Physics

Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a computational approach to solve the problems related to fractional Lane-Emden differential equations based on neural networks. Such a solution will help solve the fractional polytropic gas spheres problems which have different applications in physics, astrophysics, engineering, and several real-life issues. We used Artificial Neural Network (ANN) framework in its feedforward back propagation learning scheme. The efficiency and accuracy of the presented algorithm are checked by testing it on four fractional Lane-Emden equations and compared with the exact solutions for the polytopic indices n=0,1,5 and those of the series expansions for the polytropic index n=3. The results we obtained prove that using the ANN method is feasible, accurate, and may outperform other methods.

In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field solutions and real-world physics. To study the emergence, propagation and evolution of uncertainties from molecular to hydrodynamic level poses great opportunities and challenges to develop both sound theories and reliable multi-scale algorithms. In this paper, we study the stochastic behavior of multi-scale gas dynamic systems, especially focusing on the non-equilibrium effects. The theoretical analysis is presented on the basis of kinetic model equation and its upscaling macroscopic system, with the reformulation from the stochastic Galerkin method. A newly developed stochastic kinetic scheme is employed to conduct numerical simulation of homogeneous relaxation, normal shock structure, shear layer and lid-driven cavity problems. Different kinds of uncertainties are involved in conjunction with the gas evolutionary processes. New physical observations, such as the synergistic propagation pattern between mean fields and uncertainties, sensitivity of different orders of uncertainties, and the influence of boundary effects from continuum to rarefied regimes, will be identified and analyzed theoretically. The paper serves as a heuristic study of quantifying the uncertainties within multi-scale flow dynamics.

This paper develops the equilibrium equations describing the flexoelectric effect in soft dielectrics under large deformations. Previous works have developed related theories using a flexoelectric coupling tensor of mixed material-spatial character. Here, we formulate the model in terms of a flexoelectric tensor completely defined in the material frame, with the same symmetries of the small-strain flexocoupling tensor and leading naturally to objective flexoelectric polarization fields. The energy potential and equilibrium equations are first expressed in terms of deformation and polarization, and then rewritten in terms of deformation and electric potential, yielding an unconstrained system of fourth order partial differential equations (PDEs). We further develop a theory of geometrically nonlinear extensible flexoelectric rods under open and closed circuit conditions, with which we examine analytically cantilever bending and buckling under mechanical and electrical actuation. Besides being a simple and explicit model pertinent to slender structures, this rod theory also allows us to test our general theory and its numerical implementation using B-splines. This numerical implementation is robust as it handles the electromechanical instabilities in soft flexoelectric materials.

We present a hybrid approach to groundwater transport modeling, "CTRW-on-a-streamline", that allows continuous-time random walk (CTRW) particle tracking on large-scale, explicitly-delineated heterogeneous groundwater velocity fields. The combination of a non-Fickian transport model (in this case, the CTRW) with general heterogeneous velocity fields represents an advance of the current state of the art, in which non-Fickian transport models or heterogeneous velocity fields are employed, but generally not both. We present a general method for doing this particle tracking that fully separates the model parameters characterizing macroscopic flow, subscale advective heterogeneity, and mobile-immobile mass transfer, such that each can be directly specified a priori from available data. The method is formalized and connections to classic CTRW and subordination approaches are made. Numerical corroboration is presented.

We present a mesoscale representation of near-contact interactions between colliding droplets which permits to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focussing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet/bubble-based mesoscale porous materials.

Estimating the heat loads on re-entry vehicles is a crucial part of preparing for atmospheric re-entry manoeuvres. Re-entry flows at high altitudes are in the rarefied regime and are governed by high enthalpies and thermodynamic non-equilibrium. Additionally, catalytic gas-surface reactions change the gas flow composition and can have a major influence on the heat transfer. Our goal is to estimate the heat loads without a priori fitting of simulation parameters to experiments. We use the tool PICLas for simulations of such rarefied gas flows. It combines different particle methods, including the Direct Simulation Monte Carlo method, for modelling of gases. Recently it has been extended to include different catalysis models to treat reactions on surfaces. We evaluate a kinetic Monte Carlo approach to model catalytic gas-surface interactions in combination with flow simulations using particle methods. Here, the adsorbate distribution is modelled by reproducing a surface system using a kinetic Monte Carlo approach and estimating the necessary parameters using model assumptions. This catalytic model is compared to a simple recombination model. We present simulations that show the capability of the implemented models for a Si O 2 surface in an Oxygen flow. Furthermore, simulation results are compared to heat fluxes and recombination coefficient obtained from the respective experiment. The results show that simulations using the kinetic Monte Carlo approach match the experimentally obtained values. Thus, the approach can be used to estimate the reactivity of oxygen flows over Si O 2 surfaces.

Ionic polymer-metal composites consist in a thin film of electro-active polymers (Nafion R for example) sandwiched between two metallic electrodes. They can be used as sensors or actuators. The polymer is saturated with water, which causes a complete dissociation and the release of small cations. The strip undergoes large bending motions when it is submitted to an orthogonal electric field and vice versa. We used a continuous medium approach and a coarse grain model; the system is depicted as a deformable porous medium in which flows an ionic solution. We write microscale balance laws and thermodynamic relations for each phase, then for the complete material using an average technique. Entropy production, then constitutive equations are deduced : a Kelvin-Voigt stress-strain relation, generalized Fourier's and Darcy's laws and a Nernst-Planck equation. We applied this model to a cantilever E.A.P. strip undergoing a continuous potential difference (static case); a shear force may be applied to the free end to prevent its displacement. Applied forces and deflection are calculated using a beam model in large displacements. The results obtained are in good agreement with the experimental data published in the literature.

Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous all-atom molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous all-atom simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce all-atom molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates.

Many key industrial processes, from electricity production, conversion and storage to electrocatalysis or electrochemistry in general, rely on physical mechanisms occurring at the interface between a metallic electrode and an electrolyte solution, summarized by the concept of electric double layer, with the accumulation/depletion of electrons on the metal side and of ions on the liquid side. While electrostatic interactions play an essential role on the structure, thermodynamics, dynamics and reactivity of electrode-electrolyte interfaces, these properties also crucially depend on the nature of the ions and solvent, as well as that of the metal itself. Such interfaces pose many challenges for modeling, because they are a place where Quantum Chemistry meets Statistical Physics. In the present review, we explore the recent advances on the description and understanding of electrode-electrolyte interfaces with classical molecular simulations, with a focus on planar interfaces and solvent-based liquids, from pure solvent to water-in-salt-electrolytes.

The molecular dynamics lattice gas method maps a molecular dynamics simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method by taking a Boltzmann average over the molecular dynamics lattice gas. A key property of the lattice Boltzmann method is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the molecular dynamics simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the molecular dynamics data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from molecular dynamics data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function.