Publications

Alex Fontana, Richard Pedurand, Ludovic Bellon, J. Stat. Mech. 073206 (2020)

doi:10.1088/1742-5468/ab97b1

Statistical physics in equilibrium grants us one of its most powerful tools: the equipartition principle. It states that the degrees of freedom of a mechanical system act as a thermometer: temperature is equal to the mean variance of their oscillations divided by their stiffness. However, when a non-equilibrium state is considered, this principle is no longer valid. In our experiment, we study the fluctuations of a micro-cantilever subject to a strong heat flow, which creates a highly non-uniform local temperature. We measure independently the temperature profile of the object and the temperature yielded from the mechanical thermometers, thus testing the validity of the equipartition principle out of equilibrium. We demonstrate how the fluctuations of the most energetic degrees of freedom are equivalent to the temperature at the base of the cantilever, even when the average temperature is several hundreds of degrees higher. We then present a model based on the localised mechanical dissipation in the system to account for our results, which correspond to mechanical losses localised at the clamping position.

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Ludovic Bellon, Physics Today 73, 5, 57 (2020)

doi:10.1063/PT.3.4477

Book Review : Atomic Force Microscopy, Bert Voigtländer, Springer, 2019 (2nd ed.)

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Benjamin Monnet, Sergio Ciliberto and Ludovic Bellon, J. Stat. Mech. 104011 (2019)

doi:10.1088/1742-5468/ab363c

The Nyquist formula quantifies the thermal noise driven fluctuations of voltage across a resistance in equilibrium. We deal here with the case of a resistance driven out of equilibrium by putting it in contact with two thermostats at different temperatures. We reach a non-equilibrium steady state where a heat flux is flowing through the resistance. Our measurements demonstrate anyway that a simple extension of the Nyquist formula to the non uniform temperature field describes with an excellent precision the thermal noise. For a metallic ohmic material, the fluctuations are actually equivalent to those of a resistance in equilibrium with a single thermostat at the mean temperature between the hot and cold sources. 

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Romina Muñoz, Felipe Aguilar-Sandoval, Ludovic Bellon, and Francisco Melo, PLoS ONE 12, e0189979 (2017)

doi: 10.1371/journal.pone.0189979

The accurate characterization of proteins in both their native and denatured states is essential to effectively understand protein function, folding and stability. As a proof of concept, a micro rheological method is applied, based on the characterization of thermal fluctuations of a micro cantilever immersed in a bovine serum albumin solution, to assess changes in the viscosity associated with modifications in the protein’s structure under the denaturant effect of urea. Through modeling the power spectrum density of the cantilever’s fluctuations over a broad frequency band, it is possible to implement a fitting procedure to accurately determine the viscosity of the fluid, even at low volumes. Increases in viscosity during the denaturant process are identified using the assumption that the protein is a hard sphere, with a hydrodynamic radius that increases during unfolding. This is modeled accordingly through the Einstein-Batchelor formula. The Einstein-Batchelor formula estimates are verified through dynamic light scattering, which measures the hydrodynamic radius of proteins. Thus, this methodology is proven to be suitable for the study of protein folding in samples of small size at vanishing shear stresses.

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Mickael Geitner, Felipe Aguilar Sandoval, Eric Bertin and Ludovic Bellon, Phys. Rev. E 95, 032138

doi: 10.1103/PhysRevE.95.032138

We study the mechanical fluctuations of a micrometer sized silicon cantilever subjected to a strong heat flow, thus having a highly non-uniform local temperature. In this non-equilibrium steady state, we show that fluctuations are equivalent to the thermal noise of a cantilever at equilibrium around room temperature, while its mean local temperature is several hundred of degrees higher. Changing the mechanical dissipation by adding a coating to the cantilever, we recover the expected rise of fluctuations with the mean temperature. Our work demonstrates that inhomogeneous dissipation mechanisms can decouple the amplitude of thermal fluctuations from the average temperature. This property could be useful to understand out-of-equilibrium fluctuating systems, or to engineer low noise instruments.

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Tianjun Li,  Lorène Champougny and Ludovic Bellon,  Journal of Applied Physics 121, 094305 (2017)

doi: 10.1063/1.4977867

We study the physics of adhesion and the contact mechanics at the nanoscale with a peeling experiment of a carbon nanotube on a flat substrate. Using an interferometric atomic force microscope and an extended force modulation protocol, we investigate the frequency response of the stiffness of the nano-contact from DC to 20 kHz. We show that this dynamic stiffness is only weakly frequency dependent, increasing by a factor 2 when the frequency grows by 3 orders of magnitude. Such behavior may be the signature of amorphous relaxations during the mechanical solicitation at the nano-scale.

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