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The composition of the lithium cation (Li + ) solvation shell in mixed linear and cyclic carbonate-based electrolytes has been re-examined using Born–Oppenheimer molecular dynamics and Li + (EC) n (DMC) m cluster calculations.
Traditionally, distribution system state estimations (DSSE) are challenged by the lack of measurements at both primary and secondary sides of the system. The widely available cable television (CATV) voltage sensors installed in low-voltage (LV) networks bring opportunities to achieve higher quality DSSE covering a broader area of the distribution network. This study proposes a medium-/low-voltage (MV/LV) joint distribution system state estimation approach using the untapped CATV measurements. It aims at addressing the need for system situational awareness at the grid edge while improving the estimation accuracy at both the primary and secondary sides compared to its disjointed counterpart. Linearized measurement functions and boundary condition uncertainty propagation rules are derived to ensure the computational efficiency and accuracy of the joint state estimator. Numerical experiments are conducted on an IEEE test feeder to demonstrate the efficacy of the proposed method and the value of CATV measurements.
We propose a method to simultaneously correct linear optics errors and linear coupling for storage rings using turn-by-turn (TbT) beam position monitor (BPM) data. The independent component analysis (ICA) method is used to isolate the betatron normal modes from the measured TbT BPM data. The betatron amplitudes and phase advances of the projections of the normal modes on the horizontal and vertical planes are then extracted, which, combined with dispersion measurement, are used to fit the lattice model. The fitting results are used for lattice correction. The method has been successfully demonstrated on the NSLS-II storage ring.
Brush block copolymers (BBCPs) enable the rapid fabrication of self-assembled one-dimensional photonic crystals with photonic band gaps that are tunable in the UV-vis-IR, where the peak wavelength of reflection scales with the molecular weight of the BBCPs. Due to the difficulty in synthesizing very large BBCPs, the fidelity of the assembled lamellar nanostructures drastically erodes as the domains become large enough to reflect IR light, severely limiting their performance as optical filters. To overcome this challenge, short linear homopolymers are used to swell the arrays to ~180% of the initial domain spacing, allowing for photonic band gaps up to~1410 nm without significant opacity in the visible, demonstrating improved ordering of the arrays. Additionally, blending BBCPs with random copolymers enables functional groups to be incorporated into the BBCP array without attaching them directly to the BBCPs. The addition of short linear polymers to the BBCP arrays thus offers a facile means of improving the self-assembly and optical properties of these materials, as well as adding a route to achieving films with greater functionality and tailorability, without the need to develop or optimize the processing conditions for each new brush polymer synthesized.
A dual linear delta assembly includes a frame, a first linear delta system, and a second linear delta system concentric with the first linear delta system. Each of the first linear delta system and the second linear delta system may include rails mounted to the frame, linear actuators, each linear actuator coupled to a respective rail of the rails and configured to translate along a longitudinal length of the respective rail, pairs of parallel rods each operably coupled to a respective linear actuator of the linear actuators, and a platform coupled to a longitudinal end of each of the pairs of parallel rods opposite the respective linear actuator of the linear actuators.
Abstract Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long‐term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin‐film technology. Additionally, non‐linearities in the wear‐out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually, in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non‐linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.
A theoretically informed entangled polymer simulation approach is presented for description of the linear and non-linear rheology of entangled polymer melts. The approach relies on a many-chain representation and introduces the topological effects that arise from the non-crossability of molecules through effective fluctuating interactions, mediated by slip-springs, between neighboring pairs of macromolecules. The total number of slip-springs is not preserved but, instead, it is controlled through a chemical potential that determines the average molecular weight between entanglements. The behavior of the model is discussed in the context of a recent theory for description of homogeneous materials, and its relevance is established by comparing its predictions to experimental linear and non-linear rheology data for a series of well-characterized linear polyisoprene melts. The results are shown to be in quantitative agreement with experiment and suggest that the proposed formalism may also be used to describe the dynamics of inhomogeneous systems, such as composites and copolymers. Importantly, the fundamental connection made here between our many-chain model and the well-established, thermodynamically consistent single-chain mean-field models provides a path to systematic coarse-graining for prediction of polymer rheology in structurally homogeneous and heterogeneous materials.
Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.
We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.
Abstract Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient K s ∝ S 8 / 5 ψ c 2 , where S = τ R τ A and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ~ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.
Abstract Previous observational studies have indicated that mesoscale convective systems (MCSs) contribute the majority of precipitation over the Bay of Bengal (BoB) during the summer monsoon season, yet their initiation and propagation remain incompletely understood. To fill this knowledge gap, we conducted a comprehensive study using a combination of 20-yr satellite observations, MCS tracking, reanalysis data, and a theoretical linear model. Satellite observations reveal clear diurnal propagation signals of MCS initiation frequency and rainfall from the west coast of the BoB toward the central BoB, with the MCS rainfall propagating slightly slower than the MCS initiation frequency. Global reanalysis data indicate a strong association between the offshore-propagating MCS initiation frequency/rainfall and diurnal low-level wind perturbations, implying the potential role of gravity waves. To verify the hypothesis, we developed a 2D linear model that can be driven by realistic meteorological fields from reanalysis. The linear model realistically reproduces the characteristics of offshore-propagating diurnal wind perturbations. The wind perturbations, as well as the offshore propagation signals of MCS initiation frequency and rainfall, are associated with diurnal gravity waves emitted from the coastal regions, which in turn are caused by the diurnal land–sea thermal contrast. The ambient wind speed and vertical wind shear play crucial roles in modulating the timing, propagation, and amplitude of diurnal gravity waves. Using the linear model and satellite observations, we further show that the stronger monsoonal flows lead to faster offshore propagation of diurnal gravity waves, which subsequently control the offshore propagation signals of MCS initiation and rainfall. Significance Statement Rainfall over the Bay of Bengal (BoB) is primarily contributed by large and organized rainfall systems in the summer monsoon season. During this season, these systems are commonly observed over the east coast of India around midnight, the western BoB in the morning, and the central BoB in the afternoon. This eastward rainfall propagation is confirmed by observations, reanalysis data, and a theoretical model to have a strong association with atmospheric diurnal gravity waves. These waves are caused by land–sea thermal contrast and can trigger rainfall systems over the offshore regions. We also found that the diurnal gravity waves, as well as their triggered rainfall systems, can be greatly modulated by the large-scale monsoonal flows. All the above findings improve our understanding of diurnal rainfall cycle over the BoB and may contribute to the future improvement of rainfall forecast over the region.
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.
The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations e.g. for design-standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system response and exploit well-established methods and tools for analyzing linear systems. This paper presents the development and verification of the new linearization functionality of the open-source engineering tool FAST v8 for land-based wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly.