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Full-Text Articles in Physical Sciences and Mathematics

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough May 2024

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough

Mechanical Engineering Undergraduate Honors Theses

Mechanical Exfoliation of Graphene is an often-overlooked portion of the fabrication of quantum devices, and to create more devices quickly, optimizing this process to generate better flakes is critical. In addition, it would be valuable to simulate test pulls quickly, to gain insight on flake quality of various materials and exfoliation conditions. Physical pulls of graphene at various temperatures, pull forces, and pull repetitions were analyzed and compared to the results of ANSYS simulations, solved for similar results. Using ANSYS’ ability to predict trends in exfoliations, flake thickness and coverage using stress and deflection analyses were investigated. Generally, both strongly …


Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley May 2024

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations & Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …


Using Cuticular Wax Alkanes And Computer Simulation To Estimate Diet Selection, Herbage Intake And Nutrient Cycling In Grazing Sheep, H Dove, R J. Simpson Mar 2024

Using Cuticular Wax Alkanes And Computer Simulation To Estimate Diet Selection, Herbage Intake And Nutrient Cycling In Grazing Sheep, H Dove, R J. Simpson

IGC Proceedings (1997-2023)

In grazing ewes, plant cuticular wax alkanes were used as markers to estimate diet selection, herbage intake, N intake and N excretion in faeces. Pasture and animal data were then used as inputs to the decision-support system GrazFeed, which simulates grazing and digestion to predict herbage intake, N intake and N excretion. Estimated and predicted intakes agreed closely, especially for N intake, and it is concluded that, subject to further investigation of the possibility that GrazFeed slightly under-estimated faecal N excretion, the close agreement between estimated and predicted OM and N intakes suggests that this combined use of alkane methods …


Modelling Leucaena Biomass Under Rainfed Production Systems Of Semiarid Regions, M. J. D. Cândido, J. L. G. Santos, A. C. R. Cavalcante, S. R. Maranhão, M. A. Santos, J. M. Osorio Leyton Jan 2024

Modelling Leucaena Biomass Under Rainfed Production Systems Of Semiarid Regions, M. J. D. Cândido, J. L. G. Santos, A. C. R. Cavalcante, S. R. Maranhão, M. A. Santos, J. M. Osorio Leyton

IGC Proceedings (1997-2023)

The climatic variability of semiarid regions is the main source of uncertainties associated with forage and animal production, indicating a need for tools that accurately estimate forage production in order to construct a forage budgeting plan for livestock. This study simulated the biomass of Leucaena (Leucaena leucocephala) using the PHYGROW model in four locations located in Brazilian Semiarid. The work was carried out based on field data collected from 2019 to 2021. After sowing in 2018, leucaena was harvested when it reached 200 cm and to a target residual height of 70 cm. The biomass (fresh matter) was …


Strategy Optimization Method Of Multi-Dimension Projection Based On Deep Reinforcement Learning, Jing An, Guangya Si, Lei Zhang Jan 2024

Strategy Optimization Method Of Multi-Dimension Projection Based On Deep Reinforcement Learning, Jing An, Guangya Si, Lei Zhang

Journal of System Simulation

Abstract: Based on the perfect performance of deep reinforcement learning (DRL) in strategy optimization, this paper proposes a strategy optimization method of action taking the multi-dimension projection action as the main research object. The method combines the simulation experiment method with the DRL method. After analyzing the current situation of strategy optimization research, the deep learning framework is selected according to the research problems, and a DRL multi-dimension projection strategy model based on the asynchronous advantage actor-critic (A3C) algorithm is constructed. Through simulation experiments, the interactive learning between the DRL model and the simulation of "out of the loop" is …


Blue Whale And Krill Populations Modeling, Li Zhang Jan 2024

Blue Whale And Krill Populations Modeling, Li Zhang

CODEE Journal

We present an intriguing topic in an undergraduate mathematical modeling course where predator-prey models are taught to our students. We describe modeling activities and the use of technology that can be implemented in teaching this topic. Through modeling activities, students are expected to use the numerical and graphical methods to observe the qualitative long-term behavior of predator and prey populations. Although there are other choices of predators and prey, we find that using blue whales and krill as predator and prey, respectively, would be most beneficial in strengthening our students' awareness of protecting endangered species and its impact on climate …


Integrating Climatological-Hydrodynamic Modeling And Paleohurricane Records To Assess Storm Surge Risk, Amirhosein Begmohammadi, Christine Y. Blackshaw, Ning Lin, Avantika Gori, Elizabeth Wallace, Kerry Emanuel, Jeffrey P. Donnelly Jan 2024

Integrating Climatological-Hydrodynamic Modeling And Paleohurricane Records To Assess Storm Surge Risk, Amirhosein Begmohammadi, Christine Y. Blackshaw, Ning Lin, Avantika Gori, Elizabeth Wallace, Kerry Emanuel, Jeffrey P. Donnelly

OES Faculty Publications

Sediment cores from blue holes have emerged as a promising tool for extending the record of long-term tropical cyclone (TC) activity. However, interpreting this archive is challenging because storm surge depends on many parameters including TC intensity, track, and size. In this study, we use climatological-hydrodynamic modeling to interpret paleohurricane sediment records between 1851 and 2016 and assess the storm surge risk for Long Island in The Bahamas. As the historical TC data from 1988 to 2016 is too limited to estimate the surge risk for this area, we use historical event attribution in paleorecords paired with synthetic storm modeling …


A New Method To Determine The Posterior Distribution Of Coefficient Alpha, John Mart V. Delosreyes Oct 2023

A New Method To Determine The Posterior Distribution Of Coefficient Alpha, John Mart V. Delosreyes

Psychology Theses & Dissertations

There is a focus within the behavioral/social sciences on non-physical, psychological constructs (i.e., constructs). These constructs are indirectly measured using measurement instruments that consist of questions that capture the manifestations of these constructs. The indirect nature of measuring constructs results in a need of ensuring that measurement instruments are reliable. The most popular statistic used to estimate reliability is coefficient alpha as it is easy to compute and has properties that make it desirable to use. Coefficient alpha’s popularity has resulted in a wide breadth of research into its qualities. Notably, research about coefficient alpha’s distribution has led to developments …


Cloud-Edge Collaborative Service Architecture For Lvc Training System, Peng Yong, Miao Zhang, Yue Hu Sep 2023

Cloud-Edge Collaborative Service Architecture For Lvc Training System, Peng Yong, Miao Zhang, Yue Hu

Journal of System Simulation

Abstract: LVC training, an important means of military training, has received great attention from military and M&S experts. As the virtual and physical elements become more abundant and deeply integrated, LVC training systems become increasingly complex. Aiming at physical-virtual connection, information interaction, simulation computation, run-time control, etc., this paper designs a cloud-edge collaborative service architecture for LVC training systems (CESA-LVC) by reference to cyber-physical systems and cloud-edge computing architectures. CESA-LVC standardizes the structures of LVC training systems from several aspects of intelligent real-time interconnection, joint simulation computation, training auxiliary service, training cognitive decision, and dynamic configuration optimization. It provides a …


Verifying Empirical Predictive Modeling Of Societal Vulnerability To Hazardous Events: A Monte Carlo Experimental Approach, Yi Victor Wang, Seung Hee Kim, Menas C. Kafatos Aug 2023

Verifying Empirical Predictive Modeling Of Societal Vulnerability To Hazardous Events: A Monte Carlo Experimental Approach, Yi Victor Wang, Seung Hee Kim, Menas C. Kafatos

Institute for ECHO Articles and Research

With the emergence of large amounts of historical records on adverse impacts of hazardous events, empirical predictive modeling has been revived as a foundational paradigm for quantifying disaster vulnerability of societal systems. This paradigm models societal vulnerability to hazardous events as a vulnerability curve indicating an expected loss rate of a societal system with respect to a possible spectrum of intensity measure (IM) of an event. Although the empirical predictive models (EPMs) of societal vulnerability are calibrated on historical data, they should not be experimentally tested with data derived from field experiments on any societal system. Alternatively, in this paper, …


Linking Community And Ecosystem Ecology By Developing A Grassland Ecosystem Model (Gemini) With Interactions Between Plant, Herbivore And Soil Microbial Populations, Jean-François Soussana, S. Witzmann, P. Loiseau, S. Fontaine, Pascal Carrère, Catherine Picon-Cochard, F. Louault Aug 2023

Linking Community And Ecosystem Ecology By Developing A Grassland Ecosystem Model (Gemini) With Interactions Between Plant, Herbivore And Soil Microbial Populations, Jean-François Soussana, S. Witzmann, P. Loiseau, S. Fontaine, Pascal Carrère, Catherine Picon-Cochard, F. Louault

IGC Proceedings (1997-2023)

Simulation models may help to understand the functional role of plant and soil biodiversity for C and N cycles and for intake by herbivores in semi-natural grassland ecosystems. Detailed models of grassland ecosystems calculate C, N, water and energy fluxes without accounting for the species dynamics in the plant and soil communities. Schwinning & Parsons (1996) proposed a simple pasture growth model that includes mixed grass and clover components. This model was, however, restricted to 2 plant functional groups and it excluded the dynamics of the soil organic matter. The role of competitive interactions between at least 2 functionally distinct …


Development Of A Model Simulating The Impact Of Management Strategies On Production From Beef Cattle Farming Systems Based On Permanent Pasture, M. Jouven, R. Baumont Aug 2023

Development Of A Model Simulating The Impact Of Management Strategies On Production From Beef Cattle Farming Systems Based On Permanent Pasture, M. Jouven, R. Baumont

IGC Proceedings (1997-2023)

Grazing systems in Europe increasingly have to meet environmental objectives, which influence management strategies. A deterministic model describing farming system dynamics is being developed in order to elucidate interactions between nature-friendly management practices, as for example late (after flowering) hay harvest or moderate stocking rate, and agricultural output.


Enhancing Grasslands Education With Decision Support Tools, Helen G. Daily, J. M. Scott, J. M. Reid Aug 2023

Enhancing Grasslands Education With Decision Support Tools, Helen G. Daily, J. M. Scott, J. M. Reid

IGC Proceedings (1997-2023)

We have successfully used Decision Support Tools (DST) relevant to the management of grazing enterprises to enhance problem solving skills of undergraduates in Australia. Tools such as GrassGrotm (Moore et al., 1997) and GrazFeedtm (Freer et al., 1997) are accessed from a central server by authorised users at many widely dispersed Universities across Australia using remote access to thin-client technology via an Internet portal. This has been supplemented with training for lecturers. Experience in developing appropriate teaching and learning materials and the reliable delivery of simulation software to many clients has enhanced learning outcomes at tertiary …


Systems Simulation Assists Land Capability Estimation In Australia’S Temperate Grasslands, Richard J. Simpson, L. Salmon, P. Graham, A. D. Moore, A. Stefanski, D. J. Marshall, J. R. Donnelly Aug 2023

Systems Simulation Assists Land Capability Estimation In Australia’S Temperate Grasslands, Richard J. Simpson, L. Salmon, P. Graham, A. D. Moore, A. Stefanski, D. J. Marshall, J. R. Donnelly

IGC Proceedings (1997-2023)

Intensification of production in the water-limited grasslands of temperate Australia has increased the need to quantify their sustainable carrying capacity. Empirical rainfall-based rules for estimating stocking rate fail when used in districts with differing weather patterns, or when soil and pasture resources limit the utilisation of rainfall. Grazing systems simulation should help to overcome these problems because local conditions can be taken into account. This study investigated the impact of soil resources on potential stocking rate, profitability and production risk in a local climatic area of the southern tablelands of NSW, Australia.


Comparing Elevator Strategies For A Parking Lot, Naveed Arafat Aug 2023

Comparing Elevator Strategies For A Parking Lot, Naveed Arafat

Major Papers

In this paper, we compare elevator strategies for a parking garage. It is assumed that the parking garage has several floors and there is an elevator which can stop on each floor. We begin by considering 4 strategies detailed in page 23. For each strategy, we loop the program 100 times, and get 100 mean values for wait times. Welch's test confirms highly significant differences among the 4 strategies. Repeating the analysis multiple times we see that the best of the 4 strategies is strategy 2, which places the elevator on floor 2 (the median floor) after use.


The Time-Dependent Ionospheric Model Using A Tec-Driven Servo: An Investigation Of The Capabilities And Limitations, Jenny Rebecca Whiteley Aug 2023

The Time-Dependent Ionospheric Model Using A Tec-Driven Servo: An Investigation Of The Capabilities And Limitations, Jenny Rebecca Whiteley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The ionosphere is a region of the atmosphere with a high density of electrons. These electrons affect the behavior of any electromagnetic wave that passes through the ionosphere. Communication and geolocation systems, such as traditional radio and Global Positioning Systems, depend on emitted electromagnetic signals being picked up by a receiver. The presence of the ionosphere affects the behavior of the signal and the quality of the service. Hence, the interactions between electromagnetic waves and the ionosphere provide a major motivation to understand, research, and successfully model and predict the ionosphere and its physical phenomena. This study focused on determining …


Numerical Design And Optimization Of Near-Infrared Band- Pass Filter, Hafiza Syeeda Faiza, Ghazi Aman Nowsherwan, Basem A. Abu Izneid, Muhammad Azhar, Saira Riaz, Syed Sajjad Hussain, Saira Ikram, Mohsin Khan, Shahzad Naseem, Mohammad Kanan, Ibrahim M. Mansour Jul 2023

Numerical Design And Optimization Of Near-Infrared Band- Pass Filter, Hafiza Syeeda Faiza, Ghazi Aman Nowsherwan, Basem A. Abu Izneid, Muhammad Azhar, Saira Riaz, Syed Sajjad Hussain, Saira Ikram, Mohsin Khan, Shahzad Naseem, Mohammad Kanan, Ibrahim M. Mansour

Applied Mathematics & Information Sciences

Band-pass filters functioning in the near-infrared (IR) range are desired for laser technology, multi-photon fluorescence, and IR imaging applications. In this study, we have designed four band-pass filters in the near Infrared spectrum (900-1200 nm) by vertically stacking different high and low-index materials. The band-pass filters are modelled by Essential Macleod software with different thicknesses. The layer’s thicknesses were optimized in such a way to provide the negligible reflectance and maximum transmission on the front side. All the simulated band-pass filters exhibit high transmittance, but TiO2/Al2O3 and Ta2O5/Al2O3 outperforms other modelled structure in terms of performance due to the better …


Evaluating The Economic And Environmental Sustainability Of Integrated Farming Systems, C. A. Rotz, M. A. Sanderson, M. Wachendorf, F. Taube Jun 2023

Evaluating The Economic And Environmental Sustainability Of Integrated Farming Systems, C. A. Rotz, M. A. Sanderson, M. Wachendorf, F. Taube

IGC Proceedings (1997-2023)

Economic and environmental sustainability has become a major concern for forage-based animal production in Europe, North America and other parts of the world. Development of more sustainable farming systems requires an assimilation of experimental and modelling research. Field research is critical for supporting the development and evaluation of models, and modelling is needed to integrate farm components for predicting the long-term effects and interactions resulting from farm management changes. Experimentally supported simulation provides a tool for evaluating and comparing farming strategies and predicting their effect on the watershed, region and beyond.


Identifying Advantages To Teaching Linear Regression In A Modeling And Simulation Introductory Statistics Curriculum, Kit Harris Clement Jun 2023

Identifying Advantages To Teaching Linear Regression In A Modeling And Simulation Introductory Statistics Curriculum, Kit Harris Clement

Dissertations and Theses

Statistical association is a key facet of statistical literacy: claims based on relationships between variables or ideas rooted in data are found everywhere in media and discourse. A key development in introductory statistics curricula is the use of simulation-based inference, which has shown positive outcomes for students, especially in regards to statistical literacy and conceptual understanding. In this dissertation project, I investigate students from the Change Agents for the Teaching and Learning of STatistics (CATALST) curriculum in activities I designed for learning statistical association and linear regression. First, I analyzed the informal line fitting strategies of CATALST students. Findings suggest …


A Monte-Carlo Simulation Of Gamma Rays In A Sodium Iodide Detector, Ben Kessler Jun 2023

A Monte-Carlo Simulation Of Gamma Rays In A Sodium Iodide Detector, Ben Kessler

Physics

Gamma rays principally interact with matter through Compton scattering, photoelectric effect, pair production, and triplet production. The focus of this simulation is to study the theoretical energy spectrum created by gamma rays from a Cesium-137 source, which produces gamma photons with an energy of 0.662 MeV. At this energy level, most interactions are results of Compton scatters and the photoelectric effect. Therefore, this simulation only models those two effects on gamma rays. Using Monte Carlo methods and the Metropolis algorithm to sample the probability distributions of the two effects allowed for the simulation of gamma rays in a Sodium Iodide …


Diffusion-Driven Aggregation Of Particles In Quasi-2d Membranes, Oscar Gullickson Rausis Jun 2023

Diffusion-Driven Aggregation Of Particles In Quasi-2d Membranes, Oscar Gullickson Rausis

Physics

Many biological membranes can be modeled as two-dimensional (2D) viscous fluid sheets surrounded by three-dimensional (3D) fluids of different viscosity. Such membranes are dubbed quasi-2D as they exhibit properties of both 2D and 3D fluids. The Saffman length is a parameter that describes the energy exchange between the membrane and bulk fluids and controls the cross-over from 2D to 3D hydrodynamics. We aim to model diffusion-driven aggregation of particles embedded in a quasi-2D membrane. It is known that hydrodynamic interactions between solute particles significantly reduce their aggregation rate in 3D fluids. It is expected that in quasi-2D membranes the reduction …


Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg Jun 2023

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …


A One-Dimensional Analysis Of A Microbial Fuel Cell For Efficient Acetate Removal And Power Density Output, David Rouhani May 2023

A One-Dimensional Analysis Of A Microbial Fuel Cell For Efficient Acetate Removal And Power Density Output, David Rouhani

UNLV Theses, Dissertations, Professional Papers, and Capstones

Microbial fuel cells (MFCs) are electrochemical devices that utilize microorganisms to convert organic matter into electrical energy. MFCs have been discussed to have potential application for sustainable wastewater treatment due to their ability to generate electricity while simultaneously treating contaminated water. To optimize MFC performance, numerical models can be used to understand the complex electrochemical and biological processes occurring in the system. In this study, a numerical model was developed to simulate the performance of MFCs under varying operating conditions and to investigate the performance of a MFC for treating wastewater fuel. More specifically, the MFC was modeled to oxidize …


Dpd Guided Insight On The Formation Process Of Polyethersulfone Membranes By Nonsolvent Induced Phase Separation And The Effects Of Additives, Eric Ledieu May 2023

Dpd Guided Insight On The Formation Process Of Polyethersulfone Membranes By Nonsolvent Induced Phase Separation And The Effects Of Additives, Eric Ledieu

Graduate Theses and Dissertations

Dissipative particle dynamics (DPD), a coarse grain simulation method, was applied to the membrane formation process of non-solvent induced phase separation (NIPS) to gain further insight on the mechanism of certain variables and how they affect the final morphology. NIPS involves two solutions, an organic polymer dissolved in an organic solvent colloquially called the dope and an aqueous coagulation bath, brought into contact with one another. The solvents then mix, causing the polymer to fall out of solution as an asymmetric membrane with a dense surface layer and a more open subsurface layer in response to the decreasing solubility. Polyethersulfone …


Analyzing And Computing Complete Solution For Dots And Boxes Game, Carl Mcaninch May 2023

Analyzing And Computing Complete Solution For Dots And Boxes Game, Carl Mcaninch

Graduate Dissertations and Theses

This thesis improves a process that analyzes all the states of a game of Dots and Boxes. We use retrograde analysis and simulations to create a solution that provides significant performance improvements over our previous best solution. Expanding upon a previous 4x4 solution using rotations, reflections, better optimization, and cloud computing to limit the processing time and gather more data efficiently. We compute a file and the number of states associated with each file and process every state starting with a completely filled board. We optimized the data for cloud computing by running simulations to find the most efficient number …


Vanet Applications Under Loss Scenarios & Evolving Wireless Technology, Adil Alsuhaim May 2023

Vanet Applications Under Loss Scenarios & Evolving Wireless Technology, Adil Alsuhaim

All Dissertations

In this work we study the impact of wireless network impairment on the performance of VANET applications such as Cooperative Adaptive Cruise Control (CACC), and other VANET applications that periodically broadcast messages. We also study the future of VANET application in light of the evolution of radio access technologies (RAT) that are used to exchange messages. Previous work in the literature proposed fallback strategies that utilizes on-board sensors to recover in case of wireless network impairment, those methods assume a fixed time headway value, and do not achieve string stability. In this work, we study the string stability of a …


Procedural City Generation With Combined Architectures For Real-Time Visualization, Griffin Poyck May 2023

Procedural City Generation With Combined Architectures For Real-Time Visualization, Griffin Poyck

All Theses

The work and research of this paper sought to build upon traditional city generation and simulation in creating a tool that both realistically simulates cities and their prominent features and also creates aesthetic and artistically rich cities using assets that combine several contemporary or near contemporary architectural styles. The major city features simulated are the surrounding terrain, road networks, individual buildings, and building placement. The tools used to both create and integrate these features were created in Houdini with Unreal Engine 5 as the intended final destination. This research was influenced by the city, town, and road networking of Ghost …


Modeling, Simulation And Control Of Microrobots For The Microfactory., Zhong Yang May 2023

Modeling, Simulation And Control Of Microrobots For The Microfactory., Zhong Yang

Electronic Theses and Dissertations

Future assembly technologies will involve higher levels of automation in order to satisfy increased microscale or nanoscale precision requirements. Traditionally, assembly using a top-down robotic approach has been well-studied and applied to the microelectronics and MEMS industries, but less so in nanotechnology. With the boom of nanotechnology since the 1990s, newly designed products with new materials, coatings, and nanoparticles are gradually entering everyone’s lives, while the industry has grown into a billion-dollar volume worldwide. Traditionally, nanotechnology products are assembled using bottom-up methods, such as self-assembly, rather than top-down robotic assembly. This is due to considerations of volume handling of large …


Uconn Baseball Batting Order Optimization, Gavin Rublewski, Gavin Rublewski May 2023

Uconn Baseball Batting Order Optimization, Gavin Rublewski, Gavin Rublewski

Honors Scholar Theses

Challenging conventional wisdom is at the very core of baseball analytics. Using data and statistical analysis, the sets of rules by which coaches make decisions can be justified, or possibly refuted. One of those sets of rules relates to the construction of a batting order. Through data collection, data adjustment, the construction of a baseball simulator, and the use of a Monte Carlo Simulation, I have assessed thousands of possible batting orders to determine the roster-specific strategies that lead to optimal run production for the 2023 UConn baseball team. This paper details a repeatable process in which basic player statistics …


Analyzing And Computing Complete Solution For Dots And Boxes Game, Carl Mcaninch Apr 2023

Analyzing And Computing Complete Solution For Dots And Boxes Game, Carl Mcaninch

Undergraduate Theses and Capstone Projects

This thesis improves a process that analyzes all the states of a game of Dots and Boxes. We use retrograde analysis and simulations to create a solution that provides significant performance improvements over our previous best solution. Expanding upon a previous 4x4 solution using rotations, reflections, better optimization, and cloud computing to limit the processing time and gather more data efficiently. We compute a file and the number of states associated with each file and process every state starting with a completely filled board. We optimized the data for cloud computing by running simulations to find the most efficient number …