Below you can find some of the projects I’ve worked on as well as ongoing research.

## Stochastic force inference

Particles in biological and soft matter systems undergo Brownian dynamics: their deterministic motion, induced by forces, competes with random diffusion due to thermal noise. More broadly, Brownian dynamics is a generic and simple model for dynamical systems with noise.

Given only the noisy trajectories resulting from such dynamics – could we determine the equations that generated them? How would we do that in practice? Of particular interest are trajectories generated by an out-of-equilibrium process, in which case one would like to be able to identify the signatures of irreversibility and quantify it.

Our proposed solutions, including a practical inference method, are based on ideas from information theory and stochastic thermodynamics.

### Read more

- Frishman, A. and Ronceray P.
*“Learning force fields from stochastic trajectories.”*Phys. Rev. X 10.2: 021009 (2020).

## 2D turbulence and coherent mean flows

Turbulence is usually viewed as the breaking up of a large scale flow into ever smaller chaotic motions. A quantitative manifestation of this picture is the energy cascade, with energy flowing from large scales to increasingly smaller ones, where it is eventually dissipated by viscosity.

On the contrary, in 2D turbulence, energy is transferred to progressively larger scales — in an inverse cascade. This process can then terminate in the self-organization of the turbulence into a coherent structure, a so-called condensate, on top of small scale fluctuations.

Although 2d turbulence may seem like an abstract concept, many natural flows are quasi two-dimensional: planetary-scale flows in the ocean and atmosphere are an example, and they are often made up of coherent currents or vortices in combination with chaotic fluctuations.

My work on condensates in 2D turbulence is centered around the following questions: what determines the condensate’s structure? Which of its features are universal, independent of the excitation mechanisms? How do the small-scale fluctuations interact with the large scale mean structures?

### Read more

- Frishman, A. and Herbert C.
*“Turbulence Statistics in a Two-Dimensional Vortex Condensate.”*Phys. Rev. Lett. 120.20: 204505 (2018). - Frishman A.
*“The culmination of an inverse cascade: mean flow and fluctuations.”*Physics of Fluids 29.12: 125102. (2017). - Frishman A., Laurie J., Falkovich G.
*“Jets or vortices – what flows are generated by an inverse turbulent cascade?”*Phys. Rev. Fluids, 2.3 032602 (2017).

## Lagrangian time irreversibility of turbulence

Turbulence is an out-of-equilibrium phenomena as evidenced by the flux of energy through scales. But how could you see that irreversibility if you are only watching particles in the flow? What is the manifestation of the energy flux, which is a property of the velocity field, for particles? What changes if the flow is compressible?

### Read more

- Grafke, T., Frishman A., and Falkovich G. “
*Time irreversibility of the statistics of a single particle in compressible turbulence*.” Phys. Rev. E 91.4, 043022, (2015). - Frishman A. and Falkovich G. “
*A new type of anomaly in turbulence*“. Phys. Rev. Lett.113.02, 024501, (2014). - Falkovich, G., and Frishman A. “
*Single Flow Snapshot Reveals the Future and the Past of Pairs of Particles in Turbulence*.” Phys. Rev. Lett.110.21 214502 (2013).

## Lagrangian conservation laws

Conservation laws and symmetries play a central role in physics. Relatively recently, it was discovered that Lagrangian statistical conservation laws, related to the dynamics of particles, play a crucial role in the field theoretic description of turbulence. Their influence was demonstrated for the statistics of a field advected by the flow, and their form could be computed in simplified models for the velocity field. It remains unclear how to obtain such laws for a real turbulent velocity field, and what their influence could be on the field’s statistics. We have made some attempts in that direction.

### Read more

- Falkovich, G., and Frishman A. “
*Single Flow Snapshot Reveals the Future and the Past of Pairs of Particles in Turbulence*.” Phys. Rev. Lett.110.21 214502 (2013). - Frishman, A., Boffetta, G., De Lillo, F., & Liberzon, A. “
*Statistical conservation law in two-and three-dimensional turbulent flows.”*Phys. Rev. E 91.3, 033018, (2015).

· *Banner Image Credit: NASA/Ocean Biology Processing Group, NASA Goddard Space Flight Center* ·