Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.     

Wavelength tunable high power laser using a double-clad Er:Yb doped fiber

We experimentally demonstrated a stable, wavelength-tunable fiber laser using a polarization-maintaining, double-clad Er:Yb doped fiber amplifier in the cavity. The output wavelength is tunable over the range from 1535 to 1567 nm using a fixed grating and the dichroic mirror placed on a rotational mount; under rotation of the dichroic mirror the tuning ratio of 50 nm/deg was found. We studied the wavelength tuning range dependence on the amplifier fiber length and achieved a maximal output power of 850 mW. This configuration can be Q-switched for high peak power and its narrow bandwidth is suitable for nonlinear optics applications, such as parametric teraherthz generator.     

Reconstructing biochemical cluster networks

Motivated by fundamental problems in chemistry and biology we study cluster graphs arising from a set of initial states S í \mathbbZⁿ₊{S\subseteq\mathbb{Z}^n_+} and a set of transitions/reactions M í \mathbbZⁿ₊×\mathbbZⁿ₊{M\subseteq\mathbb{Z}^n_+\times\mathbb{Z}^n_+}. The clusters are formed out of states that can be mutually transformed into each other by a sequence of reversible transitions. We provide a solution method from computational commutative algebra that allows for deciding whether two given states belong to the same cluster as well as for the reconstruction of the full cluster graph. Using the cluster graph approach we provide solutions to two fundamental questions: (1) Deciding whether two states are connected, e.g., if the initial state can be turned into the final state by a sequence of transition and (2) listing concisely all reactions processes that can accomplish that. As a computational example, we apply the framework to the permanganate/oxalic acid reaction.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Quantification of the pore size distribution (porosity profiles) in microfiltration membranes by SEM,TEM and computer image analysis

Transport properties of membranes are closely related to morphological properties like surface porosity and variation of their inner pore structure. Scanning electron microscopy (SEM) as well as transmission electron microscopy (TEM) are powerful tools to characterise the microscopical pore structure of membranes in a qualitative manner. In order to provide more quantitative data of surface and cross-sectional pores computer image analysis can be used. Parameters like ‘porous area fraction’ and ‘mean free path length’ have been selected to describe the pore distribution within porosity profiles in order to consider the effect that the pores within the cross-section are connected to each other.     

Self-collimation in photonic crystals with anisotropic constituents

In a photonic crystal composed of anisotropic constituents we quantify the range of input angles and the degree of collimation of the beam inside the crystal. The optical properties of a photobleached 4-dimethylamino-N-methyl-4-stilbazolium-tosylate (DAST) crystal are used in our model to demonstrate the efficacy of the self-collimation features.     

Memory effects on the quantum diffusion of a particle in a fluctuating medium

We introduce a phenomenological Hamiltonian for a particle in a medium with sitediagonal and off-diagonal disorder. Without assuming the usual white noise expression for the correlation between fluctuating variables, we arrive at a master equation using second order perturbation theory. This expression is expanded in powers of the correlation time. The mean square displacement and velocity are discussed and corrections to the diffusion coefficient are given.Partially supported by the grant of the Ministry of Education of the Japanese Government and by Sakkokai Foundation     

Statistical dynamics of conserved densities for the hard-sphere Lorentz gas

The statistical dynamics of a particle scattered by randomly positioned stationary hard spheres are investigated. We examine the somewhat unusual long-wavelength, low-frequency fluctuation spectra resulting from the existence of an infinite set of mutually coupled conserved densities of which the number density and energy density are two members. The analytically soluble infinite-mode correlation functions are compared with the corresponding functions obtained by truncating the set of slow modes at successively increasing orders. Furthermore, we evaluate the long-wavelenght number density autocorrelation function for a fixed speed, υ₀, in terms of a frequency-dependent diffusivity D(ω;υ₀) and obtain the fluctuation spectra of all conserved densities by an additional velocity average with the appropriate canonical weights. The effect of the frequency-dependent diffusivity D(ω;υ₀) on the density fluctuation spectra at frequencies small compared to the mean collision frequency is elucidated.