The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N

We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective potential at finite temperature. At next-to-leading order in a 1/N expansion one has to include the sums over "necklace" and generalized "sunset" diagrams. We find that - in contrast to the Hartree approximation - there is no spontaneous symmetry breaking in this approximation, as to be expected for the exact theory. The effective potential becomes convex throughout for all parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and temperatures between 0.2 and 1. The Green's functions obtained by solving the Schwinger-Dyson equations are enhanced in the infrared region. We also compare the effective potential as function of the external field phi with those obtained in various other approximations.Comment: 19 pages, 9 figures; v2: references added, some changes in the tex

Dynamique quantique ultra-rapide de nanogouttes d'hélium superfluide dopées

In this thesis we investigate two aspects of the dynamics of atomic impurities interacting with superfluid helium (He) nanodroplets, namely the photo-excitation of alkalis on a nanodroplet and the doping process of nanodroplets hosting quantised vortices with noble gas atoms. For the theoretical investigations we use He density functional theory and its time-dependent version. The first aspect involves a joint experimental and theoretical collaboration that focusses on the photo-excitation of the alkali rubidium (Rb). Alkalis are a very interesting probe of He droplets since they reside in their surface region, where it has been argued that almost 100% Bose-Einstein condensation could be achieved due to a density that is lower than in bulk superfluid He. In our simulations we find that states excited to the 5p and 6p manifold desorb at very different timescales, separated by 2 orders of magnitude (~100 ps and ~1 ps for 5p and 6p respectively). This is in good agreement with experimental results where the desorption behaviour of photo-excited Rb atoms is determined using a femtosecond pump-probe scheme. However, in our simulations excitation to the 5pPi_{3/2}-state results in a surface-bound RbHe exciplex, contrary to the experimental case where the RbHe exciplex desorbs from the droplets surface. Introducing spin-relaxation from Pi_{3/2} to Pi_{1/2} into the simulations, the RbHe exciplex is able to desorb from the droplet's surface, which resolves this contradiction. The second aspect concerns a purely theoretical investigation that is inspired by recent work of Gomez and Vilesov et al., where quantised vortices were visualised by doping He nanodroplets with silver atoms, subsequently "soft landing" them on a carbon screen. Electron-microscope images show long filaments of silver atom clusters that accumulated along the vortex cores. Also the formation of quantum-vortex lattices inside nanodroplets is evidenced by using X-ray diffractive imaging to visualise the characteristic Bragg patterns from xenon (Xe) clusters trapped inside the vortex cores. First, head-on collisions between heliophilic Xe and a He nanodroplet made of 1000 He atoms are studied. The results are then compared with the results of a previous study of an equivalent kinematic case with cesium (Cs), which is heliophobic. Xe acquires a "snowball" of He around itself when it traverses the droplet and much more kinetic energy is required before Xe is able to pierce the droplet completely. When it does, it takes away some He with it, contrary to the Cs case. Next, collisions between argon (Ar)/Xe and pristine superfluid He nanodroplets are performed for various initial velocities and impact parameters to determine the effective cross-section for capture. Finally, the simulations are then repeated for droplets hosting a single quantised vortex line. It is observed that the impact of the impurities induces large bending and twisting excitations of the vortex line, including the generation of helical Kelvin waves propagating along the vortex core. We conclude that Ar/Xe is captured by the quantised vortex line, although not in its core. Also we find that a He droplet, hosting a 6-vortex line array whose cores are filled with Ar atoms, results in added rigidity to the system which stabilises the droplets at low angular velocities. Our simulations involving droplets hosting quantum vortices open the way to further investigations on droplets hosting an array of vortices, involving multiple impurities.Dans cette thèse, nous étudions deux aspects de la dynamique d'impuretés atomiques interagissant avec des nanogouttes d'hélium superfluide (He) : la photo-excitation d'alcalins sur une nanogoutte et le dopage de nanogouttes contenant des tourbillons (vortex) quantiques avec des atomes de gaz rares. Nous utilisons la théorie de la fonctionnelle de la densité d'hélium ainsi que sa version dépendante du temps pour en faire la description théorique. Le premier aspect a été effectué dans le cadre d'une collaboration avec des expérimentateurs sur la photo-excitation du rubidium (Rb). Les alcalins sont une sonde très intéressante des gouttelettes d'hélium car ils résident dans leur zone de surface, où il a été prédit qu'un taux de condensation de Bose-Einstein de 100% était possible en raison d'une densité inférieure à celle de l'hélium superfluide. Nos simulations montrent que les états excités 5p et 6p désorbent à des échelles de temps très différentes, séparées par 2 ordres de grandeur (~100 ps et ~1 ps pour 5p et 6p respectivement). Ces résultats sont en accord avec ceux de l'expérience pompe-sonde à l'échelle femtoseconde qui a étudié la photodesorption d'atomes de Rb. Cependant, dans nos simulations, l'excitation vers 5pPi_{3/2} aboutit à un exciplexe RbHe lié à la surface, contrairement à l'expérience où RbHe est éjecté. L'introduction de la relaxation de spin de Pi_{3/2} à Pi_{1/2} nous a permis de résoudre ce désaccord, l'exciplexe RbHe ayant alors assez d'énergie pour désorber. Le deuxième aspect concerne une investigation purement théorique inspirée par les travaux récents de Gomez et Vilesov et al., où les tourbillons quantiques étaient visualisés en dopant les nanogouttes d'hélium avec des atomes d'argent, puis en les faisant atterrir en douceur (soft landing) sur un écran de carbone. Les images au microscope électronique montrent de longs filaments d'agrégats d'atomes d'argent qui s'étaient accumulés le long des coeurs des vortex. La formation de réseaux de tourbillons quantiques à l'intérieur de nanogoutelettes dopées par du xénon est également mise en évidence par diffraction de rayons X qui montrent des pics de Bragg caractéristiques d'agrégats de xénon piégés dans les coeurs des vortex. Nous avons d'abord étudié des collisions frontales entre un atome de xénon, héliophile, et une nanogoutte de 1000 héliums, et comparé les résultats à ceux d'une étude précédente sur le même processus avec le césium (Cs), qui est héliophobe. Dans le cas de Xe une «boule de neige» se forme autour de lui quand il entre dans la nanogoutte, et il lui faut beaucoup plus d'énergie qu'au Cs pour qu'il puisse en ressortir. Quand il le fait, il emporte des héliums avec lui, contrairement au Cs. Nous avons ensuite simulé des collisions entre Ar/Xe et des nanogouttes d'hélium superfluides pour différentes vitesses initiales et paramètres d'impact afin de déterminer leur section efficace de capture. Ces simulations ont ensuite été répétées pour des gouttelettes hébergeant un vortex quantique. On observe que l'impact des impuretés induit de grandes déformations de flexion et de torsion de la ligne de vortex, allant jusqu'à la génération d'ondes de Kelvin hélicoïdales qui se propagent le long du coeur du vortex. Ar/Xe est bien finalement capturé par le vortex, mais pas dans son coeur. Nous avons également découvert que l'existence d'un réseau de 6 lignes de vortex dont les noyaux sont remplis d'atomes d'Ar donne une rigidité accrue à la nanogoutte qui permet de stabiliser le système nano-goutte + vortex même à de faibles vitesses angulaires. Nos simulations impliquant des nanogouttes d'hélium comportant des tourbillons quantiques ouvrent la voie à d'autres investigations sur des nanogouttes hébergeant un ensemble de vortex, en collision avec de multiples impuretés

Transition from Knudsen to molecular diffusion in activity of absorbing irregular interfaces

We investigate through molecular dynamics the transition from Knudsen to molecular diffusion transport towards 2d absorbing interfaces with irregular geometry. Our results indicate that the length of the active zone decreases continuously with density from the Knudsen to the molecular diffusion regime. In the limit where molecular diffusion dominates, we find that this length approaches a constant value of the order of the system size, in agreement with theoretical predictions for Laplacian transport in irregular geometries. Finally, we show that all these features can be qualitatively described in terms of a simple random-walk model of the diffusion process.Comment: 4 pages, 4 figure

Self-consistent bounces in two dimensions

We compute bounce solutions describing false vacuum decay in a Phi**4 model in two dimensions in the Hartree approximation, thus going beyond the usual one-loop corrections to the decay rate. We use zero energy mode functions of the fluctuation operator for the numerical computation of the functional determinant and the Green's function. We thus avoid the necessity of discretizing the spectrum, as it is necessary when one uses numerical techniques based on eigenfunctions. Regularization is performed in analogy of standard perturbation theory; the renormalization of the Hartree approximation is based on the two-particle point-irreducible (2PPI) scheme. The iteration towards the self-consistent solution is found to converge for some range of the parameters. Within this range we find the corrections to the leading one-loop approximation to be relatively small, not exceeding one order of magnitude in the total transition rate.Comment: 30 pages, 12 figure

Nature-Inspired, Computer-Assisted Optimization of Hierarchically Structured Zeolites

Zeolite catalysis is often affected by transport limitations, which significantly influence overall performance. Introducing wide pores as molecular transport highways can reduce transport limitations, control the product distribution, and mitigate effects of catalyst deactivation. Nevertheless, the importance to rationally design the meso‐ and macropore space remains underappreciated. This article reviews multiscale modelling approaches to optimize overall catalytic performance. It provides a general methodology and rules of thumb to guide catalyst synthesis with optimal pore network characteristics. Inspiration is taken from nature, such as the structure of leaves and tissues, with similar requirements and associated features. In optimal hierarchically structured zeolites, the added macro‐/mesopore volume fraction, connectivity, crystal size, and minimum wide pore size are crucial. The broad pore size distribution is secondary. No uncontrolled diffusion limitations should exist within the zeolite crystals. Surface barriers, however, can significantly affect, even dominate overall transport. Understanding their origin and ways to control them is an emergent research area. Synthesis methods to realize hierarchically structured zeolites are briefly reviewed. Significant gaps exist between laboratory synthesis methods and industrial requirements. Zeolite catalysis could benefit from computer‐assisted design of their hierarchical pore network, embracing principles used by natural transport networks for scalable efficiency, selectivity, and robustness

Influence of catalyst pore network structure on the hysteresis of multiphase reactions

The effects of the catalyst pore network structure on multiphase reactions in catalyst pellets are investigated by using the experimentally validated pore network model proposed in our recent work (AIChE J, 62, 451, 2016). The simulations display hysteresis loops of the effectiveness factor. The hysteresis loop area becomes significantly larger, when having small volume-averaged pore radius, wide pore-size distribution, and low pore connectivity; however, the loop area is insensitive to pellet size, even though it affects the value of the effectiveness factor. The hysteresis loop area is also strongly affected by the spatial distribution of the pore size, in particular for a bimodal pore-size distribution. The pore network structure directly influences mass transfer, capillary condensation, and pore blocking, and subsequently passes these influences on to the hysteresis loop of the effectiveness factor. Recognizing these effects is essential when designing porous catalysts for multiphase reaction processes. © 2016 American Institute of Chemical Engineers AIChE J, 63: 78–86, 2017

Economic impact of port activity : a disaggregate analysis. The case of Antwerp

The economic impact of the port sector is usually measured at an aggregate level by indicators such as value added, employment and investment. This paper tries to define the economic relevance for the regional as well as for the national economy at a disaggregate level. It attempts to identify, quantify and locate the mutual relationships between the various port players themselves and between them and other Belgian industries. Due to a lack of information foreign trade is only tackled very briefly but the method outlined in this paper can be used to measure the national effects of changes in port activity at a detailed level. A sector analysis is made by compiling a regional (regional as geographically opposed to national, not to be mistaken for the Belgian Regions Brussels, Flanders and Wallonia) input-output table, resorting to microeconomic data: a bottom-up approach. The main customers and suppliers of the port's key players or stakeholders are identified. A geographical analysis can also be carried out by using data at a disaggregate level. Each customer or supplier can be located by means of their postcode. In so doing, the economic impact of the port is quantified, both functionally and geographically. In the case of the port of Antwerp, the results show important links between freight forwarders and agents. The geographical analysis suggests the existence of major agglomerating effects in and around the port of Antwerp, referred to as a major transhipment location point. Key words: port economics, regional input-output table, sector analysis, geographical analysis.port economics, regional input-output table, sector analysis, geographical analysis

Dynamic acoustic emission analysis of polymer electrolyte membrane fuel cells

The acoustic emission (AE) technique has been demonstrated as a non-invasive and non-destructive water management diagnostic tool for polymer electrolyte membrane fuel cells (PEMFCs). AE probes the dynamics of water generation and removal at the flow-field of a PEMFC to establish the hydration state inside the cell and has been utilised to electro-acoustically characterise the performance of a PEMFC under different operating conditions. In this study, the dynamic relationship between the acoustic activity and the rate of electrochemical reaction inside a PEMFC is explored by correlating AE from PEMFCs with their performance using different time-based characterisations (polarisation scans at 10 s, 60 s, and 120 s voltage stabilisation durations). Flooding resulted in ∼16% decrease in maximum current density generated at 60 s and 120 s conditions compared to that at 10 s. Besides, flooding at longer durations is confirmed by acoustic emission as a function of polarisation (AEfP) and electrochemical impedance spectroscopy measurements. The effectiveness of the AE technique as a direct water diagnostic tool for PEMFCs is established through forward-reverse polarisation scans. Here, the AE energy generated during cell polarisations is utilised in understanding the water uptake and release mechanism inside the fuel cell. Furthermore, cell durability testing is performed through galvanostatic and potentiostatic measurements, where a synchronous relationship between the cell performance and the measured AE is identified

Acoustic emission as a function of polarisation: Diagnosis of polymer electrolyte fuel cell hydration state

Understanding water management is a crucial aspect in the development of improved polymer electrolyte fuel cells (PEFCs). Separating the performance degradation due to dehydration, water flooding and reactant starvation in PEFCs is a major challenge. In this study, acoustic emission (AE) analysis, a non-invasive and non-destructive diagnostic tool, is utilised to probe water formation and removal inside an operating fuel cell. In the acoustic emission as a function of polarisation (AEfP) method, AE activity from the PEFC is measured in terms of cumulative absolute AE energy (CAEE) hits during operation at discrete points on the polarisation curve. AEfP can identify the presence of liquid water in flow channels and correlate its formation and removal with the level of cell polarisation, and consequent internal temperature. Correlation between acoustic activity and water generation, supply and removal is achieved by varying current (polarisation), cathode air feed relative humidity (RH) and cell temperature, respectively. Features such as initial membrane hydration, liquid water formation, ‘flushing’ and the transition from ‘wet-channel’ to ‘dry-channel’ operation are identified using AE analysis, thereby providing a powerful and easy to implement diagnostic for PEFCs

Understanding the Role of Internal Diffusion Barriers in Pt/Beta Zeolite Catalyzed Isomerization of n‐Heptane

Applications of zeolites in catalysis are plagued by strong diffusion resistance, which results from limitations to molecular transport in micropores, across external crystal surfaces, but also across internal interfaces. The first type of diffusion resistance is well understood, the second is receiving increasing attention, while the diffusion barriers at internal interfaces remain largely unclear. We take Pt/Beta catalyzed isomerization of n‐heptane as the model system to explore the role of internal diffusion barriers in zeolite catalysis. The two as‐synthesized Pt/Beta catalysts have an identical Pt loading, similar Beta particle size and acidity, but different internal structures. A Pt/Beta crystal with no observable internal interfaces can be 180 % higher in activity and 22 % higher in selectivity than its counterpart with numerous internal interfaces. This can only be attributed to the strong transport barriers across internal interfaces, as supported by directly comparing the apparent diffusivities of the two Beta samples