temperature and undergo blue shifts with decreasing polarizability. We describe here the resolution of two spectrothermal matrices of ttt-DPH UV absorption spectra into two conformer-specific components. The first matrix consists of DPH spectra measured in n-dodecane in the 283 to 374 K T range and the second of ttt-DPH absorption spectra measured in the even numbered n-alkanes (n-C(8)-n-C(16)) at temperatures selected to achieve isopolarizability (284-372 K). Principal component analysis (PCA) treatments showed that reasonable two-component systems are attained by compensation for T-induced broadening and shifting in the pure conformer spectra. The self-modeling (SM) method used to resolve the n-C(12) matrix is successfully tested on a simulated matrix closely mimicking ttt-DPH experimental spectra in n-C(12). Compensation for nonlinear effects yields robust two-component matrices from the experimental spectra. Their resolution into pure component spectra is based on the application of the Lawton and Sylvestre (LS) non-negativity criterion at the spectral onset to define the spectrum of the low energy s-trans-conformer and the optimum linearity van't Hoff (vH) plot criterion to find the spectrum of the higher-energy s-cis-conformer. Resolved spectra are somewhat sensitive to the choice of the spectral region in which the LS criterion is applied. The surprising result is that both resolutions lead to the conclusion that the molar fraction of the s-cis-conformer equals, or even exceeds, the molar fraction of the s-trans-conformer as the highest T's employed in our study are approached.     

Dynamics and self-propulsion of a spherical body shedding coaxial vortex rings in an ideal fluid

We describe a model for the dynamic interaction of a sphere with uniform density and a system of coaxial circular vortex rings in an ideal fluid of equal density. At regular intervals in time, a constraint is imposed that requires the velocity of the fluid relative to the sphere to have no component transverse to a particular circular contour on the sphere. In order to enforce this constraint, new vortex rings are introduced in a manner that conserves the total momentum in the system. This models the shedding of rings from a sharp physical ridge on the sphere coincident with the circular contour. If the position of the contour is fixed on the sphere, vortex shedding is a source of drag. If the position of the contour varies periodically, propulsive rings may be shed in a manner that mimics the locomotion of certain jellyfish. We present simulations representing both cases.     

Photoisomerization of cis-1-(2-naphthyl)-2-phenylethene in methylcyclohexane at 77 K: no hula-twist

The cis-trans photoisomerization of cis-1-(2-naphthyl)-2-phenylethene (c-NPEA and c-NPEB) was studied in methylcyclohexane glass at 77 K. The progress of the reaction was followed by fluorescence spectroscopy. Formation of the extended trans conformer (t-NPEB) is revealed by the growth of sharp vibronic bands on the broad structureless fluorescence spectrum of c-NPE. Principal component analysis with self-modeling of a matrix consisting of spectra generated by irradiation of c-NPE at different excitation wavelengths and spectra of t-NPE measured under the same conditions as a function of excitation wavelength reveals that the diabatic photoisomerization is a completely conformer-specific one-bond twist process: c-NPEB --> t-NPEB. These observations are consistent with observations in solution at ambient temperature. They demonstrate unequivocally that free volume restrictions imposed by the amorphous glassy environment do not open a hula-twist process.