Generating admissible space-time meshes for moving domains in d+1d+1-dimensions

In this paper we present a discontinuous Galerkin finite element method for the solution of the transient Stokes equations on moving domains. For the discretization we use an interior penalty Galerkin approach in space, and an upwind technique in time. The method is based on a decomposition of the space-time cylinder into finite elements. Our focus lies on three-dimensional moving geometries, thus we need to triangulate four dimensional objects. For this we will present an algorithm to generate $d+1$-dimensional simplex space-time meshes and we show under natural assumptions that the resulting space-time meshes are admissible. Further we will show how one can generate a four-dimensional object resolving the domain movement. First numerical results for the transient Stokes equations on triangulations generated with the newly developed meshing algorithm are presented

On sufficient conditions for some orthogonal designs and sequences with zero autocorrelation function

We give new sets of sequences with entries from {0, ±a, ±b, ±c, ±d} on the commuting variables a, b, c, d and zero autocorrelation function. Then we use these sequences to construct some new orthogonal designs. This means that for order 28 only the existence of the following five cases, none of which is ruled out by known theoretical results, remain in doubt: OD(28; 1, 4, 9, 9), OD(28; 1, 8, 8, 9), OD(28; 2, 8, 9, 9), OD(28; 3, 6, 8, 9), OD(28; 4, 4, 4, 9). We consider 4 - N PAF(Sl, S2, S3, S4) sequences or four sequences of commuting variables from the set {0, ±a, ±b, ±c, ±d} with zero nonperiodic autocorrelation function where ±a occurs Sl times, ±b occurs S2 times, etc. We show the necessary conditions for the existence of an 0D(4n; S1,S2, S3,S4) constructed using four circulant matrices are sufficient conditions for the existence of 4 - NPAF(S1, S2, S3, S4) sequences for all lengths ≥ n, i) for n = 3, with the extra condition (S1,S2,S3,S4) ≠ (1,1,1,9), ii) for n = 5, provided there is an integer matrix P satisfying PPT = diag (S1,S2,S3,S4), iii) for n = 7, with the extra condition that (S1,S2,S3,S4) ≠ (1,1,1,25), and possibly (S1,S2,S3,S4) =I- (1,1,1,16), (1,1,8,18), (1,1,13,13), (1,4,4,9), (1,4,9,9), (1,4,10,10), (1,8,8,9), (1,9,9,9), (2,4,4,18), (2,8,9,9), (3,4,6,8), (3,6,8,9); (4,4,4,9), (4,4,9,9), (4,5,5,9), (5,5,9,9). We show the necessary conditions for the existence of an OD(4n; S1,S2) constructed using four circulant matrices are sufficient conditions for the existence of 4 - NPAF(S1,S2) sequences for all lengths ≥ n, where n = 3 or 5

Human understanding in the philosophy of R.G. Collingwood

The thesis explores the role of human understanding in R.G. Collingwood's philosophy. I examine four major areas: the role of psychology, the unity of mind (i.e. unity of thoughts and emotions), the role of art and the case of fairy tales as a source of historical knowledge. These themes taken together expound a coherent way to see human understanding: with psychology Collingwood suggests the form that human understanding cannot assume the unity of mind is Collingwood's idea of how we experience an activity, that is, as an undivided whole of emotions and thoughts (and in some respects sensations or feelings too), that exist in every activity as elements that cannot be distinguished or separated. When we come to the forms that an activity can take I argue, using art and fairy tales, that human understanding in Collingwood's system should be seen as a shift from the knowledge of the united spirit (as propounded in Speculum Mentis) to the knowledge of the historical consciousness. The knowledge of the united spirit is achieved through a dialectic scale of the different forms of experience, which individually, in isolation from one another, are not epistemologically valid. In the historical consciousness the forms of experience are epistemologically autonomous and are found within history, all being manifestations of the historical mind

On the Incorporation of Obstacles in a Fluid Flow Problem Using a Navier-Stokes-Brinkman Penalization Approach

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the solids by the moving fluid. Such problems appear in various contexts, ranging from numerous technical applications such as turbines to medical problems such as the regulation of hemodyamics by valves. Typically, the numerical treatment of such problems is posed within a fluid structure interaction (FSI) framework. General FSI models are able to capture bidirectional interactions, but are challenging to solve and computationally expensive. Simplified methods offer a possible remedy by achieving better computational efficiency to broaden the scope to demanding application problems with focus on understanding the effect of solids on altering fluid dynamics. In this study we report on the development of a novel method for such applications. In our method rigid moving obstacles are incorporated in a fluid dynamics context using concepts from porous media theory. Based on the Navier-Stokes-Brinkman equations which augments the Navier-Stokes equation with a Darcy drag term our method represents solid obstacles as time-varying regions containing a porous medium of vanishing permeability. Numerical stabilization and turbulence modeling is dealt with by using a residual based variational multiscale formulation. The key advantages of our approach -- computational efficiency and ease of implementation -- are demonstrated by solving a standard benchmark problem of a rotating blood pump posed by the Food and Drug Administration Agency (FDA). Validity is demonstrated by conducting a mesh convergence study and by comparison against the extensive set of experimental data provided for this benchmark

Fouling and Cleaning of Modified Stainless Steel Plate Heat Exchangers Processing Milk Products

Fouling of heat exchangers in dairy industries is still quite a severe problem both technically and economically. Altering the surface properties of the heating surfaces would be a way of solving this issue. Modified steel surfaces were tested in an Alfa Laval V2 plate heat exchanger throughout dairy product sterilization. The behavior was analyzed for 8 different surface treatments, such as coatings (Diamond Like Carbon [DLC], Silica, SiOX, Ni-P-PTFE, Excalibur®, Xylan®) and ion implantation (SiF+, MoS2). All fouling and cleaning experiments were carried out in standard and well-controlled operating conditions. After fouling, no significant difference could be seen between all the modified steels and the reference by statistical variance analysis. Cleaning efficiency of Ni-PPTFE appeared significantly the best. It could be suggested that the free surface energy plays a predominant role and the roughness a minor role in the level of fouling and cleaning efficiency