An intergranular strain concept for material models formulated as rate equations.

The intergranular strain concept was originally developed to capture the small-strain behaviour of the soil with hypoplastic models. A change of the deformation direction leads to an increase of the material stiffness. To obtain elastic behaviour for smallstrains, only the elastic part of the material stiffness matrix is used. Two different approaches for an application of this concept to nonhypoplastic models are presented in this article. These approaches differ in the determination of the elastic stress response, which is used for reversible deformations. The first approach determines an elastic response from the original material model, and the second one uses an additional elastic model. Both approaches are applied on barodesy. The simulations are compared with experimental results and with simulations using hypoplastic models with the original intergranular strain concept.

Co-deposition of gas hydrates by pressurized thermal evaporation.

Gas hydrates are usually synthesized by bringing together a pressurized gas and liquid or solid water. In both cases, the transport of gas or water to the hydrate growth site is hindered once an initial film of hydrate has grown at the water-gas interface. A seemingly forgotten gas-phase technique overcomes this problem by slowly depositing water vapor on a cold surface in the presence of the pressurized guest gas. Despite being used for the synthesis of low-formation-pressure hydrates, it has not yet been tested for hydrates of CO2 and CH4. Moreover, the potential of the technique for the study of hydrate decomposition has not been recognized yet. We employ two advanced implementations of the condensation technique to form hydrates of CO2 and CH4 and demonstrate the applicability of the process for the study of hydrate decomposition and the phenomenon of self-preservation. Our results show that CO2 and CH4 hydrate samples deposited on graphite at 261-265 K are almost pure hydrates with an ice fraction of less than 8%. Rapid depressurization experiments with thin deposits (approx. 330 µm thickness) of CO2 hydrate on an aluminum surface at 265 K yield identical dissociation curves when the deposition is done at identical pressure. However, hydrates deposited at 1 MPa almost completely withstand decomposition after rapid depressurization to 0.1 MPa, while samples deposited at 2 MPa decompose 7 times faster. Therefore, this synthesis technique is not only applicable for the study of hydrate decomposition but can also be used for the controlled deposition of a super-preserved hydrate.

Macroscopic defects upon decomposition of CO2 clathrate hydrate crystals.

Micrometer- and submicrometer-sized pores and macroscopic defects like cracks and tubular channels can be found in a variety of clathrate hydrates (hydrates for short) during formation and decomposition. Their origin, their evolution in time, and their effect on hydrate decomposition kinetics are unclear. We used time-lapse micro computed tomography (µCT) in combination with temperature control and pressure monitoring to study the formation and evolution of pores and macroscopic defects in decomposing CO2 hydrates at subzero (Celsius) temperature. Our results suggest that the decomposition of hydrates is always accompanied by the formation of pores and an increase of the apparent hydrate volume by more than 3%. Hydrate decomposition often starts with the formation of cracks inside the hydrate and not necessarily at the free surface of the hydrate, which frequently remains intact for a long period and seems to be self-preserved in some regions. Decomposition spreads out from these cracks in a uniform fashion yielding a variety of macroscopic features. In some cases, the propagating decomposition front seems to get blocked by planar barriers inside the hydrate yielding regions with high resistance against decomposition. This, together with a generally heterogeneous distribution of decomposition resistant regions, challenges the shrinking core model of hydrate decomposition as well as the popular ice-rind theory used to explain the effect of self-preservation.

Micro-Tomographic Investigation of Ice and Clathrate Formation and Decomposition under Thermodynamic Monitoring.

Clathrate hydrates are inclusion compounds in which guest molecules are trapped in a host lattice formed by water molecules. They are considered an interesting option for future energy supply and storage technologies. In the current paper, time lapse 3D micro computed tomographic (µCT) imaging with ice and tetrahydrofuran (THF) clathrate hydrate particles is carried out in conjunction with an accurate temperature control and pressure monitoring. µCT imaging reveals similar behavior of the ice and the THF clathrate hydrate at low temperatures while at higher temperatures (3 K below the melting point), significant differences can be observed. Strong indications for micropores are found in the ice as well as the THF clathrate hydrate. They are stable in the ice while unstable in the clathrate hydrate at temperatures slightly below the melting point. Significant transformations in surface and bulk structure can be observed within the full temperature range investigated in both the ice and the THF clathrate hydrate. Additionally, our results point towards an uptake of molecular nitrogen in the THF clathrate hydrate at ambient pressures and temperatures from 230 K to 271 K.

On the error propagation of semi-Lagrange and Fourier methods for advection problems.

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley-Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme.

Splitting methods for time integration of trajectories in combined electric and magnetic fields.

The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called ϕ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the method considered.

An almost symmetric Strang splitting scheme for the construction of high order composition methods.

In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure cannot be computed exactly. Instead, we insert a well-chosen state [Formula: see text] into the corresponding nonlinearity [Formula: see text], which results in a linear term [Formula: see text] whose exact flow can be determined efficiently. Therefore, in the spirit of splitting methods, it is still possible for the numerical simulation to satisfy certain properties of the exact flow. However, Strang splitting is no longer symmetric (even though it is still a second order method) and thus high order composition methods are not easily attainable. We will show that an iterated Strang splitting scheme can be constructed which yields a method that is symmetric up to a given order. This method can then be used to attain high order composition schemes. We will illustrate our theoretical results, up to order six, by conducting numerical experiments for a charged particle in an inhomogeneous electric field, a post-Newtonian computation in celestial mechanics, and a nonlinear population model and show that the methods constructed yield superior efficiency as compared to Strang splitting. For the first example we also perform a comparison with the standard fourth order Runge-Kutta methods and find significant gains in efficiency as well better conservation properties.

Dendritic cells: In vitro culture in two- and three-dimensional collagen systems and expression of collagen receptors in tumors and atherosclerotic microenvironments.

Dendritic cells (DCs) are immune cells found in the peripheral tissues where they sample the organism for infections or malignancies. There they take up antigens and migrate towards immunological organs to contact and activate T lymphocytes that specifically recognize the antigen presented by these antigen presenting cells. In the steady state there are several types of resident DCs present in various different organs. For example, in the mouse, splenic DC populations characterized by the co-expression of CD11c and CD8 surface markers are specialized in cross-presentation to CD8 T cells, while CD11c/SIRP-1α DCs seem to be dedicated to activating CD4 T cells. On the other hand, DCs have also been associated with the development of various diseases such as cancer, atherosclerosis, or inflammatory conditions. In such disease, DCs can participate by inducing angiogenesis or immunosuppression (tumors), promoting autoimmune responses, or exacerbating inflammation (atherosclerosis). This change in DC biology can be prompted by signals in the microenvironment. We have previously shown that the interaction of DCs with various extracellular matrix components modifies the immune properties and angiogenic potential of these cells. Building on those studies, herewith we analyzed the angiogenic profile of murine myeloid DCs upon interaction with 2D and 3D type-I collagen environments. As determined by PCR array technology and quantitative PCR analysis we observed that interaction with these collagen environments induced the expression of particular angiogenic molecules. In addition, DCs cultured on collagen environments specifically upregulated the expression of CXCL-1 and -2 chemokines. We were also able to establish DC cultures on type-IV collagen environments, a collagen type expressed in pathological conditions such as atherosclerosis. When we examined DC populations in atherosclerotic veins of Apolipoprotein E deficient mice we observed that they expressed adhesion molecules capable of interacting with collagen. Finally, to further investigate the interaction of DCs with collagen in other pathological conditions, we determined that both murine ovarian and breast cancer cells express several collagen molecules that can contribute to shape their particular tumor microenvironment. Consistently, tumor-associated DCs were shown to express adhesion molecules capable of interacting with collagen molecules as determined by flow cytometry analysis. Of particular relevance, tumor-associated DCs expressed high levels of CD305/LAIR-1, an immunosuppressive receptor. This suggests that signaling through this molecule upon interaction with collagen produced by tumor cells might help define the poorly immunogenic status of these cells in the tumor microenvironment. Overall, these studies demonstrate that through interaction with collagen proteins, DCs can be capable of modifying the microenvironments of inflammatory disease such as cancer or atherosclerosis.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

Numerical investigation of the elastic scattering of hydrogen (isotopes) and helium at graphite (0001) surfaces at beam energies of 1 to 4 eV using a split-step Fourier method.

We report simulations of the elastic scattering of atomic hydrogen isotopes and helium beams from graphite (0001) surfaces in an energy range of 1-4 eV. To this aim, we numerically solve a time-dependent Schrödinger equation using a split-step Fourier method. The hydrogen- and helium-graphite potentials are derived from density functional theory calculations using a cluster model for the graphite surface. We observe that the elastic interaction of tritium and helium with graphite differs fundamentally. Whereas the wave packets in the helium beam are directed to the centers of the aromatic cycles constituting the hexagonal graphite lattice, they are directed toward the rings in case of the hydrogen beams. These observations emphasize the importance of swift chemical sputtering for the chemical erosion of graphite and provide a fundamental justification of the graphite peeling mechanism observed in molecular dynamics studies. Our investigations imply that wave packet studies, complementary to classical atomistic molecular dynamics simulations open another angle to the microscopic view on the physics underlying the sputtering of graphite exposed to hot plasma.