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Articles 1591 - 1620 of 36223

Full-Text Articles in Physical Sciences and Mathematics

Sers Platform For Single Fiber Endoscopic Probes, Debsmita Biswas Nov 2022

Sers Platform For Single Fiber Endoscopic Probes, Debsmita Biswas

LSU Doctoral Dissertations

Molecular detection techniques have huge potential in clinical environments. In addition to many other molecular detection techniques, endoscopic Raman spectroscopy has great ability in terms of minimal invasiveness and real-time spectra acquisition. However, Raman Effect is low in sensitivity, limiting the application. Surface-Enhanced Raman Scattering (SERS), addresses this limitation. SERS brings rough nano-metallic surfaces in contact with specimen molecules which enormously enhances Raman signals. This provides Raman spectroscopy with immense capabilities for diverse fields of applications.

Generally, in clinical probe applications, the spectrometer is brought near the target molecules for detection. Typically, optical fibers are used to couple spectrometers to …


Searches For Ultra-High-Energy Photons At The Pierre Auger Observatory, The Pierre Auger Collaboration, B. Fick, D. Nitz, I. Norwood, A. Puyleart, Et Al. Nov 2022

Searches For Ultra-High-Energy Photons At The Pierre Auger Observatory, The Pierre Auger Collaboration, B. Fick, D. Nitz, I. Norwood, A. Puyleart, Et Al.

Michigan Tech Publications

No abstract provided.


Experimental Evidence That Shear Bands In Metallic Glasses Nucleate Like Cracks, Alan A. Long, Wendelin Wright, Xiaojun Gu, Anna Thackray, Mayisha Nakib, Jonathan T. Uhl, Karin A. Dahmen Nov 2022

Experimental Evidence That Shear Bands In Metallic Glasses Nucleate Like Cracks, Alan A. Long, Wendelin Wright, Xiaojun Gu, Anna Thackray, Mayisha Nakib, Jonathan T. Uhl, Karin A. Dahmen

Faculty Journal Articles

Highly time-resolved mechanical measurements, modeling, and simulations show that large shear bands in bulk metallic glasses nucleate in a manner similar to cracks. When small slips reach a nucleation size, the dynamics changes and the shear band rapidly grows to span the entire sample. Smaller nucleation sizes imply lower ductility. Ductility can be increased by increasing the nucleation size relative to the maximum (“cutoff”) shear band size at the upper edge of the power law scaling range of their size distribution. This can be achieved in three ways: (1) by increasing the nucleation size beyond this cutoff size of the …


Review Of Structural Color In The Genus Chrysochroa Dejean, 1833 (Coleoptera: Buprestidae), Able Chow Nov 2022

Review Of Structural Color In The Genus Chrysochroa Dejean, 1833 (Coleoptera: Buprestidae), Able Chow

LSU Master's Theses

The jewel beetles, (Coleoptera: Buprestidae Leach, 1815), is the eighth most speciose coleopteran family, with the majority of its members possessing diverse bright, saturated structural coloration of multilayer origin. This study focuses on the genus Chrysochroa Dejean, 1833, which includes some of the most brilliantly and charismatically colored buprestid species. While members of Chrysochroa are prised by entomologists amateurs and professional and are well-represented in museum collections, the evolution and ecology of their structural color remain underexplored. Twenty-eight select taxa including exemplars from all 13 subgenera of Chrysochroa were investigated to provide an overview of the objective optical properties and …


An Interactive Simulation And Visualization Tool For Conventional And Aberration-Corrected Transmission Electron Microscopy, Xingzhong Li Nov 2022

An Interactive Simulation And Visualization Tool For Conventional And Aberration-Corrected Transmission Electron Microscopy, Xingzhong Li

Nebraska Center for Materials and Nanoscience: Faculty Publications

Contrast transfer function (CTF) is a vital function in transmission electron microscopy (TEM). It expresses to what extent amplitudes converted from the phase changes of the diffracted waves contribute to the TEM image, including the effects of lens aberrations. Simulation is very helpful to understand the application of the function thoroughly. In this work, we develop the CTFscope as a component in the Landyne software suite, to calculate the CTF with temporal and spatial dumping envelopes for conventional TEM and to extend it to various aberrations (up to fifth order) for aberration-corrected (AC)- TEM. It also includes effects on the …


College Of Natural Sciences Newsletter, September & October 2022, College Of Natural Sciences Nov 2022

College Of Natural Sciences Newsletter, September & October 2022, College Of Natural Sciences

College of Natural Sciences Newsletters and Reports

Volume 3, Issue 6

Page 1 Dean's Message
Page 2 Awards & Recognition
Page 3 Midwest Regional ACS Meeting
Page 4 North Central ASM Meeting
Page 5 Geography Department Travel
Page 6-7 Media Coverage of CNS
Page 7 REMAST Program at SDState receives national spotlight
Page 8 Celebrating the lives of those who touched the College
Page 9 Innovative Learning Spaces
Page 10 Open PRAIRIE Data
Page 11 2022 CNS Scholarship Brunch
Page 12-14 Fall 2022 Outreach Events


Domain Wall Enabled Steep Slope Switching In Mos2 Transistors Towards Hysteresis-Free Operation, Jingfeng Song, Yubo Qi, Zhiyong Xiao, Kun Wang, Dawei Li, Seung-Hyun Kim, Angus I. Kingon, Andrew M. Rappe, Xia Hong Nov 2022

Domain Wall Enabled Steep Slope Switching In Mos2 Transistors Towards Hysteresis-Free Operation, Jingfeng Song, Yubo Qi, Zhiyong Xiao, Kun Wang, Dawei Li, Seung-Hyun Kim, Angus I. Kingon, Andrew M. Rappe, Xia Hong

Department of Physics and Astronomy: Faculty Publications

The device concept of ferroelectric-based negative capacitance (NC) transistors offers a promising route for achieving energyefficient logic applications that can outperform the conventional semiconductor technology, while viable operation mechanisms remain a central topic of debate. In this work, we report steep slope switching in MoS2 transistors back-gated by single-layer polycrystalline PbZr0.35Ti0.65O3. The devices exhibit current switching ratios up to 8 × 106 within an ultra-low gate voltage window of Vg = ±0:5 V and subthreshold swing (SS) as low as 9.7 mV decade−1 at room temperature, transcending the 60 mV decade …


Interband Transitions And Critical Points Of Single-Crystal Thoria Compared With Urania, Christina Dugan, Lu Wang, Kai Zhang, James M. Mann, Martin M. Kimani, Wai-Ning Mei, Peter A. Dowben, James C. Petrosky Nov 2022

Interband Transitions And Critical Points Of Single-Crystal Thoria Compared With Urania, Christina Dugan, Lu Wang, Kai Zhang, James M. Mann, Martin M. Kimani, Wai-Ning Mei, Peter A. Dowben, James C. Petrosky

Faculty Publications

The interband transitions of UO2 are validated independently through cathode luminescence. A picture emerges consistent with density functional theory. While theory is generally consistent with experiment, it is evident from the comparison of UO2 and ThO2 that the choice of functional can significantly alter the bandgap and some details of the band structure, in particular at the conduction band minimum. Strictly ab initio predictions of the optical properties of the actinide compounds, based on density functional theory alone, continue to be somewhat elusive.


Probing Free Nucleons With (Anti)Neutrinos, Roberto Petti Nov 2022

Probing Free Nucleons With (Anti)Neutrinos, Roberto Petti

Faculty Publications

We discuss a method to study free protons and neutrons using ν()-hydrogen (H) Charged Current (CC) inelastic interactions, together with various precision tests of the isospin (charge) symmetry using ν and CC interactions on both H and nuclear targets. Probing free nucleons with (anti)neutrinos provides information about their partonic structure, as well as a crucial input for the modeling of ν(⊽)-nucleus (A) interactions. Such measurements concurrently represent a valuable tool to address the main limitations of accelerator-based neutrino scattering experiments on nuclear targets, originating from the combined effect of the unknown (anti)neutrino energy and of the …


A Multi-Modal Volumetric Microscope With Automated Sample Handling For Surveying Microbial Life In Liquid Samples, Nathan Oborny, Eugene Serabyn, J. Kent Wallace, Kurt Liewer, Manuel Bedrossian, Stephanie Rider, Chris Lindensmith, Jay Nadeau, Multiple Additional Authors Nov 2022

A Multi-Modal Volumetric Microscope With Automated Sample Handling For Surveying Microbial Life In Liquid Samples, Nathan Oborny, Eugene Serabyn, J. Kent Wallace, Kurt Liewer, Manuel Bedrossian, Stephanie Rider, Chris Lindensmith, Jay Nadeau, Multiple Additional Authors

Physics Faculty Publications and Presentations

In the study of microbial life, microscopy plays a unique role due to its ability to detect ordered structure, motility, and fluorescence signals. As such it has also recently gained attention in the context of searching for extant life on distant Solar System bodies bearing liquid water. In this paper we introduce a multimodal volumetric microscopy system for potential future spaceflight missions that combines digital holographic microscopy (DHM) and volume fluorescence imager (VFI), which are volumetric imaging methods that provide highresolution, high-throughput examination of liquid samples. DHM provides information on the absorption, morphology, and motility of imaged objects without requiring …


Kinetic Monte Carlo Simulations Of Quantum Dot Self-Assembly, Matthew Abramson, Hunter J. Coleman, Paul J. Simmonds, Tim P. Schulze, Christian Ratsch Nov 2022

Kinetic Monte Carlo Simulations Of Quantum Dot Self-Assembly, Matthew Abramson, Hunter J. Coleman, Paul J. Simmonds, Tim P. Schulze, Christian Ratsch

Physics Faculty Publications and Presentations

In the Stranski–Krastanov growth mode for heteroepitaxial systems, layer-by-layer growth is followed by the formation and growth of three-dimensional (3D) islands. In this paper, we use a kinetic Monte Carlo method to simulate this growth mode behavior. We present a detailed and systematic investigation into the effects of key model parameters including strain, growth temperature, and deposition rate on this phenomenon. We show that increasing the strain lowers the apparent critical thickness that is defined by the onset of 3D island formation. Similarly, increasing the growth temperature lowers the apparent critical thickness, until intermixing, and the resulting relevance of entropic …


Optimizing Switching Of Non-Linear Properties With Hyperbolic Metamaterials, James A. Ethridge, John G. Jones, Manuel R. Ferdinandus, Michael J. Havrilla, Michael A. Marciniak Nov 2022

Optimizing Switching Of Non-Linear Properties With Hyperbolic Metamaterials, James A. Ethridge, John G. Jones, Manuel R. Ferdinandus, Michael J. Havrilla, Michael A. Marciniak

Faculty Publications

Hyperbolic metamaterials have been demonstrated to have special potential in their linear response, but the extent of their non-linear response has not been extensively modeled or measured. In this work, novel non-linear behavior of an ITO/SiO2 layered hyperbolic metamaterial is modeled and experimentally confirmed, specifically a change in the sign of the non-linear absorption with intensity. This behavior is tunable and can be achieved with a simple one-dimensional layered design. Fabrication was performed with physical vapor deposition, and measurements were conducted using the Z-scan technique. Potential applications include tunable optical switches, optical limiters, and tunable components of laser sources.


A Method To Solve One-Dimensional Nonlinear Fractional Differential Equation Using B-Polynomials, Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis Nov 2022

A Method To Solve One-Dimensional Nonlinear Fractional Differential Equation Using B-Polynomials, Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis

Physics and Astronomy Faculty Publications and Presentations

In this article, the fractional Bhatti-Polynomial bases are applied to solve one-dimensional nonlinear fractional differential equations (NFDEs). We derive a semi-analytical solution from a matrix equation using an operational matrix which is constructed from the terms of the NFDE using Caputo’s fractional derivative of fractional B-polynomials (B-polys). The results obtained using the prescribed method agree well with the analytical and numerical solutions presented by other authors. The legitimacy of this method is demonstrated by using it to calculate the approximate solutions to four NFDEs. The estimated solutions to the differential equations have also been compared with other known numerical and …


Orbit Propagation And Determination Algorithms For Satellite Ground Stations, Shamma Esmaeel Jamali Nov 2022

Orbit Propagation And Determination Algorithms For Satellite Ground Stations, Shamma Esmaeel Jamali

Theses

The satellite orbital parameters are essential for satellite operations. With these parameters, it is possible to estimate the satellite position in the recent past and near future, which is essential to effectively plan satellite operations and associate satellite telemetry with geographical locations.
However, for small or medium satellite operators who do not possess the infrastructure required to track their satellites, the problem of determining the satellite orbit is problematic. To access the orbit for their satellites, these organizations have to rely on third parties such as Celestrak. These entities provide the service free of charge but do not provide orbital …


Thermal Degradation Of Erythritol, Sudheendra Gamoji Nov 2022

Thermal Degradation Of Erythritol, Sudheendra Gamoji

Physics

The Insulated Solar Electric Cooker (ISEC) is a double walled Aluminum pot with a resistive heater directly connected to a solar panel whose goal is to create and disseminate cheap solar cookers in rural areas that primarily rely on biomass for cooking. Phase Change Materials (PCMs) like Erythritol, a sugar substitute, take a tremendous amount of energy to melt, and when they solidify they release the energy. Through the use of PCMs, the ISECs will produce enough heat to cook food even after the sun sets. However, PCMs like Erythritol degrade over repeated heat exposure, so the purpose of this …


Design And Modeling Of Superconducting Hardware For Implementing Quantum Stabilizers, Yebin Liu Oct 2022

Design And Modeling Of Superconducting Hardware For Implementing Quantum Stabilizers, Yebin Liu

Dissertations - ALL

Superconducting qubits are one of the leading systems for implementing quantum processors. Realizing fault-tolerant quantum computation requires some form of quantum error correction, which typically involves performing repeated stabilizer operations on groups of physical qubits in an array to form a logical qubit with enhanced protection against errors. Realizing a logical qubit that is suitable for running quantum algorithms requires an array with a significant number of physical qubits, which is extremely challenging. However, the physical qubit overhead can be reduced by lowering the error rate on the physical qubits. Current state-of-the-art superconducting qubit designs do not have robust protection …


Round Robin Tests Of Electron Irradiated Polymers Via Pulsed Electroacoustic Measurements, Zachary Gibson, J. R. Dennison, Virginie Griseri Oct 2022

Round Robin Tests Of Electron Irradiated Polymers Via Pulsed Electroacoustic Measurements, Zachary Gibson, J. R. Dennison, Virginie Griseri

Physics Student Research

Charge accumulation and migration can be studied using the pulsed electroacoustic (PEA) method to directly measure internal charge distributions in dielectric materials. This study aims to compare measurements using PEA systems constructed in labs at Utah State University and Université Paul Sabatier to establish confidence in comparing PEA results between different PEA systems. While there is good agreement in data measured for pristine samples with DC bias applied and no charge embedded, there are discrepancies in the data when measuring irradiated samples with embedded charge. The overall characteristics of charge distributions measured with both systems is clearly the same, but …


Which Countries Are Leading High-Impact Science In Astronomy?, Juan P. Madrid, Julie Steen Oct 2022

Which Countries Are Leading High-Impact Science In Astronomy?, Juan P. Madrid, Julie Steen

Physics and Astronomy Faculty Publications and Presentations

Recent news reports claim that China is overtaking the United States and all other countries in scientific productivity and scientific impact. A straightforward analysis of high-impact papers in astronomy reveals that this is not true in our field. In fact, the United States continues to host, by a large margin, the authors that lead high-impact papers. Moreover, this analysis shows that 90% of all high-impact papers in astronomy are led by authors based in North America and Europe. That is, only about 10% of countries in the world host astronomers that publish “astronomy’s greatest hits".


Influence Of Surface Water Displacement On Solvation Thermodynamics, Mia Kim Oct 2022

Influence Of Surface Water Displacement On Solvation Thermodynamics, Mia Kim

Journal of the South Carolina Academy of Science

No abstract provided.


Quantum Field Theory In Nontrivial Backgrounds And Particle Production, Yue Qiu Oct 2022

Quantum Field Theory In Nontrivial Backgrounds And Particle Production, Yue Qiu

Doctoral Dissertations

Production of particles from nontrivial backgrounds is an important phenomenon in quantum field theory. In this thesis, we review some useful formulae of Bogoliubov formalism and explain how to derive the spectra of particle production. We then apply the formalism to study several scenarios. We first study the Schwinger effect in compact $(1+1)$ dimensions spacetime. Using the in-in formalism, we compute the correction to the electric field from the creation of charged particles both when the spatial dimension is compact and when it is non-compact. Secondly, we investigate the thermodynamic properties of the Schwarzschild-de Sitter (SdS) system. We explore particle …


Applications Of Statistical Physics To Ecology: Ising Models And Two-Cycle Coupled Oscillators, Vahini Reddy Nareddy Oct 2022

Applications Of Statistical Physics To Ecology: Ising Models And Two-Cycle Coupled Oscillators, Vahini Reddy Nareddy

Doctoral Dissertations

Many ecological systems exhibit noisy period-2 oscillations and, when they are spatially extended, they undergo phase transition from synchrony to incoherence in the Ising universality class. Period-2 cycles have two possible phases of oscillations and can be represented as two states in the bistable systems. Understanding the dynamics of ecological systems by representing their oscillations as bistable states and developing dynamical models using the tools from statistical physics to predict their future states is the focus of this thesis. As the ecological oscillators with two-cycle behavior undergo phase transitions in the Ising universality class, many features of synchrony and equilibrium …


Synthesis And Assembly Of Polymer Materials At Interfaces, Xiaoshuang Wei Oct 2022

Synthesis And Assembly Of Polymer Materials At Interfaces, Xiaoshuang Wei

Doctoral Dissertations

The overarching goal of the thesis is to understand growth and assembly of polymer materials at interfaces. Chapter 2 and Chapter 3 study simultaneous polymer growth and assembly at fluid interfaces, where in-situ photopolymerization and vapor phase deposition were utilized to grow polymers, respectively. Chapter 4 leverages capillary condensation to pattern polymer growth at solid substrates. Chapter 1 provides background information on polymer materials at interfaces, and vapor phase deposition method (initiated chemical vapor deposition, iCVD) to grow polymers. This chapter also reviews polymer thin film wetting, and colloidal assemblies at interfaces. In Chapter 2, we demonstrate the preparation …


Symmetry Breaking Effects In Low-Dimensional Quantum Systems, Ke Wang Oct 2022

Symmetry Breaking Effects In Low-Dimensional Quantum Systems, Ke Wang

Doctoral Dissertations

Quantum criticality in low-dimensional quantum systems is known to host exotic behaviors. In quantum one-dimension (1D), the emerging conformal group contains infinite generators, and conformal techniques, e.g., operator product expansion, give accurate and universal descriptions of underlying systems. In quantum two-dimension (2D), the electronic interaction causes singular corrections to Fermi-liquids characteristics. Meanwhile, the Dirac fermions in topological 2D materials can greatly enrich emerging phenomena. In this thesis, we study the symmetry-breaking effects of low-dimensional quantum criticality. In 1D, we consider two cases: time-reversal symmetry (TRS) breaking in the Majorana conformal field theory (CFT) and the absence of conformal symmetry in …


Frontiers In The Self-Assembly Of Charged Macromolecules, Khatcher O. Margossian Oct 2022

Frontiers In The Self-Assembly Of Charged Macromolecules, Khatcher O. Margossian

Doctoral Dissertations

The self-assembly of charged macromolecules forms the basis of all life on earth. From the synthesis and replication of nucleic acids, to the association of DNA to chromatin, to the targeting of RNA to various cellular compartments, to the astonishingly consistent folding of proteins, all life depends on the physics of the organization and dynamics of charged polymers. In this dissertation, I address several of the newest challenges in the assembly of these types of materials. First, I describe the exciting new physics of the complexation between polyzwitterions and polyelectrolytes. These materials open new questions and possibilities within the context …


Reservoir Engineering Of Multi-Photon States In Circuit Quantum Electrodynamics, Jeffrey M. Gertler Oct 2022

Reservoir Engineering Of Multi-Photon States In Circuit Quantum Electrodynamics, Jeffrey M. Gertler

Doctoral Dissertations

The field of experimental quantum information has made significant progress towards useful computation but has been handicapped by the dissipative nature of physical qubits. Except for unwieldy and unrealized topological qubits, all quantum information systems experience natural dissipation, which limits the time scale for useful computation. However, this same dissipation, which induces errors requiring quantum error correction (QEC), can be used as a resource to perform a variety of important and unrealized tasks. In this thesis I discuss research into three uses of dissipation: manifold stabilization, state transfer, and QEC. With reservoir engineering, these tasks can be addressed in an …


Anomalous Transport, Quasiperiodicity, And Measurement Induced Phase Transitions, Utkarsh Agrawal Oct 2022

Anomalous Transport, Quasiperiodicity, And Measurement Induced Phase Transitions, Utkarsh Agrawal

Doctoral Dissertations

With the advent of the noisy-intermediate scale quantum (NISQ) era quantum computers are increasingly becoming a reality of the near future. Though universal computation still seems daunting, a great part of the excitement is about using quantum simulators to solve fundamental problems in fields ranging from quantum gravity to quantum many-body systems. This so-called second quantum revolution rests on two pillars. First, the ability to have precise control over experimental degrees of freedom is crucial for the realization of NISQ devices. Significant progress in the control and manipulation of qubits, atoms, and ions, as well as their interactions, has not …


Topological Phase Transitions And Berry-Phase Hysteresis In Exchange-Coupled Nanomagnets, Ahsan Ullah, Xin Li, Yunlong Jin, Rabindra Pahari, Lanping Yue, Xiaoshan S. Xu, Balamurugan Balasubramanian,, David J. Sellmyer, Ralph Skomski Oct 2022

Topological Phase Transitions And Berry-Phase Hysteresis In Exchange-Coupled Nanomagnets, Ahsan Ullah, Xin Li, Yunlong Jin, Rabindra Pahari, Lanping Yue, Xiaoshan S. Xu, Balamurugan Balasubramanian,, David J. Sellmyer, Ralph Skomski

Department of Physics and Astronomy: Faculty Publications

Topological phase in magnetic materials yields a quantized contribution to the Hall effect known as the topological Hall effect, which is often caused by skyrmions, with each skyrmion creating a magnetic flux quantum ±h/e. The control and understanding of topological properties in nanostructured materials is the subject of immense interest for both fundamental science and technological applications, especially in spintronics. In this work, the electron-transport properties and spin structure of exchange-coupled cobalt nanoparticles with an average particle size of 13.7 nm are studied experimentally and theoretically. Magnetic and Hall-effect measurements identify topological phase transitions in the exchange-coupled cobalt …


Electro-Optical Sensors For Atmospheric Turbulence Strength Characterization With Embedded Edge Ai Processing Of Scintillation Patterns, Ernst Polnau, Don L. N. Hettiarachchi, Mikhail A. Vorontsov Oct 2022

Electro-Optical Sensors For Atmospheric Turbulence Strength Characterization With Embedded Edge Ai Processing Of Scintillation Patterns, Ernst Polnau, Don L. N. Hettiarachchi, Mikhail A. Vorontsov

Electro-Optics and Photonics Faculty Publications

This study introduces electro-optical (EO) sensors (TurbNet sensors) that utilize a remote laser beacon (either coherent or incoherent) and an optical receiver with CCD camera and embedded edge AI computer (Jetson Xavier Nx) for in situ evaluation of the path-averaged atmospheric turbulence refractive index structure parameter C-n(2) at a high temporal rate. Evaluation of C-n(2) values was performed using deep neural network (DNN)-based real-time processing of short-exposure laser-beacon light intensity scintillation patterns (images) captured by a TurbNet sensor optical receiver. Several pre-trained DNN models were loaded onto the AI computer and used for TurbNet sensor performance evaluation in a set …


Preparation, Investigation, And Temperature Sensing Application Of Rgo/Sno2/Co3o4 Composite, Mohamed Morsy Oct 2022

Preparation, Investigation, And Temperature Sensing Application Of Rgo/Sno2/Co3o4 Composite, Mohamed Morsy

Nanotechnology Research Centre

No abstract provided.


P-39 Interdisciplinary Diffusion Lab, Sable Canales, Chloe Gaban, Mickey Kutzner Oct 2022

P-39 Interdisciplinary Diffusion Lab, Sable Canales, Chloe Gaban, Mickey Kutzner

Celebration of Research and Creative Scholarship

Diffusion is a principle in Physics, Chemistry, and Biology. The rate of diffusion is affected by temperature, particle size, concentration, and material type. Students can model the rate of diffusion based on particle size by contrasting blue and yellow dyes. Two petri dishes containing agar-agar receive a drop of dye at the center. The radius of expansion is recorded over time. The variance of the distribution grows as 𝜎2=4𝐷𝑡, where 𝜎2 is the variance, D is the diffusion constant, and t is time. Graphing variance versus time gives a slope of 4D. Diffusion constants vary by particle size, allowing for …