Cassidy Vetrovec

Certain technical details omitted due to confidentiality and export-control restrictions.

This project develops a customer-facing neural-optimization and engineering-analysis platform for evaluating multiple high-power-laser architectures against user-selected design requirements, performance objectives, and engineering constraints. The project also includes deliverable designs and test results from multiple laser architectures, with design aided by the program. The platform combines trained deep neural models with data-management, validation, visualization, and optimization workflows, allowing engineers to explore architectural alternatives and conduct design trade studies through an interactive MATLAB interface. Specific laser models, datasets, network implementations, performance requirements, and customer applications are omitted from the public description.

Certain technical details omitted due to confidentiality and export-control restrictions.

This government-funded R&D project investigates methods for maintaining laser beam-pointing stability under mechanically dynamic operating conditions. The work spans experimental disturbance reproduction, optomechanical design, adaptive-dynamic-system modeling, signal processing, machine learning, and real-time control.

Interactive 3-D computational-physics platform connecting ephemeris-driven solar-system dynamics, a modeled supermassive-black-hole binary inspiral, and LISA (Laser Interferometer Space Antenna) detector geometry. The simulator resolves evolving gravitational-wave strain and corresponding changes in LISA's laser-linked arm lengths while distinguishing physical measurements from deliberately amplified visualization.

Interactive 2-D x–z PWR (pressurized water reactor)-like forward model coupling two-group neutron diffusion, fuel and coolant thermal response, feedback effects, and control-rod motion. The simulator provides the physical and computational foundation for subsequent PINN-based (Physics-Informed Neural Network) state inference from sparse measurements.

Physics-Informed Neural Network (PINN) derivation and application for transient heat conduction using sparse temperature measurements. This self-directed project documents my derivation of the neural-network and physics-constrained training framework, then applies it to thermal-field reconstruction governed by the transient heat equation and boundary conditions. It serves as a technical precursor artifact to my later work in AI-assisted laser optimization. See the attached document for derivations, implementation details, and results.

Certain technical details omitted due to confidentiality and export-control restrictions.

Developed image-processing and computational software capable of estimating laser beam quality metrics from limited beam image measurements. A GUI was created for the program in MATLAB.

Certain technical details omitted due to confidentiality and export-control restrictions.

Developed proprietary mathematical and machine-learning frameworks for analyzing and forecasting Exchange-Traded Fund (ETF) and equity behavior, including stock market responses to disturbances. The primary framework incorporates dynamic-systems modeling, statistical learning, optimization, and other nonlinear methods with modeling procedures designed and validated across multiple market regimes and regime transitions. Separately developed volatility models for comparative analysis against option-implied volatility. This work is methodologically distinct from the market-dynamics framework. Additional methods, model structures, validation procedures, and implementation details remain proprietary. I welcome academic and mathematical discussion with researchers and practitioners in quantitative finance (especially options), applied mathematics, nonlinear dynamics, and machine learning.

Strain-Gauge Cantilever Scale: Physics-Based Estimation vs Experimental Calibration

Mechanics of Materials Laboratory: Built and instrumented a 6061-T6 aluminum cantilever scale using a bonded strain gauge, quarter-bridge Wheatstone circuit, signal amplification, a 14-bit data-acquisition device, and a custom LabVIEW interface. I developed two independent methods for inferring applied load: a first-principles model derived from beam-bending mechanics and strain-gauge response, and an empirical model obtained through four-point calibration. I compared their accuracy, repeatability, and propagated uncertainty under repeated placement and progressive unloading. The calibrated method closely matched reference measurements, while the mechanics-based method remained repeatable but exhibited a systematic sensitivity discrepancy.

This project developed a functional load-measurement system from the physical transducer through the final software interface. I prepared the aluminum cantilever, bonded and wired the strain gauge, incorporated it as the active element of a quarter-bridge Wheatstone circuit, and connected the resulting signal to an amplified data-acquisition system. A gain of 900 allowed the bridge’s millivolt-scale response to be resolved by the 14-bit analog-to-digital converter. I created a LabVIEW program to acquire the amplified bridge voltage continuously and process 1,000 samples for each saved measurement. The interface calculated and displayed the mean voltage, signal variation, inferred strain, and load estimates while retaining the data required for subsequent calibration and uncertainty analysis. A reusable sub-VI performed the mechanics-based load calculation from the measured signal and physical beam parameters. The first estimation method was derived from strain-gauge response and cantilever-beam bending theory. The amplified bridge voltage was converted into strain, the strain was converted into bending stress using the beam’s elastic modulus, and the resulting stress was related to the applied end load through the beam geometry and moment arm. The second method used four known calibration weights to establish an empirical linear relationship between amplified voltage and applied load. The resulting calibration coefficient was approximately 8.58 ± 0.642 N/V. This approach absorbed the combined response of the physical beam, bonded sensor, circuit, amplifier, and data-acquisition system rather than depending exclusively on their nominal parameters. I evaluated both methods through repeated placement of the same load and through progressive unloading of a water bottle. For a reference load of 2.471 N, the repeated-placement experiment produced a mean mechanics-based estimate of 2.755 N with a standard deviation of 0.020 N and a mean calibrated estimate of 2.471 N with a standard deviation of 0.018 N. The mechanics-based method was repeatable but consistently overpredicted the applied load, indicating a systematic difference between the idealized analytical sensitivity and the behavior of the assembled measurement system. The calibrated method produced better agreement with the reference scale, although its propagated uncertainty also included uncertainty in the fitted calibration coefficient. This distinction provided a practical comparison between repeatability, precision, accuracy, and model bias. Both methods successfully tracked progressive unloading and approached the independently measured empty-bottle weight. The experiment also revealed practical limitations involving beam oscillation, load-placement variation, sensor and amplifier uncertainty, idealized boundary conditions, and uncertainty in the effective geometry and material properties. Proposed improvements included more repeatable load positioning, mechanical damping, additional calibration points, and refinement of the analytical sensitivity model. System Outputs: - Continuous amplified-voltage acquisition. - Mean and variation across 1,000 samples. - Real-time strain estimation. - Physics-based load estimation. - Empirically calibrated load estimation. - Saved measurement history and visualization. - Repeatability and progressive-unloading analysis. - Propagated uncertainty for both estimation methods. Methods & Technologies: - Cantilever-Beam Bending - Strain-Gauge Instrumentation - Wheatstone-Bridge Circuits - Signal Amplification - LabVIEW and Sub-VI Development - 14-Bit Data Acquisition - Experimental Calibration - Uncertainty Propagation - Monte Carlo Analysis - Repeatability Testing - Model–Experiment Comparison

Cold-War Orbital Forensics: From State Vector to Ground Track

Two-Part Individual Astrodynamics Project: Developed a modular MATLAB toolchain for reconstructing and propagating an unknown spacecraft orbit from a single Earth-centered inertial position and velocity state. In Part I, I derived the true-anomaly time-of-flight integral, implemented Gauss–Legendre quadrature, recovered orbital properties and node-crossing times, and evaluated numerical convergence. Part II extended the analysis through Newton-based anomaly propagation, position and velocity reconstruction, ECI-to-ECEF transformation, geocentric longitude and latitude calculation, three-dimensional orbit visualization, and Earth-relative ground-track analysis.

This two-part project developed a small astrodynamics analysis toolchain from an initial Earth-centered inertial position and velocity vector. The work progressed from deriving the time required to move between two true anomalies to propagating the complete orbit and evaluating its motion relative to the rotating Earth. Part I began with the relationship between specific angular momentum, orbital radius, and true-anomaly rate. I combined this relationship with the conic-section orbit equation to derive an integral for elapsed flight time between two true anomalies. I then implemented the integrand and a Gauss–Legendre quadrature routine in MATLAB. Using the supplied state vector, I calculated the orbit’s angular momentum, semi-latus rectum, eccentricity, semi-major axis, period, line of nodes, and the true anomalies associated with the ascending and descending equatorial crossings. The reconstructed orbit had a period of approximately 12.03 hours and an eccentricity of approximately 0.738. I evaluated the time-of-flight integral using 10, 15, 20, and 25 Gauss points. The calculated node-to-node flight times converged to approximately 11.10158 hours along the apoapsis-side arc and 0.928043 hours along the periapsis-side arc. Their sum agreed with the independently calculated orbital period, providing a numerical consistency check. Part II extended this work into time-dependent trajectory propagation. I implemented a Newton root-finding routine that inverted the time-of-flight relation to recover true anomaly at successive timestamps. The resulting anomaly values were used to reconstruct position and velocity vectors throughout the orbit. I then developed the coordinate-processing pipeline required for Earth-relative analysis: an Earth-centered inertial to Earth-centered Earth-fixed direction-cosine matrix, time-indexed coordinate transformation, and conversion from Earth-fixed Cartesian position to geocentric longitude and latitude. These functions generated both a three-dimensional inertial trajectory and a Mercator ground track over two orbital periods. The propagated trajectory reached a maximum geocentric latitude of approximately 63.4 degrees and produced extended residence near apoapsis over two northern longitude regions. The ground track also displayed an apparent longitudinal reversal near apoapsis. This occurred because the spacecraft’s projected eastward motion decreased sufficiently that Earth’s rotation temporarily dominated its motion in the Earth-fixed frame. The geographic and mission interpretations were components of a Cold-War scenario rather than definitive spacecraft identification. The analysis used an ideal two-body orbit, constant Earth rotation, geocentric latitude, and a simplified Earth-orientation convention. Perturbations, an initial Greenwich-angle offset, atmospheric effects, and operational ephemeris corrections were outside the project scope. Computational Workflow of the Toolchain: - Accepted an initial ECI position and velocity state. - Recovered the associated classical orbital elements. - Derived and numerically evaluated time of flight between true anomalies. - Identified ascending and descending equatorial crossings. - Evaluated Gauss–Legendre quadrature convergence. - Propagated true anomaly through Newton iteration. - Reconstructed time-indexed position and velocity vectors. - Transformed positions from ECI to ECEF coordinates. - Calculated geocentric longitude and latitude. - Generated three-dimensional orbit and ground-track visualizations. - Evaluated regional residence and Earth-relative trajectory behavior. Methods & Technologies: - MATLAB - Two-Body Orbital Mechanics - State-Vector and Orbital-Element Conversion - True-Anomaly Time-of-Flight Analysis - Gauss–Legendre Quadrature - Newton Root Finding - Numerical Orbit Propagation - ECI-to-ECEF Coordinate Transformation - Direction-Cosine Matrices - Geocentric Longitude and Latitude - Ground-Track Visualization - Earth-Relative Motion Analysis

Steady 2-D Heat Conduction with Finite Differences and Successive Over-Relaxation

Independent Numerical Methods Coursework: Developed a MATLAB solver for the steady two-dimensional heat equation in a plate with prescribed boundary conditions. I discretized Laplace’s equation using finite differences, implemented an iterative relaxation solver, and evaluated temperature distributions, wall heat fluxes, and convergence behavior. A relaxation-parameter sweep identified λ=1.91 as the most efficient tested setting, converging in 258 iterations.

This project applied classical numerical methods to reconstruct the steady temperature field of a two-dimensional plate. Starting from Laplace’s equation, that is, nill temperature divergence, I derived finite-difference relationships for each interior node T_{i,j} ​and incorporated separate equations for the plate boundaries. The resulting algebraic system was solved iteratively in MATLAB using a relaxation-based update scheme. A central objective was to examine how the relaxation coefficient, λ, affected convergence efficiency. I evaluated values from 0.9 to 1.98. The standard relaxation case, λ=1.0, required 6,250 iterations to converge, while the fastest tested result occurred near λ=1.91, requiring only 258 iterations. Values beyond this point began to increase the iteration count again, illustrating the practical trade-off between under-relaxation, acceleration, and instability. The final solver generated: - A two-dimensional temperature-distribution surface. - A temperature contour map. - Finite-difference heat-flux profiles along selected plate boundaries. - Numerical heat-flow estimates using trapezoidal integration of the boundary fluxes.

Mechanical Characterization through Tensile & Compression Testing

Mechanics of Materials Laboratory: Characterized the tensile response of an unknown metal, biaxial carbon-fiber composite, and nylon, together with the compressive response of plaster of Paris, using an Instron 5967 Universal Testing Machine. I converted load, extensometer, and crosshead-displacement measurements into engineering stress–strain curves, correcting non-extensometer measurements for machine compliance. From these results, I evaluated elastic modulus, yield behavior, ultimate and fracture strengths, toughness, elongation, specific properties, failure modes, and measurement uncertainty. The unknown metal’s measured mechanical behavior was most consistent with 2014-T3 aluminum.

This experiment examined how material behavior can be reconstructed from destructive tensile and compression testing. An unknown metal, biaxial carbon-fiber composite, and nylon specimen were loaded in tension, while a cylindrical plaster-of-Paris specimen was loaded in compression. Testing was performed with an Instron 5967 Universal Testing Machine and a 30-kN load cell; an Instron extensometer provided direct strain measurements for the unknown metal. For specimens measured through crosshead displacement, I modeled the testing machine and specimen as a coupled compliance system and subtracted the machine’s calculated deformation from the total measured displacement. I then converted the corrected measurements into engineering stress and strain and generated a stress–strain curve for each material. From these curves, I extracted elastic modulus, yield strength, 0.2% offset yield strength, ultimate strength, fracture strength, toughness, and elongation where applicable. I also compared strength- and stiffness-to-density relationships among the materials and examined their post-failure geometries to distinguish ductile and brittle behavior. The unknown-metal specimen received additional analysis. I used repeated micrometer measurements to estimate its cross-sectional geometry, created a SolidWorks model to estimate specimen volume, propagated dimensional and instrumentation uncertainties through the calculated properties, and used Monte Carlo sampling to estimate uncertainty in the fitted elastic modulus. I also transformed the response into true stress and true strain and explored a strain-hardening model over the plastic region. The unknown specimen produced an elastic modulus of approximately 77.13 GPa, a yield strength of 284.36 MPa, an ultimate tensile strength of 458.6 MPa, and elongation of approximately 19–21%. Comparison with published material properties indicated that its measured mechanical response was most consistent with 2014-T3 aluminum. Because the identification was based on a single specimen and not every measured property aligned equally well with reference data, the result was treated as an engineering approximation rather than definitive alloy verification. Key Results: - The unknown metal exhibited ductile behavior, including substantial plastic deformation and an approximately 45-degree fracture surface. - The biaxial carbon-fiber composite achieved the greatest measured ultimate strength and highest specific strength but fractured without appreciable yielding. - Nylon underwent extensive plastic deformation and exhibited substantially lower stiffness and strength than the metal and composite. - Plaster of Paris failed brittly under compression and exhibited the lowest measured toughness. Machine-compliance correction materially improved strain estimation for specimens without direct extensometer measurements. - Uncertainty analysis connected instrument precision and dimensional variation to confidence in the derived mechanical properties. Methods & Technologies: - Instron 5967 Universal Testing Machine - Instron 2630-series extensometer - Engineering and true stress–strain analysis - Machine-compliance correction - 0.2% offset-yield determination - Numerical toughness integration - Failure-surface interpretation - Monte Carlo uncertainty estimation - SolidWorks volume modeling - Excel data processing and visualization