Entwicklung und Optimierung eines Produktionsverfahrens zur Herstellung neuartiger 4HV-haltiger Biopolyester im Pilotmaßstab

Wildtyp- und rekombinante Stämme von P. putida und R. eutropha akkumulierten mit Lävulinsäure (LS) 4Hydroxyvalerat (4HV)-haltige Polyester (PHF). Ein zweistufiger 20 Liter Fed-Batch-Prozeß mit Octansäure und LS führte zu einer Zell-Trockenmassekonzentration (TM) von 20 g/l und einem PHF-Gehalt von 50 % (w/w) mit den Monomeren 4HV (15 mol%), 3HB, 3HV, 3HHx und 3HO. Glucose als Wachstumssubstrat reduzierte die PHF Monomere auf 3HB, 3HV und 4HV und verdoppelte als Co-Substrat während der Speicherphase den Umsatz von Lävulinsäure in PHF. Der Scale-up in den 500 l-Maßstab war erfolgreich: TM (20 g/l), Polyestergehalt (50 %, w/w) und 4HV-Anteil (35 mol %). Der neue PHF zeigte erhöhte Schmelzeviskosität, niedrige Schmelztemperaturen (ab 25°C) und hohe Elastizität (Bruchdehnung ca. 1000 %) Die Fluoreszenzintensität (550/600 nm) von mit Nilrot angefärbten Zellen ermöglichte die schnelle Bestimmung des Zell-PHF-Gehaltes Durch Speicherversuche mit Mutanten von R. eutropha mit Defekt im Katabolismus von Lävulinsäure wurde ein hypothetischer Stoffwechselweg zum Abbau von LS entwickelt

Fractional wave equation and damped waves

In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of the same order $\alpha,\ 1\le \alpha \le 2$ both in space and in time. We show that this feature is a decisive factor for inheriting some crucial characteristics of the wave equation like a constant propagation velocity of both the maximum of its fundamental solution and its gravity and mass centers. Moreover, the first, the second, and the Smith centrovelocities of the damped waves described by the fractional wave equation are constant and depend just on the equation order $\alpha$. The fundamental solution of the fractional wave equation is determined and shown to be a spatial probability density function evolving in time that possesses finite moments up to the order $\alpha$. To illustrate analytical findings, results of numerical calculations and numerous plots are presented.Comment: 21 pages, 10 figure

Distributed Order Derivatives and Relaxation Patterns

We consider equations of the form $(D_{(\rho)}u)(t)=-\lambda u(t)$, $t>0$, where $\lambda >0$, $D_{(\rho)}$ is a distributed order derivative, that is the Caputo-Dzhrbashyan fractional derivative of order $\alpha$, integrated in $\alpha\in (0,1)$ with respect to a positive measure $\rho$. Such equations are used for modeling anomalous, non-exponential relaxation processes. In this work we study asymptotic behavior of solutions of the above equation, depending on properties of the measure $\rho$

Fractional Fokker-Planck Equation for Ultraslow Kinetics

Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability distribution of particle's position at long times is a double-sided exponential. We show that such behaviors can be adequately described by a distributed-order fractional Fokker-Planck equations with a power-law weighting-function. We discuss the equations and the properties of their solutions, and connect this description with a scheme based on continuous-time random walks

Fractional Equations of Curie-von Schweidler and Gauss Laws

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.Comment: 11 pages, LaTe

Polymer translocation through a nanopore - a showcase of anomalous diffusion

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {\em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $\alpha = 2/(2\nu+2-\gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {\em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $$, and $- < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev.

Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology

The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin-Voigt, Maxwell, Zener, anti-Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.Comment: 41 pages, 8 figure

Transport Equations from Liouville Equations for Fractional Systems

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.Comment: 11 pages, LaTe

Mapping the Sensitive Volume of an Ion-Counting Nanodosimeter

We present two methods of independently mapping the dimensions of the sensitive volume in an ion-counting nanodosimeter. The first method is based on a calculational approach simulating the extraction of ions from the sensitive volume, and the second method on probing the sensitive volume with 250 MeV protons. Sensitive-volume maps obtained with both methods are compared and systematic errors inherent in both methods are quantified.Comment: 27 pages, 8 figures. Submitted to JINST, Jan. 16 200

Universal Electromagnetic Waves in Dielectric

The dielectric susceptibility of a wide class of dielectric materials follows, over extended frequency ranges, a fractional power-law frequency dependence that is called the "universal" response. The electromagnetic fields in such dielectric media are described by fractional differential equations with time derivatives of non-integer order. An exact solution of the fractional equations for a magnetic field is derived. The electromagnetic fields in the dielectric materials demonstrate fractional damping. The typical features of "universal" electromagnetic waves in dielectric are common to a wide class of materials, regardless of the type of physical structure, chemical composition, or of the nature of the polarizing species, whether dipoles, electrons or ions.Comment: 19 pages, LaTe