Acoustic Scattering and the Extended Korteweg deVries hierarchy

The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scattering problem associated with the Camassa-Holm flows on the real line is solved explicitly for a special case, which is used to reduce a general class of such problems to scattering problems on finite intervals.Comment: 18 page

Multipeakons and a theorem of Stieltjes

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.Comment: 6 page

A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator

\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations $u_t+(u^2/2+w)_x=0, w_t\pm u_{xxx}+(uw)_x=0$ for suitably restricted, complementary classes of initial data

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works

Terpenylic Acid and Related Compounds from the Oxidation of α-Pinene: Implications for New Particle Formation and Growth above Forests

Novel secondary organic aerosol (SOA) products from the monoterpene α-pinene with unique dimer-forming properties have been identified as lactone-containing terpenoic acids, i.e., terpenylic and 2-hydroxyterpenylic acid, and diaterpenylic acid acetate. The structural characterizations were based on the synthesis of reference compounds and detailed interpretation of mass spectral data. Terpenylic acid and diaterpenylic acid acetate are early oxidation products generated upon both photooxidation and ozonolysis, while 2-hydroxyterpenylic acid is an abundant SOA tracer in ambient fine aerosol that can be explained by further oxidation of terpenylic acid. Quantum chemical calculations support that noncovalent dimer formation involving double hydrogen bonding interactions between carboxyl groups of the monomers is energetically favorable. The molecular properties allow us to explain initial particle formation in laboratory chamber experiments and are suggested to play a role in new particle formation and growth above forests, a natural phenomenon that has fascinated scientists for more than a century

Reactive intermediates revealed in secondary organic aerosol formation from isoprene

Isoprene is a significant source of atmospheric organic aerosol; however, the oxidation pathways that lead to secondary organic aerosol (SOA) have remained elusive. Here, we identify the role of two key reactive intermediates, epoxydiols of isoprene (IEPOX = β-IEPOX + δ-IEPOX) and methacryloylperoxynitrate (MPAN), which are formed during isoprene oxidation under low- and high-NO_x conditions, respectively. Isoprene low-NO_x SOA is enhanced in the presence of acidified sulfate seed aerosol (mass yield 28.6%) over that in the presence of neutral aerosol (mass yield 1.3%). Increased uptake of IEPOX by acid-catalyzed particle-phase reactions is shown to explain this enhancement. Under high-NO_x conditions, isoprene SOA formation occurs through oxidation of its second-generation product, MPAN. The similarity of the composition of SOA formed from the photooxidation of MPAN to that formed from isoprene and methacrolein demonstrates the role of MPAN in the formation of isoprene high-NO_x SOA. Reactions of IEPOX and MPAN in the presence of anthropogenic pollutants (i.e., acidic aerosol produced from the oxidation of SO_2 and NO_2, respectively) could be a substantial source of “missing urban SOA” not included in current atmospheric models

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

The formation, properties and impact of secondary organic aerosol: current and emerging issues

Secondary organic aerosol (SOA) accounts for a significant fraction of ambient tropospheric aerosol and a detailed knowledge of the formation, properties and transformation of SOA is therefore required to evaluate its impact on atmospheric processes, climate and human health. The chemical and physical processes associated with SOA formation are complex and varied, and, despite considerable progress in recent years, a quantitative and predictive understanding of SOA formation does not exist and therefore represents a major research challenge in atmospheric science. This review begins with an update on the current state of knowledge on the global SOA budget and is followed by an overview of the atmospheric degradation mechanisms for SOA precursors, gas-particle partitioning theory and the analytical techniques used to determine the chemical composition of SOA. A survey of recent laboratory, field and modeling studies is also presented. The following topical and emerging issues are highlighted and discussed in detail: molecular characterization of biogenic SOA constituents, condensed phase reactions and oligomerization, the interaction of atmospheric organic components with sulfuric acid, the chemical and photochemical processing of organics in the atmospheric aqueous phase, aerosol formation from real plant emissions, interaction of atmospheric organic components with water, thermodynamics and mixtures in atmospheric models. Finally, the major challenges ahead in laboratory, field and modeling studies of SOA are discussed and recommendations for future research directions are proposed

Toxicological Responses of α-Pinene-Derived Secondary Organic Aerosol and Its Molecular Tracers in Human Lung Cell Lines

Secondary organic aerosol (SOA) is a major component of airborne fine particulate matter (PM2.5) that contributes to adverse human health effects upon inhalation. Atmospheric ozonolysis of α-pinene, an abundantly emitted monoterpene from terrestrial vegetation, leads to significant global SOA formation; however, its impact on pulmonary pathophysiology remains uncertain. In this study, we quantified an increasing concentration response of three well-established α-pinene SOA tracers (pinic, pinonic, and 3-methyl-1,2,3-butanetricarboxylic acids) and a full mixture of α-pinene SOA in A549 (alveolar epithelial carcinoma) and BEAS-2B (bronchial epithelial normal) lung cell lines. The three aforementioned tracers contributed ∼57% of the α-pinene SOA mass under our experimental conditions. Cellular proliferation, cell viability, and oxidative stress were assessed as toxicological end points. The three α-pinene SOA molecular tracers had insignificant responses in both cell types when compared with the α-pinene SOA (up to 200 μg mL-1). BEAS-2B cells exposed to 200 μg mL-1 of α-pinene SOA decreased cellular proliferation to ∼70% and 44% at 24- and 48-h post exposure, respectively; no changes in A549 cells were observed. The inhibitory concentration-50 (IC50) in BEAS-2B cells was found to be 912 and 230 μg mL-1 at 24 and 48 h, respectively. An approximate 4-fold increase in cellular oxidative stress was observed in BEAS-2B cells when compared with untreated cells, suggesting that reactive oxygen species (ROS) buildup resulted in the downstream cytotoxicity following 24 h of exposure to α-pinene SOA. Organic hydroperoxides that were identified in the α-pinene SOA samples likely contributed to the ROS and cytotoxicity. This study identifies the potential components of α-pinene SOA that likely modulate the oxidative stress response within lung cells and highlights the need to carry out chronic exposure studies on α-pinene SOA to elucidate its long-term inhalation exposure effects. © 2021 American Chemical Society

Chemical Composition of Secondary Organic Aerosol Formed from the Photooxidation of Isoprene

Recent work in our laboratory has shown that the photooxidation of isoprene (2-methyl-1,3-butadiene, C5H8) leads to the formation of secondary organic aerosol (SOA). In the current study, the chemical composition of SOA from the photooxidation of isoprene over the full range of NO_x conditions is investigated through a series of controlled laboratory chamber experiments. SOA composition is studied using a wide range of experimental techniques:  electrospray ionization−mass spectrometry, matrix-assisted laser desorption ionization−mass spectrometry, high-resolution mass spectrometry, online aerosol mass spectrometry, gas chromatography/mass spectrometry, and an iodometric-spectroscopic method. Oligomerization was observed to be an important SOA formation pathway in all cases; however, the nature of the oligomers depends strongly on the NO_x level, with acidic products formed under high-NO_x conditions only. We present, to our knowledge, the first evidence of particle-phase esterification reactions in SOA, where the further oxidation of the isoprene oxidation product methacrolein under high-NO_x conditions produces polyesters involving 2-methylglyceric acid as a key monomeric unit. These oligomers comprise ∼22−34% of the high-NO_x SOA mass. Under low-NO_x conditions, organic peroxides contribute significantly to the low-NO_x SOA mass (∼61% when SOA forms by nucleation and ∼25−30% in the presence of seed particles). The contribution of organic peroxides in the SOA decreases with time, indicating photochemical aging. Hemiacetal dimers are found to form from C_5 alkene triols and 2-methyltetrols under low-NO_x conditions; these compounds are also found in aerosol collected from the Amazonian rainforest, demonstrating the atmospheric relevance of these low-NO_x chamber experiments