Nonlinear dynamical systems,first integrals,Bose operators,and Lie algebras

A connection between nonlinear autonomous systems of ordinary differential equations, first integrals, Bose operators and Lie algebras is described. An extension to nonlinear partial differential equations is given.     

A note on Wick's theorem

In analogy to Gaudin, but in a more complicated case, Wick's theorem in statistical mechanics is proved by using the commutation rules. As a special case we obtain the result of Gaudin. An application to the Hubbard model is given.     

Relativistic classical mechanics and canonical formalism

The analysis of interacting relativistic many-particle systems provides a theoretical basis for further work in many diverse fields of physics. After a discussion of the nonrelativisticN-particle systems we describe two approaches for obtaining the canonical equations of the corresponding relativistic forms. A further aspect of our approach is the consideration of the constants of the motion.     

A low‐cost X‐ray‐transparent experimental cell for synchrotron‐based X‐ray microtomography studies under geological reservoir conditions

A new modular X‐ray‐transparent experimental cell enables tomographic investigations of fluid rock interaction under natural reservoir conditions (confining pressure up to 20 MPa, pore fluid pressure up to 15 MPa, temperature ranging from 296 to 473 K). The portable cell can be used at synchrotron radiation sources that deliver a minimum X‐ray flux density of 10⁹ photons mm^?2 s^?1 in the energy range 30–100 keV to acquire tomographic datasets in less than 60 s. It has been successfully used in three experiments at the bending‐magnet beamline 2BM at the Advanced Photon Source. The cell can be easily machined and assembled from off‐the‐shelf components at relatively low costs, and its modular design allows it to be adapted to a wide range of experiments and lower‐energy X‐ray sources.     

Microseparations of cesium and barium in glass

A chemical micro-separation of Cs and Ba in complex glass with a high lanthanide content is presented. High purity silica, with and without Cs and Ba fortification, was subjected to identical dissolution, microseparation, and analysis as a control glass matrix. Dissolution was performed with hot concentrated nitric and hydrofluoric acids followed by fluoride complexation with boric acid, evolution of excess boric acid as methyl borate, and finally conversion to soluble nitrate species in 3 M nitric acid. Separation was performed with a miniature gas pressurized extraction chromatography system using a column packed with Eichrom Sr resin^™. High purity 3 M nitric acid was used to rinse Cs through the column and high purity 1% acetic acid was used to strip Ba from the resin. Quantitative recovery of both Cs (99.5 ± 0.7%) and Ba (99.1 ± 2.0%) was achieved in the lanthanide glass matrix and no statistically significant difference was observed in Cs or Ba recovery in the control high purity silica.     

Efficient electronic communication between two identical ferrocene centers in a hydrogen-bonded dimer

A novel ferrocene derivative that contains a donor-donor-acceptor-acceptor (DDAA) hydrogen bonding motif forms highly stable, noncovalent dimers in chloroform and dichloromethane solutions. Its voltammetric behavior and the observation of an intervalence charge-transfer band reveal that the two equivalent ferrocene centers in the hydrogen-bonded dimer exhibit a surprisingly efficient level of electronic communication.     

Analysis and modeling of the hydro-mechanics of deformable fractures

In the present contribution, we investigate and model the flow of a viscous fluid into a single deformable fracture and the associated elastic deformation of the surrounding porous rock. Due to the coupled nature of the problem, conceptually and technically different strategies can be applied to model and solve the resulting hydro-mechanical system. Therefore, two different modeling approaches are analyzed. On the one hand, we derive the governing equations from the conservation of mass avoiding any of the frequently used approximations or simplifications. On the other hand, we describe the physics based on Biot's quasi-static poroelastic equations. We compare and critically discuss the results obtained with the presented different solution approaches. The results show that both models are able to capture the same physical effects, also those caused by the fracture deformation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On response functions in linear thermoelastic models of shape memory polymers

This paper is concerned with the broad class of Liner Thermoelastic (LTE) models for Shape Memory Polymers (SMPs) which unifies numerous constitutive theories proposed in the literature for this kind of smart material. It is shown that the response functions for the general model of this class may be determined directly from experimental data measured in standard thermomechanical cyclic tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microscopical investigation of wave propagation phenomena in residual saturated porous media

Wave propagation is used in many fields for measurement and characterization. Corresponding multiphase models usually use a continuous approach. Nevertheless, systems like wetted rocks may be saturated residually in certain situations. In such cases, one fluid is distributed as clusters, each different in size and shape. One single, continuous phase cannot account for a variety of fluid clusters, either disconnected from each other or connected only about thin liquid films. Therefore, we present a model that considers a heterogeneous distribution of disconnected fluid clusters in the form of harmonic oscillators. These oscillators are described and distinguished by their mass, damping and eigenfrequency. Hence, the model allows to characterize different clusters and includes an additional damping mechanism due to oscillations of the fluid clusters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Smoothed Particle Hydrodynamics modelling of poroelastic media

Numerical modelling of poroelastic properties in porous media allows widely varied investigations at low costs and relatively short times. The study of porous media is of high interest at different scales, in this case we focus our analysis at meso- and macroscale which is highly relevant e.g. in geothermal explorations. We model a biphasic poroelastic media assuming incompressible fluid and solid grains and a large solid-fluid density ratio. Meshfree methods are nowadays more widely used due to the advantages that present in the simulation of large deformations. In this case we choose to employ the Smoothed Particle Hydrodynamics method (SPH), a Lagrangian method where the domain is discretized in particles. The solution is computed in parallel, which allows to simulate large domains more representative of the scale of our study cases. We validate our implementation with a classical consolidation problem and compare the simulated diffusion process with Terzaghi's analytical solution. Future work includes simulation of fractures initiation and propagation in the porous media at reservoir scale. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)