Traveling Wave Solutions in a Generalized Theory for Macroscopic Capillarity

One-dimensional traveling wave solutions for imbibition processes into a homogeneous porous medium are found within a recent generalized theory of macroscopic capillarity. The generalized theory is based on the hydrodynamic differences between percolating and nonpercolating fluid parts. The traveling wave solutions are obtained using a dynamical systems approach. An exhaustive study of all smooth traveling wave solutions for primary and secondary imbibition processes is reported here. It is made possible by introducing two novel methods of reduced graphical representation. In the first method the integration constant of the dynamical system is related graphically to the boundary data and the wave velocity. In the second representation the wave velocity is plotted as a function of the boundary data. Each of these two graphical representations provides an exhaustive overview over all one-dimensional and smooth solutions of traveling wave type, that can arise in primary and secondary imbibition. Analogous representations are possible for other systems, solution classes, and processes.</p

Treatment of bipolar disorder: a complex treatment for a multi-faceted disorder

Background: Manic-depression or bipolar disorder (BD) is a multi-faceted illness with an inevitably complex treatment. Methods: This article summarizes the current status of our knowledge and practice of its treatment. Results: It is widely accepted that lithium is moderately useful during all phases of bipolar illness and it might possess a specific effectiveness on suicidal prevention. Both first and second generation antipsychotics are widely used and the FDA has approved olanzapine, risperidone, quetiapine, ziprasidone and aripiprazole for the treatment of acute mania. These could also be useful in the treatment of bipolar depression, but only limited data exists so far to support the use of quetiapine monotherapy or the olanzapine-fluoxetine combination. Some, but not all, anticonvulsants possess a broad spectrum of effectiveness, including mixed dysphoric and rapid-cycling forms. Lamotrigine may be effective in the treatment of depression but not mania. Antidepressant use is controversial. Guidelines suggest their cautious use in combination with an antimanic agent, because they are supposed to induce switching to mania or hypomania, mixed episodes and rapid cycling. Conclusion: The first-line psychosocial intervention in BD is psychoeducation, followed by cognitive-behavioral therapy. Other treatment options include Electroconvulsive therapy and transcranial magnetic stimulation. There is a gap between the evidence base, which comes mostly from monotherapy trials, and clinical practice, where complex treatment regimens are the rule

Simulation and interpretation of multiphase processes in porous and fractured-porous media

A numerical model concept for simulating multi phase flow processes is presented. The conceptual model involves the approximation of heterogeneous porous and fractured porous media, by application of one-, two- and threedimensional elements in space that can be combined arbitrarily in a single model. The mathematical formulation of multiphase flow is valid for both saturated and unsaturated regions, so that dynamic front propagation behaviour as well as different geology-related retention characteristics can be accounted for in the model. For every Finite Element model problems arise when capillary pressure effects can be neglected and the governing equations are of hyperbolic type. To overcome these difficulties, the differential equations were formulated in terms of pressure and saturation as primary variables. To provide an accurate representation of the resulting saturation-front velocities and to avoid numerical oscillations a modified Petrov-Galerkin method was employed. To verify the code, the Buckley-Leverett problem was solved, and together with an adaptive finite element algorithm excellent results were obtained

Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations

In previous work, a new adaptive meshfree advection scheme for numerically solving linear transport equations has been proposed. The scheme, being a combination of an adaptive semi-Lagrangian method and local radial basis function interpolation, is essentially a method of backward characteristics. The adaptivity of the meshfree advection scheme relies on customized rules for the refinement and coarsening of scattered nodes. In this paper, the method is extended to nonlinear transport equations. To this end, in order to be able to model shock propagation, an artificial viscosity term is added to the scheme. Moreover, the local interpolation method and the node adaption rules are modified accordingly. The good performance of the resulting method is finally shown in the numerical examples by using two specific nonlinear model problems: Burgers equation and the Buckley-Leverett equation, the latter describing a two-phase fluid flow in a porous medium