Measuring cellulase activity

An approach is presented for obtaining relative filter paper activities for enzyme preparations having activities below that required for application of the traditional International Union of Pure and Applied Chemistry filter paper assay. The approach involves the utilization of protein stabilizers to retard the time-dependent enzyme inactivation that may occur under traditional filter paper assay conditions. Enzyme stabilization allows extended reaction times and the calculation of relative activities based on the time required for saccharification of 3.6% of the traditional substrate, making results proportional to those obtained in the traditional International Union of Pure and Applied Chemistry assay. The assay is demonstrated using a commercial cellulase preparation along with KCl and bovine serum albumin as protein stabilizers.     

Progress in pulsed-current Karl Fischer coulometry using diaphragm-free cells

Factors influencing the accuracy of water determinations using diaphragm-free, pulsed current Karl Fischer (KF) coulometry were investigated with the new Metrohm 756 instrument. Results obtained with commercially available reagents from Riedel-deHaen and Merck were compared with home-made ones that were especially designed to minimize the formation of iodine-consuming reduction products generated in the cathode reaction. Positive errors in the range 2-5% were found for the commercial reagents as compared to 0.2-1% for the home-made ones which were buffered at about pH 10 containing modifiers like chloroform, hexanol or ethylene glycol. Except for the composition of the KF-reagent, the cathode current density and the titration rate were found to be critical parameters for the accuracy of the determinations. For all reagents investigated, the best results were obtained for the maximum generator current 400 mA (corresponding to a current density of 1,400 mA cm(-2)) in combination with a maximum titration rate of 2,000 microg min(-1). Surprisingly, the errors found under optimum conditions for the pulse technique were always somewhat larger than the corresponding values obtained with continuous coulometry.     

Optimum conditions for pulse generation in diaphragm-free Karl Fischer coulometry

A flexible instrument was designed in order to investigate the influence of current magnitude, current duration and the frequency of the pulse generation on the error obtained in coulometric Karl Fischer titrations carried out in diaphragm-free cells. For a given current magnitude the lowest errors were obtained for current durations more than 60% of the total time for the pulse cycle. No significant influence of the pulse frequency (5–1000 Hz) was found independently of the pulse current duration for three different types of reagents intended for diaphragm-free coulometry. For all reagents, the errors obtained with the home-built instrument were significantly smaller than those obtained with an optimized commercial titrator based on pulsed current generation. Using optimum conditions for the former instrument, in combination with an imidazole-buffered reagent at pH 10 containing chloroform as modifier, the accuracy was close to 100%. Thus, it is now possible to achieve the same high accuracy with diaphragm-free coulometry as with the conventional diaphragm based technique. The precision of the water determinations was affected by the size of the background. Received: 16 March 2000 / Revised: 17 May 2000 / Accepted: 22 May 2000     

Discontinuity-induced bifurcations in systems with impacts and friction: Discontinuities in the impact law

This paper concerns the non-smooth dynamics of planar mechanical systems with isolated contact in the presence of Coulomb friction. Following Stronge [Impact Mechanics, Cambridge University Press, Cambridge, 2000], a set of closed-form analytic formulae is derived for a rigid-body impact law based on an energetic coefficient of restitution and a resolution of the impact phase into distinct segments of relative slip and stick. Thus, the impact behavior is consistent both with the assumption of Coulomb friction and with the dissipative nature of impacts. The analysis highlights the presence of boundaries between open regions of initial conditions and parameter values corresponding to distinct forms of the impact law and investigates the smoothness properties of the impact law across these boundaries. It is shown how discontinuities in the impact law are associated with discontinuity-induced bifurcations of periodic trajectories, including non-smooth folds and persistence scenarios. Numerical analysis of an example mechanical model is used to illustrate and validate the conclusions.     

Simulation and stability analysis of impacting systems with complete chattering

This paper considers dynamical systems that are derived from mechanical systems with impacts. In particular we will focus on chattering—accumulation of impacts—for which local discontinuity mappings will be derived. We will first show how to use these mappings in simulation schemes, and secondly how the mappings are used to calculate the stability of limit cycles with chattering by solving the first variational equations.     

Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems

A rich variety of dynamical scenarios has been shown to occur when a fixed point of a non-smooth map undergoes a border-collision. This paper concerns a closely related class of discontinuity-induced bifurcations, those involving equilibria of n-dimensional piecewise-smooth flows. Specifically, transitions are studied which occur when a boundary equilibrium, that is one lying within a discontinuity manifold, is perturbed. It is shown that such equilibria can either persist under parameter variations or can disappear giving rise to different bifurcation scenarios. Conditions to classify among the possible simplest scenarios are given for piecewise-smooth continuous, Filippov and impacting systems. Also, we investigate the possible birth of other attractors (e.g. limit cycles) at a boundary-equilibrium bifurcation.     

Experiments on the Onset of Impacting Motion Using a Pipe Conveying Fluid

The transition from stable periodic nonimpacting motion to impacting motion, due to variations of parameters, is observable in a wide range of vibro-impact systems. Recent theoretical studies suggest a possible scenario for this type of transition. A key element in the proposed scenario is fulfilled if the oscillatory motion involved in the transition is born in a supercritical Hopf bifurcation. If the onset of impacting motion is close to the Hopf bifurcation, the impacting motion is likely to be chaotic. A numerical simulation of a system of articulated pipes conveying fluid is used to illuminate the theory. An experimental setup is presented, where a cantilevered pipe conveying fluid is unilaterally constrained. Results from experiments are found to be in good qualitative agreement with the theory.