Orientador: Prof. Dr. Roberto Venegeroles / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015. / Discutiremos uma classe de sistemas dinâmicos intermitentes na qual o espaço de fase é composto de duas regiões distintas: uma região laminar, onde a partícula desenvolve uma dinâmica lenta e quase regular até saltar para uma região turbulenta, onde a mesma desenvolve uma dinâmica caó- tica de curta duração até ser reinjetada de volta para a fase laminar, num processo que assim se repete. A fase laminar é causada pela existência de medida invariante innita, e a composição regularidade-caos resulta numa modalidade de caos fraco na qual a separação de trajetórias inicialmente muito próximas torna-se subexponencial (em sistemas caóticos usuais, essa separação é exponencial). Por conta desse tipo intermitência, o mapa apresentará um comportamento ergódico diferente daquele observado pelo teorema de Birkho, de modo que a distribuição de médias temporais de observáveis (com fatores próprios de normalização) é descrita essencialmente por uma estatística Mittag-Leer, ao invés de distribuições com limites assintóticos para delta de Dirac. Apresentaremos a lei responsável por tal comportamento, o teorema de Aaronson-Darling-Kac, que nos permitirá estender adequadamente certos observáveis, tais como o expoente de Lyapunov e a entropia de Kolmogorov- Sinai, de modo a inferir precisamente a existência desse tipo de instabilidade. Após um estudo das principais características ergódicas de tais sistemas, investigamos o número de primeiras-passagens da fase laminar para a turbulenta, e como obter informações-chave por meio dessa quantidade. Mostraremos também que a teoria de processos de renovação, usualmente empregada na literatura para esse m, é insuciente para descrever precisamente esse tipo de intermitência. Historicamente, esse tipo de sistema surgiu do estudo de mapas de primeiro retorno de certas seções do atrator de Lorenz, realizado nos anos 80 por Pomeau e Manneville. Atualmente, cadeias de tais mapas são empregadas no estudo de difusão anômala e passeios aleatórios com tempos de espera. / We discuss a class of intermittent dynamical systems in which the phase space is made up of two distinct regions: a laminar region, where the particle develops a slow and almost regular dynamic until it jumps to a turbulent region, where it develops a chaotic dynamic of short duration that is reinjected back into the laminating step, in a repeating process. The laminar phase is caused by the existence of innite invariant measure, and the regularity-chaos composition results in a weak mode in which the trajectories separation of two initial nearly points becomes subexponential (in usual chaotic systems, this separation is exponential). Because of this type of intermittency, the map will present a dierent behavior from that observed by ergodic Birkho's theorem, so that the distribution of average observable time (with its own normalization factors) is described essentially by a Mittag-Leer statistics, rather than distributions with asymptotic limit to the Dirac delta. We will present the law responsible for such behavior, the theorem Aaronson-Darling-Kac, which will allow us to extend properly certain observables, such as the Lyapunov exponent and entropy Kolmogorov-Sinai, in order to infer precisely the existence of such instability . After a study of the main ergodic characteristics of such systems, we investigate the number of rst-passages of the laminar stage for the turbulence, and how to get key information by that amount. We will also show that the theory of renewal processes, usually used in the literature for this purpose, is insucient to accurately describe this type of intermittency. Historically, this type of system emerged from the study of rst return maps of certain sections of the Lorenz attractor was accomplished in the 80's by Pomeau and Manneville. Currently chains of these maps are used in the study of anomalous diusion and random walks with waiting times.

Les marches aléatoires avec recherche de cible peuvent modéliser des réactions nucléaires ou la quête de nourriture par des animaux. Dans cette thèse, nous identifions des stratégies qui minimisent le temps moyen de première rencontre d’une cible (MFPT) pour plusieurs types de marches aléatoires. Premièrement, pour des marches symétriques ou avec biais, nous déterminons la distribution des temps de première sortie par une ouverture dans une paroi en forme de secteur angulaire, d’anneau ou de rectangle. Nous concluons sur la minimisation du MFPT en termes de la géométrie du confinement. Deuxièmement, pour des marches alternant entre diffusions volumique et surfacique, nous déterminons le temps moyen de première sortie par une ouverture dans la surface de confine- ment. Nous montrons qu’il existe un taux de désorption optimal qui minimise le MFPT. Nous justifions la généralité de l’optimalité par l’étude des rôles de la géométrie, de l’adsorption sur la surface et d’un biais en phase volumique. Troisièmement, pour des marches actives composées de phases balistiques entrecoupées par des réorientations aléatoires, nous obtenons l’expression du taux de réorientation qui minimise le MFPT en géométries sphériques de dimension deux ou trois. Dans un dernier chapitre, nous modélisons le mouvement de cellules eucaryotes par des marches browniennes actives. Nous expliquons pourquoi le temps de persistance évolue expo- nentiellement avec la vitesse de la cellule. Nous obtenons un diagramme des phases des types de trajectoires. Ce modèle minimal permet de quantifier l’efficacité des processus de recherche d’antigènes par des cellules immunitaires. / Random search processes can model nuclear reactions or animal foraging. In this thesis, we identify optimal search strategies which minimize the mean first passage time (MFPT) to a target for various processes. First, for symmetric and biased Brownian particles, we compute the distribution of exit times through an opening within the boundary of angular sectors, annuli and rectangles. We conclude on the optimizability of the MFPT in terms of geometric parameters. Second, for walks that switch between volume and surface diffusions, we determine the mean exit time through an opening inside the bounding surface. Under analytical criteria, an optimal desorption rate minimizes the MFPT. We justify that this optimality is a general property through a study of the roles of the geometry, of the adsorption properties and of a bias in the bulk random walk. Third, for active walks composed of straight runs interrupted by reorientations in a random direction, we obtain the expression of the optimal reorientation rate which minimizes the MFPT to a centered spherical target within a spherical confinement, in two and three dimensions. In a last chapter, we model the motion of eukaryotic cells by active Brownian walks. We explain an experimental observation: the persistence time is exponentially coupled with the speed of the cell. We also obtain a phase diagram for each type of trajectories. This model is a first step to quantify the search efficiency of immune cells in terms of a minimal number of biological parameters.

Contingent Convertibles (CoCos) are a new type of hybrid debt instrument characterized by forced equity conversion or write-down under a specified trigger event, usually indicating a state of near non-viability of the Additional Tier 1 capital category, giving them additional features such as possible coupon cancellation. In this thesis, the structure of CoCos is presented and different pricing approaches are introduced. A special focus is put on structural models with the Analytically Tractable First Passage Time(AT1P) Model and its extensions. Two models are applied on the write-down CoCo issued by Svenska Handelsbanken, starting with the equity derivative model and followed by the AT1P model. / Contingent Convertibles (Cocos) - villkorade konvertibla obligationer, är en ny typ av hybridinstrument som kännetecknas av konvertering till eget kapital eller nedskrivning av lånet vid en viss utlösande händelse, som vanligtvis indikerar ett tillstånd där den emitterande banken har behov av att absorbera förluster. Under strikta villkor kan dessa CoCo obligationer tillhöra primärkapital, där de kännetecknas av bland annat möjlig inställning av kuponger. I denna avhandling presenteras CoCons struktur och olika prissättningsmodeller läggs fram. Ett särskilt fokus läggs på strukturella modeller med “Analytically Tractable First Passage Time (AT1P) Model” och dess utvidgningar. Två modeller tillämpas på CoCon emitterad av Svenska Handelsbanken: “equity derivative” modellen och AT1P modellen.

The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature.

no / The paper deals with the problem of predicting the maximum response statistics of Multi-Degree-of-Freedom (MDoF) linear structures subjected to non-stationary non-white noises. The extension of two different censored closures of Gumbel type, originally proposed by the authors for the response of Single-Degree-of-Freedom oscillators, it is presented. The improvement associated with the introduction in the closure of a consistent censorship factor, accounting for the response bandwidth, it is pointed out. Simple and effective step-by-step procedures are formulated and described in details. Numerical applications on a realistic 25-storey moment-resisting frame along with comparisons with classical approximations and Monte Carlo simulations are also included.

En présence de diffusions multiples, les algorithmes de Monte-Carlo sont trop coûteux pour être employés dans les algorithmes de reconstruction d'images de géométries tridimensionnelles réalistes. Pour des trajectoires de premiers retours, l'approximation de diffusion est communément employée afin de représenter la statistique des chemins aux nombres de Knudsen tendant vers zéro. En formulant des problèmes équivalents sur des trajectoires de premiers passages, l'usage de l'approximation est étendue en un développement théorique. Cette nouvelle formulation assure un bon niveau de précision, sur une large plage de valeurs du nombre de Knudsen en ce qui concerne l'évaluation des moments de la distribution des longueurs des chemins de premier retour. La résolution numérique du modèle formulé est confrontée aux simulations numériques type Monte- Carlo sur des géométries mono-dimensionnelles et un cas tridimensionel ouvrant des perspectives vers une généralisation aux applications réelles. / For multiple scattering, Monte-Carlo algorithms are computationally too demanding for use in image reconstruction of 3D realistic geometries. In the study of first return path, the diffusion approximation is commonly used to represent their statistical behaviour when the Knudsen number tends to zero. With the formulation of equivalent problems for first passage path, the use of the approximation is extended in a theoretical development. The new model provides a good level of accuracy, for a wide distribution of Knudsen numbers when evaluating the moments distribution of the first return paths length. Numerical application of the model is confronted to Monte-Carlo simulations on one dimension geometries and a simple three-dimension case opening perspectives for the generalization to practical applications.

Dans cette thèse, nous étudions les propriétés d’un mouvement de diffusion intermittent dans un milieu confiné.Dans ce but, nous considérons un modèle minimal de catalyse hétérogène, mettant en jeu une particule soumise à un mouvement de diffusion “surface-mediated”, alternant des phases de diffusion volumique à l’intérieur d’un disque, et des phases de diffusion surfacique sur le pourtour du disque. Pour un tel mouvement, nous obtenons des résultats pour plusieurs observables de premier passage (i) le temps moyen de premier passage d'atteindre une cible, (ii) la probabilité de splitting d’atteindre une cible spécifique, (iii) le territoire exploré avant de sortir du disque (iv) la probabilité de réaction avec des sites catalytiques. Selon la position relative de départ de de ces quantités vis-à-vis du temps d'adsorption moyen sur la surface. Nous avons montré que des excursions volumiques peuvent minimiser le temps de recherche d’une cible, même si celle-ci est située sur la surface. Nous présentons également un modèle simple de milieu poreux ordonné, constitué d’un réseau hypercubique de cavités identiques. Nous présentons deux modèles : (i) pour un mouvement brownien simple, (ii) pour un mouvement intermittent, en introduisant un paramètre de persistance. Nous montrons que ces deux modèles, dans la limite de non-persistance, converge vers le même résultat. Nous avons aussi etudié le comportement et l’optimisation du coefficient de diffusion vis-à-vis du temps moyen d’adsorption. Pour évaluer nos résultats théoriques, nous utilisons des simulations de Monte-Carlo et des résolutions numériques par le méthode des éléments finis. / In this thesis, we study first-passage properties for an intermittent Brownian motion inside a confining domain. We consider a minimal model of heterogenous catalysis in which a molecule performs surface-mediated diffusion inside a confining domain whose boundary contains catalytic sites. We obtain results for several observables : (i) the mean first-passage time to reach a target, (ii) the splitting probabilities that the molecule reach a specific target, (iii) the covered territory on the confining surface before the molecule exits the domain, (iv) the probability of reacting with catalytic sites. These results are exact for point like-targets, and are shown to be accurate also for extended targets, located on the surface or inside the bulk. Depending of the relative positions of the entrance and exit points, very different behaviors with respect to the mean adsorption time of the molecule on the surface are found. Although non-intuitive for bulk targets, it is found that boundary excursions, can minimize the search time. We also present a simple model of an ordered porous media. We present two models : (i) for a simple Brownian motion, (ii) for a surface-mediated diffusion with a parameter of persistence b. This model leads to a less simple result for the efficient diffusion coefficient. Our main result shows that in the limit of non persistence (b=0), both results are the same. We also provide an analysis of the behaviors of the efficient diffusion coefficient with respect to the mean adsorption time, showing optimisation possibilities. Numericals Monte-Carlo simulations and finite element solver have been used to evaluate our theoretical results.

In dieser Arbeit werden zwei intrazelluläre Signalwege, betreffend den Tumorsuppressor p53 und das Signalmolekül Ca2+ , diskutiert und modelliert. Einzelzellmessungen des Tumorsuppressors p53 zeigen pulsatile Antwor- ten nach Zufügung von DNA Doppelstrangbrüchen (DSBs). Außer für sehr hohe Schadensdosen, ist das zeitliche auftreten dieser Pulse unregelmäßig. Mithilfe eines Wavelet basierten Pulsdetektors werden die einzelzell Trajek- torien untersucht und die inter-Puls Intervall (IPI) Verteilungen extrahiert. Diese weisen auf nicht-oszillatorische Regime in den Daten hin. Die Theorie der anregbaren Systeme angewendet auf regulatorische Netzwerke ermöglicht dieses komplexe Verhalten mathematisch zu beschreiben. Die Kopplung von Schadens-Sensor-Kinase Dynamik mit dem kanonischen p53 negativen feedback loop, ergibt ein anregbares p53 Modell. Detaillier- te Bifurkationsanalysen zeigen ein robustes anregbares Regime, welches durch ein starkes Schadenssignal auch in Oszillationen überführt werden kann. Treibt man das p53 Modell mit einem stochastischen DNA-Schadens-Prozess, kann sowohl das oszillatorische Verhalten nach hohem Schaden, als auch das unregelmäßige pulsatile Verhalten ohne äußere Stimulation reproduziert werden. Intrazelluläre Ca 2+ Spikes entstehen durch eine hierarchische Kaskade stochastischer prozesse. Die Anwendung einer semi-markovschen Beschreibung führt zu praktischen analytischen Lösungen des erstpassagezeiten Problems. Eine hierbei entdeckte Zeitskalenseparation ermöglicht ein neues allgemeines Ca2+ -Modell. Dieses erklärt auf äußerst prägnante Weise viele wesentliche experimentelle Ergebnisse, insbesondere die Momentenbeziehungen der inter-Spike Intervall Verteilungen. Schließlich erlaubt die hier vorgestellte Theorie Berechnungen der Stimulus-Enkodierung, also die Adaption des Ca 2+ Signals auf veränderliche extrazelluläre Stimuli. Die Vorhersage einer fold change Enkodierung kann durch Experimente gestützt werden. / In this work two signaling pathways, involving the tumor suppressor p53 and the second messenger Ca2+ , are to be discussed and modelled. The tumor suppressor p53 shows a pulsatile response in single cells after induction of DNA double strand breaks (DSBs). Except for very high amounts of damage, these pulses appear at irregular times. The concept of excitable systems is employed as a convenient way to model such observed dynamics. An application to biomolecular reaction networks shows the need for a positive feedback within the p53 regulatory network. Exploiting the reported ultrasensitive dynamics of the upstream damage sensor kinases, leads to a simplified excitable kinase-phosphatase model. Coupling that to the canonical negative feedback p53 regulatory loop, is the core idea behind the construction of the excitable p53 model. A detailed bifurcation analysis of the model establishes a robust excitable regime, which can be switched to oscillatory dynamics via a strong DNA damage signal. Driving the p53 model with a stochastic DSB process yields pulsatile dynamics which reflect different experimental scenarios. Intracellular Ca 2+ concentration spikes arise from a hierarchic cascade of stochastic events. An analytical solution strategy, employing a semi-Markovian description and involving Laplace transformations, is devised and successfully applied to a specific Ca2+ model. The new gained insights are then used, to construct a new generic Ca2+ model, which elegantly captures many known features of Ca2+ signaling. In particular the experimentally observed relations between the average and the standard deviation of the inter spike intervals (ISIs) can be explained in a concise way. Finally, the theoretical considerations allow to calculate the stimulus encoding relation, which governs the adaption of the Ca 2+ signals to varying extracellular stimuli. This is predicted to be a fold change response and new experimental results display a strong support of this idea.

Der Charakter der Schwellwertdynamik vieler physikalischer, chemischer und biologischer Systeme hat sich in neueren Experimenten als im wesentlichen nicht Markowsch herausgestellt. In diesem Fall sind die "Ubergangsraten von der Zeit und den Anfangsbedingungen abh"angig und es stellen sich komplexe Wahrscheinlichkeitsverteilungen f"ur die erste Durchgangszeit ein. In dieser Arbeit werden verschiedene Aspekte nicht Markowscher Schwellwertprobleme und deren Anwendung bei der Beschreibung der Dynamik von Neuronen untersucht. In dieser Arbeit entwickeln wir einen analytischen Zugang zu nicht Markowschen Problemen, dem die Theorie der Schwellwert"uberschreitung zu Grunde liegt. Im Ergebnis erhalten wir mehrere analytische N"aherungen f"ur die Wahrscheinlichkeitsverteilung der ersten Durchgangszeit f"ur Zufallsprozesse mit differenzierbaren Trajektorien. Die Qualit"at und der G"ultigkeitsbereich der N"aherungen werden von uns sorgf"altig untersucht. Die abgeleiteten N"aherungen decken dabei den gesamten Bereich zwischen fast Markowschen und stark nicht Markowschen Problemen ab. Diese analytischen N"aherungen werden in Kombination mit numerischen Methoden genutzt, um Spikemuster in resonanten und nicht-resonanten Neuronen zu untersuchen. Im Besonderen haben wir uns dabei f"ur die Entstehung spontaner, durch zellinternes Rauschen hervorgerufener, Spikemuster in stellaten (resonanten) und pyramidalen (nicht-resonanten) Zellen des entorhinalen Kortex in Ratten interessiert. Diese zwei Neuronentypen zeigten deutliche Unterschiede in den Spikemustern, die den jeweiligen Unterschieden in den unterschwelligen Dynamiken zuzuordnen sind. Des weiteren wurden negative Korrelationen in den Spikesequenzen f"ur beide Neuronentypen gefunden. Um diese negativen Korrelationen angemessen zu beschreiben, haben wir einen nicht erneuerbaren Schwellenmechanismus in das Resonate-and-Fire Modell integriert. / Recent experiments revealed the non-Markovian character of the escape dynamics in many physical, chemical and biological systems on time scales prior to relaxation. The escape rates in the non-Markovian case are time-dependent and the escape times are dictated by the initial conditions. Complex, multipeak distributions of the first passage time are characteristic for the non-Markovian case. In this thesis we investigate various aspects of the non-Markovian first passage time problem and in particular its application to the dynamics of neurons. We elaborate an analytical approach to the non-Markovian first passage time problem, which is based on the theory of level-crossings, and obtain several analytical approximations for the first passage time density of a random process with differentiable trajectories. We compare the quality of these approximations and ascertain their regions of validity. Our approximations are applicable and provide accurate results for different types of dynamics, ranging from almost Markovian to strongly non-Markovian cases. These analytical approximations in combination with numerical methods are applied to investigate the spike patterns observed in resonant and nonresonant neurons. In particular, we focus on spontaneous (driven by intrinsic noise) spike patterns obtained in stellate (resonant) and pyramidal (nonresonant) cells in the entorhinal cortex in rat. These two types of neurons exhibit striking different spike patterns attributed to the differences in their subthreshold dynamics. We show that the resonate-and-fire model with experimentally estimated parameter values can quantitatively reproduce the interspike interval distributions measured in resonant as well as in nonresonant cells. We also found negative interspike interval correlations in both types of neurons. To capture these negative correlations, we introduce a novel nonrenewal threshold mechanism in the resonate-and-fire model.

In this thesis the interplay between hydrodynamic transport and specific adhesion is theoretically investigated. An important biological motivation for this work is the rolling adhesion of white blood cells experimentally investigated in flow chambers. There, specific adhesion is mediated by weak bonds between complementary molecular building blocks which are either located on the cell surface (receptors) or attached to the bottom plate of the flow chamber (ligands). The model system under consideration is a hard sphere covered with receptors moving above a planar ligand-bearing wall. The motion of the sphere is influenced by a simple shear flow, deterministic forces, and Brownian motion. An algorithm is given that allows to numerically simulate this motion as well as the formation and rupture of bonds between receptors and ligands. The presented algorithm spatially resolves receptors and ligands. This opens up the perspective to apply the results also to flow chamber experiments done with patterned substrates based on modern nanotechnological developments. In the first part the influence of flow rate, as well as of the number and geometry of receptors and ligands, on the probability for initial binding is studied. This is done by determining the mean time that elapses until the first encounter between a receptor and a ligand occurs. It turns out that besides the number of receptors, especially the height by which the receptors are elevated above the surface of the sphere plays an important role. These findings are in good agreement with observations of actual biological systems like white blood cells or malaria-infected red blood cells. Then, the influence of bonds which have formed between receptors and ligands, but easily rupture in response to force, on the motion of the sphere is studied. It is demonstrated that different states of motion-for example rolling-can be distinguished. The appearance of these states depending on important model parameters is then systematically investigated. Furthermore, it is shown by which bond property the ability of cells to stably roll in a large range of applied flow rates is increased. Finally, the model is applied to another biological process, the transport of spherical cargo particles by molecular motors. In analogy to the so far described systems molecular motors can be considered as bonds that are able to actively move. In this part of the thesis the mean distance the cargo particles are transported is determined. / In der vorliegenden Arbeit wird das Zusammenspiel zwischen hydrodynamischem Transport und spezifischer Adhäsion theoretisch untersucht. Eine wichtige biologische Motivation für diese Arbeit ist die rollende Adhäsion weißer Blutkörperchen, die experimentell in Flusskammern untersucht wird. Die spezifische Adhäsion wird durch schwache Bindungen zwischen komplementären molekularen Bausteinen vermittelt, die sich einerseits auf der Zelloberfläche, Rezeptoren genannt, andererseits auf der unteren begrenzenden Platte der Flusskammer, Liganden genannt, befinden. Das untersuchte Modellsystem besteht aus einer festen Kugel, die mit Rezeptoren bedeckt ist und sich unter dem Einfluss einer einfachen Scherströmung, deterministischer Kräfte und der Brownschen Molekularbewegung oberhalb einer mit Liganden bedeckten Wand bewegt. Es wird ein Algorithmus angegeben, mit dessen Hilfe diese Bewegung sowie das Entstehen und Reißen von Bindungen zwischen Rezeptoren und Liganden numerisch simuliert werden kann. In der numerischen Modellierung werden die Positionen von Rezeptoren und Liganden räumlich aufgelöst, wodurch sich die Möglichkeit ergibt, die Ergebnisse auch mit Flusskammerexperimenten, in denen moderne nanotechnologisch strukturierte Substrate verwendet werden, zu vergleichen. Als Erstes wird der Einfluss von Strömungsrate sowie Zahl und Form der Rezeptoren bzw. Liganden auf die Wahrscheinlichkeit, mit der es zu einer Bindung kommen kann, untersucht. Hierfür wird die mittlere Zeit bestimmt, die vergeht bis zum ersten Mal ein Rezeptor mit einem Liganden in Kontakt kommt. Dabei stellt sich heraus, dass neben der Anzahl der Rezeptoren auf der Kugel insbesondere der Abstand, welchen die Rezeptoren von der Oberfläche haben, eine große Rolle spielt. Dieses Ergebnis ist in sehr guter Übereinstimmung mit tatsächlichen biologischen Systemen wie etwa weißen Blutkörperchen oder mit Malaria infizierten roten Blutkörperchen. Als Nächstes wird betrachtet, welchen Einfluss Bindungen haben, die sich zwischen Rezeptoren und Liganden bilden, aber unter Kraft auch leicht wieder reißen. Dabei zeigt sich, dass verschiedene Bewegungstypen auftreten, beispielsweise Rollen, deren Erscheinen in Abhängigkeit wichtiger Modellparameter dann systematisch untersucht wird. Weiter wird der Frage nachgegangen, welche Eigenschaften von Bindungen dazu führen können, dass Zellen in einem großen Bereich von Strömungsraten ein stabiles Rollverhalten zeigen. Abschließend wird das Modell auf einen etwas anderen biologischen Prozess angewendet, nämlich den Transport kugelförmiger Lastpartikeln durch molekulare Motoren. In Analogie zu den bisher beschriebene Systemen können diese molekularen Motoren als sich aktiv bewegende Bindungen betrachtet werden. In diesem Teil der Arbeit wird ermittelt, wie weit die Lastpartikel im Mittel transportiert werden.