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Title: Thermal Fluctuations of Active and Anisotropic Elastic Membranes
Authors: Bahri, Mohamed El Hedi
Advisors: Kosmrlj, Andrej
Contributors: Mechanical and Aerospace Engineering Department
Keywords: Active
Statistical Physics
Thermal Fluctuations
Subjects: Statistical physics
Condensed matter physics
Materials Science
Issue Date: 2023
Publisher: Princeton, NJ : Princeton University
Abstract: Atomically thin sheets, such as graphene, are widely used in nanotechnology. In the 80s it was shown that if one takes an isotropic elastic material and allows it to thermally fluctuate then beyond a thermal length scale, the effective Lamé constants scale as $\lambda_R(q),\mu_R(q) \sim q^{\eta_u}$ (where $q$ is the Fourier scale and $\eta_u \approx .4$). On the other hand the effective bending rigidity diverged as $\kappa_R(q) \sim q^{-\eta}$ ($\eta \approx .8$). Given that this thermal length scale is generally around 2 nm for nano-materials at room temperature, it thus becomes of interest for us to study the effects of temperature on elastic membranes. However, the spectrum of 2-D materials is quite wide, including anisotropies (such as black phosphorus) and non-equilibrium properties. Motivated by this, we investigate elastic membranes in three different scenarios using field theory and simulations. Firstly, we examine the effect of a uni-axial stress on the scaling exponents $\eta, \eta_u$. We find that the scaling theory no longer remains the same and that the elastic moduli become explicitly anisotropic. We furthermore establish a non-linear stress-strain relation for intermediate stresses. Secondly, we investigate the effect of elastic anisotropies on the scaling exponents $\eta,\eta_u$; in particular we would like to know if an elastic modulus anisotropy persists (potentially diverging) or washes away. Our simulations indicate that the latter is the case whereas the theory is much less trivial and our work indicates that further calculations are necessary. Lastly, we investigate what impact non-equilibrium forces may have on the established equilibrium behavior. We do this by generalizing to odd elasticity, permitting the presence of moduli that break conservation of energy and angular momentum, $A_{odd},K_{odd}$. $A_{odd}$ couples torques to dilations whereas $K_{odd}$ couples pure and simple shears. We find that fluctuation-dissipation is an unstable condition. If, however, it is satisfied then $K_{odd}$ is an irrelevant parameter that converges to zero with an exponent $2 \eta_u$ whereas $A_{odd}$ acts as a marginal parameter that only converges to zero with exponent $\eta_u$.
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mechanical and Aerospace Engineering

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