Energy systems
Near-real-time computation for CO₂ transport
Composite stiff-system methods for rapid estimates of phase behavior, impurity effects, and operational transitions in carbon-dioxide pipelines.
Research · Computation · Field Intelligence
Mathematics for systems
that refuse to be simple.
DigitronX, LLC is a Missouri research and scientific-software company developing computational methods for multiphase flow, carbon capture, utilization and storage, stiff dynamical systems, and behavioral health measurement.
Springfield, MissouriEstablished 2026Independent research
Research programs
Where hard science meets usable computation.
Our work is organized around problems in which conventional computation becomes too slow, too fragile, or too detached from physical reality.
01
Multiphase flow
Fast, physically grounded computation for complex gas–liquid flow, measurement, and real-time operational decisions.
Explore topic →02CCUS measurement
Methods for CO₂ transport, impurity effects, custody transfer, and defensible uncertainty assessment.
Explore topic →03Stiff systems
Singular-perturbation and composite methods designed to turn severe stiffness from a burden into a computational advantage.
Explore topic →04Computational psychiatry
Mathematical approaches to diagnostic agreement, population heterogeneity, biomarkers, and clinical decision-making.
Explore topic →Current work
Problems under active investigation.
DigitronX is building a focused research portfolio rather than a catalog of generic services. These programs share a common aim: results that are mathematically sound, physically interpretable, and useful on the timescale of a real decision.
Measurement
Defensible CCUS custody transfer
A measurement framework linking equation-of-state uncertainty, multiphase behavior, instrument response, and the evidence required for an auditable transfer certificate.
Numerical methods
The stiffer the better
A renewed program in singular perturbation: identify the fast structure, replace brute-force integration where justified, and preserve physical constraints across regimes.
Behavioral health
The mathematics of diagnostic reliability
Research showing how apparent agreement depends not only on diagnosticians, but also on thresholds, population heterogeneity, and where subjects lie relative to a decision boundary.
Research descriptions identify active directions; they are not claims of completed commercial products.
The DigitronX method
From a difficult measurement to a defensible decision.
- 01Field measurements
Pressure, temperature, density, composition, and operating context
- 02Physical model
Conservation laws, phase behavior, instrument response, and uncertainty
- 03Stiff-system reduction
Exploit separated time scales instead of resolving every transient
- 04Validity diagnostic
Identify when the reduced model is—and is not—trustworthy
- 05Operational estimate
A fast, interpretable answer with its limits made explicit
Phase-flow capability
Models fast enough for the control room—and honest enough to say when they should not be trusted.
DigitronX occupies an uncommon intersection: numerical methods for severely stiff dynamic systems, firsthand field measurement of two-phase pipeline flow, and CO₂/acid-gas process chemistry. This combination supports physics-based monitoring and prediction that is fast enough for operational use, continuously recalibrated from available measurements, and equipped to indicate when its reduced model should no longer be trusted.
Real-time transient modeling
Reduced-order and composite methods for stiff pipeline dynamics, transient forecasting, virtual flow metering, and continuous recalibration against sparse pressure and temperature measurements.
Two-phase flow measurement
Interpretation of gas–liquid flow regimes in offshore and hilly-terrain pipelines, grounded in firsthand field measurement and the practical limits of instrumentation.
CO₂ transport and acid-gas chemistry
Analysis of impurity effects, selective H₂S removal, high-pressure gas purification, phase behavior, and measurement consequences for CCUS transport.
Measurement models and diagnostics
Measurement equations, uncertainty models, dynamic response, failure signatures, self-validating diagnostics, and instrument-selection strategy—not measurement-hardware development.
Stability, safety, and control criteria
Perturbation-derived, criterion-based analysis for stiff reacting and transport systems—designed to produce interpretable go/no-go boundaries rather than opaque numerical output.
Field and scientific foundation
Digitron, Inc. field systems studied offshore and hilly-terrain gas-condensate pipelines for Shell, Mobil, and Standard Oil of California (Chevron), with results reported through the American Gas Association. Related peer-reviewed work addressed stiff computation, CO₂/H₂S separation, gas purification, stability, and process control.
Engagements
Technical consulting and algorithm development · CCUS measurement strategy · independent technical review · advisory work with metering, digital-twin, and virtual-flow-metering teams · lecturing and training
Why the method is different
Conventional solvers can spend their greatest effort resolving dynamics that have already relaxed. DigitronX uses singular-perturbation structure to remove that unnecessary computational burden—while retaining a diagnostic that indicates when the reduced model is no longer trustworthy.
What DigitronX can deliver
Technical work products—not generic advice.
- 01Reduced-order transient models
- 02Virtual-flow-metering algorithms
- 03In-line model-validity diagnostics
- 04CO₂ impurity and phase-transition analyses
- 05Measurement uncertainty assessments
- 06Prototype scientific software and computational proofs of concept
Selected field record
Measurement where the physics becomes inconvenient.
1985 · Hilly-terrain system
Rickman–Painter
Two-phase measurement in a hilly-terrain gas-condensate pipeline, where elevation changes, liquid accumulation, and intermittent behavior complicated conventional interpretation.
1986 · Offshore system
Matagorda offshore system
Field observations using gamma-transmission measurement to characterize gas–liquid behavior through a steel offshore pipeline system under operating conditions.
Selected technical foundations
Evidence behind the capability.
A selective record of the field, computational, chemical, and stability work underlying current DigitronX programs.
Stiff Computation
Oxford University Press edited volume bringing together state-of-the-art mathematical and numerical approaches to stiff systems.
Rickman–Painter
Two-phase flow measurement in a hilly-terrain pipeline system; American Gas Association research publication.
Matagorda offshore system
Field observations of two-phase flow in an offshore pipeline system; American Gas Association research publication.
Parameter estimation
Stage-wise parameter estimation for stiff differential equations, published in AIChE Journal.
CO₂ and H₂S chemistry
Peer-reviewed work on selective H₂S removal from CO₂ streams and high-pressure selective gas purification.
Stability criteria
A graded damping-factor criterion for explosion limits in H₂–O₂ kinetics, published in Combustion and Flame.
An Effective Numerical Integration Method for Typical Stiff Systems
AIChE Journal paper with Leon Lapidus establishing the equivalence between stiff and singularly perturbed systems as the basis of a practical numerical method.
Selected published work
A technical record spanning computation, chemistry, and field measurement.
A selective list relevant to current DigitronX programs. A fuller scholarly record is available through the founder's ORCID profile.
An Effective Numerical Integration Method for Typical Stiff Systems
AIChE Journal 20, 368 · with Leon Lapidus
Pseudo Steady State Approximation for the Numerical Integration of Stiff Kinetic Systems
AIChE Journal 21, 917 · with Leon Lapidus
Problem Approximation for Stiff Ordinary Differential Equations
AIChE Journal 21, 1227 · with Leon Lapidus
Selective Removal of H₂S from CO₂ by Absorption and Reaction in Sprays
AIChE Journal 29, 66 · with E. Bendall
Two-Phase Flow Measurement of the Rickman–Painter System
American Gas Association research publication
Field Observations of Two-Phase Flow in the Matagorda Offshore Pipeline System
American Gas Association research publication
Stage-wise Parameter Estimation for Stiff Differential Equations
AIChE Journal 32, 195–199 · with V. Srinivasan
Selective Absorption of H₂S from CO₂—Factors Controlling Selectivity Toward H₂S
Fuel Processing Technology · with V. Srinivasan
Underlying methods
The stiffer,
the better.
DigitronX revives a distinctive line of work: using asymptotic structure to extract reliable answers from systems that defeat ordinary numerical approaches.
- 01Composite asymptotic methods for stiff differential equations
- 02Near-real-time scientific computation
- 03Multiphase-flow measurement and interpretation
- 04CO₂ and H₂S thermodynamics
- 05Diagnostic reliability and psychometric modeling
- 06Translation between mathematical theory and field practice
Current scholarship
Research in motion.
Current work is listed transparently by status. Manuscripts under consideration have not yet been accepted or published. Statuses were last updated in August 2026.
Psychoneuroimmunology
Selective Tightening of Acute-Phase Coupling in Depression
Examines how depression changes the coordination of acute-phase biomarkers, using MIDUS 2 data to distinguish altered coupling from simple changes in biomarker levels.
Revision in progress · 2026
Biomarker psychiatry
Why Biomarker Studies in Depression Disagree
Shows how differences in biomarker covariance can change subtype classification and diagnostic agreement even when marginal biomarker distributions are identical.
Under editorial review · 2026
Dynamical psychology
Stability and Recovery in Coupled Psychological Systems
Separates coupling from recovery through Lyapunov and input-to-state stability, yielding estimable contraction, perturbation, and threshold-crossing quantities.
Under editorial review · 2026
Reliability methods
Standardizing Inter-rater and Test–retest Reliability Across Populations
Develops a latent-response transport method for separating population heterogeneity from measurement error and comparing reliability across populations.
Under review · 2026
CCUS measurement
Impurity-Aware CO₂ Custody-Transfer Measurement
Builds a defensible custody-transfer framework around composition, phase behavior, equation-of-state uncertainty, and the limits of real instruments.
Under review · 2026
CCUS measurement
Dynamic Composition-Sampling Bias in CO₂ Custody Transfer
Analyzes how sampling lag and changing composition can create systematic transfer errors that static uncertainty calculations do not reveal.
Under review · 2026
CO₂ pipeline modeling
Trajectory-Based Verification of Thermodynamic Tables for Transient Pure-CO₂ Pipeline Depressurization
Tests thermodynamic tables along transient depressurization trajectories, focusing verification on the states actually encountered by a pipeline model.
Under review · 2026
CCS thermodynamics
Acoustically Optimal State Points for Constraining CCS Mixture Models
Identifies sound-speed measurements that are most informative for constraining CO₂ mixture models in the region most important to custody-transfer metering.
Under review · 2026
CCUS field measurement
Gamma Densitometry of Two-Phase CO₂ Pipeline Flow
Reanalyzes a 1987 field record to examine what gamma densitometry can still contribute to modern two-phase CO₂ pipeline measurement and assurance.
Under review · 2026
Additional work in development extends these programs into composite CO₂ decompression models, correction-induced measurement error, observability limits, multirate estimation, and equation-of-state diagnostics.
Forthcoming book
Under contract with Routledge
A Practitioner's Guide to Clinical Presence:
Staying Engaged and Preventing Burnout
A practical, research-grounded framework for detecting attentional drift, regulating emotional activation, and preventing carryover between clinical encounters.
1983 → 2026
From measurement in the field to computation at decision speed.
The original Digitron, Inc. combined gamma-ray sensing, mathematical inversion, and field engineering to examine multiphase flow through steel pipelines for major oil and gas operators.
DigitronX, LLC is a newly established and legally distinct company. It carries forward the intellectual method—not a claim of continuous corporate operation: begin with the physics, respect the measurement, and make the mathematics serve the field decision.
Founder
Richard C. Aiken, MD, PhD
A career spanning numerical analysis, field engineering, psychiatry, and scientific entrepreneurship.
Dr. Aiken earned his PhD at Princeton University and developed early composite asymptotic methods for stiff chemical systems. His academic and research work has included the University of Utah, ETH Zürich, KTH Stockholm, Washington University in St. Louis, and the University of Illinois.
In 1983 he founded Digitron, Inc., applying gamma-ray measurement and mathematical modeling to multiphase petroleum pipelines. DigitronX is a new company—and a new chapter—bringing that combination of theory, measurement, and field judgment to today’s energy and behavioral-health problems.
Company
Serious work.
Independent thinking.
DigitronX, LLC
Research and scientific software
Springfield, Missouri, USA
Current programs include computational methods for multiphase flow and CCUS, with selected work in behavioral-health measurement.
Conversations are welcome with pipeline operators, metering and instrumentation companies, CCUS developers, research consortia, and teams seeking independent review of difficult computational or measurement problems.