Internal erosion of granular materials – Identification of erodible fine particles as a basis for numerical calculations

In geohydromechanics internal erosion is a process which is still hardly to be quantified both spatially as well as temporally. The transport of fine particles, which is caused by increased hydraulic gradients, is influenced by the pore structure of the coarse grained fabric. The microstructural information of the pore constriction size distribution (CSD) of the solid skeleton has therefore to be taken into account when internal erosion is analyzed either analytically or numerically. The CSD geometrically defines the amount of fine particles, which potentially can be eroded away for a given hydraulic force. The contribution introduces experimental and numerical calculations which aim at the quantification of the amount of erodible fines. Based on this approach a multiphase continuum-based numerical model is used to back calculate the process of internal erosion for one material of the well-known experimental investigation of Skempton & Brogan (1994)[1]

SHynergie: Development of a virtual project laboratory for monitoring hydraulic stimulations

Hydraulic stimulations are the primary means of developing subsurface reservoirs regarding the extent of fluid transport in them. The associated creation or conditioning of a system of hydraulic conduits involves a range of hydraulic and mechanical processes but also chemical reactions, such as dissolution and precipitation, may affect the stimulation result on time scales as short as hours. In the light of the extent and complexity of these processes, the steering potential for the operator of a stimulation critically depends on the ability to integrate the maximum amount of site-specific information with profound process understanding and a large spectrum of experience. We report on the development of a virtual project laboratory for monitoring hydraulic stimulations within the project SHynergie (http://www.ruhr-uni-bochum.de/shynergie/). The concept of the laboratory envisioned product that constitutes a preparing and accompanying rather than post-processing instrument ultimately accessible to persons responsible for a project over a web-repository. The virtual laboratory consists of a data base, a toolbox, and a model-building environment. Entries in the data base are of two categories. On the one hand, selected mineral and rock properties are provided from the literature. On the other hand, project-specific entries of any format can be made that are assigned attributes regarding their use in a stimulation problem at hand. The toolbox is interactive and allows the user to perform calculations of effective properties and simulations of different types (e.g., wave propagation in a reservoir, hydraulic test). The model component is also hybrid. The laboratory provides a library of models reflecting a range of scenarios but also allows the user to develop a site-specific model constituting the basis for simulations. The laboratory offers the option to use its components following the typical workflow of a stimulation project. The toolbox incorporates simulation instruments developed in the course of the SHynergie project that account for the experimental and modeling results of the various sub-projects

A Geometrical Method of Decoupling

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as for instance the method of Teng and Edwards. In a preceeding paper it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all thinkable cases. Hence a systematic derivation of a more general treatment seemed advisable. In a second paper the author suggested the use of real Dirac matrices as basic tools to coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. It is shown that this algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec P$, that were introduced with the so-called "electromechanical equivalence". We present a structure-preserving block-diagonalization of symplectic or Hamiltonian matrices, respectively. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires ${\cal O}(n^2)$ iterations to converge to a given precision.Comment: 13 pages, 1 figur

Painlev\'{e} test of coupled Gross-Pitaevskii equations

Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied. Computer algebra is applied to evaluate j=4 compatibility condition for admissible external potentials. Appearance of an arbitrary real potential embedded in the external potentials is shown to be the consequence of the coupling. Connection with recent experiments related to stability of two-component Bose-Einstein condensates of Rb atoms is discussed.Comment: 13 pages, no figure

Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term

An exact time-dependent solution of field equations for the 3-d gauge field model with a Chern-Simons (CS) topological mass is found. Limiting cases of constant solution and solution with vanishing topological mass are considered. After Lorentz boost, the found solution describes a massive nonlinear non-abelian plane wave. For the more complicate case of gauge fields with CS mass interacting with a Higgs field, the stochastic character of motion is demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure

Function reconstruction as a classical moment problem: A maximum entropy approach

We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we reconstruct a set of functions using an iterative entropy optimization scheme, and study the convergence profile as the number of moments is increased. We consider a wide variety of functions that include a distribution with a sharp discontinuity, a rapidly oscillatory function, a distribution with singularities, and finally a distribution with several spikes and fine structure. The last example is important in the context of the determination of the natural density of the logistic map. The convergence of the method is studied by comparing the moments of the approximated functions with the exact ones. Furthermore, by varying the number of moments and iterations, we examine to what extent the features of the functions, such as the divergence behavior at singular points within the interval, is reproduced. The proximity of the reconstructed maximum entropy solution to the exact solution is examined via Kullback-Leibler divergence and variation measures for different number of moments.Comment: 20 pages, 17 figure

Stochastic resonance in pattern recognition by a holographic neuron model

The recognition rate of holographic neural synapses, performing a pattern recognition task, is significantly higher when applied to natural, rather than artificial, images. This shortcoming of artificial images can be largely compensated for, if noise is added to the input pattern. The effect is the result of a trade-off between optimal representation of the stimulus (for which noise is favorable) and keeping as much as possible of the stimulus-specific information (for which noise is detrimental). The observed mechanism may play a prominent role for simple biological sensors

Palmitoylation of the β4-Subunit Regulates Surface Expression of Large Conductance Calcium-activated Potassium Channel Splice Variants

Regulatory β-subunits of large conductance calcium- and voltage-activated potassium (BK) channels play an important role in generating functional diversity and control of cell surface expression of the pore forming α-subunits. However, in contrast to α-subunits, the role of reversible post-translational modification of intracellular residues on β-subunit function is largely unknown. Here we demonstrate that the human β4-subunit is S-acylated (palmitoylated) on a juxtamembrane cysteine residue (Cys-193) in the intracellular C terminus of the regulatory β-subunit. β4-Subunit palmitoylation is important for cell surface expression and endoplasmic reticulum (ER) exit of the β4-subunit alone. Importantly, palmitoylated β4-subunits promote the ER exit and surface expression of the pore-forming α-subunit, whereas β4-subunits that cannot be palmitoylated do not increase ER exit or surface expression of α-subunits. Strikingly, however, this palmitoylation- and β4-dependent enhancement of α-subunit surface expression was only observed in α-subunits that contain a putative trafficking motif (… REVEDEC) at the very C terminus of the α-subunit. Engineering this trafficking motif to other C-terminal α-subunit splice variants results in α-subunits with reduced surface expression that can be rescued by palmitoylated, but not depalmitoylated, β4-subunits. Our data reveal a novel mechanism by which palmitoylated β4-subunit controls surface expression of BK channels through masking of a trafficking motif in the C terminus of the α-subunit. As palmitoylation is dynamic, this mechanism would allow precise control of specific splice variants to the cell surface. Our data provide new insights into how complex interplay between the repertoire of post-transcriptional and post-translational mechanisms controls cell surface expression of BK channels

Lagrangian Description of the Variational Equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system