I am interested in theoretical soft matter physics and biophysics. Modeling of complex fluids and elastic materials.

I am currently a research fellow at the Flatiron Institute division of the Simons Foundation working
 with Michael Shelley.

Email: naomiop_at_gmail.com

Membrane rotors: from Euler vorticity dynamics to quasi-geostrophic flows
We show that the dynamics of rotors embedded in a quasi 2D membrane exhibit a power law transition in their interactions from Euler fluid at small distances (1/r), to quasi-geostrophic at large distances (1/r^2).  We derive a Hamiltonian for a discrete system of rotors and describe the conserved quantities. We develop a coarse-grained description for a density field of rotors. We work on theory and simulations for both the discrete and the continuous cases. 

Broken time reversibility of a sphere in a viscous fluid falling near an elastic wall

When a sphere moves next to a solid wall it experiences an increased drag, but no normal force. If, however, elasticity is introduced, then coupling between hydrodynamics and elasticity can break the time-reversal symmetry of the Stokes equations. We describe (theoretically and experimentally) a case in which a sphere is falling due to gravity next to a suspended elastic sheet. We predict the induced normal force created on the sphere in the lubrication limit and verify the predictions via experiments. The sphere will move away from the sheet with a velocity which is proportional to the square of its translational velocity and inversely proportional to the bending modulus and the tension of the sheet. 

Motion of hot sphere in viscous fluids

Imagine a sphere falling through a fluid, what will be the connection between the force acting on the sphere and its velocity? 
For a regular sphere the result is the known Stokes' law. We found the leading order correction in the case of a particle with some heat distribution on it. We show that in the case of a Janus sphere there will be coupling between translation and rotation.
  • N. Oppenheimer, S. Navardi and H. A. Stone
    Physical Review Fluids, 1, 014001 (2016)

Non-dissipative shapable sheet

A sheet of paper that has been crumpled and flattened retains some amount of shapability that a bare, uncrumpled, sheet does not have: when deformed by external forces, it retains the deformed shape after the forces are removed.  Using a frustrated two dimensional lattice of springs, we show that such shapability can be attained in a non-dissipative system.  Numerical investigations suggest an extensive number of bistable energy minima using several variants of this scheme. The numerical sheet can be bent into a nearly-closed cylinder that holds its shape.  We verify that the deformed shape is locally stable and compare its bending modulus in the deformed state with that in the initial flat state.  We investigate the threshold for non-elastic deformation using various kinds of forcing.
      •   Shapeable sheet without plastic deformations. 
          N. Oppenheimer and T. Witten
          Physical Review E 92, 052401, (2015)

Why do sleeping nematodes develop a hockey-stick-like posture? 

C. elegans exhibits a sleep-like state during a stage termed lethargus, during which they are commonly observed in a hockey-stick-like posture. Biron et. al. showed that this posture is actively maintained. They also see that the animals flip almost exclusively when they have a single bent. We describe a simple biomechanical model using springs to simulate the muscles, and show that it is sufficient for generating rotation about the anterior-posterior body axis 

  • Why do sleeping nematodes develop a hockey-stick-like posture? 
    N. Tramm, N. Oppenheimer, S. Nagy, E. Efrati and D. Biron

    PlosOne 9(7):e101162 (2014)

Anomalously fast kinetics of lipid monolayer jerks

A monolayer of lipids is sitting on top of water and compressed on both sides. As the pressure increases the monolayer buckles with the observation of fast "jerks" spanning the entire range of the system. What can account for this fast motion? We survey the folding mechanism, believed to accounts for this motion, and show that even the most generous energy it can supply does not account for the kinetic energy observed in experiments. So what is actually taking place? We do not know, but we offer some alternative possibilities.

  • Anomalously fast kinetics of lipid monolayer buckling
    N. Oppenheimer, H. Diamant, T. A. Witten
    Physical Review E 88, 022504 (2013)

Dynamics of heterogeneous membranes

The dynamics of biomembranes and membrane proteins is a key ingredient in a host of vital cellular processes.  We model the membrane as a two-dimensional fluid surrounded by a three-dimensional different fluid (the solution). The mixed dimensionality results in a rich physical behavior. We have focused on three scenarios: (i) a membrane surrounded by an unbounded fluid; (ii) a membrane adjacent to a rigid surface; and (iii) a membrane containing immobile inclusions (such as the ones anchoring the membrane to the cytoskeleton). Each of the three scenarios exhibits different physics,
stemming from different implications of the conservation laws for mass and momentum, and from the symmetry of the problem. We have found long-range correlations between the motions of membrane proteins, leading to anomalous concentration affects.
  • Correlated diffusion of membrane proteins and their effect on membrane viscosity 
    N. Oppenheimer, H. Diamant 
    Biophysical Journal 96, 3041-3049 (2009) 
    doi/journal link  arxived preprint 

  • Correlated dynamics of inclusions in a supported membrane 
    N. Oppenheimer, H. Diamant 
    Physical Review E 82, 041912 (2010) 
    doi/journal link  arxived preprint 

  • Dynamics of membranes with immobile inclusions 
    N. Oppenheimer, H. Diamant 
    Physical Review Letters 107, 258102 (2011) 
    doi/journal link  arxived preprint