Physics

In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson--Nernst--Planck (PNP) equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically found multiple steady-state solutions, we obtain S -shaped current-voltage and current-concentration curves, showing hysteretic response of ion conductance to voltages and boundary concentrations with memory effects. Boundary value problems are proposed to locate bifurcation points and predict the local bifurcation diagram near bifurcation points on the S -shaped curves. Numerical approaches for linear stability analysis are developed to understand the stability of the steady-state solutions that are only numerically available. Finite difference schemes are proposed to solve a derived eigenvalue problem involving differential operators. The linear stability analysis reveals that the S -shaped curves have two linearly stable branches of different conductance levels and one linearly unstable intermediate branch, exhibiting classical bistable hysteresis. As predicted in the linear stability analysis, transition dynamics, from a steady-state solution on the unstable branch to a one on the stable branches, are led by perturbations associated to the mode of the dominant eigenvalue. Further numerical tests demonstrate that the finite difference schemes proposed in the linear stability analysis are second-order accurate. Numerical approaches developed in this work can be applied to study linear stability of a class of time-dependent problems around their steady-state solutions that are computed numerically.

The onset of hydrodynamic instabilities is of great importance in both industry and daily life, due to the dramatic mechanical and thermodynamic changes for different types of flow motions. In this paper, modern machine learning techniques, especially the convolutional neural networks (CNN), are applied to identify the transition between different flow motions raised by hydrodynamic instability, as well as critical non-dimensionalized parameters for characterizing this transit. CNN not only correctly predicts the critical transition values for both Taylor-Couette (TC) flow and Rayleigh- Bénard (RB) convection under various setups and conditions, but also shows an outstanding performance on robustness and noise-tolerance. In addition, key spatial features used for classifying different flow patterns are revealed by the principal component analysis.

Magnetic reconnection is a fundamental process that quickly releases magnetic energy stored in a plasma.Identifying, from simulation outputs, where reconnection is taking place is non-trivial and, in general, has to be performed by human experts. Hence, it would be valuable if such an identification process could be automated. Here, we demonstrate that a machine learning algorithm can help to identify reconnection in 2D simulations of collisionless plasma turbulence. Using a Hybrid Vlasov Maxwell (HVM) model, a data set containing over 2000 potential reconnection events was generated and subsequently labeled by human experts. We test and compare two machine learning approaches with different configurations on this data set. The best results are obtained with a convolutional neural network (CNN) combined with an 'image cropping' step that zooms in on potential reconnection sites. With this method, more than 70% of reconnection events can be identified correctly. The importance of different physical variables is evaluated by studying how they affect the accuracy of predictions. Finally, we also discuss various possible causes for wrong predictions from the proposed model.

Water near detonation nanodiamonds (DNDs) forms a Hydrogen Bond (HB) network, whose strength influences DNDs' fluorescence intensity and colloidal stability in aqueous suspensions. However, effects of dissolved ions and DND's surface chemistry on dynamics of water that manifest in rupture and formation of HBs still remain to be elucidated. Thus, we carried out molecular dynamics simulations to investigate the aforementioned effects in the aqueous salt (any of KCl, NaCl, CaCl\_2, or MgCl\_2) solution of DND functionalized with any of -H, -NH\_2, -COOH, or -OH groups. We observed the specific cation effects on both translational and reorientational dynamics of water around the negatively charged DND-COOH. In the whole hydration shell of this DND, we obtained K\{+} < Na\{+} < Ca\{2+} < Mg\{2+} ordering for the impact of the cation on reducing the translational diffusion coefficient of water. In the immediate vicinity of the charged DND-COOH, the slowdown impacts of cations on the reorientational dynamics of dipole and OH vectors of water were according to Na\{+} < K\{+} < Ca\{2+} < Mg\{2+} and Na\{+} < Ca\{2+} < K\{+} < Mg\{2+} ordering, respectively. Furthermore, regardless of the type of dissolved ions, positively charged DND-NH\_2 and negatively charged DND-COOH induced, respectively, the slowest dipole and OH reorientational dynamics in the first hydration layer of DND. Our results led us to conclude that charged groups on the surface of DNDs on the one hand and the adsorbed counterions on the other hand cooperatively slow down the reorientational dynamics of water in multiple directions.

The H-formulation, used abundantly for the simulation of high temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well known H- ϕ formulation in COMSOL Multiphysics in order to compare the numerical performance of the H and H- ϕ formulations in the context of computing the magnetization of bulk superconductors. We show that the H- ϕ formulation can reduce the number of degrees of freedom and computation times by nearly a factor of two for a given relative error. The accuracy of the magnetic fields obtained with both formulations are demonstrated to be similar. The computational benefits of the H- ϕ formulation are shown to far outweigh the added complexity of its implementation, especially in 3-D. Finally, we identify the ideal element orders for both H and H- ϕ formulations to be quartic in 2-D and cubic in 3-D, corresponding to the highest element orders implementable in COMSOL.

The Independent Reaction Time method is a computationally efficient Monte-Carlo based approach to simulate the evolution of initially heterogeneously distributed reaction-diffusion systems that has seen wide-scale implementation in the field of radiation chemistry modeling. The method gains its efficiency by preventing multiple calculations steps before a reaction can take place. In this work we outline the development and implementation of this method in the Geant4 toolkit to model ionizing radiation induced chemical species in liquid water. The accuracy and validity of these developed chemical models in Geant4 is verified against analytical solutions of well stirred bimolecular systems confined in a fully reflective box.

Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive methods for computing the C-G coefficients are often unstable for large quantum numbers due to numerical overflow or underflow. In this paper, we present an improved method, the so-called sign-exponent recurrence, for the recursive computation of C-G coefficients. The result shows that the proposed method can significantly improve the stability of the computation without losing its efficiency, producing accurate values for the C-G coefficients even with very large quantum numbers.

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretisations that track the moving phase boundary. However standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic field near the geometric edges of wedge-shaped structures. Several algorithms for incorporating treatment of singularities into methods for solving Maxwell's equations in two-dimensional structures by the examples of the analytical modal method and the spectral element method are discussed. In test calculations, for which we use diffraction gratings, the significant accuracy improvement and convergence ac-celeration were demonstrated. In the considered cases of spectral methods an enhancement of convergence from algebraic to exponential or close to exponential is observed. Diffraction efficiencies of the gratings, for which the conventional methods fail to converge due to the special values of permittivities, were calculated.

We develop new transfer learning algorithms to accelerate prediction of material properties from ab initio simulations based on density functional theory (DFT). Transfer learning has been successfully utilized for data-efficient modeling in applications other than materials science, and it allows transferable representations learned from large datasets to be repurposed for learning new tasks even with small datasets. In the context of materials science, this opens the possibility to develop generalizable neural network models that can be repurposed on other materials, without the need of generating a large (computationally expensive) training set of materials properties. The proposed transfer learning algorithms are demonstrated on predicting the Gibbs free energy of light transition metal oxides.