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Neste trabalho caracterizamos dispersões aquosas de vesículas lipídicas por espalhamento de luz. Utilizamos os diferentes métodos da técnica: espalhamento de luz estático (SLS) e espalhamento de luz dinâmico (DLS) no estudo desses sistemas. No SLS a intensidade da luz espalhada foi coletada em vários ângulos de espalhamento para diferentes concentrações, e obtivemos os seguintes parâmetros: peso molecular, Mw, raio de giração, Rg, que esta relacionado _a forma do centro espalhador e segundo coeficiente do virial, A2, que está relacionado a interações entre partículas. No DLS a correlação da luz espalhada foi obtida em função do tempo, para vários ângulos e concentrações. As medidas de DLS fornecem o coeficiente de difusão dos centros espalhadores, que estão relacionados a seus diâmetros efetivos. Em especial a técnica de SLS foi amplamente estudada para desenvolvimento de uma apostila coordenada pela Profa. Vera B. Henriques. Nesta apostila a teoria de espalhamento de luz estático está apresentada através de uma abordagem diferente da convencional, sob o ponto de vista da mecânica estatística. O principal objeto de estudo neste trabalho foram as dispersões aquosas de dimiristoil fosfatidil glicerol (DMPG). O DMPG, lipídio aniônico, saturado, com 14 carbonos nas cadeias hidrocarbônicas, em baixa força iônica, exibe um comportamento termo-estrutural muito peculiar, apresentando uma larga região de transição de fase, entre as fases gel e fluida. O lipídio dimiristoil fosfatidil colina (DMPC) com as mesmas cadeias carbônicas mas cabeça polar neutra, foi utilizado como controle, pois não apresenta esta anomalia. Os tamanhos efetivos obtidos pelos diferentes métodos (SLS) e (DLS) são semelhantes nas fases gel e fluída de ambos os lipídios, mas isso não ocorre na região de transição do DMPG. Ambos os métodos indicam um aumento na dimensão das vesículas de DMPG, nesta região de temperatura. No entanto, por SLS temos que o Rg triplica na região de transição, levando a um raio efetivo muito maior que o observado por DLS. Como é sabido que não há fusão entre as vesículas, considerando os dados de espalhamento de luz e a literatura, discutimos um modelo em que o agregado lipídico apresente grandes deformações isotrópicas e grandes flutuações de forma. / Light scattering used to structurally characterize lipid dispersions. In the present work light scattering was used to characterize aqueous dispersions of lipid vesicles. Two different methods were applied: static light scattering (SLS) and dynamic light scattering (DLS). With SLS, the intensity of the scattered light was measured at several scattering angles and different lipid concentrations. The following parameters were obtained: molecular weight (Mw) and radius of gyration (Rg), related to the mass and form of the scattering particle, and the second Virial coefficient (A2), related to interactions among particles. With DLS, the autocorrelation of the intensity of the scattered light was obtained, also at several scattering angles and lipid concentrations. Measurements of DLS provide the difusion coefficient of the particles, which are related to their hydrodynamic radii. In particular, the theory of SLS was largely studied to the elaboration of a manuscript, under the supervision of Dr. Vera B. Henriques, which presents an unconventional approach to the technique. Here, the main object of investigation was the aqueous dispersion of the anionic lipid dimyristoyl phosphatidylglycerol (DMPG), a saturated anionic lipid, with 14 C-atoms in the hydrophobic chains. At low ionic strength, this lipid exhibits a very peculiar thermo-structural behavior, presenting a large region of transition, between the gel and fluid phases. The lipid dimyristoyl phosphatidylcholine (DMPC), with the same hydrocarbon chains but zwitterionic polar headgroup, was used as a control, since it does not present such anomaly. Lipid dispersions were extruded through 100 nm filters (pore diameter). In the gel and fluid phases of DMPC and DMPG, both SLS and DLS indicate similar dimensions for the lipid vesicles, assuming them spherical. For DMPC, the obtained effective radius (Reff ) values were around 53 and 62nm for the gel and fluid phases, respectively, indicating the expected expansion of the uid bilayer, and radii compatible with the extrusion process. For DMPG, the fluid vesicle (Reff _ 30nm) was also found to be larger than the gel vesicle (Reff _ 27nm), but much smaller than the dimensions of the filter pore (R = 50nm). More interesting, over the DMPG transition region, SLS indicated a three times increase for the vesicle radius of gyration, whereas the hydrodynamic radius, measured by DLS, increased by 30% only. Besides, no light depolarization could be detected, indicating that the DMPG aggregates are isotropic particles, in average, at all temperatures. Considering the results presented here, and those in the literature, the presence of large bilayer fluctuations over the DMPG transition region will be discussed, possibly including the existence of bilayer pores.

Homogeneous crystal nucleation in binary hard sphere mixtures is an active area of research for last two decades. Although Classical nucleation theory (CNT) gives a qualitative picture, it fails at high super saturations because of the following reasons. CNT assumes that the cluster formed is spherical in shape, its properties can be modeled using the bulk properties of the stable solid phase and the interfacial free energy γ between the nucleus and the surrounding metastable fluid is equal to the planar surface tension between two phases at coexistence. These assumptions get increasingly tenuous at higher degrees of super saturations where the critical nucleus formed is microscopic in size leading to breakdown in the predictions of CNT. In addition direct experimental observation of critical nucleus is very difficult because, 1. Critical nucleus is microscopic in size, consisting of few hundreds of particles. 2. Formation of critical cluster is very rare (typically of the order of 101– 106nuclei/cm3/s) 3. Its life time is very short (it either rapidly grows to form a solid phase or melts back to fluid) In these circumstances molecular simulations are an attractive tool to study the crystal nucleation, because in these simulations microscopic size critical nucleus properties can be calculated. However, brute force molecular dynamic (MD) simulation techniques to study the homogeneous crystal nucleation is currently not feasible due to long times involved. Hence, an indirect approach is needed. In this work, Monte Carlo Abstract v (MC) molecular simulation techniques are used to calculate free energy barrier height during the crystal nucleation. Phase behavior of Binary hard sphere mixtures with varying ratios of smaller diameter to larger diameter (α) is very similar to that of binary organic liquids. By studying the crystal nucleation in hard sphere system, the physics behind the nucleation for binary organic liquids can be understood. This is the key motivation to study the homogeneous crystal nucleation in binary hard sphere mixtures using MC simulations. Simulations were done using umbrella sampling in combination with local bond order analysis for the identification of crystal nuclei and to compute shape and height of nucleation barrier. Parallel tempering scheme of Geyer and Thomson was utilized to sample phase space more efficiently. Parallel tempering technique was implemented using Message passing interface (MPI) libraries. By using all the above Monte-Carlo simulation techniques, nucleation barrier was calculated during crystallization of binary hard sphere mixtures under the moderate degrees of super cooling in Isothermal-Isobaric semi grand ensembles. Crystal nucleation in binary hard sphere mixtures has been studied for size ratios α = 0.85, 0.42 and 0.43. For α=0.85, phase diagram contains eutectic point. In this system, the effect of eutectic composition on the nucleation barrier height was observed, by calculating nucleation barriers at various fluid mixture compositions keeping Laplace pressure constant. It is observed that as the fluid mixture composition move towards the eutectic point, free energy barrier height, surface tension and critical cluster sizes are increased and the nucleation rate is drastically decreased by a factor of 10-31. Thus the difficulty of homogenous crystal nucleation increases near the eutectic point. For α=0.42 and 0.43 in the hard sphere system, compound solids such as AB and AB2 solids are stable respectively. In these systems crystal nucleation study was done to observe the compound solid formation. It is observed that in these systems crystallization kinetics are very slow and more advanced simulation techniques need to be developed in order to study crystal nucleation.

Contemporary laser research involves the development of spectroscopic techniques to understand the microscopic structural aspects of a simple molecular system in chemical and materials to more complex biological systems such as cells. In particular, Raman spectroscopy, which provides bond specific information, has attracted considerable attention. Further with the advent of femtosecond (fs) laser, the recent trend in the field of fs chemistry is to develop nonlinear Raman techniques that allow one to acquire vibrational structural information with both fs temporal resolution as well as good spectral resolution. Among many advanced nonlinear Raman techniques, the development of fs Stimulated Raman scattering (SRS) has gathered momentum in the recent decade due to its ability to (1) provide vibrational structural information of various system including fluorescent molecules with good signal to noise ratio and (2) circumvent the limitation imposed on the spectral resolution by the necessary pulse durations according to the energy-time uncertainty principle where ‘K’ is a constant that depends on the pulse shape) unlike in the case of fs normal resonance Raman spectroscopy. We have developed a technique named “Ultrafast Raman loss spectroscopy (URLS)” that is analogues to SRS, but is more advantageous as compared to SRS and has the potential to be an alternative if not competitive tool as a vibrational structure elucidating technique. The concept and the design of this novel technique, URLS, form the core of the thesis entitled “Ultrafast Raman Loss Spectroscopy (URLS)”. Chapter 1 lays the theoretical groundwork for ultra-short pulses and nonlinear spectroscopy which forms the heart of URLS. It presents a detailed discussion on the basis behind the elementary experimental problems associated with the ultra-short laser pulses when they travel through a medium, the characterization of these ultrashort pulses as well as various non-linear phenomena induced within a medium due to the propagation of these pulses. Chapter 2 focuses on the concept of SRS which resulted into the foundation of URLS. It illustrates the theoretical as well as the experimental aspects of SRS and demonstrates the sensitivity of SRS over normal Raman spectroscopy. Chapter 3 introduces the conceptual and the technical basis which ensued into the development of URLS while Chapter 4 demonstrates its application and efficiency over its analogue SRS. URLS involves the interaction of two laser sources, viz. a picosecond (ps) pulse and a fs white light (WL), with a sample leading to the generation of loss signal on the higher energy (blue) side with respect to the wavelength of the ps pulse unlike the gain signal observed on the lower energy (red) side in SRS. These loss signals are at least 1.5 times more intense than SRS signals. Also, the very prerequisite of the experimental protocol for signal detection to be on the higher energy side by design eliminates the interference from fluorescence, which appears on the red side. Thus, the rapid data acquisition, 100% natural fluorescence rejection and experimental ease ascertain “Ultrafast Raman Loss Spectroscopy (URLS)” as a unique valuable structure determining technique. Further, the effect of resonance on the line shape of the URLS signal has been studied which forms the subject of discussion in Chapter 5. The objective of the study is to verify whether the variation of resonance Raman line shapes in URLS could provide an understanding of the mode specific response on ultrafast excitation. It is found that the URLS signal’s line shape is mode dependent and can provide information similar to Raman excitation profile (REP) in the normal Raman studies. This information can have impact on the study of various dynamical process involving vibrational modes like structural dynamics and coherent control. Chapter 6 demonstrates the application of URLS as a structure elucidating technique for monitoring ultrafast structural and reaction dynamics in both chemical and biological systems using α-terthiophene (3T) as the model system. The objective is to understand the mechanism of the molecular structure dependent electronic relaxation of the first singlet excited state, S1, of α-terthiophene using fs URLS. The URLS data along with the ab-initio calculations indicate that the electronic transition is associated with a structural rearrangement from a non-planar to a planar configuration in the singlet manifold along the ring deformation co-ordinate. The experimental findings suggest that the singlet state decays exponentially with a decay time constant ( 1/e) of about 145 ps and this decay could be assigned to the intersystem crossing (ISC) pathway from the relaxed S1 state to the vibrationally hot triplet state, T1*. Lastly, Chapter 7 summarizes the entire thesis and presents some possible future prospects for URLS. Considering the advantages of URLS, it is proposed that URLS can be exploited [1] to determine the structure of any fluorescent/non-florescent condensed materials and biological systems with a very good spectral resolution (10- 40 cm-1); [2] to obtain the vibrational signature of weak Raman scattering molecules and vibrational modes with relatively small Raman cross-section owing to its high detection sensitivity with good signal to noise ratio; [3] for performing fs time-resolved study by introducing an additional fs pulse for photo-excitation of the molecule and using URLS to probe the excited state dynamics with good temporal (fs) and spectral (10-40 cm-1) resolution; and lastly, [4] the high chemical selectivity of URLS and the fact that the signal is generated only within the focal volume of the lasers where all the beams overlap can be utilized for developing this method into a microscopy for labeled-free effective vibrational study of biological samples. Consequently, it is hoped that this technique, “Ultrafast Raman Loss Spectroscopy (URLS)”, would be a suitable alternative to other nonlinear Raman methods like coherent anti-Stokes Raman spectroscopy (CARS) that has made major inroads into biology, medicine and materials.

Nanomaterials such as graphene oxide and carbon nanotubes, have demonstrated excellent properties for membrane desalination, including decrease of maintenance, increase of flux rate, simple solution casting, and impressive chemical inertness. Here, two projects are studied to investigate nanocarbon based membrane desalination. The first project is to prepare hybrid membranes with amyloid fibrils intercalated with graphene oxide sheets. The addition of protein amyloid fibrils expands the interlayer spacing between graphene oxide nanosheets and introduces additional functional groups in the diffusion pathways, resulting in increase of flux rate and rejection rate for the organic dyes. Amyloid fibrils also provide structural assistance to the hybrid membrane, which supresses cracking and instability of graphene oxide sheets. The second project is to fabricate polymer nanocomposite membranes with carbon nanotubes encapsulated by polymerized surfactants. The designed polymerizable surfactant forms lyotropic liquid crystalline mesophases in an aqueous medium with hexagonal packing of cylindrical micelles. The adsorption of surfactants on the surface of carbon nanotubes allows a stable dispersion of carbon nanotubes encapsulated in the cylindrical micelles, resulting in the ordered structure. After photo-polymerization, the composite membranes display enhanced dye rejection. Both projects have shown promising ways to improve membrane filtration by using nanomaterials.

: Le rouge à lèvres est un produit incontournable du marché des cosmétiques. C’est un produit de formulation complexe et aux fonctionnalités multiples, parmi lesquelles la sensorialité est centrale et dépend principalement des corps gras mis en œuvre. Face à la multiplicité des ingrédients disponibles et aux pratiques de formulation s’appuyant largement sur l’expertise empirique des formulateurs, cette thèse répond à une problématique industrielle de mise en place d’une méthodologie de formulation raisonnée pilotée par la fonctionnalité sensorielle. Mettre en place une telle démarche d’ingénierie sensorielle nécessite d’intégrer la connaissance des liens entre la formulation, la structure et les fonctionnalités du produit. Pour ce faire, nous avons proposé une démarche en sept étapes, s’appuyant sur la réalisation d’une formule simplifiée et réaliste. Ce système a permis de structurer une approche hypothético-déductive concernant le rôle de différentes catégories d’ingrédients sur les propriétés sensorielles du produit. Nous avons ainsi pu montrer que les huiles et les cires ont un rôle majeur sur ces propriétés. Les huiles affectent principalement le glissant, le fondant, l’huileux, la douceur, le collant et la présence sur les lèvres. Les cires, quant à elles, ont une influence sur l’opacité et la quantité de rouge à lèvres déposé. Ce travail s’appuie sur une compréhension approfondie des mécanismes physicochimiques à l’origine de la structure du rouge à lèvres, observée à différentes échelles, et des propriétés résultantes. Enfin, sur deux cas concrets d’ingénierie inverse, nous avons validé cette démarche ainsi que les relations entre les propriétés des ingrédients, la structure et les propriétés mécaniques et sensorielles du rouge à lèvres. / Lipstick is a must-have product of the cosmetics market. It is made from a complex formulation and it has multiple functionalities, among which the sensoriality is central and depends mainly on fats and oils used. Given the multiplicity of available ingredients, formulation practices are largely based on the formulators’ empirical expertise. In this industrial context, this thesis aims at setting up a reasoned formulation methodology driven by the sensory functionality. Implementing such a sensory engineering approach requires integrating knowledge of the relationships between formulation, structure and product functionalities. In order to do this, we proposed a seven-step approach, based on the realization of a simplified and realistic formula. This system allowed to structure a deductive reasoning approach concerning the role of different categories of ingredients in the sensory properties of the product. Thanks to this approach, we have shown that oils and waxes have a major role in these properties. The oils mainly affect the slipperiness, the melting quality, the oiliness, the softness, the stickiness and the presence on the lips. Waxes, on the other hand, have an influence on the opacity and the amount of lipstick deposited. This work is based on a thorough understanding of the physicochemical mechanisms at the origin of the structure of lipsticks, observed at different scales, and of the resulting properties. Finally, we validated this approach, as well as the relationships between the properties of the ingredients, the structure and the mechanical and sensory properties of lipsticks, on two concrete cases of reverse engineering.

Indiana University-Purdue University Indianapolis (IUPUI) / Molecular polarizability plays a significant role in chemistry, biology, and medicine. Classical prediction of polarizability often relies on atomic-type specific polarizability optimized for training set molecules, which limits the calculations to systems of similar chemical environment. Although ab initio (AI) quantum mechanical (QM) methods are more transferable in predicting molecular polarizability, their high computational costs especially when used with large basis sets for obtaining quantitatively reliable results make them less practical. To obtain accurate QM polarizability in an efficient manner, we have developed a dual-level approach, where the polarizability (α) obtained from the efficient semiempirical QM (SE) method is corrected using a set of element-base atomic polarizabilities derived from the atomic dipole interaction model (ADIM) to reproduce the density functional theory (DFT) results. We have optimized the atomic polarizability correction parameters for CHON-containing systems using a small training set of molecules and tested the resulting SE-ADIM model on the neutral drug-like molecules in the QM7B database. SE-ADIM corrected AM1 showed substantial improvement with its relative percent error (RPE) compared to B3LYP reduced from 33.81% to 3.35%. To further test its robustness for larger molecules in broader chemical bonding situations, we applied this method to a collection of drug molecules from the e-Drug3D database. For the 1004 molecules tested, our SE-ADIM model, which only contains four empirical parameters, greatly reduces the RPE in AM1 polarizability relative to B3LYP from 26.8% to 2.9%. Error decomposition shows consistent improvements across molecules with diverse bond saturations, molecular sizes, and charge states. In addition, we have applied AlphaML, a promising machine learning (ML) technique for predicting molecular polarizability, to the e-Drug3D dataset to compare its performance with our SE-ADIM correction of AM1. We found SE-ADIM performs competitively with AlphaML bolstering our confidence in the value of our method. Errors distinct to AlphaML were also discovered. We found four molecules for which AlphaML predicts negative molecular polarizabilities, all of which were peroxides. In contrast, SE-ADIM has no such issue with these molecules or this chemical type. Finally, to improve performance of SE-ADIM when correcting AM1 molecular polarizability calculations for charged molecules, we introduce a charge dependent polarizability (CDP) enabled SE-ADIM. Training the CDP enabled SE-ADIM with a single additional parameter, B, we were able to reduce error in AM1 molecular polarizability calculations of charged molecules relative to B3LYP from 29.57% to 5.16%. By contrast, SE-ADIM without CDP corrected AM1 relative to B3LYP had an RPE of 8.56%. The most benefit of CDP was evident within negatively charged molecules where AM1 error relative to B3LYP fell from 32.20% to 3.77% while SE-ADIM without CDP enabled error for these same negative molecules was 10.06%.

<p>In this thesis, the ripple formation at the interface of SiO2 and Si were studied in a systematic fashion by irradiating the SiO2-Si samples with ultrashort laser pulses under a broad variety of experimental conditions. They consist of di↵erent irradiating laser wavelengths, incident laser energies, translation speeds, translation directions, spot sizes of the laser beam, as well as oxide thicknesses. The ripples produced by laser irradiation are examined using various microscopy techniques in order to characterize their surface morphology, detailed structures, crystalline properties, and so on. For the experiments carried out at ! = 800 nm, the ripples formed on the SiO2-Si sample with an oxide thickness of 216 nm were first observed under optical microscopy and SEM. After removing the oxide layer with HF solution, the surface features of the ripples on the Si substrate were investigated using SEM and AFM techniques. Subsequently, by means of TEM and EDX analysis, the material composition and crystallinity of the ripples were determined. It is concluded that the ripples are composed of nano-crystalline silicon. In addition to the 216 nm oxide thickness, other oxide samples with di↵erent oxide thicknesses, such as 24, 112, 117, 158 and 1013 nm, were also processed under laser irradiation. The ripple formation as a function of the laser energy, the translation direction and the spot size is discussed in detail. Furthermore, the ripples created at the SiO2-Si interface are compared with</p> <p>the LIPSS created on pure silicon samples that were processed under similar laser irradiation conditions. The spatial periodicities of the ripples were evaluated to be in the range of between 510 nm and 700 nm, which vary with the oxide thickness and other laser parameters. For the experiments using the ! = 400 nm laser pulses, it is found that ripples can also be formed at the SiO2-Si interface, which have spatial periodicities in the range of between 310 nm and 350 nm depending on the oxide thickness. The ripple formation at this 400 nm wavelength as a function of the laser energy, the translation speed, and translation direction is considered as well. For the case of ! = 400 nm irradiation, a comparison is also made between the interface ripples on the SiO2-Si samples and the LIPSS on a pure Si sample. Through FIB-TEM and EDX analysis, it confirmed that the ripples were produced in the substrate while the oxide layer maintained its structural integrity. In addition, the ripples are composed of nano-crystalline silicon whose crystallite sizes are on the order of a few nanometers. Apart from irradiating oxide samples with femtosecond laser pulses, which applies to the two cases of ! = 800 and 400 nm mentioned above, oxide samples with an oxide thickness of 112 nm were irradiated with picosecond laser pulses at ! = 800 nm whose pulse durations are 1 ps and 5 ps, respectively. However, no regular ripples can be produced at the SiO2-Si interface while maintaining the complete integrity of the oxide layer.</p> / Master of Applied Science (MASc)

<p>The class of meteorites called carbonaceous chondrites are examples of material from the solar system which have been relatively unchanged from the time of their initial formation. We investigate the carbonaceous chondrite subclasses CI, CM, CR, CV, and CO, which contain high levels of water and organic material, including amino acids. These subclasses span petrologic types 1 through 3, indicating the degree of internal chemistry undergone by the meteoritic parent body. The goal of this thesis is two-fold: to obtain a comprehensive view of amino acid abundances and relative frequencies in carbonaceous chondrites, and to recreate these patterns via thermodynamic computational models.</p> <p>We collate available amino acid abundance data for a variety of meteorites to identify patterns in total abundance and relative frequencies. We consider only a set of 20 proteinogenic alpha-amino acids created via a specific chemical pathway called Strecker synthesis. We plot abundances of individual amino acids for each subclass, as well as total abundances across all subclasses. We see a predominance in abundance and variety of amino acids in the CM and CR subclasses, which contain concentrations of amino acids greater by several orders of magnitude than other carbonaceous subclasses. These subclasses correspond to an aqueous alteration temperature range of 200 deg. C to 400 deg. C. Within the CM2 and CR2 meteorites, we identify trends in the relative frequencies of amino acids in preparation for computational modeling.</p> <p>Now having a baseline observed amino acid abundance plot, we recreate both the total amino acid abundance pattern as well as the relative frequency of amino acids within the CM2 chondrite subclass using computational models. We use thermodynamic theory of Gibbs free energies to calculate the output of amino acids in a meteoritic parent body assuming chemical equilibrium and some set of initial concentrations of organic material. Our model recreates abundance patterns in the temperature range 200 deg. C to 400 deg. C, ~10⁵ parts-per billion (ppb), and the temperature range 400 deg. C to 500 deg. C, ~10² ppb. Our model does not fit well between temperatures of 150 deg. C to 200 deg. C. Our current model assumes a uniform composition of initial chemical reactants; likely an inhomogeneous composition would be a more accurate physical representation of a parent body. In addition, we match relative frequencies to observed frequencies for each amino acid in the CM2 subclass to well within an order of magnitude.</p> / Master of Science (MSc)

We analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations. Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown. We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations. Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency. / text