publications

2025

1. Learning constitutive models and rheology from partial flow measurements

   Alp M. Sunol , James V. Roggeveen , Mohammed G. Alhashim , and 2 more authors

   Oct 2025

   Abs arXiv

   Constitutive laws are at the core of fluid mechanics, relating the fluid stress to its deformation rate. Unlike Newtonian fluids, most industrial and biological fluids are non-Newtonian, exhibiting a nonlinear relation. Accurately characterizing this nonlinearity is essential for predicting flow behavior in real-world engineering and translational applications. Yet current methods fall short by relying on bulk rheometer data and simple fits that fail to capture behaviors relevant in complex geometries and flow conditions. Data-driven approaches can capture more complex behaviors, but lack interpretability or consistency. To close this gap, we leverage automatic differentiation to build an end-to-end framework for robust rheological learning. We develop a differentiable non-Newtonian fluid solver with a tensor basis neural network closure that learns stress directly from arbitrary flow measurements, such as velocimetry data. In parallel, we implement differentiable versions of major constitutive relations, enabling Bayesian model parametrization and selection from rheometer data. Our framework predicts flows in unseen geometries and ensures physical consistency and interpretability by matching neural network responses to known constitutive laws. Ultimately, this work lays the groundwork for advanced digital rheometry capable of comprehensively characterizing non-Newtonian and viscoelastic fluids under realistic in-situ or in-line operating conditions.

2. CMT-Benchmark: A Benchmark for Condensed Matter Theory Built by Expert Researchers

   Haining Pan , James V. Roggeveen , Erez Berg , and 16 more authors

   Oct 2025

   Abs arXiv Code

   Large language models (LLMs) have shown remarkable progress in coding and math problem-solving, but evaluation on advanced research-level problems in hard sciences remains scarce. To fill this gap, we present CMT-Benchmark, a dataset of 50 problems covering condensed matter theory (CMT) at the level of an expert researcher. Topics span analytical and computational approaches in quantum many-body, and classical statistical mechanics. The dataset was designed and verified by a panel of expert researchers from around the world. We built the dataset through a collaborative environment that challenges the panel to write and refine problems they would want a research assistant to solve, including Hartree-Fock, exact diagonalization, quantum/variational Monte Carlo, density matrix renormalization group (DMRG), quantum/classical statistical mechanics, and model building. We evaluate LLMs by programmatically checking solutions against expert-supplied ground truth. We developed machine-grading, including symbolic handling of non-commuting operators via normal ordering. They generalize across tasks too. Our evaluations show that frontier models struggle with all of the problems in the dataset, highlighting a gap in the physical reasoning skills of current LLMs. Notably, experts identified strategies for creating increasingly difficult problems by interacting with the LLMs and exploiting common failure modes. The best model, GPT5, solves 30% of the problems; average across 17 models (GPT, Gemini, Claude, DeepSeek, Llama) is 11.4\pm2.1%. Moreover, 18 problems are solved by none of the 17 models, and 26 by at most one. These unsolved problems span Quantum Monte Carlo, Variational Monte Carlo, and DMRG. Answers sometimes violate fundamental symmetries or have unphysical scaling dimensions. We believe this benchmark will guide development toward capable AI research assistants and tutors.

3. Meshless solutions of PDE inverse problems on irregular geometries

   James V. Roggeveen , and Michael P. Brenner

   Oct 2025

   Abs arXiv

   Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis is defined on a hyperrectangle containing the true domain. We find the coefficients of the basis expansion by solving an optimization problem whereby both the equations, the boundary conditions and any optimization targets are enforced by a loss function, building on a key idea from Physics-Informed Neural Networks (PINNs). Since the representation of the function natively has exponential convergence, so does the solution of the optimization problem, as long as it can be solved efficiently. We find empirically that the optimization protocols developed for machine learning find solutions with exponential convergence on a wide range of equations. The method naturally allows for the incorporation of data assimilation by including additional terms in the loss function, and for the efficient solution of optimization problems over the PDE solutions.

4. HARDMath2: A Benchmark for Applied Mathematics Built by Students as Part of a Graduate Class

   James V. Roggeveen , Erik Y. Wang , Will Flintoft , and 42 more authors

   May 2025

   Abs arXiv Code

   Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based problems ubiquitous in applied science and engineering. To fill this gap, we build on prior work and present , a dataset of 211 original problems covering the core topics in an introductory graduate applied math class, including boundary-layer analysis, WKB methods, asymptotic solutions of nonlinear partial differential equations, and the asymptotics of oscillatory integrals. This dataset was designed and verified by the students and instructors of a core graduate applied mathematics course at Harvard. We build the dataset through a novel collaborative environment that challenges students to write and refine difficult problems consistent with the class syllabus, peer-validate solutions, test different models, and automatically check LLM-generated solutions against their own answers and numerical ground truths. Evaluation results show that leading frontier models still struggle with many of the problems in the dataset, highlighting a gap in the mathematical reasoning skills of current LLMs. Importantly, students identified strategies to create increasingly difficult problems by interacting with the models and exploiting common failure modes. This back-and-forth with the models not only resulted in a richer and more challenging benchmark but also led to qualitative improvements in the students’ understanding of the course material, which is increasingly important as we enter an age where state-of-the-art language models can solve many challenging problems across a wide domain of fields.

5. Micropipette aspiration reveals differential RNA-dependent viscoelasticity of nucleolar subcompartments

   Holly H. Cheng , James V. Roggeveen , Huan Wang , and 3 more authors

   Proceedings of the National Academy of Sciences, May 2025

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   The nucleolus is a multiphasic biomolecular condensate that facilitates ribosome biogenesis, a complex process involving hundreds of proteins and RNAs. The proper execution of ribosome biogenesis likely depends on the material properties of the nucleolus. However, these material properties remain poorly understood due to the challenges of in vivo measurements. Here, we use micropipette aspiration (MPA) to directly characterize the viscoelasticity and interfacial tensions of nucleoli within transcriptionally active Xenopus laevis oocytes. We examine the major nucleolar subphases, the outer granular component (GC) and the inner dense fibrillar component (DFC), which itself contains a third small phase known as the fibrillar center (FC). We show that the behavior of the GC is more liquid-like, while the behavior of the DFC/FC is consistent with that of a partially viscoelastic solid. To determine the role of ribosomal RNA in nucleolar material properties, we degrade RNA using RNase A, which causes the DFC/FC to become more fluid-like and alters interfacial tension. Together, our findings suggest that RNA underlies the partially solid-like properties of the DFC/FC and provide insights into how material properties of nucleoli in a near-native environment are related to their RNA-dependent function.

6. Drift of elastic hinges in quasi-two-dimensional oscillating shear flows

   J. V. Roggeveen , and H. A. Stone

   Physical Review Fluids, Mar 2025

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   In low-Reynolds-number flows, time reversibility makes it impossible for rigid particles to self-propel using reciprocal motions. When passive particles are freely suspended in a background flow that sinusoidally oscillates and is on average stationary, rigid particles are likewise stationary on average. However, as we demonstrate, an elastic particle in such a flow may experience net translation over each period of the flow oscillation. In this paper we analytically and numerically explore the dynamics of particles in steady and oscillatory shear flows. In particular, we study hinges, which we define as a particle consisting of two slender rigid rods joined at one of their ends at a hinge point. We focus on two classes of hinges: rigid hinges, where the two arms of the hinge are fixed relative to each other, and elastic hinges, where the two arms are allowed to rotate relative to each other with a restoring torque provided by a linear torsional spring. Hinges serve as qualitative analogs for curved fibers, which are an important class of particles in many biological and industrial flow applications. We first analyze the motion of elastic hinges in flow-free environments, providing an asymptotic theory to explain the emergence of symmetry breaking in the net translation between a hinge that is initially open versus one that is initially closed. We next turn to studying hinges in flows. In steady shear, both rigid and elastic hinges undergo periodic motions similar to Jeffery orbits with no steady cross-streamline motion. When the hinges are placed in a shear flow whose shear rate oscillates with time, the rigid hinge undergoes no net motion while an elastic hinge’s motion is characterized by attracting cycles in the phase space, which undergo bifurcations as the geometric and flow parameters vary. These cycles lead to nonreciprocal translational motions of the hinge, related to the symmetry-breaking motion presented in the flow-free case, which vary in both magnitude and direction as a function of the controlling parameters. This raises the possibility of designing hinges with particular geometric parameters and then tuning the macroscopic flow properties to control and manipulate the particles while also aiding in particle separation, or, conversely, mixing.

2023

1. Transport of a passive scalar in wide channels with surface topography: An asymptotic theory

   J V Roggeveen , H A Stone , and C Kurzthaler

   Journal of Physics: Condensed Matter, Apr 2023

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   We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our asymptotic theory relies on a domain perturbation approach for small roughness amplitudes of the channel and holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e. the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion diffusion tensor.

2. A calibration-free model of micropipette aspiration for measuring properties of protein condensates

   James V. Roggeveen , Huan Wang , Zheng Shi , and 1 more author

   Biophysical Journal, Oct 2023

   Abs HTML Poster

   There is growing evidence that biological condensates, which are also referred to as membraneless organelles, and liquid-liquid phase separation play critical roles regulating many important cellular processes. Understanding the roles these condensates play in biology is predicated on understanding the material properties of these complex substances. Recently, micropipette aspiration (MPA) has been proposed as a tool to assay the viscosity and surface tension of condensates. This tool allows the measurement of both material properties in one relatively simple experiment, in contrast to many other techniques that only provide one or a ratio of parameters. While this technique has been commonly used in the literature to determine the material properties of membrane-bound objects dating back decades, the model describing the dynamics of MPA for objects with an external membrane does not correctly capture the hydrodynamics of unbounded fluids, leading to a calibration parameter several orders of magnitude larger than predicted. In this work we derive a new model for MPA of biological condensates that does not require any calibration and is consistent with the hydrodynamics of the MPA geometry. We validate the predictions of this model by conducting MPA experiments on a standard silicone oil of known material properties and are able to predict the viscosity and surface tension using MPA. Finally, we reanalyze with this new model the MPA data presented in previous works for condensates formed from LAF-1 RGG domains.

2022

1. Motion of asymmetric bodies in two-dimensional shear flow

   James V. Roggeveen , and Howard A. Stone

   Journal of Fluid Mechanics, Mar 2022

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   At low Reynolds numbers, axisymmetric ellipsoidal particles immersed in a shear flow undergo periodic tumbling motions known as Jeffery orbits, with the orbit determined by the initial orientation. Understanding this motion is important for predicting the overall dynamics of a suspension. While slender fibres may follow Jeffery orbits, many such particles in nature are neither straight nor rigid. Recent work exploring the dynamics of curved or elastic fibres have found Jeffery-like behaviour along with chaotic orbits, decaying orbital constants and cross-streamline drift. Most work focuses on particles with reflectional symmetry; we instead consider the behaviour of a composite asymmetric slender body made of two straight rods, suspended in a two-dimensional shear flow, to understand the effects of the shape on the dynamics. We find that for certain geometries the particle does not rotate and undergoes persistent drift across streamlines, the magnitude of which is consistent with other previously identified forms of cross-streamline drift. For this class of particles, such geometry-driven cross-streamline motion may be important in giving rise to dispersion in channel flows, thereby potentially enhancing mixing.

2017

1. Analysis of alternative energy harvesting methods to power atmospheric robotic explorers on Jupiter

   James Roggeveen , Adrian Stoica , and Marco Dolci

   In 2017 IEEE Aerospace Conference , Mar 2017

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   WindBots is a NIAC funded concept for a longduration atmospheric robot explorer targeting the region between 0.3 bar and 10 bar on Jupiter. The WindBot would explore this region, which extends from 15km above to 125km below the reference surface at 1 bar. Proposed WindBot mission scenarios include a glider which would use updrafts to gain altitude before gliding to find another updraft, mimicking the action of soaring birds such as frigate birds. In another mission scenario, a balloon-like WindBot would use buoyancy to maintain altitude within its operational region. An important requirement of a WindBot is survival with energy obtained in-situ to provide power for the 30-50W avionic payload envisioned for the mission. The solar intensity below Jupiter’s clouds is small and a solar solution as well as a nuclear solution have been ruled out from this study. This paper analyzes methods of energy generation and harvesting in Jupiters atmosphere and offers a comparison of the relative power densities. Wind, thermal, and magnetic energy, as well as other modalities, are sources of energy for a WindBot to transform into mechanical or electrical energy. Mechanisms evaluated include vibration harvesting and turbine technologies to utilize smallscale wind velocity gradients. Natural atmospheric thermal and pressure gradients may be tapped to provide power to a WindBot. The possibility of inductive generation using Jupiters strong magnetic field is also considered. Finally, these methods are evaluated on their power density and applicability to proposed WindBot designs.