Search results for "Geometry"
showing 10 items of 4487 documents
On the Reception of Grassmann’s Work in Germany during the 1870’s
1996
It has often been remarked that Grassmann’s mathematics was not widely appreciated during his lifetime. Although awareness of the dimensions of his achievements began to spread in the early 1870’s, even in Germany relatively few mathematicians appear to have been well acquainted with either the original 1844 edition of Grassmann’s Ausdehnungslehre or the mathematically more accessible edition of 1862. The main reasons for this weak and rather delayed reception have been described often enough---Grassmann’s isolated working environment and his nearly impenetrable language---but there are a number of related aspects that still deserve closer consideration.1
Introducing History of Mathematics Education Through Its Actors: Peter Treutlein’s Intuitive Geometry
2018
This paper deals with the questions why and how to introduce into teacher education the history of teaching practices and educational reforms. In particular, we are interested in the developments of curricular school geometry during the 19th century and the reforms at the beginning of the last century in Germany. The life and work of Peter Treutlein—a contemporary of Felix Klein—and a conceptual reformist of geometry instruction, schoolbook author, committed teacher and school principal with educational experience of many years opens to us many opportunities to link present teaching practices in Geometry to its traditions, some of which we will discuss.
Optimizing and Modeling the drying process of the Natural Gas through the Taguchi method
2018
The aim of this study is to highlight the optimization method of the drying process of natural gas, using the Taguchi method. The natural gas undergoes several stages from its extraction until reaching its end consumer. As the natural gas contains several impurities and a certain quantity of water and vapors, the drying process is very important to obtain a product of high quality. Gas dehydration can be obtained through several methods, the method presented here being the absorption method - by use of a drying station with triglycol. This method is considered to be the most convenient one taking into account the obtained results. Nevertheless, cost reducing is the main objective for compan…
A probabilistic approach to radiant field modeling in dense particulate systems
2016
Radiant field distribution is an important modeling issue in many systems of practical interest, such as photo-bioreactors for algae growth and heterogeneous photo-catalytic reactors for water detoxification.In this work, a simple radiant field model suitable for dispersed systems showing particle size distributions, is proposed for both dilute and dense two-phase systems. Its main features are: (i) only physical, independently assessable parameters are involved and (ii) its simplicity allows a closed form solution, which makes it suitable for inclusion in a complete photo-reactor model, where also kinetic and fluid dynamic sub-models play a role. A similar model can be derived by making us…
Multi-physical modelling of reverse electrodialysis
2017
Abstract Reverse electrodialysis (RED) is an electrochemical membrane process that directly converts the energy associated with the concentration difference between two salt solutions into electrical energy by means of a selective controlled mixing. The physics of RED involves the interaction of several phenomena of different nature and space-time scales. Therefore, mathematical modelling and numerical simulation tools are crucial for performance prediction. In this work, a multi-physical modelling approach for the simulation of RED units was developed. A periodic portion of a single cell pair was simulated in two dimensions. Fluid dynamics was simulated by the Navier-Stokes and continuity …
A COMPARISON BETWEEN COMBUSTION PHASE INDICATORS FOR OPTIMAL SPARK TIMING
2008
The closed-loop control of internal combustion engine spark timing may be accomplished by means of a combustion phase indicator, i.e., a parameter, derived from in-cylinder pressure analysis, whose variation is mainly referable to combustion phase shift and assumes a fixed reference value under optimal spark timing operation. The aim of the present work is a comparison between different combustion phase indicators, focusing on the performance attainable by a feedback spark timing control, which uses the indicator as pilot variable. An extensive experimental investigation has been carried out, verifying the relationship between indicators’ optimal values and the main engine running parameter…
Performance improvement of a Savonius water rotor with novel blade shapes
2021
Abstract Savonius water rotor is a prominent drag based turbine able to extract energy available in flowing water with low velocity like river streams, tidal currents or other man made water canals. However, in view of its low performance, an enhanced design of the rotor blades is necessary to better its efficiency. Therefore, the present study aims to improve the efficiency of Savonius rotor by changing the blade design. Different blade shapes were investigated numerically using computational fluid dynamics (CFD). Using conventional design, the peak power coefficient was found to be 0.166 at tip-speed ratio of 0.78. However, the peak power coefficient reaches 0.184 using the optimal blade …
Scenery Flow, Conical Densities, and Rectifiability
2015
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
Beyond ideal two-dimensional metals: Edges, vacancies, and polarizabilities
2018
Recent experimental discoveries of graphene-stabilized patches of two-dimensional (2D) metals have motivated also their computational studies. However, so far the studies have been restricted to ideal and infinite 2D metallic monolayers, which is insufficient because in reality the properties of such metallic patches are governed by microstructures pervaded by edges, defects, and several types of perturbations. Here we use density-functional theory to calculate edge and vacancy formation energies of hexagonal and square lattices of 45 elemental 2D metals. We find that the edge and vacancy formation energies are strongly correlated and decrease with increasing Wigner-Seitz radii, analogously…