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Full-Text Articles in Physical Sciences and Mathematics

Do Limestone Quarries Act As “Engineered Sinkholes”? Analysis Of Exfiltration Of Groundwater From Limestone Quarries In The Boone Formation, Ozark Physiographic Province, Arkansas, Usa, Noel Turner Aug 2016

Do Limestone Quarries Act As “Engineered Sinkholes”? Analysis Of Exfiltration Of Groundwater From Limestone Quarries In The Boone Formation, Ozark Physiographic Province, Arkansas, Usa, Noel Turner

Graduate Theses and Dissertations

Limestone quarries are a source of construction materials that are utilized in our everyday lives. Karst landscapes cover up to 15 percent of the Earth’s surface, and limestone quarries are found in these environmentally sensitive regions where groundwater and surface-water interactions are dynamic and complex. Several studies have provided conceptual models of groundwater flow to and out of quarries. The goal of this research was to describe the geochemistry of water exfiltration from limestone quarries in karst regions via joints, fractures, faulting, or karst features and to determine if limestone quarries are “engineered sinkholes”; that is to say: did quarries, …


Determination Of Optimum Fall And Spring Nitrogen Fertilizer Rate For Maximizing Grain Yield Of Soft Red Winter Wheat Sown At Variable Planting Dates, Lucas Vasconcelos Vieira Aug 2016

Determination Of Optimum Fall And Spring Nitrogen Fertilizer Rate For Maximizing Grain Yield Of Soft Red Winter Wheat Sown At Variable Planting Dates, Lucas Vasconcelos Vieira

Graduate Theses and Dissertations

An optimum planting date is important for winter wheat nitrogen (N) management as it dramatically changes the growing environment including temperature and moisture, ultimately affecting fertilizer efficiency and grain yield (GY). In Arkansas, high precipitation in the fall often forces farmers to delay planting and current Arkansas recommendations include the application of fall N when soft red winter wheat (SRWW) is sown later than optimum, despite the lack of data supporting this practice. This study evaluated the effect of rate and timing of N application on GY of SRWW sown at variable planting dates in Arkansas. Granular urea was split …


Initial Structural Subsidence As Reflected In Morrowan And Atokan (Pennsylvanian) Subsurface Stratigraphy, Northern Arkoma Basin, North-Central Arkansas, Fatimah Taher Nahi Al Asadi Aug 2016

Initial Structural Subsidence As Reflected In Morrowan And Atokan (Pennsylvanian) Subsurface Stratigraphy, Northern Arkoma Basin, North-Central Arkansas, Fatimah Taher Nahi Al Asadi

Graduate Theses and Dissertations

The Arkoma Basin is a carboniferous foreland basin that is known for its prolific gas production. The objective of this research is to study the initial subsidence of the basin by analyzing the strati-graphic and structural features of the study area. This was accomplished through IHS Petra, Surf-er 13, and Win-Tensor software. Field work studies comprised a large part of this study. Also, a seismic profile and Google earth elevation profiles are among the methods used to study the initial subsidence of the Arkoma Basin. The study area within the basin represents a transitional zone from the shelf into the …


Conformally Invariant Operators In Higher Spin Spaces, Chao Ding Aug 2016

Conformally Invariant Operators In Higher Spin Spaces, Chao Ding

Graduate Theses and Dissertations

In this dissertation, we complete the work of constructing arbitrary order conformally invariant operators in higher spin spaces, where functions take values in irreducible representations of Spin groups. We provide explicit formulas for them.

We first construct the Dirac operator and Rarita-Schwinger operator as Stein Weiss type operators. This motivates us to consider representation theory in higher spin spaces. We provide corrections to the proof of conformal invariance of the Rarita-Schwinger operator in [15]. With the techniques used in the second order case [7, 18], we construct conformally invariant differential operators of arbitrary order with the target space being degree-1 …


Implications For The North American Lower Crustal 7.Xx Km/S Layer From An Exhumed Crustal Root, Western Canadian Shield, Calvin Everette Johnson Aug 2016

Implications For The North American Lower Crustal 7.Xx Km/S Layer From An Exhumed Crustal Root, Western Canadian Shield, Calvin Everette Johnson

Graduate Theses and Dissertations

Studies of the Thorsby magnetic low, the southern extent of the 2,800 km-long Snowbird

Tectonic Zone (STZ) in Alberta, Canada, show pronounced lower crustal seismic reflectivity and preservation of a crustal root. These features may be correlative to the well-exposed central STZ, where two lower crustal tectonic events have been identified at 2.6-2.55 Ga and 1.92-1.89 Ga. High-resolution cross-sections of the central STZ reveal the late-stage interaction of Paleoproterozoic intracontinental thrust and strike-slip shear zones responsible for juxtaposing ca. >20,000 km2 of lower continental crust (0.9-1.5 GPa) with middle continental crust (0.5 GPa) (Mahan and Williams, 2005; Dumond et al., …


The Role Of Organic Matter In The Fate And Transport Of Antibiotic Resistance, Metals, And Nutrients In The Karst Of Northwest Arkansas, Victor Lee Roland Ii Aug 2016

The Role Of Organic Matter In The Fate And Transport Of Antibiotic Resistance, Metals, And Nutrients In The Karst Of Northwest Arkansas, Victor Lee Roland Ii

Graduate Theses and Dissertations

Organic matter (OM) in the environment acts as a nutrient, but may also act as a transport vector for harmful chemical compounds and bacteria. Acetate is a labile form of OM produced during fermentation in anaerobic lagoons used to store animal fecal-waste from concentrated animal feeding operations (CAFOs). Dry and liquid fertilizers from CAFOs pose a threat to groundwater by introducing excessive amounts of nutrients (e.g. OM, nitrate and ammonia), metals, and antibiotic compounds. In the epikarst of Northern Arkansas in the Buffalo River watershed additional input of labile dissolved organic carbon (DOC) from liquid CAFO waste-fertilizers was hypothesized to …


Investigation Of The Interaction Of Dimeric Ruthenium Complexes With Cytochrome B5, Christopher Dain Rupar Aug 2016

Investigation Of The Interaction Of Dimeric Ruthenium Complexes With Cytochrome B5, Christopher Dain Rupar

Graduate Theses and Dissertations

Photoreactive complexes to study the kinetics of electron transfer of proteins have been in use for a long time. It has always been speculated that complexes bind near the heme or the electron transfer reaction would not occur. But it is unkown exactly how the complex interacts with the protein. The structural, thermodynamic, and kinetic properties of rat liver microsomal cytochrome b5 were investigated when bound to ruthenium dimer complexes. Heteronuclear Single Quantum Coherence studies support a dynamic binding model of a dimer Ru complex bound near the protein’s heme involving residues H39, E44, G42, V61, G62, and H63. The …


Studies In The Asymmetric Synthesis Of The C21-C34 Fragment Of The Natural Product, Antascomicin B, Brian Lee Walker Aug 2016

Studies In The Asymmetric Synthesis Of The C21-C34 Fragment Of The Natural Product, Antascomicin B, Brian Lee Walker

Graduate Theses and Dissertations

This dissertation describes studies in the asymmetric synthesis of the C21 – C34 fragment of the natural product, antascomicin B. Antascomicin B is structurally related to FK506, binds strongly to FKBP12, yet does not shown immunosuppressive activity. Small ligand FKBP12 binding complexes were shown to have potent neuroprotective and neuroregenerative properties in mouse models of Parkinson’s disease. The highlighted chemical reactions include an asymmetric transfer hydrogenation (ATH), Ireland-Claisen rearrangement (ICR), directed hydrogenation and allylic diazene rearrangement.


3d Seismic Interpretation Of Paleokarst Sinkholes, Boone Limestone, Lower Mississippian: Subsurface Eastern Arkoma Basin, Conway County, Arkansas, Daniel James Moser Aug 2016

3d Seismic Interpretation Of Paleokarst Sinkholes, Boone Limestone, Lower Mississippian: Subsurface Eastern Arkoma Basin, Conway County, Arkansas, Daniel James Moser

Graduate Theses and Dissertations

Unconventional natural gas discoveries in the Fayetteville Shale of the eastern Arkoma Basin have led to improved understanding of subsurface geology in central Arkansas. This study interprets 3D seismic data for evidence of paleokarst within the Mississippian formations in a portion of the subsurface of Conway County, Arkansas. Quantitative data interpretation suggests that sinkholes developed during the Mississippian portion of the eastern Arkoma Basin record.

In a nine square mile area, 3D seismic mapping of Mississippian formations show 14 closed depressions interpreted as karst sinkholes. Time and depth structure maps were created and utilized to estimate the timing of dissolution …


The Impact Of Climate Change In Bangladesh On The Rice Market And Farm Households, Mst Ashrafun Nahar Aug 2016

The Impact Of Climate Change In Bangladesh On The Rice Market And Farm Households, Mst Ashrafun Nahar

Graduate Theses and Dissertations

Bangladesh is trying to achieve self-sufficiency in domestic rice production but climate change effects on agricultural production makes it challenging to attain the goal. The country is highly vulnerable to the effects of climate change since it is the major cause to rise in sea level, more warm summer, and happening food and cyclone in the country.

This study develops an Aggregate Farm Household Model to analyze the impact of potential land loss and yield reduction from climate change on production, consumption, prices, welfare, and the ability of government to achieve self-sufficiency in rice production. The model is calibrated to …


Photoluminescence Measurement On Low-Temperature Metal Modulation Epitaxy Grown Gan, Yang Wu Aug 2016

Photoluminescence Measurement On Low-Temperature Metal Modulation Epitaxy Grown Gan, Yang Wu

Graduate Theses and Dissertations

A low-temperature photoluminescence (PL) study was conducted on low-temperature metal modulation epitaxy (MME) grown GaN. By comparing the PL signal from high temperature grown GaN buffer layers, and MME grown cap layers on top of the buffer layers, it was found that MME grown GaN cap has a significantly greater defect-related emission. The band edge PL from MME grown GaN found to be 3.51eV at low temperature. The binding energy of the exciton in GaN is determined to be 21meV through temperature dependence analysis. A PL peak at 3.29eV was found in the luminescence of the MME grown cap layer, …


Early And Middle Atokan Lithostratigraphy And Reservoir Development, Northern Arkoma Basin, Northwestern Arkansas, Matthew Alan Blaylock Aug 2016

Early And Middle Atokan Lithostratigraphy And Reservoir Development, Northern Arkoma Basin, Northwestern Arkansas, Matthew Alan Blaylock

Graduate Theses and Dissertations

The Arkoma Basin is a peripheral foreland arc basin associated with the Ouachita orogenic belt. In Arkansas, the basin is bounded by the Ouachita belt to the south and the Ozark Dome to the north. Sedimentary rocks of early to middle Atokan age are present in the shallow subsurface at the northern margin of the Arkoma Basin in northwestern Arkansas. Sedimentary units of this time interval reflect basinal subsidence, and the transition of the Arkoma Basin from a passive margin shelf to a rapidly evolving foreland arc basin. Sediment sources from the north and east produced a thickened Lower and …


Mechanism Of Rapid Electron Transfer Reactions Involving Cytochrome Bc1, Cytochrome C And Cytochrome Oxidase, Jeremy Erik Durchman Aug 2016

Mechanism Of Rapid Electron Transfer Reactions Involving Cytochrome Bc1, Cytochrome C And Cytochrome Oxidase, Jeremy Erik Durchman

Graduate Theses and Dissertations

Electron transfer between mitochondrial proteins complexes represents the primary means by which living things acquire the requisite energy for survival. The coupling of electron transfer to proton translocation creates an electrochemical gradient that drives the synthesis of highly energetic compounds such as ATP. The purpose of these studies is to measure rates of electron transfer and elucidate the important governing factors in the redox events involving cytochrome bc1, cytochrome c and cytochrome oxidase. Using rapid initiation of redox events triggered by laser flash excitation of ruthenium compounds, and strategically monitoring unique spectral properties of these proteins in the visible region …


Asbestos Cement Pipe Condition Assessment And Remaining Service Life Prediction, Abiy Melles Ghirmay Aug 2016

Asbestos Cement Pipe Condition Assessment And Remaining Service Life Prediction, Abiy Melles Ghirmay

Graduate Theses and Dissertations

This research details a condition assessment of asbestos cement (AC) pipe within in the Bella Vista Village Property Owners Association water distribution system. Bella Vista Village contains appropriately 300 miles of AC pipe with nominal diameters from 6-14 inch. The goal of the research is to determine the current condition of AC pipe within the system and predict future performance of the pipes. AC pipe samples were obtained from 23 locations disturbed across the distribution system with nominal pipe diameters of 6-8 inch. Estimates of current level of degradation were obtained using phenolphthalein staining and hardness measurements of each sample. …


Heparin-Peptide Interactions, Jacqueline Anastasia Morris Aug 2016

Heparin-Peptide Interactions, Jacqueline Anastasia Morris

Graduate Theses and Dissertations

Heparin is a polydispersed sulfated molecule that is part of the family called glycosaminoglycans found in the extracellular matrix and cell surfaces. This molecule is extremely important for the activation of proteins and protein-receptor interactions that are responsible for downstream cell signaling pathways. Heparin has been isolated from porcine intestine and used as an anticoagulant for the prevention of embolisms, heart thrombosis, and clotting during heart surgeries. This so-called miracle drug was in use until 2008, when isolated batches were found to be contaminated with other glycosaminoglycans similar to heparin. From 2008, there has been a dire need for a …


Bella Vista Lakes Project: Fertility Management, J. Thad Scott Jun 2016

Bella Vista Lakes Project: Fertility Management, J. Thad Scott

Technical Reports

No abstract provided.


A Support Vector Machine Base Model For Predicting Heparin-Binding Proteins Using Biological Metrics And Xb Patterns As Features, Joseph W. Sirrianni May 2016

A Support Vector Machine Base Model For Predicting Heparin-Binding Proteins Using Biological Metrics And Xb Patterns As Features, Joseph W. Sirrianni

Computer Science and Computer Engineering Undergraduate Honors Theses

Heparin is a highly sulphated and negatively charged polysaccharides belonging to the glycosamino- glycans(GAGs) family. It is widely used in medical treatments as an injectable anticoagulant. Although many heparin-binding proteins have been identified through experimental studies, there are still many proteins needing to be classified as heparin-binding or not. Many studies have been aimed at prediction of heparin binding patterns or motifs in the primary structure of proteins. For example XBBXBX and XBBBXXBX are two well-known patterns or motifs. In spite of intensive studies, still no good model has emerged which reasonably predicts proteins in the protein database as heparin-binding …


Acceleration Of Ddscat Computation By Parallelization On A Supercomputer, Manoj V. Seeram May 2016

Acceleration Of Ddscat Computation By Parallelization On A Supercomputer, Manoj V. Seeram

Chemical Engineering Undergraduate Honors Theses

The DDSCAT software is enabled for use of MPI or OpenMP to distribute calculation of different particle orientations amongst multiple processors on a high performance system. Run times for these simulations have been tested to take hours or days however and simulating varying orientations is not always necessary. If a simulation with only one particle orientation is submitted, DDSCAT could still potentially parallelize the simulation by wavelength calculations but it is unknown if this is the case. In this paper, we will be (i) quantifying the reduction in computation time that MPI provides relative to an equivalent MPI disabled simulation …


Nitrogen And Phosphorus Enrichment Effects On Nutrient Supply In Reservoirs: A Small-Scale Approach, Jessalyn G. Kohn May 2016

Nitrogen And Phosphorus Enrichment Effects On Nutrient Supply In Reservoirs: A Small-Scale Approach, Jessalyn G. Kohn

Crop, Soil and Environmental Sciences Undergraduate Honors Theses

Eutrophication is a problem in many lakes, but the reduction of nutrient inputs such as nitrogen (N) and phosphorus (P) to combat eutrophication can lead to an oligotrophic state, which may be unable to support healthy aquatic ecosystems. This study examined how different rates of chemical fertilization with N and P during times of nutrient limitation (mid-summer) could affect particulate N and C concentrations in four lakes in northwest Arkansas. Fertilization experiments were conducted in microcosms during the month of July 2014. Water samples from each lake were collected and divided into six treatments: control, P-only, N:P 10, 20, 40, …


Validation Of An Internal Camera Based Volume Determination System For Triaxial Testing, Leah D. Miramontes May 2016

Validation Of An Internal Camera Based Volume Determination System For Triaxial Testing, Leah D. Miramontes

Civil Engineering Undergraduate Honors Theses

Accurate strain and volume measurements are critical to phase relationships and strength determination for saturated and unsaturated soils. In recent years, laboratory-based photographic techniques of monitoring soil specimens have become more common. These techniques have been used to reconstruct 3D models and to determine strain and volumetric changes of triaxial specimens. A new technique that utilized digital photographs of the soil specimen, captured from within a triaxial testing cell, was utilized. Photographs were processed using photogrammetry software to reconstruct 3D models of the soil specimens. By placing camera equipment within the cell, the technique eliminated the need to account for …


Cfd Model For Ventilation In Broiler Holding Sheds, Christian Heymsfield May 2016

Cfd Model For Ventilation In Broiler Holding Sheds, Christian Heymsfield

Biological and Agricultural Engineering Undergraduate Honors Theses

Broiler production in Arkansas was valued at over $3.6 billion in 2013 (University of Arkansas Extension of Agriculture). Consequently, improvement in any phase of the production process can have significant economic impact and animal welfare implications. From the time poultry leave the farm and until they are slaughtered, they can be exposed to harsh environmental conditions, both in winter and in summer. After road transportation, birds are left to wait in holding sheds once they arrive at the processing plant, for periods of approximately 30 minutes to two hours. This project was interested in this holding shed waiting time during …


Microdialysis Studies Using Porcine Pancreatic Elastase To Guide Mathematical Modeling Of Microdialysis Sampling For In Vivo Measurements., Mason W. Young May 2016

Microdialysis Studies Using Porcine Pancreatic Elastase To Guide Mathematical Modeling Of Microdialysis Sampling For In Vivo Measurements., Mason W. Young

Biomedical Engineering Undergraduate Honors Theses

Microdialysis sampling uses a semi-permeable membrane to allow solute collection by diffusion. When used in conjunction with other instruments, analytes in question can be quantified. Matrix Metalloproteinases (MMPs) are enzymes involved in numerous biological processes where they serve the role of degrading extracellular matrix. Microdialysis sampling, in coordination with further analysis methods, can be used in order to measure the activity of these enzymes in a region of the body instantaneously. The intention of this project is to determine ways of measuring in vitro activity of elastase from porcine pancreas using determined activity values and the collection of elastase products. …


Synthesis Of Microgel Polymers As Catalysts, Hannah N. Miller May 2016

Synthesis Of Microgel Polymers As Catalysts, Hannah N. Miller

Chemistry & Biochemistry Undergraduate Honors Theses

New developments in organic synthesis show promise in achieving the best catalytic properties for the hydrolysis of glycosidic bonds through microgel polymers and transition metal complexes. A monomer mix of ethylene glycol dimethacrylate, butyl acrylate, and styrene form miniemulsion polymers after sonication and exposure to UV light. Gravimetrical analysis is used to determine the most suitable polymerization conditions by performing experiments at varying pH values, temperatures, monomer amounts, initiator amounts, and lamp heights. The final data show that the best polymerization conditions are a pH of 10.50 at 0°C with a high monomer ratio, 20% initiator amount, and a lamp …


Improving Photocatalytic Activity By Appending A Quinone To Ruthenium Polypyridyl Complex, Amy N. James May 2016

Improving Photocatalytic Activity By Appending A Quinone To Ruthenium Polypyridyl Complex, Amy N. James

Chemistry & Biochemistry Undergraduate Honors Theses

By converting natural light energy into chemical energy, chemists are studying ways to take advantage of clean energy. The rising precedence of “green chemistry” has led to academic interest in the activity of photocatalysts and harnessing visible light in an efficient, accessible, and safe manner. Photochemistry is an upcoming and fascinating field of study that has made significant progress, but also has great potential for future work. By utilizing light as a natural energy source, many reaction processes in chemistry can be viewed with a new perspective. Ru(bpy)32+ is one of the most widely used photocatalysts. An efficient …


Staphylococcal Nuclease And Ubiquitin Local Folding Energies And Rates Using Peps-Hdx-Esi-Ms, Julie Rhee May 2016

Staphylococcal Nuclease And Ubiquitin Local Folding Energies And Rates Using Peps-Hdx-Esi-Ms, Julie Rhee

Chemistry & Biochemistry Undergraduate Honors Theses

In this study, Protein Equilibrium Population Snapshot Hydrogen-Deuterium Exchange Electrospray Ionization Mass Spectrometry (PEPS-HDX-ESI-MS) was applied to study the local regions of model proteins, staphylococcal nuclease and ubiquitin. The hydrogen deuterium exchange (HDX) has become a key technique for studying the structural and dynamic aspects of proteins in solution. This technique creates a rapid exchange between all of the exchangeable hydrogen ions with deuterium when the protein is exposed to a solvent. The PEPS method is an equilibrium-based method used to determine the populations of the closed native and open denatured states of a protein. By combining the applications of …


Regulation Of The Reaction Between Cytochrome C And Cytochrome Oxidase, Jennifer Silva-Nash May 2016

Regulation Of The Reaction Between Cytochrome C And Cytochrome Oxidase, Jennifer Silva-Nash

Chemistry & Biochemistry Undergraduate Honors Theses

Irreversible brain damage is commonly seen in patients that have suffered strokes, cardiac arrest, or other brain ischemia events. The hypoxic conditions result in neuron death, and previous studies have shown that additional damage occurs when blood flow is restored. It is thought that the lack of energy production during post-ischemia events also causes severe brain damage, as the brain heavily depends on oxidative phosphorylation. Cytochrome c (Cyt c) plays a crucial role in this energy production by means of the electron transport chain (ETC), transferring electrons between complexes ΙΙΙ (cytochrome bc1) and ΙV (cytochrome c oxidase, CcO). Mitochondrial …


A Geochemical Analysis Of The Arkansas Novaculite And Comparison To The Siliceous Deposits Of The Boone Formation, John Byron Scott Philbrick May 2016

A Geochemical Analysis Of The Arkansas Novaculite And Comparison To The Siliceous Deposits Of The Boone Formation, John Byron Scott Philbrick

Graduate Theses and Dissertations

Geochemical analyses of the Arkansas Novaculite, located within core structures of the Ouachita Mountains in west-central Arkansas, and penecontemporaneous chert of the lower Boone Formation, located atop the Springfield Plateau of southwest Missouri, northwest Arkansas, and northeast Oklahoma, have identified a significant concentration of both aluminum and potassium. This would seem to eliminate a biogenic origin and favor a volcanic source of the silica that comprises these units. Trace and rare earth element (REE) analysis also suggests that the Arkansas Novaculite and the chert in the lower Boone Formation may have both been formed from the same volcanic source.

The …


Ant Colony Optimization For Continuous Spaces, Rachel Findley May 2016

Ant Colony Optimization For Continuous Spaces, Rachel Findley

Computer Science and Computer Engineering Undergraduate Honors Theses

Ant Colony Optimization (ACO) is an optimization algorithm designed to find semi-optimal solutions to Combinatorial Optimization Problems. The challenge of modifying this algorithm to effectively optimize over a continuous domain is one that has been tackled by several researchers. In this paper, ACO has been modified to use several variations of the algorithm for continuous spaces. An aspect of ACO which is crucial to its success when optimizing over a continuous space is choosing the appropriate object (solution component) out of an infinite set to add to the ant's path. This step is highly important in shaping good solutions. Important …


Developing A Risk Analysis Model To Improve Study Abroad Awareness, Tyler Spain May 2016

Developing A Risk Analysis Model To Improve Study Abroad Awareness, Tyler Spain

Industrial Engineering Undergraduate Honors Theses

As international education opportunities increase in popularity among U.S. college students (McMurtrie, 2007), it is becoming more and more necessary for study abroad organizations to be aware of the risks students face as they travel abroad. While some international cities are riskier than others, it can be difficult to distinguish between cities which truly carry a high degree of risk for visiting students, and which cities are only perceived to be risky based on various personal misconceptions. The University of Arkansas Office of Study Abroad & International Exchange currently lacks a way to quantifiably analyze the risk of study abroad …


Nanoscale Frictional Properties Of Nickel With One-Dimensional And Two-Dimensional Materials, Timothy K. Schlenger May 2016

Nanoscale Frictional Properties Of Nickel With One-Dimensional And Two-Dimensional Materials, Timothy K. Schlenger

Mechanical Engineering Undergraduate Honors Theses

When looking at the nanoscale, material interface interactions have been observed to exhibit particularly interesting properties. Our research looks into various combinations of carbyne and graphene atop a nickel block to look into the interface friction properties between them. Both the carbyne and graphene are tested using steered molecular dynamics (SMD) in sheering and peeling directions along the surface of the nickel block. These tests are then analyzed by comparing the magnitude of the acting force versus the displacement of the carbon allotrope sample across the nickel block. It is found that as the width of a carbon allotrope sample …