Physical Sciences and Mathematics Commons^™

Variational Iteration Method For The Burgers' Flow With Fractional Derivatives—New Lagrange Multipliers, Guo-Cheng Wu, Dumitru Baleanu

G.C. Wu

The flow through porous media can be better described by fractional models than the classical ones since they include inherently memory effects caused by obstacles in the structures. The variational iteration method was extended to find approximate solutions of fractional differential equations with the Caputo derivatives, but the Lagrange multipliers of the method were not identified explicitly. In this paper, the Lagrange multiplier is determined in a more accurate way and some new variational iteration formulae are presented.

Computing Immutable Regions For Subspace Top-K Queries, Kyriakos Mouratidis, Hwee Hwa Pang

Research Collection School of Information Systems (Open Access)

Given a high-dimensional dataset, a top-k query can be used to shortlist the k tuples that best match the user’s preferences. Typically, these preferences regard a subset of the available dimensions (i.e., attributes) whose relative significance is expressed by user-specified weights. Along with the query result, we propose to compute for each involved dimension the maximal deviation to the corresponding weight for which the query result remains valid. The derived weight ranges, called immutable regions, are useful for performing sensitivity analysis, for finetuning the query weights, etc. In this paper, we focus on top-k queries with linear preference ...

Discovering Divergence: A Framework For Finding Unexpected Behavior Using Directed Exploration, Heath G. Roehr

Computer Science and Engineering: Theses, Dissertations, and Student Research

Systems that are written to achieve the same high level specifications can vary in subtle ways. Depending on a programmer's objective, using one variant of a program or algorithm over another may be beneficial, and this objective may change over time. However we do not have sufficient techniques to compare two different system variants side-by-side to find specific behavioral differences, particularly in the absence of source code. Assuming two system implementations take the same inputs and produce the same outputs or exhibit the same behavior under most conditions, we want to find input instances where the behavior diverges for ...

Airborne Dual-Polarization Observations Of The Sea-Surface Nrcs At C-Band In High Winds, Joseph W. Sapp, Stephen J. Frasier, Jason Dvorsky, Paul S. Chang, Zorana Jelenak

Joseph W Sapp

Airborne dual-polarization observations of sea-surface normalized radar cross-section (NRCS) were conducted over the North Atlantic during Jan–Feb 2011. Observations were made using the University of Massachusetts’ Imaging Wind and Rain Airborne Profiler (IWRAP) radar system installed on the National Oceanic and Atmospheric Administration’s (NOAA) WP-3D research aircraft during several winter storm events to determine the high-wind response of the sea-surface NRCS for both horizontal and vertical polarizations. During the flights, the aircraft performed several constant-roll circle maneuvers to allow collection of NRCS over a range of incidence angles. We find consistency with prior reports in the polarization ratio ...

Raman Spectroscopic Analysis Of Human Skin Tissue Sections Ex-Vivo: Evaluation Of The Effects Of Tissue Processing And Dewaxing, Syed Mehmood Ali, Franck Bonnier, Ali Tfayli, Helen Lambkin, Kathleen Flynn, Vincent Mcdonagh, Claragh Healy, Thomas Lee, Fiona Lyng, Hugh Byrne

Articles

Raman spectroscopy coupled with K-means clustering analysis (KMCA) is employed to elucidate the biochemical structure of human skin tissue sections, and the effects of tissue processing. Both hand and thigh sections of human cadavers were analysed in their unprocessed and formalin fixed paraffin processed (FFPP) and subsequently dewaxed forms. In unprocessed sections, KMCA reveals clear differentiation of the stratum corneum, intermediate underlying epithelium and dermal layers for sections from both anatomical sites. The stratum corneum is seen to be relatively rich in lipidic content; the spectrum of the subjacent layers is strongly influenced by the presence of melanin, while that ...

Spring­11: Pdc In Cs1/2 And A Mobile/Cloud Intermediate Mobile/Cloud Intermediate Software Design Course, Joseph P. Kaylor, Konstantin Läufer, Chandra N. Sekharan, George K. Thiruvathukal

Computer Science: Faculty Publications & Other Works

Recent changes in the environment of Loyola University Chicago’s Department of Computer Science include a better differentiation of our four undergraduate majors, growing interest in computing among science majors, and an increased demand for graduates with mobile and cloud skills. In our continued effort to incorporate parallel and distributed computing topics into the undergraduate curriculum, we are focusing on these three existing courses:

CS1: In response to a request from the physics department, we started to offer a CS1 section aimed at majors in physics and other hard sciences this spring semester. This section includes some material on numerical ...

Probing The Low Temperature Oxidation Of Furanic Biofuels, 2-Methyltetrahydrofuran And 2,5-Dimethylfuran, Utilizing Orthogonal Time-Of-Flight Mass Spectrometry Coupled To Synchrotron Radiation, Matthew Mcmanus

Master Theses

Concern over natural resources and global climate shifts has increased the focus of sourcing transportation fuels from depleting oil wells to regenerative, biological based solutions. One avenue of biologically sourced fuel involves the extraction of C5 and C6 sugars from the woody, fibrous, and inedible plant materials, otherwise known as lignocellulosic biomass. These cellulosic sugars can be converted to target biofuels and biofuel additives like the furanic compounds, 2,5-dimethylfuran and 2-methylfuran. In this thesis, the low temperature oxidation of two compounds, 2,5-dimethylfuran and 2-methylfuran, are explored. These reactions were conducted at the Advanced Light Source in Berkeley, CA ...

Balancing Score Adjusted Targeted Minimum Loss-Based Estimation, Samuel D. Lendle, Bruce Fireman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment specific mean with ...

Speleothem Laminae Counting And Growth Rate, Corey Wilson

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to determine if there is a correlation between annual laminae in speleothems and Uranium dating. To do this, we counted laminae using high-resolution images and calculated a line of the best fit for the resulting data. We found that our data could supplement Uranium dating, but unless more data is obtained, laminae counting gives relatively imprecise age and growth rate estimates.

Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald

Undergraduate Journal of Mathematical Modeling: One + Two

In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research ...

The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project was to determine the area-to-depth relationship in Lake Behnke, which acts as the principal stormwater drainage basin for the University of South Florida campus in Tampa, Florida. Data previously collected in a stormwater management study by Jeffery Earhart illustrated a linear correlation between the lake's area and depth; however, that study was conducted in 1998, and this present work serves to double check that correlation. We analyzed a bathymetric map of Lake Behnke that displayed several contour lines indicating depth and approximated the area inside each closed curve with a contour integral. The resulting ...

Overfishing Of The Common Snook, Allison Ashcroft

Undergraduate Journal of Mathematical Modeling: One + Two

The chief aim of this project is to determine if the populations of the common snook, Centropomus Undecimalis, in the Atlantic and Gulf coast are being affected by overfishing. This is established by evaluating the intrinsic rate of change for these populations and their carrying capacities. It turns out that the carrying capacity for the population of the Atlantic coast is approximately one million snook and its intrinsic rate is 0.00621, while the carrying capacity of the Gulf coast's population is 2.9 million snook and its intrinsic rate is 0.00165. The decline of both populations is ...

Complexity Of Mitochondrial Genome Sequences, Brandon Toun

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to compare the complexities of different species' mitochondrial genome sequences. Using an implementation of Deflate compression algorithm from Java standard library, we were able to compress mitochondrial genomes of nine different species. The complexity of each sequence is estimated as a ratio of the original sequence length to the length of the compressed sequence. In addition, we show how a notion of topological entropy from symbolic dynamics can be used as another complexity measure of nucleotide sequences.

The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon

Undergraduate Journal of Mathematical Modeling: One + Two

The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum ...

U.S. Oil Reserves And Peak Oil, Trang Luong

Undergraduate Journal of Mathematical Modeling: One + Two

We use calculus methods to estimate the quantity of U.S. oil reserves. We consider a model that consists of an exponential function with four unknown constants. We fit real oil production data to determine the unknown constants. With the constants determined we use the function to find the year in which the U.S. oil production reached its peak. We also estimate the amount of petroleum produced until the end of 2006, and the undiscovered oil reserves to be produced in the future.

Average Light Intensity Inside A Photobioreactor, Herby Jean

Undergraduate Journal of Mathematical Modeling: One + Two

For energy production, microalgae are one of the few alternatives with high potential. Similar to plants, algae require energy acquired from light sources to grow. This project uses calculus to determine the light intensity inside of a photobioreactor filled with algae. Under preset conditions along with estimated values, we applied Lambert-Beer's law to formulate an equation to calculate how much light intensity escapes a photobioreactor and determine the average light intensity that was present inside the reactor.

Model For Facial Cooling, Jacalyn Sampson

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to estimate the ambient temperature and the wind speed that cause painful sensation in a cheek. Our findings confirm that the higher the wind speed, the less cold air is required to cause cheek pain.

Optimal Operation Of A Concentrator, Katrina Stine

Undergraduate Journal of Mathematical Modeling: One + Two

Concentrators are used in the industrial world to remove water from a chemical or substance by heating the liquid until the water evaporates thereby concentrating the remaining substance. The goal of this project is to find the optimum cycle time, number of cycles per year, and the heating element area that would minimize the total annual cost and hours of operation of an industrial concentrator. It was found that the specified concentrator would achieve a minimum total cost of $48,720.50 per year and take 993.8 hours to meet the production goal of evaporating one million kilograms of ...

Design Of A Rainwater Catchment System, Neil Cammardella

Undergraduate Journal of Mathematical Modeling: One + Two

Certain dimensions of a rainwater catchment and storage system were optimized using climatological and sociological data. Using only daily demand and average daily rain fall data, the following dimensions were optimized: 1) The horizontal roof area needed to collect the daily demand of water, 2) The tank size needed to store all the water collected during a heavy rain event, 3) When full, how long the tank will be able to provide water without rain, and 4) The diameter of the outlet flow orifice. With these calculations, we can design a rainwater catchment system that can capture the daily demand ...

Going Ballistic: Bullet Trajectories, Amanda Wade

Undergraduate Journal of Mathematical Modeling: One + Two

This project seeks to answer at what angle does a gun marksman have to aim in order to hit the center of a target one meter off the ground and 1000 meters away? We begin by modeling the bullet's trajectory using Euler's method with the help of a Microsoft Excel spreadsheet solver, and then systematically search for the angle corresponding to the center of the target. It was found that a marksman shooting a target 1000 meters away and 1 meter off the ground has to aim the rifle 0.436° above horizontal to hit the center.

Length Of A Hanging Cable, Eric Costello

Undergraduate Journal of Mathematical Modeling: One + Two

The shape of a cable hanging under its own weight and uniform horizontal tension between two power poles is a catenary. The catenary is a curve which has an equation defined by a hyperbolic cosine function and a scaling factor. The scaling factor for power cables hanging under their own weight is equal to the horizontal tension on the cable divided by the weight of the cable. Both of these values are unknown for this problem. Newton's method was used to approximate the scaling factor and the arc length function to determine the length of the cable. A script ...

Optimization Of A Pressure-Treating Process, Josean Velez

Undergraduate Journal of Mathematical Modeling: One + Two

A company that pressure-treats wood wants to minimize its annual cost without using more than 250 days of operation per year. In addition, they want to find the corresponding value of time, batches and cost for each category. We develop an expression in terms of boards per batch to model the total cost of the treatment process. We then take the derivative and use Newton's Method to find the number of boards per batch that minimizes total cost.

The Effects Of Age On Short-Term Memory Loss Due To Proactive Interference, Alisha Berkauzer

Undergraduate Journal of Mathematical Modeling: One + Two

This project focused on how proactive interference affects the short-term memory of people based on their age. The goal was to find the prime age for learning information and storing it in one's memory. Seven people from ages fifteen to forty were tested individually, using a set color pattern, in order to see how well each individual could remember the different color patterns as difficulty of the pattern increased. The obtained data was fitted by the polynomial regression. The “fitted” curve shows that as age increases, the individual's performance in memorizing the more difficult patterns decreases. Also, the ...

Comparison Of First Gear Performance For Manual And Automatic Transmissions, Kyle Stottlemyer

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to compare the first gear performance of an automobile for both its manual and automatic transmission options. Each transmission type has a different gear ratio, which yields a different acceleration curve for each transmission throughout the torque-rpm curve of the engine. The method of integral calculus was used to find an equation which could be used to solve for time at any point in the car's acceleration. The automobile velocity versus time was then graphed to compare each transmissions acceleration trend. This process is similar to that which automotive companies may use when ...

Arc Length Of A Pipe Needed For A Directional Drill, Kenneth Cabana

Undergraduate Journal of Mathematical Modeling: One + Two

Underground contracting has come a long way in recent years. As communities and buildings are being built, services like water, sewer, and gas are needed to allow people to perform their day to day activities. This research has led to the idea and design of a way to find the arc length of the pipe put into the ground at given points. The pipe length was estimated using the formulas for distance and arc length together with two different modeling methods: Lagrange interpolation and polynomial regression. Both techniques yielded similar results; however this may be situational and in other circumstances ...

Blood Glucose Levels, Carlos Estela

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this study was to establish a mathematical model which can be used to estimate glucose levels in the blood over time. The equations governing this process were manipulated with the use of techniques such as separation of variables and integration of first order differential equations, which resulted in a function that described the glucose concentration in terms of time. This function was then plotted, which allowed us to find when glucose concentration was at its highest. The model was then used to analyze two cases where the maximum glucose level could not exceed a certain level while ...

Study Of Consciousness, Samuel Lee

Undergraduate Journal of Mathematical Modeling: One + Two

The human brain is a powerful organ that controls most of the body. Researchers around the world have long tried to uncover how the brain operates, how memories are formed and stored. Our understanding of neurological diseases such as Alzheimer's and Parkinson's disease has been rapidly improving, yet much remains to be done. In this work, we attempt to study changes in intracranial pressure (ICP) for a 12-hour period and discuss whether the resulting estimates could be used as a measure of consciousness.

Sizing Of An Ammonia Discharge Tank, Tuliagenda Beckfords

Undergraduate Journal of Mathematical Modeling: One + Two

Phosphate companies use well-stirred tanks to regulate the concentration of ammonia they discharge via their wastewater, preventing ammonia spikes from exceeding the cap set by the Environmental Protection Agency. This report discusses the methods used to determine the minimum possible volume of the tank required to regulate wastewater discharge. With this information, it was determined that the use of a stirring tank is an efficient and cost effective way to regulate ammonia discharge. Based on these results many other companies may use this method to decrease the negative effects of ammonia on the environment.

Pallet Physics, Lauren Woodbridge

Undergraduate Journal of Mathematical Modeling: One + Two

This project explores whether it is safe to unload a 907kg pallet from a supply truck with a bed 1.5m off the ground by sliding it down a metal ramp. First we calculated the critical angle for which the pallet would overcome the friction of the wood on the metal and begin to slide. Next we calculated velocity of the pallet as it reaches the bottom of the ramp. Finally we calculate the distance the pallet travels on the concrete after leaving the ramp. Based on these calculations of acceleration, velocity, and displacement, we conclude that it would not ...

Optimization Of A Wall Built On A Slope, John Hanna

Undergraduate Journal of Mathematical Modeling: One + Two

This project focuses on optimizing the construction of a wall with identical segments built on a slope. Faced with certain variable and fixed cost limitations, one can find the width of a segment that will minimize the total production cost. In this case, the lowest total cost comes from using 10 segments of width 3m.