Inelastic proton scattering to the first excited 2+ state of the doubly magic ' Ni nucleus was investigated in inverse kinematics, using a secondary beam of radioactive Ni nuclei. At an incident energy of 101 MeV/nucleon, a value B(E2, 0+ 2+) = 600~120 e~fm4 was measured. This result completes the set of experimental data for the first excited 2+ states in the 1f 2p shell with a closed shell of neutrons or protons. These data are compared to recent shell-model calculations.

In standard multi-phase flow models on porous media, a capillary pressure saturation relationship developed under static conditions is assumed. Recent experiments have shown that this static relationship cannot explain dynamic effects as seen for example in outflow experiments. In this paper, we use a static capillary pressure model and a dynamic capillary pressure model based on the concept of Hassanizadeh and Gray and examine the behavior with respect to material interfaces. We introduce a new numerical scheme for the one-dimensional case using a Lagrange multiplier approach and develop a suitable interface condition. The behavior at the interface is discussed and verified by various numerical simulations.

Abstract. In this paper, we consider two error estimators for one-body contact problems. The first error estimator is defined in terms of H(div)-conforming stress approximations and equilibrated fluxes while the second is a standard edge-based residual error estimator without any modification with respect to the contact. We show reliability and efficiency for both estimators. Moreover, the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order. The second estimator is used in a control-based AFEM refinement strategy, and the decay of the error in the energy is shown. Several numerical tests demonstrate the performance of both estimators.

One of the driving forces in porous media flow is the capillary pressure. In standard models, it is given depending on the saturation. However, recent experiments have shown disagreement between measurements and numerical solutions using such simple models. Hence, we consider in this paper two extensions to standard capillary pressure relationships. Firstly, to correct the nonphysical behavior, we use a recently established saturation-dependent retardation term. Secondly, in the case of heterogeneous porous media, we apply a model with a capillary threshold pressure that controls the penetration process. Mathematically, we rewrite this model as inequality constraint at the interfaces, which allows discontinuities in the saturation and pressure. For the standard model, often finite-volume schemes resulting in a nonlinear system for the saturation are applied. To handle the enhanced model at the interfaces correctly, we apply a mortar discretization method on nonmatching meshes. Introducing the flux as a new variable allows us to solve the inequality constraint efficiently. This method can be applied to both the standard and the enhanced capillary model. As nonlinear solver, we use an active set strategy combined with a Newton method. Several numerical examples demonstrate This work was supported in part by IRTG NUPUS. the efficiency and flexibility of the new algorithm in 2D and 3D and show the influence of the retardation term.Keywords Porous media · Entry pressure · Variational inequality · Mortar · Active set strategy MotivationFlow processes in porous media involving two immiscible fluids need to be understood and predicted when dealing with subsurface hydrosystems or industrial applications. For example, in the unsaturated zone, the spatial distribution of the water and air phase, as well as their fluxes, serves as a basis for modeling transport of contaminants, such as pesticides or heavy metals (e.g., [8]). As examples for industrial applications in two-phase flow, the movement of fluids through a filter or the infiltration of ink into paper (see [24]) can be considered. All these applications have in common that the porous media structure is, in general, highly heterogeneous. The challenges are to combine the complex multiphase flow processes with the heterogeneity distribution of the porous media properties.The physical-mathematical model underlying simulations of two-phase flow on the Darcy scale usually requires a constitutive relationship between (wetting phase) saturation S w and the capillary pressure p c . Traditionally, one assumes that this relationship is determined under quasistatic or steady-state conditions but can also be applied to any transient flow processes fulfilling the Reynolds number criterion. However, recently, some works have questioned this assumption (see, e.g., [25]). The authors were able to improve numerical simulation results by applying a model

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