Multiplication of solutions for linear overdetermined systems of partial differential equations

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains the Cauchy-Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebraic way, large classes of non-trivial solutions that can be constructed by forming convergent power series of trivial solutions.Comment: 27 page

Using natural means to reduce surface transport noise during propagation outdoors

This paper reviews ways of reducing surface transport noise by natural means. The noise abatement solutions of interest can be easily (visually) incorporated in the landscape or help with greening the (sub)urban environment. They include vegetated surfaces (applied to faces or tops of noise walls and on building façades and roofs ), caged piles of stones (gabions), vegetation belts (tree belts, shrub zones and hedges), earth berms and various ways of exploiting ground-surface-related effects. The ideas presented in this overview have been tested in the laboratory and/or numerically evaluated in order to assess or enhance the noise abatement they could provide. Some in-situ experiments are discussed as well. When well-designed, such natural devices have the potential to abate surface transport noise, possibly by complementing and sometimes improving common (non-green) noise reducing devices or measures. Their applicability strongly depends on the available space reserved for the noise abatement and the receiver position

Endothelial cells stimulate growth of normal and cancerous breast epithelial cells in 3D culture

<p>Abstract</p> <p>Background</p> <p>Epithelial-stromal interaction provides regulatory signals that maintain correct histoarchitecture and homeostasis in the normal breast and facilitates tumor progression in breast cancer. However, research on the regulatory role of the endothelial component in the normal and malignant breast gland has largely been neglected. The aim of the study was to investigate the effects of endothelial cells on growth and differentiation of human breast epithelial cells in a three-dimensional (3D) co-culture assay.</p> <p>Methods</p> <p>Breast luminal and myoepithelial cells and endothelial cells were isolated from reduction mammoplasties. Primary cells and established normal and malignant breast cell lines were embedded in reconstituted basement membrane in direct co-culture with endothelial cells and by separation of Transwell filters. Morphogenic and phenotypic profiles of co-cultures was evaluated by phase contrast microscopy, immunostaining and confocal microscopy.</p> <p>Results</p> <p>In co-culture, endothelial cells stimulate proliferation of both luminal- and myoepithelial cells. Furthermore, endothelial cells induce a subpopulation of luminal epithelial cells to form large acini/ducts with a large and clear lumen. Endothelial cells also stimulate growth and cloning efficiency of normal and malignant breast epithelial cell lines. Transwell and gradient co-culture studies show that endothelial derived effects are mediated - at least partially - by soluble factors.</p> <p>Conclusion</p> <p>Breast endothelial cells - beside their role in transporting nutrients and oxygen to tissues - are vital component of the epithelial microenvironment in the breast and provide proliferative signals to the normal and malignant breast epithelium. These growth promoting effects of endothelial cells should be taken into consideration in breast cancer biology.</p

Systems of Linear First Order Partial Differential Equations Admitting a Bilinear Multiplication of Solutions

The Cauchy–Riemann equations admit a bilinear multiplication of solutions, since the product of two holomorphic functions is again holomorphic. This multiplication plays the role of a nonlinear superposition principle for solutions, allowing for construction of new solutions from already known ones, and it leads to the exceptional property of the Cauchy–Riemann equations that all solutions can locally be built from power series of a single solution z = x + iy ∈ C. In this thesis we have found a differential algebraic characterization of linear first order systems of partial differential equations admitting a bilinear ∗-multiplication of solutions, and we have determined large new classes of systems having this property. Among them are the already known quasi-Cauchy–Riemann equations, characterizing integrable Newton equations, and the gradient equations ∇f = M∇g with constant matrices M. A systematic description of linear systems of PDEs with variable coefficients have been given for systems with few independent and few dependent variables. An important property of the ∗-multiplication is that infinite families of solutions can be constructed algebraically as power series of known solutions. For the equation ∇f = M∇g it has been proved that the general solution, found by Jodeit and Olver, can be locally represented as convergent power series of a single simple solution similarly as for solutions of the Cauchy–Riemann equations

Utveckling av insatsmodul till en Arcam S12 EBM-maskin : För möjliggörande av småskaliga tester med mindre pulveråtgång

Arbetet behandlar utvecklingsprocessen för en insats till en ARCAM S12 Electron Beam Melting-maskin.   Behovet består i att dagens maskin kräver en full tank med tillverk-ningsmaterial för att kunna användas. Den överdrivna materialtillför-seln leder till att maskinen ej kan ses som lämplig för materialforskning, då nya material måste tillverkas i stora satser varav en stor del går som svinn. Målet med arbetet blev därför att utveckla en insats till maskinen, som skulle göra den gångbar att använda vid materialforskning, utan att permanent påverka ursprungsfunktionen.   Den utvecklade insatsen har som funktion att sänka materialanvänd-ningen i maskinen, och därigenom göra maskinen applicerbar för materialforskning. Detta genom att minska byggytan och skapa en mer sofistikerad materialmatning än originalutförandets. Materialmatningen är också modulär, på så sätt att mängden materialpulver som matas ut per cykel kan varieras med olika insatser.   Under arbetets gång behandlas alla processens steg, från målspecifikat-ionen till det slutgiltiga konstruktionsunderlaget. Projektet startade med en funktionsanalys och uppställande av en målspecifikation. Därefter startade konceptgenereringsprocessen med både kreativa och mer stringenta utvecklingsmetoder. Efter detta genomfördes konceptval med flera strukturerade konceptvalsmetoder. Det valda konceptet modellerades sedan i sin slutgiltiga form i SolidWorks. Via SolidWorks interna ritningssystem ritades även konstruktionsunderlag till insatts-modulen.   Projektets resultat är ett färdigt konstruktionsunderlag för en modul som passar i en ARCAM S12 EBM-maskin. Denna modul minskar byggvolymen till 110x110xbygghöjden i millimeter, och likriktar mängden material applicerat mellan lagerna.This thesis work is focused on the product development of an insert module for an ARCAM S12 Electron Beam Melting machine The need for an insert module comes from the fact that the machine requires a full tank of building material to operate as intended. With concern to the large building volume the original machine cannot be seen as a viable alternative for materials research, because such research often uses expensive experimental materials. The goal for the module is therefore to lower the use of building material, and trough that make the machine viable for materials research without permanently affecting the original function. Another important function of the new module is the possibility to control and synchronize the amount of material dispensed between layers of the build.     During the length of the thesis, the entire development process of the module is discussed. From the target specification, to the finished blueprints.   The process started with the establishment of a target specification, followed by a phase of concept development containing both creative and stringent methods. After these concepts had been evaluated and culled through structured methods a final concept was selected. This concept was then modeled in Solid Works and technical drawings of the model was made for the blueprint.   The result of the thesis work is a finished blueprint for an insert module that fits an ARCAM S12 EBM machine. This module has lowered the build volume to 110x110xthe build height in millimeters, and has the possibility to synchronize the amount of material dispensed between layers.Betyg 190909</p

Utveckling av insatsmodul till en Arcam S12 EBM-maskin : För möjliggörande av småskaliga tester med mindre pulveråtgång

Arbetet behandlar utvecklingsprocessen för en insats till en ARCAM S12 Electron Beam Melting-maskin.   Behovet består i att dagens maskin kräver en full tank med tillverk-ningsmaterial för att kunna användas. Den överdrivna materialtillför-seln leder till att maskinen ej kan ses som lämplig för materialforskning, då nya material måste tillverkas i stora satser varav en stor del går som svinn. Målet med arbetet blev därför att utveckla en insats till maskinen, som skulle göra den gångbar att använda vid materialforskning, utan att permanent påverka ursprungsfunktionen.   Den utvecklade insatsen har som funktion att sänka materialanvänd-ningen i maskinen, och därigenom göra maskinen applicerbar för materialforskning. Detta genom att minska byggytan och skapa en mer sofistikerad materialmatning än originalutförandets. Materialmatningen är också modulär, på så sätt att mängden materialpulver som matas ut per cykel kan varieras med olika insatser.   Under arbetets gång behandlas alla processens steg, från målspecifikat-ionen till det slutgiltiga konstruktionsunderlaget. Projektet startade med en funktionsanalys och uppställande av en målspecifikation. Därefter startade konceptgenereringsprocessen med både kreativa och mer stringenta utvecklingsmetoder. Efter detta genomfördes konceptval med flera strukturerade konceptvalsmetoder. Det valda konceptet modellerades sedan i sin slutgiltiga form i SolidWorks. Via SolidWorks interna ritningssystem ritades även konstruktionsunderlag till insatts-modulen.   Projektets resultat är ett färdigt konstruktionsunderlag för en modul som passar i en ARCAM S12 EBM-maskin. Denna modul minskar byggvolymen till 110x110xbygghöjden i millimeter, och likriktar mängden material applicerat mellan lagerna.This thesis work is focused on the product development of an insert module for an ARCAM S12 Electron Beam Melting machine The need for an insert module comes from the fact that the machine requires a full tank of building material to operate as intended. With concern to the large building volume the original machine cannot be seen as a viable alternative for materials research, because such research often uses expensive experimental materials. The goal for the module is therefore to lower the use of building material, and trough that make the machine viable for materials research without permanently affecting the original function. Another important function of the new module is the possibility to control and synchronize the amount of material dispensed between layers of the build.     During the length of the thesis, the entire development process of the module is discussed. From the target specification, to the finished blueprints.   The process started with the establishment of a target specification, followed by a phase of concept development containing both creative and stringent methods. After these concepts had been evaluated and culled through structured methods a final concept was selected. This concept was then modeled in Solid Works and technical drawings of the model was made for the blueprint.   The result of the thesis work is a finished blueprint for an insert module that fits an ARCAM S12 EBM machine. This module has lowered the build volume to 110x110xthe build height in millimeters, and has the possibility to synchronize the amount of material dispensed between layers.Betyg 190909</p

Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales

We study the homogenization of a certain linear hyperbolic-parabolic problem exhibiting two rapid spatial scales {ε; ε2}. The homogenization is performed by means of evolution multiscale convergence, a generalization of the concept of two-scale convergence to include any number of scales in both space and time. In particular we apply a compactness result for gradients. The outcome of the homogenization procedure is that we obtain a homogenized problem of hyperbolic-parabolic type together with two elliptic local problems, one for each rapid scale, for the correctors