Reaction–Diffusion Models for Marine Population Dynamics (MS, PhD)
Model spatial spread, recruitment, mortality, and patch formation in seagrass, oysters, benthic invertebrates, or plankton.

Poroelastic Modeling of Marine Sediments or Biological Tissues (MS, PhD)
Apply poroelastic models to sediment compaction, burrowing organisms, coral tissue deformation, or mangrove root–sediment interactions.

Phase‑Field Modeling of Marine Aggregates, Biofilms, or Marine Snow (MS, PhD)
Simulate aggregation, adhesion, and breakup of marine snow or biofilms using phase‑field methods.

Energetic Variational Models for Coastal Fluid–Structure Interaction (MS, PhD)
Model interactions between vegetation (kelp, seagrass) and coastal flows using energetic variational principles.

Mechanistic Models of Hypoxia, HABs, or Coastal Water Quality (MS, PhD)
Develop mechanistic ODE/PDE models for oxygen depletion, harmful algal bloom initiation, or nutrient cycling.

Hybrid PDE–Agent Models for Marine Organism Behavior (MS, PhD)
Couple PDE environmental fields with agent‑based models of fish, larvae, or plankton.

Multiscale Modeling of Marine Ecosystem Processes (MS, PhD)
Integrate microscale diffusion, mesoscale behavior, and macroscale population dynamics.

Variational Tumor‑Like Growth Models for Marine Organisms (MS, PhD)
Adapt poroelastic + reaction–diffusion tumor models to coral polyps, sponges, or bivalve growth under mechanical stress.

Phase‑Field Models of Coral Skeleton Formation or Biomineralization (MS, PhD)
Apply sintering‑inspired phase‑field models to coral calcification or shell formation.

Poroelastic–Fluid Coupling in Coastal Sediment–Root Systems (MS, PhD)
Model sediment deformation and stabilization by mangrove or seagrass roots.

Reaction–Diffusion–Mechanics Models of Marine Biofilm Expansion (MS, PhD)
Combine reaction–diffusion, phase‑field, and mechanical stress to model biofilm growth on marine structures.

Variational Modeling of Marine Snow Compaction and Settling (MS, PhD)
Treat marine snow aggregates as deformable porous bodies with fluid flow through them.

Energy-Stable Numerical Schemes for Variational Models (UG, MS)
Design numerical schemes that preserve energy dissipation for phase–field, poroelastic, or reaction–diffusion models.

Adaptive Mesh Refinement for Reaction–Diffusion or Phase–Field Models (MS)
Implement AMR for sharp interfaces or moving biological fronts.

GPU Acceleration of PDE Solvers (MS)
Port PDE solvers to GPU using CUDA, JAX, or Numba.

Numerical Bifurcation Analysis for Nonlinear PDE Models (MS)
Use continuation methods to study pattern formation and steady-state transitions.

Numerical Methods for Poroelastic Reaction–Diffusion Systems (MS)
Implement and test schemes for coupled poroelastic + R–D systems.

Energy-Law-Preserving Schemes for Phase–Field–Mechanics Models (MS)
Extend sintering numerical analysis to new physical systems.

Efficient Solvers for Coupled Fluid–Structure Variational Systems (MS)
Develop preconditioners or splitting schemes for variational PDE systems.

NEPA Data Pipelines for Environmental Indicators (UG, MS)
Build reproducible Python workflows to extract timelines, project characteristics, and environmental indicators.

Mechanistic Modeling Driven by Public Environmental Datasets (UG, MS)
Use NOAA, USGS, EPA, or NASA data to drive mechanistic ODE/PDE models.

ML-Assisted Feature Extraction for Environmental or Biological Systems (MS)
Use ML for dimensionality reduction, clustering, or pattern detection.

Integrating Mechanistic Models with Environmental Data for Marine Systems (MS)
Combine mechanistic PDE models with real environmental datasets.

Genetic Data Analysis for Tumor Microenvironment Profiling (MS)
Analyze gene‑expression datasets to estimate immune cell composition, similar to digital cytometry and tumor‑deconvolution methods used in cancer modeling. Build reproducible pipelines for bulk RNA‑seq processing and integrate results into mechanistic tumor models.

Medical Image Processing Pipeline Using TCIA (MS)
Develop a Python‑based workflow to segment tumors from medical images (e.g., TCIA), estimate boundaries, and track tumor shape and location over time. A practical example is analyzing patients with primary colonic tumors to study metastatic spread. Extracted shapes can be used as inputs for mathematical tumor‑growth models.

Particle Methods for Nonlocal Social Interaction Models (UG, MS)
Extend particle methods for Hegselmann–Krause‑type systems to multidimensional or network‑structured interactions.

Control and Intervention in Opinion Dynamics (MS)
Study how interventions shift equilibria in ODE/PDE opinion models.

Multi‑Species Analogs of Opinion Dynamics for Marine Ecology (MS)
Map bounded‑confidence or candidate‑voter dynamics to interacting species with influence kernels.

Nonlocal Interaction Kernels for Marine Species Behavior (MS)
Adapt opinion‑dynamics kernels to model schooling, aggregation, or avoidance in marine organisms.