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Full-Text Articles in Physical Sciences and Mathematics

Quantum Chaos, Integrability, And Hydrodynamics In Nonequilibrium Quantum Matter, Javier Lopez Piqueres Mar 2024

Quantum Chaos, Integrability, And Hydrodynamics In Nonequilibrium Quantum Matter, Javier Lopez Piqueres

Doctoral Dissertations

It is well-known that the Hilbert space of a quantum many-body system grows exponentially with the number of particles in the system. Drive the system out of equilibrium so that the degrees of freedom are now dynamic and the result is an extremely complicated problem. With that comes a vast landscape of new physics, which we are just recently starting to explore. In this proposal, we study the dynam- ics of two paradigmatic classes of quantum many-body systems: quantum chaotic and integrable systems. We leverage certain tools commonly employed in equilibrium many-body physics, as well as others tailored to the …


A Field-Programmable Metamaterial Using Memristor As A Stable Switcher, Taekuk Hong Jan 2023

A Field-Programmable Metamaterial Using Memristor As A Stable Switcher, Taekuk Hong

Theses and Dissertations

Before the memristor was discovered, there were RLC circuits as representative passive devices. However, the fourth fundamental two-terminal circuit has been discovered by Dr. Leon Chua in 1971 and has been called a memristor. The memristor is a compound word of memory and resistor, and is an element whose resistive value is not constant and whose resistive value changes depending on the applied voltage and is recorded as a memory. It is mainly used in resistive switching and is the center of this research theme. A metamaterial is artificially created material that has never been found in nature. The theory …


An Entropic Approach To Dynamics, Pedro Henrique Moreira Pessoa May 2022

An Entropic Approach To Dynamics, Pedro Henrique Moreira Pessoa

Legacy Theses & Dissertations (2009 - 2024)

The present thesis deals with different aspects of probability, the method of maximum entropy, information geometry, and dynamical systems and their applications to statistical physics and complex systems. Those topics come together in the framework for dynamics termed entropic dynamics. Work on the topic was initiated by my PhD advisor Professor Ariel Caticha and many colleagues at University at Albany as a method for explaining the dynamical processes in quantum mechanics from first principles of probability theory.


In Silico Identification Of Vaccine Candidates Against Viral Infections, Prabin Baral Mar 2022

In Silico Identification Of Vaccine Candidates Against Viral Infections, Prabin Baral

FIU Electronic Theses and Dissertations

There are many viral diseases without effective treatments or vaccines. These viruses can cause catastrophic epidemics such as the Lassa, Ebola, and Marburg viruses. Similarly, the recent coronavirus pandemic is of great concern as new variants are continuously emerging with decreased susceptibility to antibodies and vaccines that were developed for earlier strains. A critical step in the immune system’s fight against viruses involves an immunological protein molecule binding to a viral protein molecule. I investigate the atomic and molecular details of binding site recognition and binding interactions and dynamics for three important viruses.

Antigens are molecules, such as viral proteins, …


12 C(E,E'Pn) Measurements Of Short Range Correlations In The Tensor-To-Scalar Interaction Transition Region, I. Korover, J. R. Pybus, A. Schmidt, F. Hauenstein, M. Duer, O. Hen, E. Piasetzky, L. B. Weinstein, D. W. Higinbotham, S. Adhikari, K. Adhikari, M. J. Amaryan, Giovanni Angelini, H. Atac, L. Barion, M. Battaglieri, A. Beck, I. Bedlinkskiy, Fatiha Benmokhtar, Steffen Strauch, Ralf W. Gothe, Krishna Chandra Neupane, Et. Al. Aug 2021

12 C(E,E'Pn) Measurements Of Short Range Correlations In The Tensor-To-Scalar Interaction Transition Region, I. Korover, J. R. Pybus, A. Schmidt, F. Hauenstein, M. Duer, O. Hen, E. Piasetzky, L. B. Weinstein, D. W. Higinbotham, S. Adhikari, K. Adhikari, M. J. Amaryan, Giovanni Angelini, H. Atac, L. Barion, M. Battaglieri, A. Beck, I. Bedlinkskiy, Fatiha Benmokhtar, Steffen Strauch, Ralf W. Gothe, Krishna Chandra Neupane, Et. Al.

Faculty Publications

High-momentum configurations of nucleon pairs at short-distance are probed using measurements of the C-12(e, e' p) and C-12(e, e' pN) reactions (where N is either n or p), at high-Q(2) and x(B) > 1.1. The data span a missing-momentum range of 300-1000 MeV/c and are predominantly sensitive to the transition region of the strong nuclear interaction from a Tensor to Scalar interaction. The data are well reproduced by theoretical calculations using the Generalized Contact Formalism with both chiral and phenomenological nucleon-nucleon (NN) interaction models. This agreement suggests that the measured high missing-momentum protons up to 1000 MeV/c predominantly belong to short-ranged …


¹² C(E,E'Pn) Measurements Of Short Range Correlations In The Tensor-To-Scalar Interaction Transition Region, I. Korover, J. R. Pybus, A. Schmidt, F. Hauenstein, M. Duer, L. B. Weinstein, M. J. Amaryan, D. Bullumulla, M. Hattawy, X. Zheng, Et Al., The Clas Collaboration Jan 2021

¹² C(E,E'Pn) Measurements Of Short Range Correlations In The Tensor-To-Scalar Interaction Transition Region, I. Korover, J. R. Pybus, A. Schmidt, F. Hauenstein, M. Duer, L. B. Weinstein, M. J. Amaryan, D. Bullumulla, M. Hattawy, X. Zheng, Et Al., The Clas Collaboration

Physics Faculty Publications

High-momentum configurations of nucleon pairs at short-distance are probed using measurements of the 12C(e,'p) and 12C (e,e'pN) reactions (where N is either n or p), at high Q2 and 𝒙B > 1.1. The data span a missing-momentum range of 300-1000 MeV/c and are predominantly sensitive to the transition region of the strong nuclear interaction from a tensor to scalar interaction. The data are well reproduced by theoretical calculations using the generalized contact formalism with both chiral and phenomenological nucleon-nucleon (NN) interaction models. This agreement suggests that the measured high missing-momentum protons up to 1000 MeV/c predominantly …


Quantifying Confinement Of Chain Dynamics For Chains Tethered To Self-Assembling Crystalline Nanodomains Using Neutron Spin Echo Spectroscopy, Logan Benninghoff Jan 2021

Quantifying Confinement Of Chain Dynamics For Chains Tethered To Self-Assembling Crystalline Nanodomains Using Neutron Spin Echo Spectroscopy, Logan Benninghoff

Williams Honors College, Honors Research Projects

Polyisobutylene (PIB) rubbers can be reinforced with crystalline β-alanine nanodomains. Progress has been made in understanding the morphology of the nanodomains, but the dynamics of the PIB molecule chains attached to the surface of the nanodomains and in the matrix are not well understood. It is possible to observe the motion of these PIB chains using Neutron Spin Echo (NSE) experiments, since the experimental technique can give data for smaller timescales. Data collection for reinforced rubber samples has already been performed, but the data still need to be analyzed. For my honors project I will be comparing the data to …


Composite Network Of Actin And Microtubule Filaments, Self-Organization And Steady-State Dynamics, Leila Farhadi Dec 2020

Composite Network Of Actin And Microtubule Filaments, Self-Organization And Steady-State Dynamics, Leila Farhadi

Doctoral Dissertations

Actin and microtubule filaments, with their auxiliary proteins, enable the cytoskeleton to perform vital processes in the cell by tuning the organizational, mechanical properties and dynamics of the network. Despite their critical importance and interactions in cells, we are only beginning to uncover information about the composite network. Here, I use florescence microscopy to explore the role of filaments characteristics, interactions and activities in the self-organization and steady-state dynamics of the composite network of filaments. First, I discuss active self-organization of semiflexible actin and rigid microtubule filaments in the 2D composite network while myosin II and kinesin-1 motor proteins propel …


Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan Dec 2020

Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan

Doctoral Dissertations

Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed …


Mechani-Kits Senior Design Project, Jake Utley, Sophie Carson, Vincent Seguin Jun 2020

Mechani-Kits Senior Design Project, Jake Utley, Sophie Carson, Vincent Seguin

Mechanical Engineering

Studies suggest that when designed and executed well, hands-on activities can enhance student understanding of key mechanics concepts. Current products are expensive and typically not designed to meet a variety of learning objectives. Through the Mechanics of Inclusion and Inclusivity in Mechanics grant, the Cal Poly Physics and Engineering Departments are seeking to incorporate new hands-on activities into their courses. Our team has designed three inexpensive ”MechaniKits” to be used in physics, statics and dynamics courses [1]. This Final Design Review outlines our findings, objectives, and final designs for this project. It also explains our manufacturing and design verification plans. …


A Numerical Survey Of Multi-Planet Systems’ Inclination Excitation And Survival Under The Influence Of An Oblate, Tilted Star, Kathleen M T Schultz May 2020

A Numerical Survey Of Multi-Planet Systems’ Inclination Excitation And Survival Under The Influence Of An Oblate, Tilted Star, Kathleen M T Schultz

Electronic Theses and Dissertations

Among the many exciting and thought-provoking discoveries facilitated by the Kepler telescope, one of the most puzzling is the very large proportion of systems with only a single transiting planet in them, relative to the number of systems with multiple transiting planets. Given that most of these multis are close together and have low mutual inclinations, and that planetary systems tend to form in such a configuration, the next logical step is to guess that at least some of the singles are part of multi-planet systems with large mutual inclinations between planets, excited by some other object’s gravitational perturbations. A …


Characterizing Complexity In A Semiconductor With Optical Feedback From Two Mirrors, Layla M. Abrams Jan 2020

Characterizing Complexity In A Semiconductor With Optical Feedback From Two Mirrors, Layla M. Abrams

2020 Symposium Posters

Lasers are stable devices with a broad spectrum of applications. They can be perturbed to induce complex dynamics in their output intensity. One interesting regime in semiconductor lasers is that the output intensity of the laser emits a sequence of non-regular optical spikes. This behavior resembles that of neurons. We use a semiconductor laser with optical feedback from two mirrors to characterize the behavior of the laser's power output. The data is then analyzed by transforming the intensity time series into a sequence of patterns or words. By doing this we want to explore how the laser changes its preferred …


Extreme Dynamics Of Nanomaterials Under High-Rate Mechanical Stimuli, Wanting Xie Oct 2019

Extreme Dynamics Of Nanomaterials Under High-Rate Mechanical Stimuli, Wanting Xie

Doctoral Dissertations

Nanomaterials demonstrate novel mechanical properties attributed to the extremely large interfacial area. At quasi-static rates, the interfacial interactions are crucial in mechanical behaviors, however, materials under extreme mechanical stimuli are rarely studied at nanoscale. With an advanced laser-induced projectile impact test, we perform supersonic impact of micro-projectiles on polymer films, multilayer graphene, carbon- based nanocomposites membranes as well as individual micro-fibers, to study the interface interactions in the high-rate regime, and develop a simplified model to characterize the ballistic performance of materials.


Comparing Proton Momentum Distributions In A = 2 And 3 Nuclei Via 2H 3H And 3He (E,E′P) Measurements, R. Cruz-Torres, F. Hauenstein, A. Schmidt, D. Nguyen, D. Abrams, H. Albataineh, S. Alsalmi, D. Androic, K. Aniol, W. Armstrong, J. Arrington, H. Atac, D. Bulumulla, C. E. Hyde, V. Khachatryan, M. N.H. Rashad, L. B. Weinstein, Z. Y. Ye, J. Zhang, Jefferson Lab Hall A Tritium Collaboration Oct 2019

Comparing Proton Momentum Distributions In A = 2 And 3 Nuclei Via 2H 3H And 3He (E,E′P) Measurements, R. Cruz-Torres, F. Hauenstein, A. Schmidt, D. Nguyen, D. Abrams, H. Albataineh, S. Alsalmi, D. Androic, K. Aniol, W. Armstrong, J. Arrington, H. Atac, D. Bulumulla, C. E. Hyde, V. Khachatryan, M. N.H. Rashad, L. B. Weinstein, Z. Y. Ye, J. Zhang, Jefferson Lab Hall A Tritium Collaboration

Physics Faculty Publications

We report the first measurement of the (e, e' p) reaction cross-section ratios for Helium-3 (3He), Tritium (3H), and Deuterium (d). The measurement covered a missing momentum range of 40 ≤ pmiss ≤ 550 MeV/c, at large momentum transfer ({Q2} ≈ 1.9 (GeV/c)2) and xB > 1, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The data is compared with planewave impulse approximation (PWIA) calculations using realistic spectral functions and momentum distributions. The measured and PWIA-calculated cross-section ratios for 3He/d and 3H/d extend to just above the typical …


Muon Capture In Nuclei: An Ab Initio Approach Based On Green's Function Monte Carlo Methods, A. Lovato, N. Rocco, Rocco Schiavilla Sep 2019

Muon Capture In Nuclei: An Ab Initio Approach Based On Green's Function Monte Carlo Methods, A. Lovato, N. Rocco, Rocco Schiavilla

Physics Faculty Publications

An ab initio Green’s function Monte Carlo (GFMC) method is introduced for calculating total rates of muon weak capture in light nuclei with mass number A ≤ 12. As a first application of the method, we perform a calculation of the rate in 3H and 4He in a dynamical framework based on realistic two- and three-nucleon interactions and realistic nuclear charge-changing weak currents. The currents include one- and two-body terms induced by π-and ρ-meson exchange, and N-to-Δ excitation, and are constrained to reproduce the empirical value of the Gamow-Teller matrix element in tritium. We investigate the sensitivity of …


Water Entry Of Spheres At Various Contact Angles, Nathan B. Spiers, Mohammad M. Mansoor, Jesse Belden, Tadd T. Truscott Jan 2019

Water Entry Of Spheres At Various Contact Angles, Nathan B. Spiers, Mohammad M. Mansoor, Jesse Belden, Tadd T. Truscott

Mechanical and Aerospace Engineering Faculty Publications

It is well known that the water entry of a sphere causes cavity formation above a critical impact velocity as a function of the solid-liquid contact angle (Duez et al. 2007). Using a rough sphere with a contact angle of 120, Aristoff & Bush (2009) showed that there are four different cavity shapes dependent on the Bond and Weber numbers (i.e., quasi-static, shallow, deep and surface). We experimentally alter the Bond number, Weber number and contact angle of smooth spheres and find two key additions to the literature: 1) Cavity shape also depends on the contact angle; 2) …


Instability Of Flux Flow And Production Of Vortex-Antivortex Pairs By Current-Driven Josephson Vortices In Layered Superconductors, Ahmad Sheikhzada, Alex Gurevich Jan 2019

Instability Of Flux Flow And Production Of Vortex-Antivortex Pairs By Current-Driven Josephson Vortices In Layered Superconductors, Ahmad Sheikhzada, Alex Gurevich

Physics Faculty Publications

We report numerical simulations of the nonlinear dynamics of Josephson vortices driven by strong dc currents in layered superconductors. Dynamic equations for interlayer phase differences in a stack of coupled superconducting layers were solved to calculate a drag coefficient η(J) of the vortex as a function of the perpendicular dc current density J. It is shown that Cherenkov radiation produced by a moving vortex causes significant radiation drag increasing η(v) at high vortex velocities v and striking instabilities of driven Josephson vortices moving faster than a terminal vc. The steady-state flux flow breaks down at ν > v …


Current-Driven Production Of Vortex-Antivortex Pairs In Planar Josephson Junction Arrays And Phase Cracks In Long-Range Order, Francisco Estellés-Duart, Miguel Ortuño, Andrés M. Somoza, Valerii M. Vinokur, Alex Gurevich Oct 2018

Current-Driven Production Of Vortex-Antivortex Pairs In Planar Josephson Junction Arrays And Phase Cracks In Long-Range Order, Francisco Estellés-Duart, Miguel Ortuño, Andrés M. Somoza, Valerii M. Vinokur, Alex Gurevich

Physics Faculty Publications

Proliferation of topological defects like vortices and dislocations plays a key role in the physics of systems with long-range order, particularly, superconductivity and superfluidity in thin films, plasticity of solids, and melting of atomic monolayers. Topological defects are characterized by their topological charge reflecting fundamental symmetries and conservation laws of the system. Conservation of topological charge manifests itself in extreme stability of static topological defects because destruction of a single defect requires overcoming a huge energy barrier proportional to the system size. However, the stability of driven topological defects remains largely unexplored. Here we address this issue and investigate numerically …


Catalysis Of Stark-Tuned Interactions Between Ultracold Rydberg Atoms, A. L. Win, W. D. Williams, T. J. Carroll, C. I. Sukenik Sep 2018

Catalysis Of Stark-Tuned Interactions Between Ultracold Rydberg Atoms, A. L. Win, W. D. Williams, T. J. Carroll, C. I. Sukenik

Physics Faculty Publications

We have experimentally investigated a catalysis effect in the resonant energy transfer between ultracold 85Rb Rydberg atoms. We studied the time dependence of the process, 34p + 34p → 34s + 35s, and observed an enhancement of 34s state population when 34d state atoms are added. We have also performed numerical model simulations, which are in qualitative agreement with experiment and indicate that the enhancement arises from a redistribution of p-state atoms due to the presence of the d-state atoms.


Developing A Femtosecond Stimulated Raman Spectroscopy Experiment For Solid State Materials, Daniel Hammerland Aug 2018

Developing A Femtosecond Stimulated Raman Spectroscopy Experiment For Solid State Materials, Daniel Hammerland

Electronic Theses and Dissertations

Femtosecond Stimulated Raman Spectroscopy (FSRS) is a ultrafast spectroscopy technique first implemented by chemists to understand isomerization and other ultrafast molecular morphology changes by resolving vibrational dynamics[1, 2, 3]. FSRS has an unparalleled temporal and spectral resolution [4, 1, 5, 6] that arises as a result of a clever combination of picosecond and femtosecond pulses. However, despite this capability, FSRS has yet to be applied to modern materials in condensed matter physics. This thesis explores the design and implementation of FSRS to study two-dimensional materials in order to measure their quantum confined vibrational dynamics on utlrafast time scales.


Emergent Phenomena In Quantum Critical Systems, Kun Chen Jul 2018

Emergent Phenomena In Quantum Critical Systems, Kun Chen

Doctoral Dissertations

A quantum critical point (QCP) is a point in the phase diagram of quantum matter where a continuous phase transition takes place at zero temperature. Low-dimensional quantum critical systems are strongly correlated, therefore hosting nontrivial emergent phenomena. In this thesis, we first address two decades-old problems on quantum critical dynamics. We then reveal two novel emergent phenomena of quantum critical impurity problems. In the first part of the thesis, we address the linear response dynamics of the $(2+1)$-dimensional $O(2)$ quantum critical universality class, which can be realized in the ultracold bosonic system near the superfluid (SF) to Mott insulator (MI) …


Elementary Computational Fluid Dynamics Using Finite-Difference Methods, Jason Turner, Scott Labrake Jun 2018

Elementary Computational Fluid Dynamics Using Finite-Difference Methods, Jason Turner, Scott Labrake

Honors Theses

Fluids permeate all of human existence, and fluid dynamics serves as a rich field of research for many physicists. Although the mathematics involved in studying fluids tends to get complicated, the physical intuition gained through daily exposure to such systems bridges the gap between abstract calculations and their physical meaning. We discuss the mathematical treatment and simulations of fluid flows found in everyday life, such as flow in a cavity and through a pipe. Our discussions follow the example set by several notable texts, referenced in the document.


Toy Blocks And Rotational Physics, Gabriele U. Varieschi, Isabel R. Jully Dec 2016

Toy Blocks And Rotational Physics, Gabriele U. Varieschi, Isabel R. Jully

Gabriele Varieschi

Have you ever observed a child playing with toy blocks? A favorite game is to build towers and then make them topple like falling trees. To the eye of a trained physicist this should immediately look like an example of the physics of “falling chimneys,” when tall structures bend and break in mid-air while falling to the ground. The game played with toy blocks can actually reproduce well what is usually seen in photographs of falling towers, such as the one that appeared on the cover of the September 1976 issue of The Physics Teacher.1 In this paper we describe …


Toy Models For The Falling Chimney, Gabriele U. Varieschi, Kaoru Kamiya Dec 2016

Toy Models For The Falling Chimney, Gabriele U. Varieschi, Kaoru Kamiya

Gabriele Varieschi

In this paper we review the theory of the ‘‘falling chimney,’’ which deals with the breaking in mid-air of tall structures when they fall to the ground. We show that these ruptures can be caused by either shear forces typically developing near the base, or by the bending of the structure which is caused primarily by the internal bending moment. In the latter case the breaking is more likely to occur between one-third and one-half of the height of the chimney. Small scale toy models are used to reproduce the dynamics of the falling chimney. By examining photos taken during …


Random Field Disorder At An Absorbing State Transition In One And Two Dimensions, Hatem Barghathi, Thomas Vojta Feb 2016

Random Field Disorder At An Absorbing State Transition In One And Two Dimensions, Hatem Barghathi, Thomas Vojta

Physics Faculty Research & Creative Works

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, …


Yoyo Lab (Prelab), David Abbott Jan 2016

Yoyo Lab (Prelab), David Abbott

Handouts

No abstract provided.


Yoyo Lab (In-Lab), David Abbott Jan 2016

Yoyo Lab (In-Lab), David Abbott

Handouts

No abstract provided.


Rate Kinetics And Molecular Dynamics Of The Structural Transitions In Amyloidogenic Proteins, Timothy Michael Steckmann Jan 2016

Rate Kinetics And Molecular Dynamics Of The Structural Transitions In Amyloidogenic Proteins, Timothy Michael Steckmann

FIU Electronic Theses and Dissertations

Amyloid fibril aggregation is associated with several horrific diseases such as Alzheimer’s, Creutzfeld-Jacob, diabetes, Parkinson’s and others. The process of amyloid aggregation involves forming myriad different metastable intermediate aggregates. Amyloid fibrils are composed of proteins that originate in an innocuous α-helix or random-coil structure. The α-helices convert their structure to β-strands that aggregate into β-sheets, and then into protofibrils, and ultimately into fully formed amyloid fibrils. On the basis of experimental data, I have developed a mathematical model for the kinetics of the reaction pathways and determined rate parameters for peptide secondary structural conversion and aggregation during the entire fibrillogenesis …


Fragmentation Of Fast Josephson Vortices And Breakdown Of Ordered States By Moving Topological Defects, Ahmad Sheikhzada, Alex Gurevich Jan 2015

Fragmentation Of Fast Josephson Vortices And Breakdown Of Ordered States By Moving Topological Defects, Ahmad Sheikhzada, Alex Gurevich

Physics Faculty Publications

Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the topologically-protected stability of such defects driven by strong external forces. We focus on Josephson vortices that appear at planar weak links of suppressed superconductivity which have attracted much attention for electronic applications, new sources of THz radiation, and low-dissipative computing. Our numerical simulations show that a rapidly moving vortex driven by a constant current becomes unstable with respect to generation of vortex-antivortex pairs caused by Cherenkov radiation. As a result, …


Algebraic Semi-Classical Model For Reaction Dynamics, Tim Glenn Wendler Dec 2014

Algebraic Semi-Classical Model For Reaction Dynamics, Tim Glenn Wendler

Theses and Dissertations

We use an algebraic method to model the molecular collision dynamics of a collinear triatomic system. Beginning with a forced oscillator, we develop a mathematical framework upon which inelastic and reactive collisions are modeled. The model is considered algebraic because it takes advantage of the properties of a Lie algebra in the derivation of a time-evolution operator. The time-evolution operator is shown to generate both phase-space and quantum dynamics of a forced oscillator simultaneously. The model is considered semi-classical because only the molecule's internal degrees-of-freedom are quantized. The relative translation between the colliding atom and molecule in an exchange reaction …