BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.     

Ring structures on groups of arithmetic functions

Using the theory of Witt vectors, we define ring structures on several well-known groups of arithmetic functions, which in another guise are formal Dirichlet series. The set of multiplicative arithmetic functions over a commutative ring R is shown to have a unique functorial ring structure for which the operation of addition is Dirichlet convolution and the operation of multiplication restricted to the completely multiplicative functions coincides with point-wise multiplication. The group of additive arithmetic functions over R also has a functorial ring structure. In analogy with the ghost homomorphism of Witt vectors, there is a functorial ring homomorphism from the ring of multiplicative functions to the ring of additive functions that is an isomorphism if R is a Q-algebra. The group of rational arithmetic functions, that is, the group generated by the completely multiplicative functions, forms a subring of the ring of multiplicative functions. The latter ring has the structure of a Bin(R)-algebra, where Bin(R) is the universal binomial ring equipped with a ring homomorphism to R. We use this algebra structure to study the order of a rational arithmetic function, as well the powersfα for α∈Bin(R) of a multiplicative arithmetic function f. For example, we prove new results about the powers of a given multiplicative arithmetic function that are rational. Finally, we apply our theory to the study of the zeta function of a scheme of finite type over Z.     

Untersuchung von Vitaminen

Ohne Zusammenfassung     

Optical behavior of antibiofouling additives in environment‐friendly coverglass materials for bio‐sensors and solar panels

Solar panels and bio‐optical sensors play a significant and growing role in a number of applications that are of importance to many organizations. Many of these instruments require a high transmission of radiation into the device for it to work properly. A major issue faced is that harsh marine environments often aid in the growth or development of fouling on the coverglass used to protect the instruments. Over a period of time in an ocean environment, some plant or animal may attach itself to the coverglass, ultimately obscuring the glass and rendering the instrument useless. As such, an antifouling mechanism is needed for these instruments that is inexpensive, long‐lasting, and environment friendly. The approach discussed herein involves the use of known antifouling chemicals which have been incorporated into the polymer matrix. Polymethylmethacrylate (PMMA), bisphenol A polycarbonate (Bis A PC), and a co‐polyterephthalate (CPTE) were examined. The plaques are optically transparent and previous work has shown that, for most samples, the materials display a minimal decrease in mechanical behavior upon the addition of the algaecides. This paper will discuss the effects on the materials' optical properties when exposed to both harsh marine conditions as well as high intensity UV light. Specifically, the decrease in transmission of visible light was examined over a 6 month period of time. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of toluene LIF thermometry detection strategies applied in an internal combustion engine

In the context of toluene laser-induced fluorescence (LIF) thermometry, the two common LIF detection strategies, namely one-color and two-color detection, have been simultaneously applied to compare each strategy’s ability to accurately resolve thermal gradients during an engine cycle within an optically accessible internal combustion (IC) engine. Temperature images are obtained from high-speed toluene LIF measurements and are combined with high-speed particle image velocimetry. The combination with flow data and Mie scattering images facilitates the interpretation of differences between the toluene LIF detection strategies. Two-color temperature images are limited in their ability to detect thermal gradients near the end of compression due to larger precision uncertainties. Local regions of cold gases in the two-color images are better identified with the guidance of the one-color images when homogeneous toluene mixtures preside. During expansion, large differences exist between one- and two-color temperature images and likely caused by local mixture fraction heterogeneities that bias the one-color detection strategy. Toluene condensation occurs during the expansion and exhaust stroke and causes local mixture fraction heterogeneities in the combustion chamber. Liquid toluene is in contact with solid surfaces and crevices of the combustion chamber and can evaporate during compression or expansion causing both local temperature and mixture stratification. This work demonstrates the advantage of high-speed imaging and use of multiple image diagnostics to reveal the development of natural temperature and mixture stratification in a motored IC engine. This work also suggests that natural temperature stratification typically regarded from gas-wall heat transfer may also be caused by liquid droplet evaporation on solid surfaces. Such phenomenon, however, is expected to be pertinent for all modern-day engine operating systems.     

3,4,9,10-Perylenetetracarboxylicdiimide as an interlayer for ultraviolet organic light emitting diodes

Ultraviolet organic light emitting diodes with 3,4,9,10-perylenetetracarboxylicdiimide (PTCDI) interlayer have been achieved. The emission spectrum and intensity were strongly dependent on the thickness of PTCDI interlayer, in spite of the fact that PTCDI has neither much lower HOMO nor much higher LUMO level, which is considered necessary for efficient charge blocking layers. The influence of PTCDI layer was investigated in three different device configurations and obtained results are discussed. For optimal device configuration, OLED with emission centered at 370 nm and turn-on voltage of 4.5 V is obtained.