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Physical Sciences and Mathematics Commons™
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- Optimization (7)
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- Deflection (3)
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Articles 1 - 30 of 180
Full-Text Articles in Physical Sciences and Mathematics
The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz
The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz
Undergraduate Journal of Mathematical Modeling: One + Two
For this project, I wanted to incorporate calculus into agriculture and environmental science methods. More in detail, the problem used asked for the maximum levels of nitrogen (N) and phosphorus (P) that would be best for a current crop yield. This allowed incorporating partial derivatives, and critical points to find the maximum values for the equation. The results show that in order to demonstrate maximum crop yield production, the levels of nitrogen (N) and phosphorus (P) were to be both at 2, with the correct corresponding units. The drawback from this problem is that although the problem showed effective nitrogen …
The Effects Of Effluent Discharge Into The Santa Fé River, João Vito Bezerra Dragone
The Effects Of Effluent Discharge Into The Santa Fé River, João Vito Bezerra Dragone
Undergraduate Journal of Mathematical Modeling: One + Two
The discharge of effluents into rivers is something that has occurred a lot throughout our history, rivers like the Mississippi River and the Tiete River (São Paulo, Brazil) have been targets for many years. Therefore, in this paper I choose to show, through hard data and some assumptions, the impact of sewage dumping in water bodies, in this case the Santa Fé River, Florida and the reason why we should avoid dumping these effluents into the rivers.
Internal Combustion Engines: Modeling Internal Temperature As A Function Of Time, Garrett Fandrich
Internal Combustion Engines: Modeling Internal Temperature As A Function Of Time, Garrett Fandrich
Undergraduate Journal of Mathematical Modeling: One + Two
Just like any thermodynamic system, combustion engines must be cooled to eliminate friction due to heat. Without proper cooling, internal components, such as connecting rods, rod bearings, and pistons can be severely damaged due to thermal expansion, leading to severe damage to the engine block or outright catastrophic failure. Modern engines are cooled using coolant, which flows through internal passageways within the engine block to pull heat away from the system. The use of coolant and external components, such as a water pump, radiator, and thermostat allow an engine to efficiently warm to standard operating temperature and remain at said …
The Distribution Of Energies, Dung Tien Do
The Distribution Of Energies, Dung Tien Do
Undergraduate Journal of Mathematical Modeling: One + Two
The application of calculus is of great importance in physics. It is used to calculate energy, acceleration, velocity, and much more. In this paper, to calculate the internal energy of an ideal gas (gas molecules) we will use Maxwell-Boltzmann statistical distribution based entirely on calculus. The technique represents the mathematical concept that depends on integration and substitution in calculus to solve a problem.
Application Of Calculus In The Elastic Curve (Deflection), Ryan Hillock
Application Of Calculus In The Elastic Curve (Deflection), Ryan Hillock
Undergraduate Journal of Mathematical Modeling: One + Two
Beams are extremely important structure members that are used in nearly every application where significant loads need to be supported. In mechanical and civil engineering being able to appropriately design beams to withstand the expected-to-be loads is a foundational skill. Proper beam design is what keeps large machines from failing and buildings from collapsing. One important aspect of beam design to consider is the deflection of the beam due to the applied loads. It is often useful to determine the deflection along any given point in the beam in order to make sure the loaded beam does not displace any …
Converting Velocity Pressure Into Cubic Feet Per Minute (Cfm), Darrian Robinette
Converting Velocity Pressure Into Cubic Feet Per Minute (Cfm), Darrian Robinette
Undergraduate Journal of Mathematical Modeling: One + Two
Almost every building in the United States has a HVAC (Heating, ventilation, and air conditioning) system that relies on balancing Velocity Pressure and calculated CFM to properly control the atmosphere in a building. This is ensured and tested by Field Engineers whose job it is to maintain the efficiency and proper output of these HVAC systems. These systems are used to improve indoor air quality, control moisture and condensation, and contaminants while satisfying comfort needs of occupants. Just with any mechanical system, HVAC systems function efficiently with multiple formulas derived from calculus and physics. Every building is equipped with a …
Volume And Cost Of Longboard Using Aircrete, Mira Stimac
Volume And Cost Of Longboard Using Aircrete, Mira Stimac
Undergraduate Journal of Mathematical Modeling: One + Two
This project utilizes integral calculus to find the volume of a longboard-style surfboard. The cost for using AirCrete as the material for the longboard will then be calculated. Due to the longboard's shape, the longboard is divided into four sections, and the volume of each is found. The final volume for the longboard with the measurements provided is approximately 3821 cubic inches. The cost of making the longboard out of AirCrete was then calculated by using ratios. The final cost for the longboard is $4.70.
Monitoring Drug Concentration In Emergency Medicine, Andrew Woods
Monitoring Drug Concentration In Emergency Medicine, Andrew Woods
Undergraduate Journal of Mathematical Modeling: One + Two
The careful monitoring of a drug’s concentration in the body of a patient is of the utmost importance in modern medicine. Many of the lifesaving medications that are administered in an emergency medicine environment have a narrow window of efficacy. This effective concentration is in an ever-changing state, as the body processes and eliminates exogenous compounds that are introduced to maintain homeostasis. To ensure the proper treatment and/or management of ailments, special attention must be given to the concentration of a given drug in the body as time progresses. These changing concentrations can be evaluated and tracked using the mathematical …
Area Of Irregular Shaped Roof, Omar Alkhawaldeh
Area Of Irregular Shaped Roof, Omar Alkhawaldeh
Undergraduate Journal of Mathematical Modeling: One + Two
This project makes use of calculus, specifically integration, to find the exact area of a roof garden to minimize the cost of material used in flooring it. Since the roof is of irregular shape, it is divided into four sections, the integral of each section is taken, and a relationship between the integrals is generated. Positive results are found, and the data reveal that the area of the grass floor is 175.3 m2 while the area of the wooden floor is 23.4 m2 with the total price being 2472 US dollars.
Using Calculus To Plan An Open-Air Concert, Timur Kalandarov
Using Calculus To Plan An Open-Air Concert, Timur Kalandarov
Undergraduate Journal of Mathematical Modeling: One + Two
A concert is a mass entertainment event held indoors, at concert halls, or outdoors (open-air festivals). These two formats differ greatly from each other. However, the goal of both events remains the same – to allow the audience to enjoy the musical performance. Indoor halls are designed for the best acoustics of sound. They are often circular and let sound waves travel around the inside of the building, like an echo bouncing back and forth. This makes the audience feel like they are surrounded by sound. Such places already have outlined spots for mounting music equipment with the highest efficiency. …
The Dangers Of Lift On Parked Planes: General Aviation Airport Safety, Robert Malloy
The Dangers Of Lift On Parked Planes: General Aviation Airport Safety, Robert Malloy
Undergraduate Journal of Mathematical Modeling: One + Two
The focus of this paper is to investigate proper aircraft management for safety on an airfield. This is accomplished by looking at lift caused by powerful winds to the aircrafts stored on an airfield, and the tension it places on the rope that secures them. This work could be used to determine when aircrafts are in high-risk and need to be stored either in hangars or moved to other airports prior to storms. The calculations used to determine these conclusions are also explored in the paper.
Mathematical Reconstruction Of A Traffic Crash, Benjamin Covert
Mathematical Reconstruction Of A Traffic Crash, Benjamin Covert
Undergraduate Journal of Mathematical Modeling: One + Two
The objective is to find the impact speeds of two motor vehicles involved in a traffic crash. The calculations take into account the approach (pre-collision) and departure (post collision) angles, as well as weights and post collision speeds of both vehicles. The data is provided by Timothy Sleyzack who investigated this traffic collision. The conclusions confirm the validity of the use of Conservation of Linear Momentum in the field of traffic crash reconstruction.
Calculating Probable Theoretical Offspring Genotype In Fruit Flies, Megan Keller
Calculating Probable Theoretical Offspring Genotype In Fruit Flies, Megan Keller
Undergraduate Journal of Mathematical Modeling: One + Two
Being able to calculate an offspring's theoretical genotype is critical in genetic sciences. We calculate the theoretical genotype and phenotype of fruit fly offspring. Using the product rule, we determine the probability for each trait and then for each genotype. In conclusion, we calculate 64 different genotypes that are supposed to be possible, but only 8 phenotypes are possible.
Emergency Communications Deficiency Locator, Austin Collins
Emergency Communications Deficiency Locator, Austin Collins
Undergraduate Journal of Mathematical Modeling: One + Two
The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall …
Analyzing Piney Point’S Wastewater Discharge Rate, Josephina Reyman
Analyzing Piney Point’S Wastewater Discharge Rate, Josephina Reyman
Undergraduate Journal of Mathematical Modeling: One + Two
Implicit differentiation is used in order to find the cubic feet of water dumped into Tampa Bay per hour from the Piney Point reservoir. To get to moles from cubic feet, a series of conversions is done while Le Chatelier’s principle explains how an increase in HPO4 2- (hydrogen phosphate) in Tampa Bay is going to affect algae growth. The rate of moles of HPO4 2- is analyzed as well as the consequences that come with dumping copious amounts of fertilizer water into an aquatic environment.
Evaluating The Improvement In Dna Fingerprinting, Dani Dray
Evaluating The Improvement In Dna Fingerprinting, Dani Dray
Undergraduate Journal of Mathematical Modeling: One + Two
DNA fingerprinting is a forensic technique used to create patterns that are unique to a person’s DNA. Previously, these fingerprints were made from 13 different segments of DNA, but today they are made from the 20 ones. The fundamental principle of counting is used to determine how much of an improvement was made after adding the 7 additional DNA segments. It is found that this addition greatly reduces the likelihood of two people having the same exact fingerprint, therefore improving the accuracy and reliability of DNA fingerprinting.
Predicting The Cost Of Dental Care Using A Probability Model, Nadine Wehbe
Predicting The Cost Of Dental Care Using A Probability Model, Nadine Wehbe
Undergraduate Journal of Mathematical Modeling: One + Two
This paper uses survey data to present a probability model that allows dental offices to predict patient costs. The quantitative model is useful for developing and accepting capitation rates. It accounts for whether the care is initial care or maintenance care, the type of dental care (such as operative, prosthetics, or periodontics), and different age groups, all of which affect the cost of dental treatment.
Possible Contamination From Rainwater In Community Pool, David Mcgregor
Possible Contamination From Rainwater In Community Pool, David Mcgregor
Undergraduate Journal of Mathematical Modeling: One + Two
The project is meant to create an equation that can be used to estimate the amount of organic pollutant – bacteria - that is present in a swimming pool per day from rainwater. This equation is derived through a differential equation of the rate in minus the rate out. The created differential equation is an ordinary linear differential equation and is solved using an integration factor. The general solution is then converted into a specific equation using an initial condition. The resulting equation provides an approximate number of organic contaminants x(t) present in the pool after an …
Volume And Cost Of Cylindrical Shaped Silo With Conical Roof, Gabriel Mitzakoff Parola
Volume And Cost Of Cylindrical Shaped Silo With Conical Roof, Gabriel Mitzakoff Parola
Undergraduate Journal of Mathematical Modeling: One + Two
This project utilizes integral calculus to find the exact volume of a non-uniform cylindrical-shaped silo used to store wheat and calculate the cost of material utilized to build such silo. Due to its non-uniform shape, the silo is divided into two sections and the volume of each is calculated. The final volume for the silo with the measurements provided is approximately 2330.02 meters cubic and surface area of 1074.96 meters squared, which is considered to be a large capacity silo. With such a large capacity silo there are costs to be considered, such as the material cost which is calculated …
Calculating The Probability Of Constitutional Isomers Of Pentane, Mary-Margaret Dare
Calculating The Probability Of Constitutional Isomers Of Pentane, Mary-Margaret Dare
Undergraduate Journal of Mathematical Modeling: One + Two
Depending on the reagent, and orientation of collisions within a chemical reaction, organic molecules can be present as different constitutional isomers of the same molecule. We can analyze the likelihood of getting a mixture of pentane with certain conformers. Based on this, we find that there are 16 potential conformers, but 13 are identical structures, meaning only three are distinct from each other. Using the product rule, we then demonstrate how to go about calculating the probability of specific conformers, including specific identical structures, being present in a mixture, and then we demonstrate that process is strictly within the three …
Surge Functions And Drug Interactions, Olta Tarko
Surge Functions And Drug Interactions, Olta Tarko
Undergraduate Journal of Mathematical Modeling: One + Two
The objective of this project is to analyze how surge functions work to understand the way drug concentration levels in the bloodstream of a human body vary over time after an initial dose. A surge function increases rapidly at the beginning of the dosage and drops slowly after it reaches its peak. It is important to realize when a certain drug reaches its peak and how long the effects will last on a patient, so a second drug can be administered without risking negative interactions. We explain the calculations used in order to properly understand the curve of a drug’s …
Moment Of Inertia In Applied Calculus, Saad Habib
Moment Of Inertia In Applied Calculus, Saad Habib
Undergraduate Journal of Mathematical Modeling: One + Two
This paper demonstrates the usefulness of calculus in structural/continuum mechanics. Calculus in structural/continuum mechanics is used to calculate mass, volume, centre of mass, moment of inertia and in solutions of differential equations. In this paper, we will use calculus to calculate moment of inertia. The area moment of inertia of a surface measures the resistance to deflection of the cross section to bending or buckling. Moment of inertia is used by engineers of inertia to determine the state of stress in a cross section and the amount of inertia. It represents a mathematical concept that depends on the size and …
Calculating The Area Within The Orbit Of Arrokoth, Aurielle Collins
Calculating The Area Within The Orbit Of Arrokoth, Aurielle Collins
Undergraduate Journal of Mathematical Modeling: One + Two
The area within the orbit of the Kuiper Belt object (KBO) Arrokoth (or 2014MU69) is approximated using the corresponding ellipse. The fact that the Sun lies at a focus of the ellipse is of interest. Attention is made to the known deviations of orbits from their models. It is at least of interest that the ellipse model is still essentially valid. Theoretically, if there were only the Sun and Arrokoth in the Universe, the orbit would be precisely described by the ellipse model.
Probabilistic Machine Learning Using Bayesian Inference, Mayank Pandey
Probabilistic Machine Learning Using Bayesian Inference, Mayank Pandey
Undergraduate Journal of Mathematical Modeling: One + Two
Machine Learning is a branch of AI (Artificial Intelligence) which expands on the idea of a computational system extending its knowledge about set methodical behaviors from the data that is fed to it to essentially develop analytical skills that can help in identifying patterns and making decisions with little to no participation of a real human being. Computer algorithms help in gaining experience to improve the facility over time for use by both consumers and corporations. In today’s technologically advanced world, Machine Learning has given us self-driving cars, speech recognition software, and AI agents like Siri and Google assistant. This …
The Relationship Between Suicide Rates And Mental Health Provider Ratio, Christian Bates
The Relationship Between Suicide Rates And Mental Health Provider Ratio, Christian Bates
Undergraduate Journal of Mathematical Modeling: One + Two
This project is an analysis of the relationship between suicide rates and mental health provider ratio within the United States. Data from 2018 are collected for each state regarding its suicide rate, mental health provider ratio, and percent of population unable to receive treatment for mental health problems. An initial analysis is made using suicide rates and mental health provider ratio, with no correlation being found. A second analysis is conducted, using multiple linear regression with the percent of individuals within each state who were unable to access treatment for their mental health problems being the confounding variable. Controlling for …
A Mathematical Modeling Of Infrared Neural Stimulation, Cesil S. Alex
A Mathematical Modeling Of Infrared Neural Stimulation, Cesil S. Alex
Undergraduate Journal of Mathematical Modeling: One + Two
Electrical stimulation is the gold standard for artificial neural stimulation. The greatest disadvantage with electrical stimulation is that it scatters in space and it is difficult to achieve specific point stimulation. Recently, infrared stimulation attracted attention to address this issue. Infrared stimulation works on the principle of heating the tissue, exploiting the energy of infrared lasers to heat the cellular aqueous solution that helps transfer the energy to the cell membrane without direct contact, and provides a discrete localization of stimulation as it does not spread in space like electric fields. In the present study, a heat transfer model for …
Prosthetic Leg Model, Dang Nguyen
Prosthetic Leg Model, Dang Nguyen
Undergraduate Journal of Mathematical Modeling: One + Two
The main goal of this paper is to introduce an imitated prosthetic leg model by analyzing the applied forces. Even though the model is based on the idea of a prosthetic leg, it is also applicable to people without disabilities. The same concept of the model can be seen in the circus, where a person maintains a balanced state while on an incredible height without falling. When all the applying forces in the system are calculated, the design achieves the ideal state which allows it to function most effectively. One of the essential factors applied to the imitated prosthetic leg …
An Exploration Of Wind Energy, Bianca De Haan
An Exploration Of Wind Energy, Bianca De Haan
Undergraduate Journal of Mathematical Modeling: One + Two
Wind energy is renewable energy extrapolated from the wind that has the potential to revolutionize our power supply in the near future as fossil fuels become outdated. Wind turbines capture the energy as the wind spins the blades of the turbine, transforming wind energy into mechanical energy and then into electrical energy through a generator. One of the techniques utilized to understand wind energy is to manipulate various variables in the formula for wind power. These variables such as the power coefficient, wind velocity, number and length of blades are explored to find its optimal value. The variable of turbine …
Finding The Growth Rate Of A Tumor, Christine Staat
Finding The Growth Rate Of A Tumor, Christine Staat
Undergraduate Journal of Mathematical Modeling: One + Two
The Gompertz method is used to analyze the growing glioblastoma data and estimate how accurate the results of growth over time are. The Gompertz curve is expressed as V(t) = αe-βe-γt. The data from the tumor is graphed in Excel along with the values from the Gompertz equation. Excel solver is used to assist in determining the constant values of α, β, and γ. The data of the tumor is overall very close to the outcome of the Gompertz model following a sigmoidal “S” curve.
Optimization Of Handicap Ramp, Tyler Schilling
Optimization Of Handicap Ramp, Tyler Schilling
Undergraduate Journal of Mathematical Modeling: One + Two
The objective of this project is to minimize the cost of building a handicap ramp. This is done by introducing an equation that represents the total cost of the construction, including labor and materials. Variables are then defined in terms of block length l, allowing for an equation with one variable to be graphed and derived. This equation then undergoes the first derivative test to find a value of l that would create a minimum output for cost. This value is then compared to the physical constraints of the project allowing for a realistic minimum cost to be found. …