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Hyperassociative semigroups
(1994)
Pre-solid varieties
(1994)
Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.
A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.
Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
The prepaparation of amorphous, homogeneous blends of zwitterionic polymers and transition metal salts was investigated. Homogeneous miscibility was achieved in many cases up to equimolar amounts of salt, depending on the anion and cation chosen. Various analytical techniques point to a solid state solution of the inorganic ions in the polymer matrix.
We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.
In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.
German
(1994)
Throughfall measurements were made under primary terra firme rainforest in the Rio Pichis valley, in the Upper Amazon Basin of Peru. Based on 214 precipitation events over nearly 18 months, throughfall was estimated to be 83.1±8.8% of gross precipitation. Regression analysis of all events revealed that gross precipitation is the only significant explanatory variable; the use of one-burst events does not significantly improve the regression relationship. Gross precipitation is, however, a poor predictor of throughfall for small rainfall events. The two forest structure parameters, canopy capacity, S, and free throughfall coefficient, p, were determined to be 1.3±0.2 mm and 0.32±0.18 mm. Rainfall intensity was found to influence these parameters. New methods which attempt to minimize the influence of meteorologic variables are used to estimate the potential values of these canopy parameters.
Solubilization by polysoaps
(1994)
The aqueous solubilization power of several series of micellar homopolymers and copolymers (polysoaps) is investigated. Using five insoluble or poorly water-soluble dyes, comparisons of the capacities are made with respect ot the influence of structural variables such as the polymer backbone, the polymer geometry, the comonomer content, and the charge of the hydrophilic group. Some guidelines for polysoap structures suited for efficient solubilization are established. Noteworthy is that the solubilization capacities of the polysoaps are neither linked to the ability to reduce the surface tension of water, nor to the polarity of the solubilization sites deduced from spectroscopic probes.
In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n).
In cultured rat hepatocytes the key gluconeogenic enzyme phosphoenolpyruvate carboxykinase (PCK) is known to be induced by glucagon via an elevation of cAMP. Prostaglandin E₂ has been shown to antagonize the glucagon-activated cAMP formation, glycogen phosphorylase activity and glucose output in hepatocytes. It was the purpose of the current investigation to study the potential of PGE₂ to inhibit the glucagon-induced expression of PCK on the level of mRNA and enzyme activity. PCK mRNA and enzyme activity were increased by 0.1 nM glucagon to a maximum after 2 h and 4 h, respectively. This increase was completely inhibited if 10 μM PGE2 was added concomitantly with glucagon. This inhibition by PGE₂ of glucagon-induced PCK activity was abolished by pertussis toxin treatment. When added at the maximum of PCK mRNA at 2 h, PGE₂ accelerated the decay of mRNA and reduced enzyme activity. This effect was not reversed by pertussis toxin treatment. Since in liver PGE₂ is derived from Kupffer cells, which play a key role in the local inflammatory response, the present data imply that during inflammation PGE₂ may reduce the hepatic gluconeogenic capacity via a Gᵢ-linked signal chain.
Rat hepatocytes have previously been reported to possess prostaglandin E₂ receptors of the EP₃-type (EP₃-receptors) that inhibit glucagonstimulated glycogenolysis by decreasing cAMP. Here, the isolation of a functional EP₃ϐ receptor cDNA clone from a rat hepatocyte cDNA library is reported. This clone can be translated into a 362-amino-acid protein, that displays over 95% homology to the EP₃ϐ receptor from mouse mastocytoma. The amino- and carboxy-terminal region of the protein are least conserved. Transiently transfected HEK 293 cells expressed a single binding site for PGE₂ with an apparent Kd of 15 nM. PGE₂ > PGF₂α > PGD₂ competed for [³H]PGE₂ binding sites as did the EP₃ receptor agonists M&B 28767 = sulprostone > misoprostol but not the EP₁ receptor antagonist SC 19220. In stably transfected CHO cells M&B 28767 > sulprostone = PGE₂ > misoprostol > PGF₂α inhibited the forskolin-elicited cAMP formation. Thus, the characteristics of the EP₃ϐ receptor of rat hepatocytes closely resemble those of the EP₃ϐ receptor of mouse mastocytoma.