About

Roberto Camassa is a Kenan Distinguished Professor in the Department of Mathematics at the University of North Carolina at Chapel Hill. His research interests include applied mathematics, applied analysis, and fluid dynamics. His work involves understanding complex phenomena in these fields, contributing to the advancement of knowledge through his investigations into particulate aggregation, self-assembly in stratified fluids, and chemical delivery in microfluidic systems. His publications reflect a focus on the mathematical mechanisms underlying physical processes, emphasizing the application of mathematical analysis to problems in fluid mechanics and related areas.

Research topics

• Mathematical analysis
• Mathematics
• Physics
• Computer Science
• Mechanics
• Geography
• Meteorology
• Geometry
• Ecology
• Environmental resource management
• Classical mechanics
• Optics
• Thermodynamics
• Environmental science

Selected publications

• Tauberian Identities and Suspended Falls: A Wile E. Coyote Time Lag in the Fall of Stretched Elastic Bodies

  SIAM Review · 2026-05-13

  article1st authorCorresponding
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• Gravitational collapse of liquid layer cavities near boundaries

  Physica D Nonlinear Phenomena · 2025-11-11

  article1st authorCorresponding
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• Diffusion-limited settling of highly porous particles in density-stratified fluids

  Proceedings of the National Academy of Sciences · 2025-06-20

  articleOpen access

  The vertical transport of solid material in a stratified medium is fundamental to a number of environmental applications, with implications for the carbon cycle and nutrient transport in marine ecosystems. In this work, we study the diffusion-limited settling of highly porous particles in a density-stratified fluid through a combination of experiment, analysis, and numerical simulation. By delineating and appealing to the diffusion-limited regime wherein buoyancy effects due to mass adaptation dominate hydrodynamic drag, we derive a simple expression for the steady settling velocity of a sphere as a function of the density, size, and diffusivity of the solid, as well as the density gradient of the background fluid. In this regime, smaller particles settle faster, in contrast with most conventional hydrodynamic drag mechanisms. Furthermore, we outline a general mathematical framework for computing the steady settling speed of a body of arbitrary shape in this regime and compute exact results for the case of general ellipsoids. Using hydrogels as a highly porous model system, we validate the predictions with laboratory experiments in linear stratification for a wide range of parameters. Last, we show how the predictions can be applied to arbitrary slowly varying background density profiles and demonstrate how a measured particle position over time can be used to reconstruct the background density profile.

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• Spontaneous wall suction in stratified fluids: a new phenomenon exhibiting Aristotle’s ancient view of motion

  Research Square · 2025-12-02

  preprintOpen access
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• Video: Diffusion-limited settling of highly porous particles in density-stratified fluids

  2024-11-21

  articleOpen access
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• Hamiltonian shocks

  Studies in Applied Mathematics · 2024-07-09 · 1 citations

  article

  Abstract Wave propagation in the form of fronts or kinks, a common occurrence in a wide range of physical phenomena, is studied in the context of models defined by their Hamiltonian structure. Motivated, for dispersive wave evolution equations such as a strongly nonlinear model of two‐layer internal waves in the Boussinesq limit, by the symmetric properties of a class of front‐propagating solutions, known as conjugate states or solibores, a generalized formulation based purely on the dispersionless reduction of a system is introduced, and a class of undercompressive shock solutions, here referred to as “Hamiltonian shocks,” is defined. This analysis determines whether a Hamiltonian shock, representing locally a kink for the parent dispersive equations, will interact with a sufficiently smooth background wave without inducing loss of regularity, which would take the form of a classical dispersive shock for the parent equations. This property is also related to an infinitude of conservation laws, drawing a parallel to the case of completely integrable systems.

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• Traveling Faraday waves

  UNC Libraries · 2024-06-15

  articleOpen access

  This paper is associated with a video winner of a 2022 American Physical Society's Division of Fluids Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2022.GFM.V0040

  PublisherDOI

• Evolution of Derivative Singularities in Hyperbolic Quasilinear Systems of Conservation Laws

  SIAM Journal on Applied Mathematics · 2024-12-12 · 2 citations

  articleOpen access

  Motivated by problems arising in the piecewise construction of physically relevant solutions to models of shallow water fluid flows, we study the initial value problem for quasilinear hyperbolic systems of conservation laws in 1+1 dimensions when the initial data are continuous with ``corners,” i.e., derivative discontinuities. While it is well known that generically such discontinuities propagate along characteristics, under which conditions the initial corner points may fission into several ones, and which characteristics they end up following during their time evolution, seems to be less understood; this study aims at filling this knowledge gap. To this end, a distributional approach to moving singularities is constructed, and criteria for selecting the corner-propagating characteristics are identified. The extreme case of initial corners occurring with at least a one-sided infinite derivative is special. Generically, these gradient catastrophe initial conditions for hyperbolic systems (or their parabolic limits) can be expected to evolve instantaneously into either shock discontinuities or rarefaction waves. It is shown that when genuine nonlinearity does not hold uniformly and fails at such singular points, the solutions' continuity along with their infinite derivatives persist for finite times. All the results are demonstrated in the context of explicit solutions of problems emerging from applications to fluid flows.

  PublisherOA PDFDOI

• A Hamiltonian set-up for 4-layer density stratified Euler fluids

  arXiv (Cornell University) · 2024-11-15

  preprintOpen access1st authorCorresponding

  By means of the Hamiltonian approach to two-dimensional wave motions in heterogeneous fluids proposed by Benjamin, we derive a natural Hamiltonian structure for ideal fluids, density stratified in four homogenous layers, constrained in a channel of fixed total height and infinite lateral length. We derive the Hamiltonian and the equations of motion in the dispersionless long-wave limit, restricting ourselves to the so-called Boussinesq approximation. The existence of special symmetric solutions, which generalize to the four-layer case the ones obtained in the paper for the three-layer case, is examined.

  PublisherOA PDFDOI

• A Hamiltonian Set-Up for 4-Layer Density Stratified Euler Fluids

  Springer proceedings in mathematics & statistics · 2024-01-01

  book-chapter1st authorCorresponding
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Recent grants

• A Combined Theoretical and Experimental Approach for Internal Wave Dynamics: Coupling to Free Surface and Instabilities

  NSF · $180k · 2015–2019

• "CMG Collaborative Research": A Systematic Approach to Large Amplitude Internal Wave Dynamics: An Integrated Mathematical, Observational, and Remote Sensing Model

  NSF · $153k · 2006–2010

• Strongly Nonlinear Wave and Transport Models in Stratified Fluids

  NSF · $157k · 2005–2009

Frequent coauthors

• Richard M. McLaughlin

  66 shared

• G. Ortenzi

  24 shared

• Gregorio Falqui

  21 shared

• Marco Pedroni

  20 shared

• Daniel M. Harris

  17 shared

• Long Lee

  16 shared

• Claudio Viotti

  14 shared

• Mark Alber

  University of California, Riverside

  13 shared