Physical Sciences and Mathematics Commons^™

Problem Set #12, David Peak

Problems

Solid stuff

Problem Set #6, David Peak

Problems

3D, 1-particle systems

Problem Set #3, David Peak

Problems

Comparing classical electromagnetic waves with photon probability waves.

Problem 1 refers to: A standing electric field wave (one with lots of photons) in a quantum wire stretching between x = 0 and x = L is described by E(x,t)=E_maxsin(3πx/L)cos(3πct/L). Let L = 900 nm.

Problem Set #1, David Peak

Problems

A little E&M practice

Problems 1-2 refer to: The electric field in a laser beam is given by E( x,t) = (1000V/m)sin[(πx10⁷rad/m) x + (3πx10¹⁵rad/s)t].

Problem Set #7, David Peak

Problems

Atom stuff

Problem Set #8, David Peak

Problems

A bit of stat mech

Problems 1-3 refer to: N identical, noninteracting, and distinguishable spin-1/2 particles (i.e., their separation is much greater than their de Broglie wavelength) are placed in an external magnetic field. Assume the ground state energy of one such particle is 0 and the excited state energy is ε , and the system is in thermal equilibrium at temperature T.

Problem Set #5, David Peak

Problems

Expectations & 1D finite wells

Problem Set #2, David Peak

Problems

A little energy and momentum practice (and units)

Problems 1-2 deal with “rest” energy and relativity.

Problem Set #9, David Peak

Problems

Another bit of stat mech

Problems 1-3 refer to: N identical, noninteracting, and distinguishable quantum harmonic oscillators (i.e., their separation is much greater than their de Broglie wavelength) are in thermal equilibrium at temperature T. The energy of each oscillator can be expressed as ε_n = nε , where ε is the level spacing and n = 0, 1, 2, … .

Schrödinger, 2, David Peak

Schrodinger

The finite square well

The infinite square well potential energy rigorously restricts the associated wavefunction to an exact region of space: it is infinitely “hard.” Potential energies encountered in more realistic physical scenarios are “softer” in that they permit wavefunctions to spread throughout less well-defined regions. An important toy example of the latter is the finite square well. In this problem, the potential energy function is U(x) = 0, if 0 < x < L, and U₀ otherwise.

Schrödinger, 3, David Peak

Schrodinger

The 3D infinite square well: quantum dots, wells, and wires

In the preceding discussion of the Schrödinger Equation the particle of interest was assumed to be “moving in the x -direction.” Of course, it is not possible for a particle to be moving in one spatial direction only. If that were true, according to the HUP it could be anywhere in the y - and z -directions and therefore be undetectable with finite volume detectors. Now, we consider the more realistic case of motion in all three spatial directions. For this purpose, we start with the 3D infinite square well. …

Schrödinger, 1, David Peak

Schrodinger

The Schrödinger equation: the quantum description of one massive, slow-moving particle

To establish a probability wave equation for one photon, it was useful to note that probability density and electromagnetic energy density were proportional. The governing equation for EM radiation fields is the Maxwell wave equation, which is also the governing equation for photon probability wave functions. Converting from EM radiation to photon information is made plausible by identifying energy and momentum operators with time- and space-derivatives, respectively. Thus, the Maxwell wave equation can be interpreted as being equivalent to the energy-momentum relation for photons. Though we don’t have a …

Schrödinger, 5, David Peak

Schrodinger

Transitions

Schrödinger, 4, David Peak

Schrodinger

The sanitized hydrogen atom: separating the variables

Separation of variables in the Schrödinger Equation for the hydrogen problem requires expressing Ψ as a product, Ψ(r,θ,φ,t) = R(r)Θ(θ )Φ(φ)T(t) , substituting into the partial differential equation [(5) in Sc3], and then dividing by Ψ. As in the square well problems, the separation constant for the t part of the separation is the particle’s eigen-energy, E.

Physics 2710: Introductory Modern Physics, David Peak

Syllabus

No abstract provided.

Controls On Erosion In The Western Tarin Basin: Implications For The Uplift Of Northwest Tibet And The Parmir, Peter D. Clift, Hongbo Zheng, Andrew Carter, Philipp Böning, Tara N. Jonell, Hannah Schorr, Xin Shan, Katharina Pahnke, Xiaochun Wei, Tammy M. Rittenour

Geosciences Faculty Publications

We present here bulk sediment major element chemistry, Nd and Sr isotope ratios, and detrital apatite fission-track (AFT) and U-Pb zircon ages to characterize the provenance of the southwestern Taklimakan Desert (northwest China) and the three major rivers draining this region. We establish the spatial and temporal controls on erosion and sediment transport in the modern Tibetan rain shadow. The Hotan River drains the North Kunlun block and is characterized by zircon populations at 160–230 Ma and 370–520 Ma. The Yarkand River shares these grains with the Hotan, but also has a very prominent zircon population at 40–160 Ma, which …

Gravitation And Black Hole Electrodynamics, Maria Rodriguez

Funded Research Records

No abstract provided.

Foundations, 2, David Peak

Foundations

The double slit experiment in dim light – photons!

Let’s imagine doing the double slit experiment again, but now in very dim light. To do so requires putting the laser, plate, and collector in a sealed, light-tight box. Inserting neutral density filters in the beam between the laser and the double slit plate decreases the intensity of the beam striking the plate. In fact, the experiment can be done at such a low intensity that a human eye will not see any light on the CCD collector; but the CCD can. Under these conditions, the number of pixels that “light …

Many-Particle Systems, 10, David Peak

Many Particles

Intrinsic semiconductors

Intrinsic semiconductors have negligible concentrations of impurity atoms. Their electrical conductivity arises primarily from electrons excited into the otherwise empty conduction band from the otherwise filled valence band—usually by absorbing sufficient energy from phonons at finite temperature. Exciting an electron into the conduction band leaves a vacant state in the valence band. An electron at lower energy in the valence band can fill this vacant state. That, in turn, makes available a possible state for yet another valence band electron to fill. In other words, the excitation of the electron provides a mobile charge in the conduction band …

Uv Screening In Native And Non-Native Plant Species In The Tropical Alpine: Implications For Climate Change-Driven Migration Of Species To Higher Elevations, Paul W. Barnes, Ronald J. Ryel, Stephan D. Flint

Wildland Resources Faculty Publications

Ongoing changes in Earth’s climate are shifting the elevation ranges of many plant species with non-native species often experiencing greater expansion into higher elevations than native species. These climate change-induced shifts in distributions inevitably expose plants to novel biotic and abiotic environments, including altered solar ultraviolet (UV)-B (280–315 nm) radiation regimes. Do the greater migration potentials of non-native species into higher elevations imply that they have more effective UV-protective mechanisms than native species? In this study, we surveyed leaf epidermal UV-A transmittance (TUVA) in a diversity of plant species representing different growth forms to test whether native and non-native species …

Secondary Gravity Wave Generation Over New Zealand During The Deepwave Campaign, K. Bossert, C. G. Kruse, C. J. Heale, D. C. Fritts, B. P. Williams, J. B. Snively, Pierre-Dominique Pautet, Michael J. Taylor

All Physics Faculty Publications

Multiple events during the Deep Propagating Gravity Wave Experiment measurement program revealed mountain wave (MW) breaking at multiple altitudes over the Southern Island of New Zealand. These events were measured during several research flights from the National Science Foundation/National Center for Atmospheric Research Gulfstream V aircraft, utilizing a Rayleigh lidar, an Na lidar, and an Advanced Mesospheric Temperature Mapper simultaneously. A flight on 29 June 2014 observed MWs with horizontal wavelengths of ~80_120ækm breaking in the stratosphere from ~10 to 50ækm altitude. A flight on 13 July 2014 observed a horizontal wavelength of ~200_240ækm MW extending from 20 to 90ækm …

Supergravity Tools For Holography, Oscar Varela

Funded Research Records

No abstract provided.

Universal Surface Engineering Of Transition Metals For Superior Electrocatalytic Hydrogen Evolution In Neutral Water, Bo You, Xuan Liu, Guoxiang Hu, Sheraz Gul, Junko Yano, De-En Jiang, Yujie Sun

Chemistry and Biochemistry Faculty Publications

The development of low-cost hybrid water splitting-biosynthetic systems that mimic natural photosynthesis to achieve solar-to-chemical conversion is of great promise for future energy demands, but often limited by the kinetically sluggish hydrogen evolution reaction (HER) on the surface of nonprecious transition metal catalysts in neutral media. It is thus highly desirable to rationally tailor the reaction interface to boost the neutral HER catalytic kinetics. Herein, we report a general surface nitrogen modification of diverse transition metals (e.g. iron, cobalt, nickel, copper, and nickel-cobalt alloy), accomplished by a facile low-temperature ammonium carbonate treatment, for significantly improved hydrogen generation from neutral water. …

Single-Grain Optically Stimulated Luminescence Ages Of Brownware Pottery In The Central Rocky Mountains And The Spread Of Numic Ceramic Technology, Judson Byrd Finley, Carlie J. Ideker, Tammy M. Rittenour

Geosciences Faculty Publications

This study presents the results of a single-grain optically stimulated luminescence (SG-OSL) analysis of brownware pottery from four Late Prehistoric-period sites in the Middle Rocky Mountains, Wyoming, USA. SG-OSL of quartz ceramic temper provides improved age control for sites where radiocarbon dating has proven problematic due to old wood, recent wildfires, and calibration uncertainties. SG-OSL results are compared to fine-grain infrared stimulated luminescence (FG-IRSL) results from the same sherds and associated radiocarbon ages. We find that the single-grain technique applied to quartz sand temper provides improved accuracy and precision over both FG-IRSL and radiocarbon. We compare our results to directly …

Frg: Collaborative Research: Homotopy Renormalization Of Topological Field Theories, Nathan Geer

Funded Research Records

No abstract provided.

Imputation For Random Forests, Joshua Young

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project introduces two new methods for imputation of missing data in random forests. The new methods are compared against other frequently used imputation methods, including those used in the randomForest package in R. To test the effectiveness of these methods, missing data are imputed into datasets that contain two missing data mechanisms including missing at random and missing completely at random. After imputation, random forests are run on the data and accuracies for the predictions are obtained. Speed is an important aspect in computing; the speeds for all the tested methods are also compared.

One of the new methods …

Tree-Based Regression For Interval-Valued Data, Chih-Ching Yeh

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore development of nonlinear regression tools for intervalvalued data is crucial. In this project, we propose a tree-based regression method for interval-valued data, which is well applicable to both linear and nonlinear problems. Unlike linear regression models that usually require additional constraints to ensure positivity of the predicted interval length, the proposed method estimates the regression function in a nonparametric way, so the …

The Dynamic Relationship Between The Bear River, Quaternary Basaltic Center, Normal Faults, And The Resulting Rearrangement Of Rivers In The Northeast Edge Of The Great Basin, Southeast Idaho, Brady Utley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The objective of this research project in Gem Valley graben, southeast Idaho is to identify the location, age and history of the Quaternary diversion of the Bear River into paleo-Lake Thatcher, and then into the Lake Bonneville basin from the Columbia River basin. Mapping, geochemical analysis, cross-cutting relationships, and five new age determinations, together with prior published research, shed new light on the complex history of interaction between the volcanic rocks, rivers, lakes, and faults in Gem Valley. Research goals were to test the hypothesis that local faulting and volcanism drove the diversion of the Bear River and controlled the …

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log₂(α)³ + 16.5log₂(α)² + …

Stratigraphy, Petrology, And Paleontology Of The Late Cretaceous Campanian Mesaverde Group In Northeastern Utah, Christopher Ward

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project examines a poorly studied sandstone ridge called Snake John Reef located 22 miles southeast of Vernal, in northeastern Utah. Previously this ridge was mapped as exposures of late Cretaceous, undifferentiated Mesaverde Group, and recently unidentified dinosaur fossils have been found along the ridge by the Utah Field House of Natural History State Park Museum. Stratigraphic sections, petrographic thin sections, and collection and study of fossils from Snake John Reef were undertaken to understand the stratigraphic relationship as well as to reconstruct the depositional environment of the dinosaur bearing units. Snake John Reef represents exposures of three late Cretaceous …