Discrete Levels Research Articles

Anchoring of Metal Complexes on Au25 Nanocluster for Enhanced Photocoupled Electrocatalytic CO2 Reduction

AbstractAtomically precise Au nanoclusters (NCs) with discrete energy levels can be used as photosensitizers for CO2 reduction. However, tight ligand capping of Au NCs hinders CO2 adsorption on its active sites. Here, a new hybrid material is obtained by anchoring of thiol functionalized terpyridine metal complexes (metal=Ru, Ni, Fe, Co) on Au NCs by ligand exchange reactions (LERs). The anchoring of Ru and Ni complexes on Au25 NC (Au25−Ru and Au25−Ni) leads to adequate CO2 to CO conversion for photocoupled electrocatalytic CO2 reduction (PECR) in terms of high selectivity, with Faradaic efficiency of CO (FECO) exceeding 90 % in a wide potential range, remarkable activity (CO production rate up to two times higher than that for pristine Au25PET18) and extremely large turnover frequencies (TOFs, 63012 h−1 at −0.97 V for Au25−Ru and 69989 h−1 at −1.07 V vs. RHE for Au25−Ni). Moreover, PECR stability test indicates the excellent long‐term stability of the modified NCs in contrast with pristine Au NCs. The present approach offers a novel strategy to enhance PECR activity and selectivity, as well as to improve the stability of Au NCs under light illumination, which paves the way for highly active and stable Au NCs catalysts.

Anchoring of Metal Complexes on Au25 Nanocluster for Enhanced Photocoupled Electrocatalytic CO2 Reduction.

Atomically precise Au nanoclusters (NCs) with discrete energy levels can be used as photosensitizers for CO2 reduction. However, tight ligand capping of Au NCs hinders CO2 adsorption on its active sites. Here, a new hybrid material is obtained by anchoring of thiol functionalized terpyridine metal complexes (metal=Ru, Ni, Fe, Co) on Au NCs by ligand exchange reactions (LERs). The anchoring of Ru and Ni complexes on Au25 NC (Au25 -Ru and Au25 -Ni) leads to adequate CO2 to CO conversion for photocoupled electrocatalytic CO2 reduction (PECR) in terms of high selectivity, with Faradaic efficiency of CO (FECO ) exceeding 90 % in a wide potential range, remarkable activity (CO production rate up to two times higher than that for pristine Au25 PET18 ) and extremely large turnover frequencies (TOFs, 63012 h-1 at -0.97 V for Au25 -Ru and 69989 h-1 at -1.07 V vs. RHE for Au25 -Ni). Moreover, PECR stability test indicates the excellent long-term stability of the modified NCs in contrast with pristine Au NCs. The present approach offers a novel strategy to enhance PECR activity and selectivity, as well as to improve the stability of Au NCs under light illumination, which paves the way for highly active and stable Au NCs catalysts.

A flexible z-layers approach for the accurate representation of free surface flows in a coastal ocean model (SHYFEM v. 7_5_71)

Abstract. We propose a discrete multilayer shallow water model based on z-layers, which, thanks to the insertion and removal of surface layers, can deal with an arbitrarily large tidal oscillation independently of the vertical resolution. The algorithm is based on a classical two-step procedure used in numerical simulations with moving boundaries (grid movement followed by a grid topology change, that is, the insertion/removal of surface layers), which avoids the appearance of surface layers with very small or negative thickness. With ad hoc treatment of advection terms at nonconformal edges that may appear owing to insertion/removal operations, mass conservation and the compatibility of the tracer equation with the continuity equation are preserved at a discrete level. This algorithm called z-surface-adaptive, can be reduced, as a particular case when all layers are moving, to the z-star coordinate. With idealized and realistic numerical experiments, we compare the z-surface-adaptive against z-star and we show that it can be used to simulate coastal flows effectively.

Regulating intragap states in colloidal quantum dots for universal photocatalytic hydrogen evolution

Understanding and manipulating intragap states in semiconductors may enable superior solar-to-hydrogen energy conversion. The effect of intragap states on photocatalysis usually remains unclear and is sometimes contradictory. Quantum-confined colloidal quantum dots (QDs) provide a unique platform to tune the density and distribution of intragap states due to their discrete energy levels. Herein, intragap active domains, composed of Cu vacancies (VCu′) and high-valent Cu (Cu*) defect states, are constructed in copper-deficient Zn-doped CuInS2 QDs. Note that these intragap states mainly exist at in-facet and on-edge defects in QDs, being away from the valence band maximum and close to Fermi level. Steady and transient optical spectra indicate that photoactivated Cu* states serving as photoinduced absorption centers can facilitate the generation of long-lived hot electrons (ca. 85 ps) as a manifestation of phonon bottleneck. Synergistically, the VCu′ states enable the holes capture and electron-hole pairs decoupling to suppress ultrafast Auger-like hot carrier cooling (ca. 178 fs). Moreover, the on-edge defects are demonstrated to play an active role in mediating proton reduction kinetics through density functional calculation. As a result, the QDs exhibit an outstanding hydrogen generation rate of 50.4 mmol g−1 h−1 without any noble metal, meanwhile, various molecule oxidation and polymer degradation can be integrated with the hydrogen generation process.

Structure-preserving discretization of fractional vector calculus using discrete exterior calculus

Fractional vector calculus is the building block of the fractional partial differential equations that model non-local or long-range phenomena, e.g., anomalous diffusion, fractional electromagnetism, and fractional advection-dispersion. In this work, we reformulate a type of fractional vector calculus that uses Caputo fractional partial derivatives and discretize this reformulation using discrete exterior calculus on a cubical complex in the structure-preserving way, meaning that the continuous-level properties curlαgradα=0 and divαcurlα=0 hold exactly on the discrete level. We discuss important properties of our fractional discrete exterior derivatives and verify their second-order convergence in the root mean square error numerically. Our proposed discretization has the potential to provide accurate and stable numerical solutions to fractional partial differential equations and exactly preserve fundamental physics laws on the discrete level regardless of the mesh size.

Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the unsteady thermally coupled magnetohydrodynamic equations with variable density

In this article, we propose a fully decoupled first-order time discrete scheme for the unsteady thermally coupled magnetohydrodynamics (MHD) equations with variable density, which is a large nonlinear strongly coupled system consisting of incompressible Navier-Stokes equations with variable density, heat equation and Maxwell equations. The proposed scheme is highly efficient because only the linearised subproblems need to be solved at the discrete level. Furthermore, unconditional stability analysis is established which is a vital issue in the field of multiphysics. We also construct and implement a fully discrete scheme based on conforming finite elements in space. Several 2D/3D numerical tests are conducted to confirm the efficiency and accuracy of the developed scheme with large density differences.

Energy-dissipative evolutionary deep operator neural networks

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seek numerical solutions for a class of partial differential equations instead of a single partial differential equation, such as partial differential equations with different parameters or different initial conditions. The network consists of two sub-networks, the Branch net and the Trunk net. For an objective operator G, the Branch net encodes different input functions f at a fixed number of sensors xi,i=1,2,⋯,m, and the Trunk net evaluates the output function at any location. By minimizing the error between the evaluated output q and the expected output G(f)(y) at the test point y, DeepONet generates a good approximation of the operator G. A key distinction in our methodology is the utilization of DeepONet for the training of the initial state, which operates as a multi-parametric operator. Further, the evolution of parameters in our model is facilitated by the Scalar Auxiliary Variable (SAV) method, leading to a formulated iterative process for the parameter's progression over time. The SAV approach is adopted to preserve essential physical properties of PDEs, particularly the Energy Dissipation Law. It introduces a kind of modified energy and establishes unconditional energy dissipation law in the discrete level. By treating the parameters of the well-trained DeepONet as a representation of the initial operator and evolving them by a dynamic system, our network can predict the accurate solution at any further time, while the training data is only the initial state. In order to validate the accuracy and efficiency of our neural networks, we provide numerical simulations of several partial differential equations, including heat equations, parametric heat equations, Allen-Cahn equations and a reaction–diffusion equation in three dimensions.

An extended quadratic auxiliary variable method for the singular Lennard-Jones droplet liquid film model

In this letter, we present an extended quadratic auxiliary variable method for a droplet liquid film model characterized by the singular Lennard-Jones potential. This innovative approach begins with the introduction of three new auxiliary variables, each satisfying a quadratic equation, with the primary objective of reformulating the original model into an equivalent system. The reformulated system exhibits remarkable properties, including the preservation of three quadratic invariants and a quadratic energy dissipation law, where these auxiliary variables satisfy consistent initial conditions. To solve it numerically, we employ the implicit midpoint method in time and the central finite difference scheme in space to produce a second-order fully discrete scheme for the original model. Under consistent initial conditions, our proposed scheme is rigorously proved to preserve the original energy dissipation law at the fully discrete level. Numerical experiments showcase the scheme’s accuracy and effectiveness. It is noteworthy that the quadratic auxiliary variable method is extended to gradient flow systems featuring rational energy functionals.

Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry

We consider parametric finite element approximations for the anisotropic surface diffusion flow in an axisymmetric setting. Based on the anisotropy function, we introduce a symmetric positive definite matrix with a suitable stabilizing function. This then gives rise to two novel weak formulations for the axisymmetric flow in terms of the generating curve of the interface. By using piecewise linear elements in space and backward Euler in time, we discretize the weak formulations to obtain different approximating methods. These include a linear approximation which has good mesh properties and nonlinear approximations which can be shown rigorously to satisfy the volume preservation or the unconditional energy stability on the discrete level. Extensive numerical results are reported to demonstrate the accuracy and efficiency of the introduced methods for computing the axisymmetric flow.

Evaluation of the spatial self-shielding impact for TRISO-based nuclear fuel depletion

Reactor physics analyses of nuclear cores with nuclear fuel concepts containing tristructural isotropic (TRISO) particles, such as pebbles or compact fuel elements, rely on various degrees of simplification to keep these highly heterogeneous problems computationally tractable. One such limitation regards the level of spatial discretization employed during burnup calculations, where traditionally only a limited number of spatial zones are modeled at the full core level and assume that the spectrum is constant within the fuel elements and TRISO particles in this depletion zone. This type of assumption neglects the impact of spatial self-shielding effect within the kernels (microscale level) as well as within the compact or pebbles (mesoscale level). The Monte Carlo code Serpent 2 contains many relevant features for efficiently modeling this type of geometry, including a collision-based domain decomposition intended for very large burnup calculations, which we leveraged for this work to quantify the impact of capturing neutron flux variations occurring at the micro- and mesoscale level on a series of high-temperature gas-cooled reactor fuel element depletion problems. While spatial self-shielding is observed at both scales, with differences from a volume-averaged burnup of ±7% within the kernels and ±2% between TRISO particles within the fuel element, the conjugated effect on nuclide inventories and multiplication factor are negligible, hence confirming that assuming a single average spectrum value may be sufficient for most applications.

Multi‐Level Optical Switching by Amorphization in Single‐ and Multi‐Phase Change Material Structures

AbstractThe optical properties of phase‐change materials (PCMs) can be tuned to multiple levels by controlling the transition between their amorphous and crystalline phases. In multi‐material PCM structures, the number of discrete reflectance levels can be increased according to the number of PCM layers. However, the effect of increasing the number of layers on quenching and reversibility has not been thoroughly studied. In this work, the phase‐change physics and thermal conditions required for reversible switching of single and multi‐material PCM switches are discussed based on thermo‐optical phase‐change models and laser switching experiments. By using nanosecond laser pulses, 16 different reflectance levels in Ge2Sb2Te5 are demonstrated via amorphization. Furthermore, a multi‐material switch based on Ge2Sb2Te5 and GeTe with four discrete reflectance levels is experimentally proven with a reversible multi‐level response. The results and design principles presented herein will impact active photonics applications that rely on dynamic multi‐level operation, such as optical computing, beam steering, and next‐generation display technologies.

Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal–dual gap estimators

We consider nonsmooth partial differential equations associated with a minimization of an energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to apply the usual Newton linearization, which is not always possible otherwise. We apply the finite element method as a discretization. We focus on the choice of the regularization parameter and adjust it on the basis of an a posteriori error estimate for the difference of energies of the exact and approximate solutions. Importantly, our estimates distinguish the different error components, namely those of regularization, linearization, and discretization. This leads to an algorithm that steers the overall procedure by adaptive stopping criteria with parameters for the regularization, linearization, and discretization levels. We prove guaranteed upper bounds for the energy difference and discuss the robustness of the estimates with respect to the magnitude of the nonlinearity when the stopping criteria are satisfied. Numerical results illustrate the theoretical developments.

Analysis of a semi-implicit and structure-preserving finite element method for the incompressible MHD equations with magnetic-current formulation

In this paper, we investigate a fully discrete finite element scheme for the incompressible magnetohydrodynamic (MHD) equations with magnetic-current formulation that was introduced in Hu et al. (2016). We discretize the system by the semi-implicit Euler scheme in time and a mixed finite element approach together with finite element exterior calculus in space. The resulting scheme enjoys the structure-preserving feature that it can always produce an exactly divergence-free magnetic induction on the discrete level. The unique solvability and unconditional stability of the scheme are also proved rigorously. By utilizing the energy argument, error estimates for the velocity, magnetic induction, current density and induced electric field are further established under the low regularity hypothesis for the exact solutions. Numerical results are provided to verify the theoretical analysis and to show the effectiveness of the proposed scheme.

Well-balanced kinetic schemes for two-phase flows

At equilibrium state of a two-phase fluid system, the chemical potential is constant and the velocity vanishes. However, such equilibrium state usually cannot be captured by numerical methods due to discretization errors. Consequently, inconsistent thermodynamic interfacial properties due to non-constant chemical potential, and spurious velocities due to discrete force imbalance, are frequently encountered in numerical simulations. Therefore, numerical schemes with well-balanced properties, which can capture the equilibrium state at discrete level, are preferred for simulating two-phase flows. In this paper, we report the progress of developing well-balanced mesoscopic numerical methods based on kinetic theory, focusing on the lattice Boltzmann equation (LBE) method and the discrete unified gas-kinetic scheme (DUGKS). First, the discrete balance property of a free-energy LBE for single-component two-phase flows is analyzed to identify the structure of force imbalance. Then, a well-balanced LBE (WB-LBE) model which has the same algorithm structure as the standard one is reviewed. The WB-LBE is theoretically shown to be able to achieve the discrete equilibrium state, and the well-balance properties are confirmed numerically. Some extensions to other two-phase LBE models are discussed with enhanced numerical stability. The well-balanced DUGKS, which can use non-uniform meshes and exhibits better numerical stability for large density ratio systems is also reported.

Symmetric Fano Profiles of Two-photon Electronic Transitions Observed in an Ultracold Rydberg Gas

Fano profiles are caused by the interference between the discrete states and continuum. It is a very common phenomenon
 in multi-electron Rydberg states, such as the Rydberg states of group II elements in the periodic table. It often leads to
 autoionization due to the fact that a discrete state couples with an autoionizing state. Unlike the typical asymmetric line
 shape, here we report a symmetric unusual Fano line shape that has been predicted. In addition, this profile is caused
 by molecular states or polymer states instead of multi-electron atomic states. Moreover, it is shown that the fano profile
 caused by the multi-electron polymer states does not necessarily lead to autoionization. We propose that the Fano profile
 studied is caused by the interference between discrete levels and the multipole-multipole coupled continuum, or energy
 band.

A decoupled, unconditionally energy-stable and conservative finite element algorithm for a constrained transport model of the incompressible MHD equations

This article mainly considers numerical approximation for a constrained transport magnetohydrodynamic (CT-MHD) model in three dimensions. The superiority of the algorithm is that the magnetic field and current density naturally satisfy divergence-free at the discrete level, the divergence of velocity is improved simultaneously, and the electromagnetic field and the fluid field are decoupled. Finally, we rigorously prove the unconditional energy stability of the proposed algorithm and display five simulations to confirm its accuracy and validity.

Orbital-free density-functional theory for metal slabs.

Orbital-Free Density-Functional Theory (OF-DFT) is known to represent a promising alternative to the standard Kohn-Sham (KS) DFT, as it relies on the electron density alone, without the need to calculate all KS single-particle orbitals and energies. Here, we investigate the behavior of the main ingredients of this theory, which are the non-interacting kinetic-energy density (KED) and the Pauli potential, for metal slabs. We derive explicit density functionals for these quantities in the quantum limit where all electrons are in the same slab discrete level of energy, and we present numerical calculations beyond this quantum limit for slabs of various widths. We have found the first explicit KED functional for a realistic many-particle fermionic system, which we prove to be generally valid with no assumption about the KS potential. We also discuss the total non-interacting kinetic energy and the corresponding enhancement factor, which represent basic quantities for the practical implementation of OF-DFT.

Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet—Andreev states

Light–matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting–semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current–phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current–phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet–Andreev states, our study rules out this scenario. The distortion of the current–phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light–matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet–Andreev states in mesoscopic devices.

Design-space dimensionality reduction in global optimization of functional surfaces: recent developments and way forward

ABSTRACT In shape optimization of complex industrial products (such as, but not limited to, hull forms, rudder and appendages, propellers), there exists an inherent similarity between global optimization (GO) and uncertainty quantification (UQ): they rely on an extensive exploration of the design and operational spaces, respectively; often, they need local refinements to ensure accurate identification of optimal solutions or probability density regions (such as distribution tails), respectively; they both are dramatically affected by the curse of dimensionality as GO and UQ algorithms' complexity and especially computational cost rapidly increase with the problem dimension. Therefore, there exists a natural ground for transferring dimensionality reduction methods from UQ to GO. These enable the efficient exploration of large design spaces in shape optimization, which, in turn, enable global optimization (possibly in a multidisciplinary and stochastic setting). The paper reviews and discusses recent techniques for design-space dimensionality reduction in shape optimization, based on the Karhunen-Loève expansion (equivalent to proper orthogonal decomposition and, at the discrete level, principal component analysis). An example is shown and discussed for the hydrodynamic optimization of a ship hull.

Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT

Despite the growing interest in parallel-in-time methods as an approach to accelerate numerical simulations in atmospheric modeling, improving their stability and convergence remains a substantial challenge for their application to operational models. In this work, we study the temporal parallelization of the shallow water equations on the rotating sphere combined with time-stepping schemes commonly used in atmospheric modeling due to their stability properties, namely an Eulerian implicit-explicit (IMEX) method and a semi-Lagrangian semi-implicit method (SL-SI-SETTLS). The main goal is to investigate the performance of parallel-in-time methods, namely Parareal and Multigrid Reduction in Time (MGRIT) when these well-established schemes are used on the coarse discretization levels and provide insights on how they can be improved for better performance. We begin by performing an analytical stability study of Parareal and MGRIT applied to a linearized ordinary differential equation depending on some temporal parallelization parameters, including the choice of a coarse scheme. Next, we perform numerical simulations of two standard tests in atmospheric modeling to evaluate the stability, convergence, and speedup provided by the parallel-in-time methods compared to a fine reference solution computed serially. We also conduct a detailed investigation on the influence of artificial viscosity and hyperviscosity approaches, applied on the coarse discretization levels, on the performance of the temporal parallelization. Both the analytical stability study and the numerical simulations indicate a poorer stability behavior when SL-SI-SETTLS is used on the coarse levels, compared to the IMEX scheme. With the IMEX scheme, a better trade-off between convergence, stability, and speedup compared to serial simulations can be obtained under proper parameters and artificial viscosity choices, opening the perspective of the potential competitiveness for realistic models.