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Wei Cai

Publications and source records attributed to Wei Cai.

At least 73 records · Page 4Linked to original sources
arXiv2024

Characterization of 3D printed micro-blades for cutting tissue-embedding material

Cutting soft materials on the microscale has emerging applications in single-cell studies, tissue microdissection for organoid culture, drug screens, and other analyses. However, the cutting process is complex and remains incompletely understood. Furthermore, precise control over blade geometries, such as the blade tip radius, has been difficult to achieve. In this work, we use the Nanoscribe 3D printer to precisely fabricate micro-blades (i.e., blades <1 mm in length) and blade grid geometries. This fabrication method enables a systematic study of the effect of blade geometry on the indentation cutting of paraffin wax, a common tissue-embedding material. First, we print straight micro-blades with tip radius ranging from ~100 nm to 10 um. The micro-blades are mounted in a custom nanoindentation setup to measure the cutting energy during indentation cutting of paraffin. Cutting energy, measured as the difference in dissipated energy between the first and second loading cycles, decreases as blade tip radius decreases, until ~357 nm when the cutting energy plateaus despite further decrease in tip radius. Second, we expand our method to blades printed in unconventional configurations, including parallel blade structures and blades arranged in a square grid. Under the conditions tested, the cutting energy scales approximately linearly with the total length of the blades comprising the blade structure. The experimental platform described can be extended to investigate other blade geometries and guide the design of microscale cutting of soft materials.

physics.med-ph↗
arXiv2024

Political Leanings in Web3 Betting: Decoding the Interplay of Political and Profitable Motives

Harnessing the transparent blockchain user behavior data, we construct the Political Betting Leaning Score (PBLS) to measure political leanings based on betting within Web3 prediction markets. Focusing on Polymarket and starting from the 2024 U.S. Presidential Election, we synthesize behaviors over 15,000 addresses across 4,500 events and 8,500 markets, capturing the intensity and direction of their political leanings by the PBLS. We validate the PBLS through internal consistency checks and external comparisons. We uncover relationships between our PBLS and betting behaviors through over 800 features capturing various behavioral aspects. A case study of the 2022 U.S. Senate election further demonstrates the ability of our measurement while decoding the dynamic interaction between political and profitable motives. Our findings contribute to understanding decision-making in decentralized markets, enhancing the analysis of behaviors within Web3 prediction environments. The insights of this study reveal the potential of blockchain in enabling innovative, multidisciplinary studies and could inform the development of more effective online prediction markets, improve the accuracy of forecast, and help the design and optimization of platform mechanisms. The data and code for the paper are accessible at the following link: https://github.com/anonymous.

cs.CY↗
arXiv2024

Deep Neural Networks with Symplectic Preservation Properties

We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used in normalizing flow techniques. Utilizing this neural network type allows for learning tasks on unknown Hamiltonian systems without breaking the inherent symplectic structure of the phase space.

math.NA↗
arXiv2024

Beam shaping by nonlinear moiré metasurfaces

This paper explores the interplay of momentum transfer and nonlinear optical processes through moiré phenomena. Momentum transfer plays a crucial role in the interaction between photons and matter. Here, we study stacked metasurfaces with tailored dispersion and rotated against each other with varying twisted angles. The stacking introduces interlayer interactions, which can be controlled by the relative angle between metasurfaces, significantly enriching the resulting response compared to the single layer counterpart. By focusing on second-harmonic generation (SHG) from these twisted metasurfaces, we delve into the realm of nonlinear moiré photonics. Through experimental observations, we unveil the emergence of intricate far-field SHG radiation patterns, showing their effective tuning by varying the twisted angles. These findings offer a fresh perspective to explore nonlinear wavefront shaping through moiré phenomena, opening new avenues for nonlinear information processing, optical steering, and nonlinear optical switching.

physics.optics↗
arXiv2024

Electro-optically Modulated Nonlinear Metasurfaces

Tunable nonlinearity facilitates the creation of reconfigurable nonlinear metasurfaces, enabling innovative applications in signal processing, light switching, and sensing. This paper presents a novel approach to electrically modulate SHG from a lithium niobate (LN) metasurface, exploiting the electro-optical (EO) effect. By fabricating a nanohole array metasurface on a thin LN film and applying an electric field, we demonstrate the alteration of the material's refractive index, resulting in resonance shifts and modulation of SHG intensity at specific wavelengths. Our findings provide valuable insights for the development of electrically tunable nonlinear light sources, quantum optics, dynamic nonlinear holography, and nonlinear information processing.

physics.optics↗
arXiv2024

Enhanced mobility of dislocation network nodes and its effect on dislocation multiplication and strain hardening

Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been developed, but its lack of atomistic resolution leaves open the possibility that certain key mechanisms may be overlooked. By comparing large-scale Molecular Dynamics (MD) with DDD simulations performed under identical conditions we uncover significant discrepancies in the predicted strength and microstructure evolution in BCC crytals under high-strain rate conditions. These are traced to unexpected behaviors of dislocation network nodes forming at dislocation intersections, that can move in ways not previously anticipated as revealed by MD. Once these newfound freedoms of nodal motion are incorporated, DDD simulations begin to closely match plastic evolution observed in MD. This additional mechanism of motion whereby non-screw dislocations can change their glide plane profoundly affects fundamental processes of dislocation multiplication, recovery and storage that define strength of metals.

cond-mat.mtrl-sci↗
arXiv2024

Modeling Shortest Paths in Polymeric Networks using Spatial Branching Processes

Recent studies have established a connection between the macroscopic mechanical response of polymeric materials and the statistics of the shortest path (SP) length between distant nodes in the polymer network. Since these statistics can be costly to compute and difficult to study theoretically, we introduce a branching random walk (BRW) model to describe the SP statistics from the coarse-grained molecular dynamics (CGMD) simulations of polymer networks. We postulate that the first passage time (FPT) of the BRW to a given termination site can be used to approximate the statistics of the SP between distant nodes in the polymer network. We develop a theoretical framework for studying the FPT of spatial branching processes and obtain an analytical expression for estimating the FPT distribution as a function of the cross-link density. We demonstrate by extensive numerical calculations that the distribution of the FPT of the BRW model agrees well with the SP distribution from the CGMD simulations. The theoretical estimate and the corresponding numerical implementations of BRW provide an efficient way of approximating the SP distribution in a polymer network. Our results have the physical meaning that by accounting for the realistic topology of polymer networks, extensive bond-breaking is expected to occur at a much smaller stretch than that expected from idealized models assuming periodic network structures. Our work presents the first analysis of polymer networks as a BRW and sets the framework for developing a generalizable spatial branching model for studying the macroscopic evolution of polymeric systems.

math-ph↗
arXiv2024

Topological valley plasmons in twisted monolayer-double graphene moiré superlattices

In topological photonics, artificial photonic structures are constructed for realizing nontrivial unidirectional propagation of photonic information. On the other hand, moiré superlattices are emerging as an important avenue for engineering quantum materials with novel properties. In this paper, we combine these two aspects and demonstrate theoretically that moiré superlattices of small-angle twisted monolayer-bilayer graphene provide a natural platform for valley protected plasmons. Particularly, a complete plasmonic bandgap appears stemming from the distinct optical conductivities of the ABA and ABC stacked triangular domains. Moreover, the plasmonic crystals exhibit nonzero valley Chern numbers and unidirectional transport of plasmonic edge states protected from inter-valley scattering is presented.

physics.optics↗
arXiv2024

Prediction of Yield Surface of Single Crystal Copper from Discrete Dislocation Dynamics and Geometric Learning

A yield surface of a material is a set of critical stress conditions beyond which macroscopic plastic deformation begins. For crystalline solids, plastic deformation occurs through the motion of dislocations, which can be captured by discrete dislocation dynamics (DDD) simulations. In this paper, we predict the yield surfaces and strain-hardening behaviors using DDD simulations and a geometric manifold learning approach. The yield surfaces in the three-dimensional space of plane stress are constructed for single-crystal copper subjected to uniaxial loading along the $[100]$ and $[110]$ directions, respectively. With increasing plastic deformation under $[100]$ loading, the yield surface expands nearly uniformly in all directions, corresponding to isotropic hardening. In contrast, under $[110]$ loading, latent hardening is observed, where the yield surface remains nearly unchanged in the orientations in the vicinity of the loading direction itself, but expands in other directions, resulting in an asymmetric shape. This difference in hardening behaviors is attributed to the different dislocation multiplication behaviors on various slip systems under the two loading conditions.

cond-mat.mtrl-sci↗
arXiv2024

Network evolution controlling strain-induced damage and self-healing of elastomers with dynamic bonds

Highly stretchable and self-healable supramolecular elastomers are promising materials for future soft electronics, biomimetic systems, and smart textiles, due to their dynamic cross-linking bonds. The dynamic or reversible nature of the cross-links gives rise to interesting macroscopic responses in these materials such as self-healing and rapid stress-relaxation. However, the relationship between bond activity and macroscopic mechanical response, and the self-healing properties of these dynamic polymer networks (DPNs) remains poorly understood. Using coarse-grained molecular dynamics (CGMD) simulations, we reveal a fundamental connection between the macroscopic behaviors of DPNs and the shortest paths between distant nodes in the polymer network. Notably, the trajectories of the material on the shortest path-strain map provide key insights into understanding the stress-strain hysteresis, anisotropy, stress relaxation, and self-healing of DPNs. Based on CGMD simulations under various loading histories, we formulate a set of empirical rules that dictate how the shortest path interacts with stress and strain. This lays the foundation for the development of a physics-based theory centered around the non-local microstructural feature of shortest paths to predict the mechanical behavior of DPNs.

cond-mat.soft↗
arXiv2024

Accelerated Sampling of Rare Events using a Neural Network Bias Potential

In the field of computational physics and material science, the efficient sampling of rare events occurring at atomic scale is crucial. It aids in understanding mechanisms behind a wide range of important phenomena, including protein folding, conformal changes, chemical reactions and materials diffusion and deformation. Traditional simulation methods, such as Molecular Dynamics and Monte Carlo, often prove inefficient in capturing the timescale of these rare events by brute force. In this paper, we introduce a practical approach by combining the idea of importance sampling with deep neural networks (DNNs) that enhance the sampling of these rare events. In particular, we approximate the variance-free bias potential function with DNNs which is trained to maximize the probability of rare event transition under the importance potential function. This method is easily scalable to high-dimensional problems and provides robust statistical guarantees on the accuracy of the estimated probability of rare event transition. Furthermore, our algorithm can actively generate and learn from any successful samples, which is a novel improvement over existing methods. Using a 2D system as a test bed, we provide comparisons between results obtained from different training strategies, traditional Monte Carlo sampling and numerically solved optimal bias potential function under different temperatures. Our numerical results demonstrate the efficacy of the DNN-based importance sampling of rare events.

cs.LG↗
arXiv2024

Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks

This study presents a Graph Neural Networks (GNNs)-based approach for predicting the effective elastic moduli of rocks from their digital CT-scan images. We use the Mapper algorithm to transform 3D digital rock images into graph datasets, encapsulating essential geometrical information. These graphs, after training, prove effective in predicting elastic moduli. Our GNN model shows robust predictive capabilities across various graph sizes derived from various subcube dimensions. Not only does it perform well on the test dataset, but it also maintains high prediction accuracy for unseen rocks and unexplored subcube sizes. Comparative analysis with Convolutional Neural Networks (CNNs) reveals the superior performance of GNNs in predicting unseen rock properties. Moreover, the graph representation of microstructures significantly reduces GPU memory requirements (compared to the grid representation for CNNs), enabling greater flexibility in the batch size selection. This work demonstrates the potential of GNN models in enhancing the prediction accuracy of rock properties and boosting the efficiency of digital rock analysis.

cs.LG↗
arXiv2023

DeepMartNet -- A Martingale Based Deep Neural Network Learning Method for Dirichlet BVPs and Eigenvalue Problems of Elliptic PDEs in R^d

In this paper, we propose DeepMartNet - a Martingale based deep neural network learning method for solving Dirichlet boundary value problems (BVPs) and eigenvalue problems for elliptic partial differential equations (PDEs) in high dimensions or domains with complex geometries. The method is based on Varadhan's Martingale problem formulation for the BVPs/eigenvalue problems where a loss function enforcing the Martingale property for the PDE solution is used for an efficient optimization by sampling the stochastic processes associated with corresponding elliptic operators. High dimensional numerical results for BVPs of the linear and nonlinear Poisson-Boltzmann equation and eigenvalue problems of the Laplace equation and a Fokker-Planck equation demonstrate the capability of the proposed DeepMartNet learning method in solving high dimensional PDE problems.

math.NA↗
arXiv2023

TigerBot: An Open Multilingual Multitask LLM

We release and introduce the TigerBot family of large language models (LLMs), consisting of base and chat models, sized from 7, 13, 70 and 180 billion parameters. We develop our models embarking from Llama-2 and BLOOM, and push the boundary further in data, training algorithm, infrastructure, and application tools. Our models yield meaningful performance gain over SOTA open-source models, e.g., Llama-2, specifically 6% gain in English and 20% gain in Chinese. TigerBot model family also achieves leading performance in major academic and industrial benchmarks and leaderboards. We believe that TigerBot represents just a snapshot of lightning-fast progression in LLM open-source community. Therefore, we are thrilled to give back by publicly releasing our models and reporting our approach behind, with additional emphases on building SOTA LLMs in a democratized way and making LLMs of use in real-world applications.

cs.CL↗
arXiv2023

High Absorptivity Nanotextured Powders for Additive Manufacturing

The widespread application of metal additive manufacturing (AM) is limited by the ability to control the complex interactions between the energy source and the feedstock material. Here we develop a generalizable process to introduce nanoscale grooves to the surface of metal powders which increases the powder absorptivity by up to 70% during laser powder bed fusion. Absorptivity enhancements in copper, copper-silver, and tungsten enables energy efficient manufacturing, with printing of pure copper at relative densities up to 92% using laser energy densities as low as 82 J/mm^3. Simulations show the enhanced powder absorptivity results from plasmon-enabled light concentration in nanoscale grooves combined with multiple scattering events. The approach taken here demonstrates a general method to enhance the absorptivity and printability of reflective and refractory metal powders by changing the surface morphology of the feedstock without altering its composition.

physics.optics↗
arXiv2023

On Spectral Bias Reduction of Multi-scale Neural Networks for Regression Problems

In this paper, we derive diffusion equation models in the spectral domain for the evolution of training errors of two-layer multi-scale deep neural networks (MscaleDNN) \cite{caixu2019,liu2020multi}, designed to reduce the spectral bias of fully connected deep neural networks in approximating oscillatory functions. The diffusion models are obtained from the spectral form of the error equation of the MscaleDNN, derived with a neural tangent kernel approach and gradient descent training and a sine activation function, assuming a vanishing learning rate and infinite network width and domain size. The involved diffusion coefficients are shown to have larger supports if more scales are used in the MscaleDNN, and thus, the proposed diffusion equation models in the frequency domain explain the MscaleDNN's spectral bias reduction capability. Numerical results of the diffusion models for a two-layer MscaleDNN training match with the error evolution of actual gradient descent training with a reasonably large network width, thus validating the effectiveness of the diffusion models. Meanwhile, the numerical results for MscaleDNN show error decay over a wide frequency range and confirm the advantage of using the MscaleDNN in approximating functions with a wide range of frequencies.

math.NA↗
arXiv2023

DeepMartNet -- A Martingale based Deep Neural Network Learning Algorithm for Eigenvalue/BVP Problems and Optimal Stochastic Controls

In this paper, we propose a neural network learning algorithm for solving eigenvalue problems and boundary value problems (BVPs) for elliptic operators and initial BVPs (IBVPs) of quasi-linear parabolic equations in high dimensions as well as optimal stochastic controls. The method is based on the Martingale property in the stochastic representation for the eigenvalue/BVP/IBVP problems and martingale principle for optimal stochastic controls. A loss function based on the Martingale property can be used for efficient optimization by sampling the stochastic processes associated with the elliptic operators or value process for stochastic controls. The proposed algorithm can be used for eigenvalue problems and BVPs and IBVPs with Dirichlet, Neumann, and Robin boundaries in bounded or unbounded domains and some feedback stochastic control problems.

math.NA↗