Cut-off and Escape Behaviors for Birth and Death Chains on Trees

We consider families of discrete time birth and death chains on trees, and show that in presence of a drift towards the root of the tree, the chains exhibit cut-off behavior along the drift and escape behavior in the opposite direction.Comment: 22 pages, 1 figure. This new version, written after referee's suggestions, is shorter and features a more clear presentation of the results. The previous proofs of Section 3, based on difference equations method, are now given in appendi

Convergence abrupte et métastabilité

The aim of this thesis is to link two phenomena concerning the asymptotical behavior of stochastic processes, which were disjoined up to now. The abrupt convergence or cutoff phenomenon on one hand, and metastability on the other hand.In the cutoff case an abrupt convergence towards the equilibrium measure occurs at a time which can be determined, whereas metastability is linked to a great uncertainty of the time at which we leave some equilibrium. We propose a common framework to compare and study both phenomena : that of discrete time birth and death chains on $\mathbb{N}$ with drift towards zero.Under the drift hypothesis, we prove that there is an abrupt convergence towards zero, metastability in the other direction, and that the last exit in the metastability is the time reverse of a typical cutoff path.We extend our approach to the Ehrenfest model, which allows us to prove abrupt convergence and metastability with a weaker drift hypothesis.Le but de cette thèse est de relier deux phénomènes relatifs au comportement asymptotique des processus stochastiques, qui jusqu'à présent étaient restés dissociés. La convergence abrupte ou phénomène de cutoff d'une part, et la métastabilité d'autre part. Dans le cas du cutoff, une convergence abrupte vers la mesure d'équilibre du processus a lieu à un instant que l'on peut déterminer, alors que la métastabilité est liée à une grande incertitude sur l'instant où l'on va sortir d'un certain équilibre. On propose un cadre commun pour étudier et comparer les deux phénomènes : celui des chaînes de naissance et de mort à temps discret sur $\mathbb{N}$, avec une dérive vers zéro.On montre que sous l'hypothèse de dérive il y a convergence abrupte vers zéro et métastabilité dans l'autre sens. De plus la dernière excursion dans la métastabilité est la renversée temporelle d'une trajectoire typique de cutoff.On étend notre approche au modèle d'Ehrenfest, ce qui nous permet de montrer la convergence abrupte et la métastabilité sous une hypothèse de dérive plus faible

Conformational Structural Changes of Bacteriorhodopsin Adsorbed onto Single-Walled Carbon Nanotubes

International audienceThe interaction between purple membranes, composed of proteins of bacteriorhodopsin (bR) and their native Surrounding lipids, and single-walled carbon nanotubes (SWNT) has been investigated. In this work, sonication has been used to debundle SWNT in buffer solution without surfactant before the addition of native purple membranes. The sample was then sonicated in a bath for a short time, followed by a centrifugation. The supernatants contain proteins in excess and SWNT as individual and small bundles covered by a bR layer with an average thickness of 1.5 nm. TEM and AFM observations support the idea that only a protein monolayer surrounds the tubes. Optical absorption and infrared spectroscopy measurements provide evidence that the proteins adsorbed onto the SWNT undergo orientational changes of the helical segments in bR and helix conformational changes. We ascribe the main driving force to the hydrophobic interactions between the sidewall of the SWNT and the hydrophobic residues of the alpha-helices of bR

Complexes nanotubes de carbone monoparois / polysaccharides (caractérisation de l'association et mécanisme)

Aujourd hui, les études sur les nanotubes de carbone (NTC) et plus particulièrement sur leur utilisation dans le domaine du biomédical sont en plein développement. Nos travaux s inscrivent dans cette dynamique et sont consacrés à la formation et à la caractérisation de complexes NTC monoparois / Polysaccharides, en vue de la réalisation, à long terme, de biocapteurs à transduction optique. Les polysaccharides utilisés sont des dérivés d amylose et de cellulose. L objectif est de comprendre les interactions entre ces biopolymères et les NTC, qui permettent la dispersion et l individualisation des NTC en milieu aqueux. Pour ce faire, les complexes sont formés en solution aqueuse en présence d ultra-sons, isolés par centrifugation et étudiés notamment par spectroscopie d absorption optique, de diffusion Raman et d émission et microscopie à force atomique. L efficacité et le rendement de la dispersion est fonction d un polysaccharide donné. C est avec la carboxyméthylcellulose que les dispersions obtenues sont les plus performantes. Par variation de la conformation du biopolymère, de son état de charge, de son hydrophobicité, du milieu réactionnel (solvant, pH, salinité) nous avons pu montrer que l interaction dominante mise en jeu est de type CH-p entre le NTC et le groupement glucosidique de la chaîne principale. Une conformation étendue du biopolymère favorise cette association. Les interactions hydrophobes et électrostatiques interviennent aussi dans le mécanisme d association et induisent une légère sélectivité envers les NTC semi conducteurs. Bien que nous n ayons pas encore pu réaliser de biocapteurs, les complexes obtenus répondent aux critères permettant de le faire.This thesis tackles the fields of carbon nanotubes and their biomedical applications. In that purpose, Single-Walled Carbon Nanotubes (SWNT) / Polysaccharides complexes are prepared in water by an ultrasound process and isolated by a centrifugation step and then characterized. The long term application of such systems could be the fabrication of a biosensor with optical detection.Different kinds of cellulose and amylose derivatives are used in order to individualize SWNT in water in a stable way. We show that the polysaccharide water solubility, its conformation in solution and its structure are as much different parameters which have to be taken into account for the determination of the effectiveness and the yield of the dispersion. To understand the mechanism of interaction between polysaccharide and SWNT, we use in particular optical absorption, Raman and emission spectroscopy and atomic force microscopy. Effectiveness and yield are function of a given polysaccharide. Carboxymethylcellulose is shown as one of the best dispersant for SWNT. Excellent individualization of the SWNT is observed. Modification of the polymer charge, of its hydrophobicity or of the reaction medium (salt, pH, solvent) prove that a flat conformation of the biopolymer favours the interaction. In this study, we have shown that the main mechanism of interaction may consist in a CH-p interaction between the glucose chain of the polysaccharide and the sidewall of the carbon nanotubes. Electrostatic and hydrophobic forces also have to be considered in the association mechanism and induce a weak selectivity of the process for semiconductor nanotubes. The complexes may be used for building biosensors.NANTES-BU Sciences (441092104) / SudocSudocFranceF

Morphology of DNA/single walled nanotubes complexes

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Macroporous hybrid Pickering foams based on carbon nanotubes and cellulose nanocrystals

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Carbon Nanotube/Cellulose Nanocrystal Hybrid Conducting Thin Films

Cellulose nanocrystals (CNCs) have a high ability to disperse single-walled carbon nanotubes (SWNTs) in aqueous media and to form hybrids. These hybrids are used to grow layer-by-layer thin films of controlled thickness. Thanks to the presence of SWNTs, these films are conducting. In this article, we describe the process by which the CNC/SWNT hybrids are obtained and discuss the electrical properties of the hybrid-based layer-by-layer films

Highly Efficient and Predictable Noncovalent Dispersion of Single-Walled and Multi-Walled Carbon Nanotubes by Cellulose Nanocrystals

Cellulose nanocrystals (CNCs) are shown to be able to disperse in a very efficient way both single-walled (SWNTs) and multiwalled carbon nanotubes (MWNTs). Optimization of the processing parameters (sonication time and power) leads to dispersion yields as high as 70 wt % for both types of carbon nanotubes (CNTs). Such a high dispersion yield obtained in a noncovalent way with biobased nanoparticles is noteworthy and deserves further attention. Atomic force microscopy and transmission electron microscopy images suggest that the CNCs and the nanotubes form hybrids, with the stabilization of the dispersion arising from both the irreversible adsorption of the CNCs onto the nanotubes and the electrostatic repulsion between the CNCs. A quantitative model is proposed, revealing that one CNC can stabilize one SWNT three times its length in the aqueous dispersion and that more CNCs are required in the case of MWNTs. This model allows us to control the dispersion yield as a function of the processing parameters