Singular double-phase systems with variable growth for the Baouendi-Grushin operator

Heterogeneous catalysts can be of varying complexity ranging from single or double phase systems to complicated mixtures of metals and oxides with additives to help promote chemical reactions, extend the life of the catalysts, prevent poisoning etc. Although catalysis occurs on the surface of most systems, detailed descriptions of the microstructure and chemistry of catalysts can be helpful for developing an understanding of the mechanism by which a catalyst facilitates a reaction. Recent years have seen continued development and improvement of various TEM, STEM and AEM techniques for yielding information on the structure and chemistry of catalysts on the nanometer scale. Here we review some quantitative approaches to catalyst characterization that have resulted from new developments in instrumentation.HREM has been used to examine structural features of catalysts often by employing profile imaging techniques to study atomic details on the surface. Digital recording techniques employing slow-scan CCD cameras have facilitated the use of low-dose imaging in zeolite structure analysis and electron crystallography. Fig. la shows a low-dose image from SSZ-33 zeolite revealing the presence of a stacking fault.

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Nonvariational and singular double phase problems for the Baouendi-Grushin operator

Journal of Differential Equations ◽

10.1016/j.jde.2021.09.033 ◽

2021 ◽

Vol 303 ◽

pp. 645-666

Author(s):

Anouar Bahrouni ◽

Vicenţiu D. Rădulescu ◽

Dušan D. Repovš

Keyword(s):

Grushin Operator ◽

Double Phase

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Double phase problems with variable growth and convection for the Baouendi–Grushin operator

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-020-01412-7 ◽

2020 ◽

Vol 71 (6) ◽

Cited By ~ 3

Author(s):

Anouar Bahrouni ◽

Vicenţiu D. Rădulescu ◽

Patrick Winkert

Keyword(s):

Elliptic Equations ◽

Quasilinear Elliptic Equations ◽

Stationary Waves ◽

Convection Term ◽

Pseudomonotone Operators ◽

Qualitative Properties ◽

Transonic Flows ◽

Grushin Operator ◽

Double Phase ◽

Quasilinear Elliptic

AbstractIn this paper we study a class of quasilinear elliptic equations with double phase energy and reaction term depending on the gradient. The main feature is that the associated functional is driven by the Baouendi–Grushin operator with variable coefficient. This partial differential equation is of mixed type and possesses both elliptic and hyperbolic regions. We first establish some new qualitative properties of a differential operator introduced recently by Bahrouni et al. (Nonlinearity 32(7):2481–2495, 2019). Next, under quite general assumptions on the convection term, we prove the existence of stationary waves by applying the theory of pseudomonotone operators. The analysis carried out in this paper is motivated by patterns arising in the theory of transonic flows.

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Biotransformation in Double-Phase Systems: Physiological Responses of Pseudomonas putida DOT-T1E to a Double Phase Made of Aliphatic Alcohols and Biosynthesis of Substituted Catechols

Applied and Environmental Microbiology ◽

10.1128/aem.70.6.3637-3643.2004 ◽

2004 ◽

Vol 70 (6) ◽

pp. 3637-3643 ◽

Cited By ~ 55

Author(s):

Antonia Rojas ◽

Estrella Duque ◽

Andreas Schmid ◽

Ana Hurtado ◽

Juan-Luis Ramos ◽

...

Keyword(s):

Pseudomonas Putida ◽

Defense Mechanisms ◽

Aliphatic Alcohols ◽

High Rate ◽

Second Phase ◽

Negative Effects ◽

Two Phase ◽

Double Phase ◽

Alcohol Water ◽

Phase Systems

ABSTRACT Pseudomonas putida strain DOT-T1E is highly tolerant to organic solvents, with a logPow (the logarithm of the partition coefficient of a solvent in a two-phase water-octanol system of ≥2.5. Solvent tolerant microorganisms can be exploited to develop double-phase (organic solvent and water) biotransformation systems in which toxic substrates or products are kept in the organic phase. We tested P. putida DOT-T1E tolerance to different aliphatic alcohols with a logPow value between 2 and 4, such as decanol, nonanol, and octanol, which are potentially useful in biotransformations in double-phase systems in which compounds with a logPow around 1.5 are produced. P. putida DOT-T1E responds to aliphatic alcohols as the second phase through cis-to-trans isomerization of unsaturated cis fatty acids and through efflux of these aliphatic alcohols via a series of pumps that also extrude aromatic hydrocarbons. These defense mechanisms allow P. putida DOT-T1E to survive well in the presence of high concentrations of the aliphatic alcohols, and growth with nonanol or decanol occurred at a high rate, whereas in the presence of an octanol double-phase growth was compromised. Our results support that the logPow of aliphatic alcohols correlates with their toxic effects, as octanol (logPow = 2.9) has more negative effects in P. putida cells than 1-nonanol (logPow = 3.4) or 1-decanol (logPow = 4). A P. putida DOT-T1E derivative bearing plasmid pWW0-xylE::Km transforms m-xylene (logPow = 3.2) into 3-methylcatechol (logPow = 1.8). The amount of 3-methylcatechol produced in an aliphatic alcohol/water bioreactor was 10- to 20-fold higher than in an aqueous medium, demonstrating the usefulness of double-phase systems for this particular biotransformation.

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