Lyotropic Liquid Crystals Incorporated with Different Kinds of Carbon Nanomaterials or Biomolecules

Liquid crystals (LCs) are considered as the “fourth state of matter,” which can display properties between crystals and isotropic liquids. LCs can be classified into lyotropic liquid crystals (LLCs) and thermotropic liquid crystals (TLCs), among which LLCs are a kind of self-assemblies formed by amphiphile molecules in a given solvent within certain concentration ranges. The structures and properties of LLCs can be tuned by the incorporation of various kinds of additives, which represents an interesting and novel route for realizing functional composites. This review focuses on recent progress on LLCs-based materials assembled with diverse additives including carbon nanotubes, graphene, graphene oxide, and biomolecules. The thermal stability and mechanical strength of the host LLCs can be greatly improved after the guests are incorporated. In addition, new functions such as conductivity, photothermal effect, and bioactivity can be introduced by the incorporation of the guests, which significantly widens the applications of LLCs-based hybrids in nanotechnology, electrochemistry, drug delivery, and life science

An Equivalence Checking Framework for Agile Hardware Design

Agile hardware design enables designers to produce new design iterations efficiently. Equivalence checking is critical in ensuring that a new design iteration conforms to its specification. In this paper, we introduce an equivalence checking framework for hardware designs represented in HalideIR. HalideIR is a popular intermediate representation in software domains such as deep learning and image processing, and it is increasingly utilized in agile hardware design.We have developed a fully automatic equivalence checking workflow seamlessly integrated with HalideIR and several optimizations that leverage the incremental nature of agile hardware design to scale equivalence checking. Evaluations of two deep learning accelerator designs show our automatic equivalence checking framework scales to hardware designs of practical sizes and detects inconsistencies that manually crafted tests have missed

8,10-Diiodo-2,6-dioxo-4λ3-ioda-3,5-dioxatricyclo­[5.3.1.04,11]undeca-1(11),7,9-triene-9-carb­oxy­lic acid

In the title compound, C9HI3O6·2H2O, the mol­ecule is located on a twofold axis that gives rise to disorder of the carboxyl group. This disorder is correlated with the disorder of one of the H atoms of the water mol­ecule. The carboxyl group is twisted relative to the attached benzene ring by 75.1 (4)°. The intra­molecular I⋯O distance is 2.112 (6) Å. Mol­ecules are linked via O—H⋯O hydrogen bonding, C—I⋯O halogen bonding, with I⋯O distances in the range 3.156 (5)–3.274 (6) Å, and dipolar C=O⋯C=O inter­actions between the carboxyl and carboxyl­ate groups, with an O⋯C distance of 2.944 (10) Å

A pseudo-reversible normalizing flow for stochastic dynamical systems with various initial distributions

We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with different initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDE, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE's final state without simulating trajectories. Existing normalizing flows for SDEs depend on the initial distribution, meaning the model needs to be re-trained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. We provide a rigorous convergence analysis of the pseudo-reversible normalizing flow model to the target probability density function in the Kullback-Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require to use reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the UCI repository

Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation

We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling approaches usually focus on approximating the deterministic component of physical model. However, this strategy necessitates knowledge of noise and resorts to auxiliary sampling methods for quantifying inverse uncertainty propagation. In this work, we develop the conditional pseudo-reversible normalizing flow model to directly learn and efficiently generate samples from the conditional probability density functions. The training process utilizes dataset consisting of input-output pairs without requiring prior knowledge about the noise and the function. Our model, once trained, can generate samples from any conditional probability density functions whose high probability regions are covered by the training set. Moreover, the pseudo-reversibility feature allows for the use of fully-connected neural network architectures, which simplifies the implementation and enables theoretical analysis. We provide a rigorous convergence analysis of the conditional pseudo-reversible normalizing flow model, showing its ability to converge to the target conditional probability density function using the Kullback-Leibler divergence. To demonstrate the effectiveness of our method, we apply it to several benchmark tests and a real-world geologic carbon storage problem

Geomagnetically Induced Current Calculation of High Voltage Power System with Long Transmission Lines using Kriging Method

Calculation of geomagnetically induced current (GIC) flowing through power system during the geomagnetic storm has attracted more attention recently. However, for high voltage power systems with transmission lines over hundreds or even thousands of kilometers, the earth model and geomagnetical field generally vary significantly. So, its essential to take them into consideration using limited earth survey sites and geomagnetic observatories. To address this problem, a Kriging method is introduced in this paper to make earth model and geomagnetical field interpolations. It has the characteristic of spatial autocorrelation by considering not only the distances between predicted points and training points but also the distances between training points themselves. Finally, a case study of the Central China 1000 kV ultra-high voltage (UHV) grid is carried out to illustrate the applicability and effectiveness of the proposed method

Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current

Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM), consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect