TY - JOUR A1 - Dybiec, Bartlomiej A1 - Capala, Karol A1 - Chechkin, Aleksei A1 - Metzler, Ralf T1 - Conservative random walks in confining potentials JF - Journal of physics : A, Mathematical and theoretical N2 - Levy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic systems, or even the dynamics in quantum systems such as cold atoms. In the simplest version Levy walks move with a finite speed. Here, we present an extension of the Levy walk scenario for the case when external force fields influence the motion. The resulting motion is a combination of the response to the deterministic force acting on the particle, changing its velocity according to the principle of total energy conservation, and random velocity reversals governed by the distribution of waiting times. For the fact that the motion stays conservative, that is, on a constant energy surface, our scenario is fundamentally different from thermal motion in the same external potentials. In particular, we present results for the velocity and position distributions for single well potentials of different steepness. The observed dynamics with its continuous velocity changes enriches the theory of Levy walk processes and will be of use in a variety of systems, for which the particles are externally confined. KW - Levy walk KW - conservative random walks KW - Levy flight Y1 - 2018 U6 - https://doi.org/10.1088/1751-8121/aaefc2 SN - 1751-8113 SN - 1751-8121 VL - 52 IS - 1 PB - IOP Publ. Ltd. CY - Bristol ER - TY - THES A1 - Wolf, Gunter T1 - Diffusionsuntersuchungen an (polymer-modifizierten) Mikroemulsionen mittels Feldgradientenimpuls-NMR-Spektroskopie T1 - Diffusion studies in (polymer-modified) microemulsions using pulsed field gradient NMR spectroscopy N2 - Aufgrund des großen Verhältnisses von Oberfläche zu Volumen zeigen Nanopartikel interessante, größenabhängige Eigenschaften, die man im ausgedehnten Festkörper nicht beobachtet. Sie sind daher von großem wissenschaftlichem und technologischem Interesse. Die Herstellung kleinster Partikel ist aus diesem Grund überaus wünschenswert. Dieses Ziel kann mit Hilfe von Mikroemulsionen als Templatphasen bei der Herstellung von Nanopartikeln erreicht werden. Mikroemulsionen sind thermodynamisch stabile, transparente und isotrope Mischungen von Wasser und Öl, die durch einen Emulgator stabilisiert sind. Sie können eine Vielzahl verschiedener Mikrostrukturen bilden. Die Kenntnis der einer Mikroemulsion zugrunde liegenden Struktur und Dynamik ist daher von außerordentlicher Bedeutung, um ein gewähltes System potentiell als Templatphase zur Nanopartikelherstellung einsetzen zu können. In der vorliegenden Arbeit wurden komplexe Mehrkomponentensysteme auf der Basis einer natürlich vorkommenden Sojabohnenlecithin-Mischung, eines gereinigten Lecithins und eines Sulfobetains als Emulgatoren mit Hilfe der diffusionsgewichteten 1H-NMR-Spektroskopie unter Verwendung gepulster Feldgradienten (PFG) in Abhängigkeit des Zusatzes des Polykations Poly-(diallyl-dimethyl-ammoniumchlorid) (PDADMAC) untersucht. Der zentrale Gegenstand dieser Untersuchungen war die strukturelle und dynamische Charakterisierung der verwendeten Mikroemulsionen hinsichtlich ihrer potentiellen Anwendbarkeit als Templatphasen für die Herstellung möglichst kleiner Nanopartikel. Die konzentrations- und zeit-abhängige NMR-Diffusionsmessung stellte sich dabei als hervorragend geeignete und genaue Methode zur Untersuchung der Mikrostruktur und Dynamik in den vorliegenden Systemen heraus. Die beobachtete geschlossene Wasser-in-Öl- (W/O-) Mikrostruktur der Mikroemulsionen zeigt deutlich deren potentielle Anwendbarkeit in der Nanopartikelsynthese. Das Gesamtdiffusionsverhalten des Tensides wird durch variierende Anteile aus der Verschiebung gesamter Aggregate, der Monomerdiffusion im Medium bzw. der medium-vermittelten Oberflächendiffusion bestimmt. Dies resultierte in einigen Fällen in einer anormalen Diffusionscharakteristik. In allen Systemen liegen hydrodynamische und direkte Wechselwirkungen zwischen den Tensidaggregaten vor. Der Zusatz von PDADMAC zu den Mikroemulsionen resultiert in einer Stabilisierung der flüssigen Grenzfläche der Tensidaggregate aufgrund der Adsorption des Polykations auf den entgegengesetzt geladenen Tensidfilm und kann potentiell zu Nanopartikeln mit kleineren Dimensionen und schmaleren Größenverteilungen führen. N2 - Owing to their large surface-to-volume ratio nanoparticles show interesting size-dependent properties that are not observable in bulk materials. Thus, they are of great scientific and technological interest. Thereby, the highly desirable preparation of as small particles as possible might be easily achieved using microemulsions as template phases. Microemulsions are thermodynamically stable, transparent and isotropic mixtures of water and oil stabilized by an emulsifying agent. However, microemulsions may form a great variety of different microstructures. Thus, it is of utmost importance to know the underlying microstructure and microdynamics of a chosen microemulsion system in order to use it as a template phase for nanoparticle formation. In the present study complex multi-component microemulsion systems based on a naturally occurring soybean lecithin mixture, purified lecithin and sulfobetaine as emulsifiers were investigated by diffusion-weighted pulsed field gradient (PFG) 1H NMR spectroscopy in the presence and absence of the polycation poly-(diallyldimethylammonium chloride) (PDADMAC). The central topic of this study was to structurally and dynamically characterize the present microemulsions with respect to their potential use in nanoparticle formation. The concentration- and time-dependent NMR diffusion measurements turned out to be a suitable and accurate tool to investigate the microstructure and microdynamics of the systems under investigation. They reveal closed water-in-oil (W/O) microemulsion microstructures which prove the potential suitability of the respective systems as template phases for the preparation of nano-sized particles. The overall diffusion behavior of surfactants were found to be governed by varying contributions from displacements of entire aggregates, monomer diffusion in the medium and bulk-mediated surface diffusion, respectively. In some cases this led to a marked anomalous diffusion characteristics. In all systems interactions between aggregates are dominated by hydrodynamic and direct forces. The addition of PDADMAC to the microemulsion systems results in a stabilization of the liquid interface of surfactant aggregates due to the adsorption of the polycation at the oppositely charged surfactant film and may potentially lead to nanoparticles of smaller dimensions and narrower size distributions. KW - Mikroemulsion KW - Mikrostruktur KW - Magnetische Kernresonanz KW - PFG-NMR-Spektroskopie KW - Selbstdiffusion KW - Anomale Diffusion KW - Polykation KW - Inverse Micelle KW - Wasser-in-Öl-Mikroemulsion KW - Tensiddynamik KW - medium-vermittelte Oberflächendiffusion KW - Levy-Bewegung KW - water-in-oil microemulsion KW - surfactant dynamics KW - bulk-mediated surface diffusion KW - Levy walk Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6259 ER - TY - JOUR A1 - Sliusarenko, Oleksii Yu A1 - Vitali, Silvia A1 - Sposini, Vittoria A1 - Paradisi, Paolo A1 - Chechkin, Aleksei A1 - Castellani, Gastone A1 - Pagnini, Gianni T1 - Finite-energy Levy-type motion through heterogeneous ensemble of Brownian particles JF - Journal of physics : A, Mathematical and theoretical N2 - Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling x similar to t(delta) with delta not equal 1/2 in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Levy Flights or Levy Walks (LWs). Levy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Levy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous (delta = 1/2) to normal (delta = 1/2) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the interevent time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation-dissipation theorem. KW - anomalous diffusion KW - heterogeneous ensemble of Brownian particles KW - biological transport KW - Langevin equation KW - Gaussian processes KW - fractional diffusion KW - Levy walk Y1 - 2019 U6 - https://doi.org/10.1088/1751-8121/aafe90 SN - 1751-8113 SN - 1751-8121 VL - 52 IS - 9 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Xu, Pengbo A1 - Deng, Weihua A1 - Sandev, Trifce T1 - Levy walk with parameter dependent velocity BT - hermite polynomial approach and numerical simulation JF - Journal of physics : A, Mathematical and theoretical N2 - To analyze stochastic processes, one often uses integral transform (Fourier and Laplace) methods. However, for the time-space coupled cases, e.g. the Levy walk, sometimes the integral transform method may fail. Here we provide a Hermite polynomial expansion approach, being complementary to the integral transform method, to the Levy walk. Two approaches are compared for some already known results. We also consider the generalized Levy walk with parameter dependent velocity. Namely, we consider the Levy walk with velocity which depends on the walking length or on the duration of each step. Some interesting features of the generalized Levy walk are observed, including the special shapes of the probability density function, the first passage time distributions, and various diffusive behaviors of the mean squared displacement. KW - Hermite polynomial expansion KW - Levy walk KW - anomalous diffusion KW - parameter KW - dependent velocity Y1 - 2020 U6 - https://doi.org/10.1088/1751-8121/ab7420 SN - 1751-8113 SN - 1751-8121 VL - 53 IS - 11 PB - IOP Publ. Ltd. CY - Bristol ER -