| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes the application of foundational physical principles to the design, analysis, and optimization of engineered systems. Covers mechanics, materials, thermodynamics, electromagnetism, photonics, acoustics, control theory, micro/nanoscale devices, energy systems, sensors, and applied computational modeling. Excludes purely theoretical physics and engineering fields that do not rely on explicit physical modeling (e.g., organizational systems). |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates from nanoscale semiconductor behavior, micron scale device physics, mesoscopic mechanical structures, and human scale machines to large scale engineered systems such as power grids, aerospace vehicles, and industrial reactors. Timescales range from microsecond transient responses to multi decade system lifetimes. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Materials, structures, devices, sensors, actuators, particles, fields, forces, circuits, control elements, energy carriers, fluids, thermal pathways, wave modes, engineered components, and system-level assemblies governed by physical laws. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Mass, stiffness, conductivity, permittivity, permeability, strength, thermal capacity, damping, stress, strain, efficiency, frequency response, energy density, and material microstructure. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | System types, material categories, device classes, mechanical regimes, electromagnetic regimes, thermal regimes, quantum vs classical behavior ranges, and linear vs nonlinear system classes. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Displacement, velocity, acceleration, stress, strain, temperature, heat flux, current, voltage, charge density, field intensity, wave amplitude, mode occupancy, control inputs, and system response variables. |
| | Parameterization | How variables encode and represent the system’s state. | States encoded through constitutive laws, boundary conditions, material parameters, load profiles, circuit parameters, mode shapes, thermal gradients, and system transfer functions. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Point mass approximations, rigid body assumptions, lumped circuit elements, linear elasticity, small deformation assumptions, ideal gas models, perfect conductors, lossless components, isotropic material assumptions, and simplified boundary conditions. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Valid when geometries are moderate, loads are small, materials remain within elastic limits, frequencies remain in linear bands, fluid flow is not strongly turbulent, and thermal gradients are mild. Breaks down under high strain, nonlinear materials, complex boundary interactions, turbulence, and quantum-dominated regimes. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes engineered systems obey classical physical laws, materials have consistent constitutive behavior, energy is conserved, signals propagate according to known EM or mechanical laws, and system behavior can be modeled with deterministic or controlled stochastic equations. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes material models apply across operational conditions, simplifications capture essential behavior, uncertainty can be bounded, and numerical or analytical models map realistically to real-world performance. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires consistency among physical models (mechanical, thermal, electrical, optical, etc.), material data, system constraints, simulation outputs, and experimental testing. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Entities, variables, and assumptions must integrate into a unified engineering framework linking physics, materials, components, signals, loads, and system-level behavior into a coherent design and analysis structure. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Observable signals include displacement, vibration spectra, stresses and strains, temperature fields, heat flux, voltage, current, electromagnetic field strength, optical intensity, acoustic pressure, fluid velocity, structural deformation, and device response curves. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by sensor resolution, sampling frequency, noise floor, bandwidth constraints, thermal drift, maximum measurable load, dynamic range limits, optical diffraction limits, and electromagnetic interference. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses meters, seconds, newtons, pascals, degrees Celsius, watts, volts, amperes, hertz, decibels, lumens, teslas, siemens, joules, and nondimensional engineering coefficients such as efficiency or gain. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Instruments include strain gauges, accelerometers, thermocouples, infrared cameras, power meters, multimeters, oscilloscopes, laser vibrometers, spectrum analyzers, flow meters, interferometers, load cells, and control system sensors. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Terms such as stiffness, damping ratio, thermal conductivity, electrical resistance, gain, efficiency, stress intensity factor, flow coefficient, and mode shape amplitude are defined through standardized engineering test protocols. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures include calibration runs, load–displacement tests, frequency sweeps, temperature cycling, flow-loop testing, optical alignment procedures, electrical characterization sweeps, and environmental chamber trials. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Data gathered using synchronized multi-sensor setups, fixed sampling rates, trigger-based capture, continuous monitoring, automated control loops, field data logging, and repeated cycling under standardized loads or conditions. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling rules include temporal sampling matched to system bandwidth, spatial sampling across structures or fields, repeated trials for statistical confidence, multi-axis sampling for mechanical systems, and frequency-domain sampling for wave-based phenomena. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Data appears as time series, frequency spectra, displacement maps, strain fields, thermal images, voltage–current curves, optical intensity profiles, flow rate logs, and structural mode shapes. |
| | Resolution | The granularity or precision with which data is captured. | Determined by sensor sensitivity, ADC resolution, noise environment, sampling frequency, optical diffraction, mechanical mounting quality, bandwidth of measurement circuits, and thermal response speed. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses reference loads, electrical standards, thermal calibration blocks, optical power standards, interferometric alignment, flow calibration tanks, vibration reference sources, and repeated zero-offset correction. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from sensor drift, electromagnetic interference, aliasing, thermal fluctuations, mounting misalignment, calibration inaccuracies, noise contamination, material heterogeneity, and hysteresis in mechanical or electrical components. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Stable patterns include Hooke-type stress–strain relations, Ohm’s law behavior, Fourier heat conduction, Navier-Stokes flow characteristics, resonance and damping patterns in mechanical systems, electromagnetic wave propagation laws, and predictable relationships between load, deformation, current, voltage, and temperature. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include conservation of mass, momentum, energy, charge, and flux; symmetry-preserving mode shapes; stable material constants within allowable ranges; and invariant transfer functions under linear system assumptions. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from mechanical forces, thermal gradients, electromagnetic interactions, wave propagation, fluid motion, material deformation, energy conversion processes, feedback loops in control systems, and coupling between multiphysics domains. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include load application leading to deformation, heating leading to thermal expansion, voltage leading to current flow, field excitation producing optical or electromagnetic responses, fluid pressure driving flow, and dynamic forcing producing resonant or damped motion. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include stress, strain, impedance, conductivity, permittivity, permeability, transfer function, damping, efficiency, resonance, thermal gradient, and energy conversion. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Classifies systems as mechanical, electrical, thermal, optical, fluidic, or hybrid; linear or nonlinear; static or dynamic; open-loop or closed-loop; and classical or quantum-enabled engineering devices. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Includes Newton’s laws, Maxwell’s equations, heat diffusion equations, Navier-Stokes equations, circuit equations, wave equations, constitutive material laws, and system transfer function representations. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Uses finite element models, circuit models, thermal models, fluid dynamic models, optical propagation models, multi-body dynamics, lumped parameter models, and multiphysics simulation frameworks. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Idealizations include linear elasticity, perfect insulation, ideal conductors, inviscid flow, neglecting friction or hysteresis, assuming rigidity, simplified geometry, ignoring temperature dependence, and ignoring manufacturing imperfections. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Valid under small deformation, low-speed flow, moderate temperatures, linear material behavior, low noise, weak coupling between domains, and well-posed boundary conditions; breaks down under high strain, high frequency, nonlinear materials, turbulence, or high thermal gradients. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Integrates mechanics, electromagnetism, thermodynamics, fluid dynamics, optics, materials science, and control theory into unified design and analysis frameworks for engineered systems. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Links to electrical engineering, mechanical engineering, materials science, optics, computer science, manufacturing, robotics, applied physics, and systems engineering. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Experiments vary loads, temperatures, voltages, currents, frequencies, optical power, fluid flow rates, material compositions, boundary conditions, and control inputs to determine causal effects on stress, strain, heat transfer, EM response, mechanical vibration, device efficiency, and system stability. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Observational methods monitor naturally occurring system behavior such as fatigue progression, thermal drift, vibration under ambient forcing, passive optical response, or uncontrolled fluid flow without imposed experimental changes. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Hypotheses evaluated by comparing measured stresses, modal frequencies, heat transfer rates, current–voltage curves, field strengths, optical outputs, or flow characteristics with model predictions from mechanical, thermal, electrical, or multiphysics simulations. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Replication achieved using repeated trials, independent instruments, varied sensor placements, different environmental conditions, multiple manufactured samples, and cross-laboratory testing to verify consistency. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Methods include regression of calibration curves, noise estimation, uncertainty quantification, modal analysis, spectral decomposition, system identification, fatigue trend prediction, Monte Carlo evaluation of uncertainty, and confidence interval estimation for performance metrics. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Models compared by accuracy, stability, convergence, predictive power, physical plausibility, computational cost, and robustness to parameter changes or environmental variability across mechanical, thermal, fluidic, and EM domains. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors arise from sensor drift, calibration mismatch, electromagnetic interference, mechanical backlash, thermal lag, optical misalignment, sampling aliasing, noisy power supplies, manufacturing tolerances, and environmental vibrations. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias minimized through blind testing, independent calibration, controlled environmental chambers, redundant sensors, randomized load sequences, cross validation with analytical predictions, and automated data capture to reduce human error. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings evaluated through design reviews, standards compliance audits, cross-team verification, multi-lab replications, engineering test reports, comparative benchmarking, and peer-reviewed publication of results and modeling methods. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Theories revised when repeated experiments reveal nonlinearities, unexpected failure modes, unpredicted damping behavior, anomalous heat flow, electromagnetic cross-coupling, or material responses not captured in existing engineering models. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires detailed disclosure of testing setups, sensor specifications, calibration methods, boundary conditions, environmental conditions, model assumptions, data processing techniques, and uncertainty bounds. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires honest reporting of performance, safe operation of test facilities, adherence to engineering standards, avoidance of selective data removal, responsible handling of hazardous materials or high-power systems, and accurate documentation throughout the engineering process. |