On the Areas of Cyclic and Semicyclic Polygons

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain variety derived from the variety of binary (2m-1)-forms having m-1 double roots. Thus we obtain explicit formulas for the areas of cyclic heptagons and octagons, and illuminate some mysterious features of Robbins' formulas for the areas of cyclic pentagons and hexagons. We also introduce a companion family of polynomials that relate the squared area of an n-gon inscribed in a circle, one of whose sides is a diameter, to the squared lengths of the other sides. By similar algebraic techniques we obtain explicit formulas for these polynomials for all n <= 7.Comment: 22 page

Optimization of the Hot Embossing Parameters and Sintering Characterization for Alumina/Berea Sandstone Sintering

The purpose of this study is to investigate the process of hot embossing on alumina based ceramics as a cost-efficient procedure for manufacturing microfluidic testing components. Alumina ceramics were used as an exploratory phase for the final objective of the project, manufacturing of Berea sandstone based ceramic samples. Previous research has shown potential in using hot embossing on Alumina based ceramics; however, complications with extrusion and micro-structure quality were observed. For this reason, the research performed aimed to produce Berea Sandstone based components by first improving upon the embossing quality of alumina ceramics. The thesis first investigates changes in the extrusion ratio and the subsequent effects observed on the quality of extrudate. Next, improving the quality of embossed microstructures is examined. This is done by varying the MFI as well as changing the embossing speed and temperature. Finally, a preliminary study into the effectiveness of Berea sandstone based ceramics is reported. The improved ram extruder demonstrated improved surface quality in post-extrusion samples which can be attributed to a greater extrusion ratio, enhanced temperature uniformity, and changing the extruder stock material to stainless steel. Alumina samples extruded from the new extruder had an average surface roughness of compared to reported for the previous design. Comparisons of optical scan data showed that a lower MFI provided sharper edges along the testing section; however, demolding from the embossing plate was a challenge often rendering samples unusable. The higher MFI was very easy to demold from the embossing plate and the resolution of the imprinted microstructures improved; therefore, the higher MFI was chosen and other embossing parameters were examined: embossing temperature and speed. It was concluded that low viscosity and slow embossing speeds provide higher quality embossed samples. After inspection of several embossing parameters on microstructure quality, an introductory study into Berea sandstone ceramics was conducted. During sintering, a properly densified sample was not obtained and SEM results indicated a loss of iron oxide on the periphery of the sample. However, this initial step in manufacturing sandstone samples provides invaluable insight into the future of the project

Optimization of the Hot Embossing Parameters and Sintering Characterization for Alumina/Berea Sandstone Ceramics

The purpose of this study is to investigate the process of hot embossing on alumina based ceramics as a cost-efficient procedure for manufacturing microfluidic testing components. Alumina ceramics were used as an exploratory phase for the final objective of the project, manufacturing of Berea sandstone based ceramic samples. These testing components are vital to the growth of various fields ranging from the retrieval of oil and natural gas to studying the water purification process of aquifers. Previous research has shown potential in using hot embossing on Alumina based ceramics; however, complications with extrusion and micro-structure quality were observed. For this reason, the research performed aimed to produce Berea Sandstone based components by first improving upon the embossing quality of alumina ceramics. The thesis first investigates changes in the extrusion ratio and the subsequent effects observed on the quality of extrudate. Next, improving the quality of embossed microstructures is examined. This is done by varying the MFI as well as changing the embossing speed and temperature. Finally, a preliminary study into the effectiveness of Berea sandstone based ceramics is reported. The improved ram extruder demonstrated improved surface quality in post-extrusion samples which can be attributed to a greater extrusion ratio and enhanced temperature uniformity, as well as a changing the extruder stock material to stainless steel. Alumina samples extruded from the new extruder had an average surface roughness of; this was compared to reported for the previous design. Comparisons of optical scan data showed that a lower MFI provided sharper edges along the testing section; however, demolding from the embossing plate was a challenge often rendering samples unusable. The higher MFI was very easy to demold from the embossing plate and the resolution of the imprinted microstructures improved; therefore, the higher MFI was chosen and other embossing parameters were examined: embossing temperature and speed. It was concluded that low viscosity and slow embossing speeds provide higher quality embossed samples. After a thorough inspection of several embossing parameters on microstructure quality, introductory study into substituting Berea sandstone for alumina was conducted. The analysis showed a loss in microstructure resolution when compared to alumina ceramics due to an increase in the average particle size of the sandstone powder. During sintering, a properly densified sample was not obtained and SEM results indicated a loss of iron oxide on the periphery of the sample. However, this initial step in manufacturing sandstone samples provides invaluable insight into the future of the projec

Stiffness of Contacts Between Rough Surfaces

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughnesses, system sizes and Poisson ratios can be collapsed using Persson's contact theory for continuous elastic media. The atomic scale response at the interface between solids has little affect on the area or normal stiffness, but can greatly reduce the lateral stiffness. The scaling of this effect with system size and roughness is discussed.Comment: 4 pages, 3 figure

Strain Hardening in Polymer Glasses: Limitations of Network Models

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. Entangled and unentangled chains show the same strain hardening when plotted against the microscopic chain orientation rather than the macroscopic strain.Comment: 4 pages, 3 figure

Contact area of rough spheres: Large scale simulations and simple scaling laws

We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.Comment: 2 figures + Supporting Materia

Cancer immunotherapy targeting neoantigens

AbstractNeoantigens are antigens encoded by tumor-specific mutated genes. Studies in the past few years have suggested a key role for neoantigens in cancer immunotherapy. Here we review the discoveries of neoantigens in the past two decades and the current advances in neoantigen identification. We also discuss the potential benefits and obstacles to the development of effective cancer immunotherapies targeting neoantigens

Powered fire nozzle for fast penetration of structures: A concept

Nozzle has been proposed with tip that will punch through wall very quickly. It would allow extinguishing agent to be delivered inside closed structure in minimum amount of time. Two versions of nozzle have been conceived: one operated from hydraulic pressure source and one activated by explosive charge

Resolving singular forces in cavity flow: Multiscale modeling from atoms to millimeters

A multiscale approach for fluid flow is developed that retains an atomistic description in key regions. The method is applied to a classic problem where all scales contribute: The force on a moving wall bounding a fluid-filled cavity. Continuum equations predict an infinite force due to stress singularities. Following the stress over more than six decades in length in systems with characteristic scales of millimeters and milliseconds allows us to resolve the singularities and determine the force for the first time. The speedup over pure atomistic calculations is more than fourteen orders of magnitude. We find a universal dependence on the macroscopic Reynolds number, and large atomistic effects that depend on wall velocity and interactions.Comment: 4 pages,3 figure