Efficient construction of free energy profiles of breathing metal–organic frameworks using advanced molecular dynamics simulations

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials

Aerodynamic Analysis of an MAV-Scale Cycloidal Rotor System Using a Stuctured Overset RANS Solver

A compressible Reynolds-Averaged Navier-Stokes solver was used to investigate the performance and flow physics of the cycloidal rotor (cyclocopter). This work employed a computational methodology to understand the complex aerodynamics of the cyclocopter and its relatively unexplored application for MAVs. The numerical code was compared against performance measurements obtained from experiment and was seen to exhibit reasonable accuracy. With validation of the flow solver, CFD predictions were used to gain qualitative insight into the flowfield. Time histories revealed large periodic variations in thrust and power. In particular, the virtual camber effect was found to significantly influence the vertical force time history. Spanwise thrust and flow visualizations showed a highly three-dimensional flowfield with large amounts of blade shedding and blade-vortex interaction. Overall, the current work seeks to provide unprecedented insight into the cyclocopter flowfield with the goal of developing an accurate predictive tool to refine the design of future cyclocopter configurations

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful

Loss of control in pattern-directed nucleation: a theoretical study

The properties of template-directed nucleation are studied close to the transition where full nucleation control is lost and additional nucleation occurs beyond the pre-patterned regions. First, kinetic Monte Carlo simulations are performed to obtain information on a microscopic level. Here the experimentally relevant cases of 1D stripe patterns and 2D square lattice symmetry are considered. The nucleation properties in the transition region depend in a complex way on the parameters of the system, i.e. the flux, the surface diffusion constant, the geometric properties of the pattern and the desorption rate. Second, the properties of the stationary concentration field in the fully controlled case are studied to derive the remaining nucleation probability and thus to characterize the loss of nucleation control. Using the analytically accessible solution of a model system with purely radial symmetry, some of the observed properties can be rationalized. A detailed comparison to the Monte Carlo data is included

Object-oriented hyperbolic solver on 2D-unstructured meshes applied to the shallow water equations

Fluid dynamics, like other physical sciences, is divided into theoretical and experimental branches. However, computational fluid dynamics (CFD) is third branch of Fluid dynamics, which has aspects of both the previous two branches. CFD is a supplement rather than a replacement to the experiment or theory. It turns a computer into a virtual laboratory, providing insight, foresight, return on investment and cost savings1. This work is a step toward an approach that realise a new and effective way of developing these CFD models

Neural Operator: Is data all you need to model the world? An insight into the impact of Physics Informed Machine Learning

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering and mathematical problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, and more. While this has led to solving many complex phenomena, there are some limitations. Conventional approaches such as Finite Element Methods (FEMs) and Finite Differential Methods (FDMs) require considerable time and are computationally expensive. In contrast, data driven machine learning-based methods such as neural networks provide a faster, fairly accurate alternative, and have certain advantages such as discretization invariance and resolution invariance. This article aims to provide a comprehensive insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems, while also noting some of the major pitfalls of machine learning-based approaches. Furthermore, we highlight, a novel and fast machine learning-based approach (~1000x) to learning the solution operator of a PDE operator learning. We will note how these new computational approaches can bring immense advantages in tackling many problems in fundamental and applied physics