Search results for: fractional Black-Scholes equations

Authors: Sebastian Kehne, Alexander Epple, Werner Herfs

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A new method for optimal selection of components for multi-axes forward-feed drive systems is proposed in which the choice of motors, gear boxes and ball screw drives is optimized. Essential is here the synchronization of electrical and mechanical frequency behavior of all axes because even advanced controls (like H∞-controls) can only control a small part of the mechanical modes – namely only those of observable and controllable states whose value can be derived from the positions of extern linear length measurement systems and/or rotary encoders on the motor or gear box shafts. Further problems are the unknown processing forces like cutting forces in machine tools during normal operation which make the estimation and control via an observer even more difficult. To start with, the open source Modelica Feed Drive Library which was developed at the Laboratory for Machine Tools, and Production Engineering (WZL) is extended from one axis design to the multi axes design. It is capable to simulate the mechanical, electrical and thermal behavior of permanent magnet synchronous machines with inverters, different gear boxes and ball screw drives in a mechanical system. To keep the calculation time down analytical equations are used for field and torque producing equivalent circuit, heat dissipation and mechanical torque at the shaft. As a first step, a small machine tool with a working area of 635 x 315 x 420 mm is taken apart, and the mechanical transfer behavior is measured with an impulse hammer and acceleration sensors. With the frequency transfer functions, a mechanical finite element model is built up which is reduced with substructure coupling to a mass-damper system which models the most important modes of the axes. The model is modelled with Modelica Feed Drive Library and validated by further relative measurements between machine table and spindle holder with a piezo actor and acceleration sensors. In a next step, the choice of possible components in motor catalogues is limited by derived analytical formulas which are based on well-known metrics to gain effective power and torque of the components. The simulation in Modelica is run with different permanent magnet synchronous motors, gear boxes and ball screw drives from different suppliers. To speed up the optimization different black-box optimization methods (Surrogate-based, gradient-based and evolutionary) are tested on the case. The objective that was chosen is to minimize the integral of the deviations if a step is given on the position controls of the different axes. Small values are good measures for a high dynamic axes. In each iteration (evaluation of one set of components) the control variables are adjusted automatically to have an overshoot less than 1%. It is obtained that the order of the components in optimization problem has a deep impact on the speed of the black-box optimization. An approach to do efficient black-box optimization for multi-axes design is presented in the last part. The authors would like to thank the German Research Foundation DFG for financial support of the project “Optimierung des mechatronischen Entwurfs von mehrachsigen Antriebssystemen (HE 5386/14-1 | 6954/4-1)” (English: Optimization of the Mechatronic Design of Multi-Axes Drive Systems).

Keywords: ball screw drive design, discrete optimization, forward feed drives, gear box design, linear drives, machine tools, motor design, multi-axes design

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Authors: D. Bianco, A. Sollazzo, M. Barbarino, G. Elia, A. Smoraldi, N. Favaloro

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The activities, described in the present paper, have been conducted in the framework of the HYPROB-New Program, carried out by the Italian Aerospace Research Centre (CIRA) promoted and funded by the Italian Ministry of University and Research (MIUR) in order to improve the National background on rocket engine systems for space applications. The Program has the strategic objective to improve National system and technology capabilities in the field of liquid rocket engines (LRE) for future Space Propulsion Systems applications, with specific regard to LOX/LCH4 technology. The main purpose of the HYPROB program is to design and build a Propulsion Test Facility (HIMP) allowing test activities on Liquid Thrusters. The development of skills in liquid rocket propulsion can only pass through extensive test campaign. Following its mission, CIRA has planned the development of new testing facilities and infrastructures for space propulsion characterized by adequate sizes and instrumentation. The IMP test cell is devoted to testing articles representative of small combustion chambers, fed with oxygen and methane, both in liquid and gaseous phase. This article describes the activities that have been carried out for the evaluation of the acoustic impact, and its consequent mitigation. The impact of the simulated acoustic disturbance has been evaluated, first, using an approximated method based on experimental data by Baumann and Coney, included in “Noise and Vibration Control Engineering” edited by Vér and Beranek. This methodology, used to evaluate the free-field radiation of jet in ideal acoustical medium, analyzes in details the jet noise and assumes sources acting at the same time. It considers as principal radiation sources the jet mixing noise, caused by the turbulent mixing of jet gas and the ambient medium. Empirical models, allowing a direct calculation of the Sound Pressure Level, are commonly used for rocket noise simulation. The model named after K. Eldred is probably one of the most exploited in this area. In this paper, an improvement of the Eldred Standard model has been used for a detailed investigation of the acoustical impact of the Hyprob facility. This new formulation contains an explicit expression for the acoustic pressure of each equivalent noise source, in terms of amplitude and phase, allowing the investigation of the sources correlation effects and their propagation through wave equations. In order to enhance the evaluation of the facility acoustic impact, including an assessment of the mitigation strategies to be set in place, a more advanced simulation campaign has been conducted using both an in-house code for noise propagation and scattering, and a commercial code for industrial noise environmental impact, CadnaA. The noise prediction obtained with the revised Eldred-based model has then been used for formulating an empirical/BEM (Boundary Element Method) hybrid approach allowing the evaluation of the barrier mitigation effect, at the design. This approach has been compared with the analogous empirical/ray-acoustics approach, implemented within CadnaA using a customized definition of sources and directivity factor. The resulting impact evaluation study is reported here, along with the design-level barrier optimization for noise mitigation.

Keywords: acoustic impact, industrial noise, mitigation, rocket noise

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Authors: Parag Katira, Frederika Rentzeperis, Zuzanna Nowicka, Giada Fiandaca, Thomas Veith, Jack Farinhas, Noemi Andor

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Resource limitations shape the outcome of competitions between genetically heterogeneous pre-malignant cells. One example of such heterogeneity is in the ploidy (DNA content) of pre-malignant cells. A whole-genome duplication (WGD) transforms a diploid cell into a tetraploid one and has been detected in 28-56% of human cancers. If a tetraploid subclone expands, it consistently does so early in tumor evolution, when cell density is still low, and competition for nutrients is comparatively weak – an observation confirmed for several tumor types. WGD+ cells need more resources to synthesize increasing amounts of DNA, RNA, and proteins. To quantify resource limitations and how they relate to ploidy, we performed a PAN cancer analysis of WGD, PET/CT, and MRI scans. Segmentation of >20 different organs from >900 PET/CT scans were performed with MOOSE. We observed a strong correlation between organ-wide population-average estimates of Oxygen and the average ploidy of cancers growing in the respective organ (Pearson R = 0.66; P= 0.001). In-vitro experiments using near-diploid and near-tetraploid lineages derived from a breast cancer cell line supported the hypothesis that DNA content influences Glucose- and Oxygen-dependent proliferation-, death- and migration rates. To model how subpopulations with variable DNA content compete in the resource-limited environment of the human brain, we developed a stochastic state-space model of the brain (S3MB). The model discretizes the brain into voxels, whereby the state of each voxel is defined by 8+ variables that are updated over time: stiffness, Oxygen, phosphate, glucose, vasculature, dead cells, migrating cells and proliferating cells of various DNA content, and treat conditions such as radiotherapy and chemotherapy. Well-established Fokker-Planck partial differential equations govern the distribution of resources and cells across voxels. We applied S3MB on sequencing and imaging data obtained from a primary GBM patient. We performed whole genome sequencing (WGS) of four surgical specimens collected during the 1ˢᵗ and 2ⁿᵈ surgeries of the GBM and used HATCHET to quantify its clonal composition and how it changes between the two surgeries. HATCHET identified two aneuploid subpopulations of ploidy 1.98 and 2.29, respectively. The low-ploidy clone was dominant at the time of the first surgery and became even more dominant upon recurrence. MRI images were available before and after each surgery and registered to MNI space. The S3MB domain was initiated from 4mm³ voxels of the MNI space. T1 post and T2 flair scan acquired after the 1ˢᵗ surgery informed tumor cell densities per voxel. Magnetic Resonance Elastography scans and PET/CT scans informed stiffness and Glucose access per voxel. We performed a parameter search to recapitulate the GBM’s tumor cell density and ploidy composition before the 2ⁿᵈ surgery. Results suggest that the high-ploidy subpopulation had a higher Glucose-dependent proliferation rate (0.70 vs. 0.49), but a lower Glucose-dependent death rate (0.47 vs. 1.42). These differences resulted in spatial differences in the distribution of the two subpopulations. Our results contribute to a better understanding of how genomics and microenvironments interact to shape cell fate decisions and could help pave the way to therapeutic strategies that mimic prognostically favorable environments.

Keywords: tumor evolution, intra-tumor heterogeneity, whole-genome doubling, mathematical modeling

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Authors: Anne Schattel, Mitja Echim, Christof Büskens

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Trajectory planning for deep space missions has become a recent topic of great interest. Flying to space objects like asteroids provides two main challenges. One is to find rare earth elements, the other to gain scientific knowledge of the origin of the world. Due to the enormous spatial distances such explorer missions have to be performed unmanned and autonomously. The mathematical field of optimization and optimal control can be used to realize autonomous missions while protecting recourses and making them safer. The resulting algorithms may be applied to other, earth-bound applications like e.g. deep sea navigation and autonomous driving as well. The project KaNaRiA ('Kognitionsbasierte, autonome Navigation am Beispiel des Ressourcenabbaus im All') investigates the possibilities of cognitive autonomous navigation on the example of an asteroid mining mission, including the cruise phase and approach as well as the asteroid rendezvous, landing and surface exploration. To verify and test all methods an interactive, real-time capable simulation using virtual reality is developed under KaNaRiA. This paper focuses on the specific challenge of the guidance during the cruise phase of the spacecraft, i.e. trajectory optimization and optimal control, including first solutions and results. In principle there exist two ways to solve optimal control problems (OCPs), the so called indirect and direct methods. The indirect methods are being studied since several decades and their usage needs advanced skills regarding optimal control theory. The main idea of direct approaches, also known as transcription techniques, is to transform the infinite-dimensional OCP into a finite-dimensional non-linear optimization problem (NLP) via discretization of states and controls. These direct methods are applied in this paper. The resulting high dimensional NLP with constraints can be solved efficiently by special NLP methods, e.g. sequential quadratic programming (SQP) or interior point methods (IP). The movement of the spacecraft due to gravitational influences of the sun and other planets, as well as the thrust commands, is described through ordinary differential equations (ODEs). The competitive mission aims like short flight times and low energy consumption are considered by using a multi-criteria objective function. The resulting non-linear high-dimensional optimization problems are solved by using the software package WORHP ('We Optimize Really Huge Problems'), a software routine combining SQP at an outer level and IP to solve underlying quadratic subproblems. An application-adapted model of impulsive thrusting, as well as a model of an electrically powered spacecraft propulsion system, is introduced. Different priorities and possibilities of a space mission regarding energy cost and flight time duration are investigated by choosing different weighting factors for the multi-criteria objective function. Varying mission trajectories are analyzed and compared, both aiming at different destination asteroids and using different propulsion systems. For the transcription, the robust method of full discretization is used. The results strengthen the need for trajectory optimization as a foundation for autonomous decision making during deep space missions. Simultaneously they show the enormous increase in possibilities for flight maneuvers by being able to consider different and opposite mission objectives.

Keywords: deep space navigation, guidance, multi-objective, non-linear optimization, optimal control, trajectory planning.

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Authors: David A. Olasehinde, Peter I. Olasehinde, Segun M. A. Adelana, Dapo O. Olasehinde

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An investigation was carried out on underground water system dynamics within Ilorin metropolis to monitor the subsurface flow and its corresponding pollution. Africa population growth rate is the highest among the regions of the world, especially in urban areas. A corresponding increase in waste generation and a change in waste composition from predominantly organic to non-organic waste has also been observed. Percolation of leachate from non-engineered landfills, the chief means of waste disposal in many of its cities, constitutes a threat to the underground water bodies. Ilorin city, a transboundary town in southwestern Nigeria, is a ready microcosm of Africa’s unique challenge. In spite of the fact that groundwater is naturally protected from common contaminants such as bacteria as the subsurface provides natural attenuation process, groundwater samples have been noted to however possesses relatively higher dissolved chemical contaminants such as bicarbonate, sodium, and chloride which poses a great threat to environmental receptors and human consumption. The Geographic Information System (GIS) was used as a tool to illustrate, subsurface dynamics and the corresponding pollutant indicators. Forty-four sampling points were selected around known groundwater pollutant, major old dumpsites without landfill liners. The results of the groundwater flow directions and the corresponding contaminant transport were presented using expert geospatial software. The experimental results were subjected to four descriptive statistical analyses, namely: principal component analysis, Pearson correlation analysis, scree plot analysis, and Ward cluster analysis. Regression model was also developed aimed at finding functional relationships that can adequately relate or describe the behaviour of water qualities and the hypothetical factors landfill characteristics that may influence them namely; distance of source of water body from dumpsites, static water level of groundwater, subsurface permeability (inferred from hydraulic gradient), and soil infiltration. The regression equations developed were validated using the graphical approach. Underground water seems to flow from the northern portion of Ilorin metropolis down southwards transporting contaminants. Pollution pattern in the study area generally assumed a bimodal pattern with the major concentration of the chemical pollutants in the underground watershed and the recharge. The correlation between contaminant concentrations and the spread of pollution indicates that areas of lower subsurface permeability display a higher concentration of dissolved chemical content. The principal component analysis showed that conductivity, suspended solids, calcium hardness, total dissolved solids, total coliforms, and coliforms were the chief contaminant indicators in the underground water system in the study area. Pearson correlation revealed a high correlation of electrical conductivity for many parameters analyzed. In the same vein, the regression models suggest that the heavier the molecular weight of a chemical contaminant of a pollutant from a point source, the greater the pollution of the underground water system at a short distance. The study concludes that the associative properties of landfill have a significant effect on groundwater quality in the study area.

Keywords: dumpsite, leachate, groundwater pollution, linear regression, principal component

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Authors: Artur Tyliszczak, Ewa Szymanek, Maciej Marek

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Flow through granular materials is important to a vast array of industries, for instance in construction industry where granular layers are used for bulkheads and isolators, in chemical engineering and catalytic reactors where large surfaces of packed granular beds intensify chemical reactions, or in energy production systems, where granulates are promising materials for heat storage and heat transfer media. Despite the common usage of granulates and extensive research performed in this field, phenomena occurring between granular solid elements or between solids and fluid are still not fully understood. In the present work we analyze the heat exchange process between the flowing medium (gas, liquid) and solid material inside the granular layers. We consider them as a composite of isolated solid elements and inter-granular spaces in which a gas or liquid can flow. The structure of the layer is controlled by shapes of particular granular elements (e.g., spheres, cylinders, cubes, Raschig rings), its spatial distribution or effective characteristic dimension (total volume or surface area). We will analyze to what extent alteration of these parameters influences on flow characteristics (turbulent intensity, mixing efficiency, heat transfer) inside the layer and behind it. Analysis of flow inside granular layers is very complicated because the use of classical experimental techniques (LDA, PIV, fibber probes) inside the layers is practically impossible, whereas the use of probes (e.g. thermocouples, Pitot tubes) requires drilling of holes inside the solid material. Hence, measurements of the flow inside granular layers are usually performed using for instance advanced X-ray tomography. In this respect, theoretical or numerical analyses of flow inside granulates seem crucial. Application of discrete element methods in combination with the classical finite volume/finite difference approaches is problematic as a mesh generation process for complex granular material can be very arduous. A good alternative for simulation of flow in complex domains is an immersed boundary-volume penalization (IB-VP) in which the computational meshes have simple Cartesian structure and impact of solid objects on the fluid is mimicked by source terms added to the Navier-Stokes and energy equations. The present paper focuses on application of the IB-VP method combined with large eddy simulation (LES). The flow solver used in this work is a high-order code (SAILOR), which was used previously in various studies, including laminar/turbulent transition in free flows and also for flows in wavy channels, wavy pipes and over various shape obstacles. In these cases a formal order of approximation turned out to be in between 1 and 2, depending on the test case. The current research concentrates on analyses of the flows in dense granular layers with elements distributed in a deterministic regular manner and validation of the results obtained using LES-IB method and body-fitted approach. The comparisons are very promising and show very good agreement. It is found that the size, number of elements and their distribution have huge impact on the obtained results. Ordering of the granular elements (or lack of it) affects both the pressure drop and efficiency of the heat transfer as it significantly changes mixing process.

Keywords: granular layers, heat transfer, immersed boundary method, numerical simulations

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Authors: Sumeyra Karatas, Veysel Karatas, Reyhan Safak, Gamze Bulut-Ozturk, Ozgul Kartal

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Productive struggle entails a student's cognitive exertion to comprehend mathematical concepts and uncover solutions not immediately apparent. The significance of productive struggle in learning mathematics is accentuated by influential educational theorists, emphasizing its necessity for learning mathematics with understanding. Consequently, supporting productive struggle in learning mathematics is recognized as a high-leverage and effective mathematics teaching practice. In this study, the investigation into the role of productive struggle in learning mathematics led to the development of a comprehensive rubric for productive struggle pedagogy through an exhaustive literature review. The rubric consists of eight primary criteria and 37 sub-criteria, providing a detailed description of teacher actions and pedagogical choices that foster students' productive struggles. These criteria encompass various pedagogical aspects, including task design, tool implementation, allowing time for struggle, posing questions, scaffolding, handling mistakes, acknowledging efforts, and facilitating discussion/feedback. Utilizing this rubric, a team of researchers and teachers designed eight 90-minute lesson plans, employing a productive struggle pedagogy, for a two-week unit on solving systems of linear equations. Simultaneously, another set of eight lesson plans on the same topic, featuring identical content and problems but employing a traditional lecture-and-practice model, was designed by the same team. The objective was to assess the impact of supporting productive struggle on students' mathematics learning, defined by the strands of mathematical proficiency. This quasi-experimental study compares the control group, which received traditional lecture- and practice instruction, with the treatment group, which experienced a productive struggle in pedagogy. Sixty-six 10th and 11th-grade students from two algebra classes, taught by the same teacher at a high school, underwent either the productive struggle pedagogy or lecture-and-practice approach over two-week eight 90-minute class sessions. To measure students' learning, an assessment was created and validated by a team of researchers and teachers. It comprised seven open-response problems assessing the strands of mathematical proficiency: procedural and conceptual understanding, strategic competence, and adaptive reasoning on the topic. The test was administered at the beginning and end of the two weeks as pre-and post-test. Students' solutions underwent scoring using an established rubric, subjected to expert validation and an inter-rater reliability process involving multiple criteria for each problem based on their steps and procedures. An analysis of covariance (ANCOVA) was conducted to examine the differences between the control group, which received traditional pedagogy, and the treatment group, exposed to the productive struggle pedagogy, on the post-test scores while controlling for the pre-test. The results indicated a significant effect of treatment on post-test scores for procedural understanding (F(2, 63) = 10.47, p < .001), strategic competence (F(2, 63) = 9.92, p < .001), adaptive reasoning (F(2, 63) = 10.69, p < .001), and conceptual understanding (F(2, 63) = 10.06, p < .001), controlling for pre-test scores. This demonstrates the positive impact of supporting productive struggle in learning mathematics. In conclusion, the results revealed the significance of the role of productive struggle in learning mathematics. The study further explored the practical application of productive struggle through the development of a comprehensive rubric describing the pedagogy of supporting productive struggle.

Keywords: effective mathematics teaching practice, high school algebra, learning mathematics, productive struggle

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