arXiv subjects

Hao Wu

Publications and source records attributed to Hao Wu.

At least 685 records · Page 38Linked to original sources

arXiv2022

Well-posedness for a Navier-Stokes-Cahn-Hilliard System for Incompressible Two-phase Flows with Surfactant

We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the difference of local concentrations of the binary fluid mixture coupled with a fourth-order Cahn-Hilliard equation for the local concentration of the surfactant. The former has a smooth potential, while the latter has a singular potential. Both equations are coupled with a Navier-Stokes system for the (volume averaged) fluid velocity. The evolution system is endowed with suitable initial conditions, a no-slip boundary condition for the velocity field and homogeneous Neumann boundary conditions for the phase functions as well as for the chemical potentials. We first prove the existence of a global weak solution, which turns out to be unique in two dimensions. Stronger regularity assumptions on the initial data allow us to prove the existence of a unique global (resp. local) strong solution in two (resp. three) dimensions. In the two dimensional case, we can derive a continuous dependence estimate with respect to the norms controlled by the total energy. Then we establish instantaneous regularization properties of global weak solutions for $t>0$. In particular, we show that the surfactant concentration stays uniformly away from the pure states $0$ and $1$ after some positive time.

math.AP↗

arXiv2022

Enhanced quantum sensing with room-temperature solid-state masers

Quantum sensing with solid-state systems finds broad applications in diverse areas ranging from material and biomedical sciences to fundamental physics. Several solid-state spin sensors have been developed, facilitating the ultra-sensitive detection of physical quantities such as magnetic and electric fields and temperature. Exploiting collective behaviour of non-interacting spins holds the promise of pushing the detection limit to even lower levels, while to date, those levels are scarcely reached due to the broadened linewidth and inefficient readout of solid-state spin ensembles. Here, we experimentally demonstrate that such drawbacks can be overcome by newly reborn maser technology at room temperature in the solid state. Owing to maser action, we observe a 4-fold reduction in the inhomogeneously broadened linewidth of a molecular spin ensemble, which is narrower than the same measured from single spins at cryogenic temperatures. The maser-based readout applied to magnetometry showcases a signal-to-noise ratio (SNR) of 30 dB for single shots. This technique would be a significant addition to the toolbox for boosting the sensitivity of solid-state ensemble spin sensors.

quant-ph↗

arXiv2022

Ergodic Deviations of Degenerate Multidimensional Actions -- Symmetric Convex Bodies

We prove that the ergodic deviation of a degenerate $\mathbb{Z}^2$-action on the torus $\mathbb{T}^2$ relative to a symmetric, strictly convex body can be decomposed into two parts, and that each part admits a limit distribution after choosing a suitable normalizer. Specifically, the first part is similar to an ergodic sum of smooth observables after being normalized by $N$, and the second part is similar to the case of a random toral translation, i.e., the $\mathbb{Z}$-action, but with a normalizer of $N^{\frac{1}{2}}$. The key difference is that we employ the product flow on the product space of $\mathbb{Z}^2$ lattices for the multidimensional action.

math.DS↗

arXiv2021

Well-posedness of a Hydrodynamic Phase-field Model for Functionalized Membrane-Fluid Interaction

In this paper, we study a hydrodynamic phase-field system modeling the deformation of functionalized membranes in incompressible viscous fluids. The governing PDE system consists of the Navier-Stokes equations coupled with a convective sixth-order Cahn-Hilliard type equation driven by the functionalized Cahn-Hilliard free energy, which describes phase separation in mixtures with an amphiphilic structure. In the three dimensional case, we first prove existence of global weak solutions provided that the initial total energy is finite. Then we establish uniqueness of weak solutions under suitable regularity assumptions only imposed on the velocity field (or its gradient). Finally, we prove the existence and uniqueness of local strong solutions for arbitrary regular initial data and derive some blow-up criteria. The results are obtained in the general setting with variable viscosity and mobility.

math.AP↗

arXiv2021

A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions

The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we briefly review the derivation, structure as well as some analytical issues for the Cahn-Hilliard equation and its variants. Our focus will be placed on the well-posedness and long-time behavior of the Cahn-Hilliard equation in the classical setting and recent progresses on the dynamic boundary conditions accounting for non-trivial boundary effects.

math.AP↗

arXiv2021

Deeptime: a Python library for machine learning dynamical models from time series data

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software.

math.DS↗

arXiv2021

Absolute Bounds for Ergodic Deviations of Toral Translations Relative to Triangles in $\mathbb{T}^2$

Following Beck's work on toral translations relative to straight boxes in $\mathbb{T}^n$, we prove a weaker upper bound and the same lower bound for ergodic discrepancies of toral translations relative to a triangle in $\mathbb{T}^2$. Specifically, given a positive increasing function $φ(n)$, we show that for a full measure set of translation vectors $α\in \mathbb{T}^2$, if the series $\sum_{N=1}^{\infty} \frac{1}{φ(N)} $ converges, then the maximal discrepancy of toral translations relative to the triangles of a given slope $τ$ is bounded from above by $Const(α,τ) (\log N)^2 φ^2(\log \log N)$, and there would be infinitely many $N$'s such that the maximal discrepancy is greater than $(\log N)^2φ(\log \log N)$ if the series $\sum_{N=1}^{\infty} \frac{1}{φ(N)} $ diverges. An important difference between our result and that of Beck' is an additional factor $φ(\log \log N)$, which is necessary in our proof for controlling the new small divisors created by the hypotenuse.

math.NT↗

arXiv2021

Room temperature energy-efficient spin-orbit torque switching in wafer-scale all-vdW heterostructure

The emergent two-dimensional (2D) ferromagnetic materials with unique magnetic properties have endowed great potential for next-generation spintronic devices with extraordinary merits of high flexibility, easy controllability, and high heretointegrability, which is expected to promote the development of Moore's Law continuously. However, it is extremely challenging to realize magnetic switching with ultra-low power consumption at room temperature. Here, we demonstrate the room-temperature spin-orbit torque (SOT) driven magnetization switching in a well-epitaxial all-van der Waals (vdW) heterostructure. The topological insulator Bi2Te3 not only helps to elevate the Curie temperature of Fe3GeTe2 (FGT) through interfacial exchange coupling but also works as a spin current source allowing to switch FGT at a low current density of 2.2 * 106 A cm2. A large SOT efficiency of 0.7 is measured at room temperature, and the thickness of FGT is further adjusted to reduce the influence of the thermal contribution on the second-harmonic signal. Furthermore, the temperature and thickness-dependent SOT efficiency prove that the large SOT in our system mainly originates from the nontrivial origin of topological materials. Our experiment has enabled an all-vdW SOT structure and lays a solid foundation for the implementation of room-temperature all-vdW spintronic devices in the future.

physics.app-ph↗

arXiv2021

Positional-Spectral-Temporal Attention in 3D Convolutional Neural Networks for EEG Emotion Recognition

Recognizing the feelings of human beings plays a critical role in our daily communication. Neuroscience has demonstrated that different emotion states present different degrees of activation in different brain regions, EEG frequency bands and temporal stamps. In this paper, we propose a novel structure to explore the informative EEG features for emotion recognition. The proposed module, denoted by PST-Attention, consists of Positional, Spectral and Temporal Attention modules to explore more discriminative EEG features. Specifically, the Positional Attention module is to capture the activate regions stimulated by different emotions in the spatial dimension. The Spectral and Temporal Attention modules assign the weights of different frequency bands and temporal slices respectively. Our method is adaptive as well as efficient which can be fit into 3D Convolutional Neural Networks (3D-CNN) as a plug-in module. We conduct experiments on two real-world datasets. 3D-CNN combined with our module achieves promising results and demonstrate that the PST-Attention is able to capture stable patterns for emotion recognition from EEG.

eess.SP↗

arXiv2021

Stabilization of stochastic McKean-Vlasov equations with feedback control based on discrete-time state observation

In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic stability and exponential stability in mean square for the solution of the controlled systems are obtained. Since the distribution of solution is difficult to be observed, we study the corresponding particle system which can be observed for the feedback control. We prove that the exponential stability of control system is equivalent to the the exponential stability of the corresponding particle system. Finally, an example is provided to show the effectiveness of the theory.

math.PR↗

arXiv2021

Berry-Esseen bound and Local Limit Theorem for the coefficients of products of random matrices

Let $μ$ be a probability measure on $\text{GL}_d(\mathbb{R})$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $μ$. Under the assumptions that $μ$ has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we prove a Berry-Esseen bound with the optimal rate $O(1/\sqrt n)$ and a general Local Limit Theorem for the coefficients of $S_n$.

math.PR↗

arXiv2021

Improving Blockchain Consistency Bound by Assigning Weights to Random Blocks

Blockchains based on the celebrated Nakamoto consensus protocol have shown promise in several applications, including cryptocurrencies. However, these blockchains have inherent scalability limits caused by the protocol's consensus properties. In particular, the \emph{consistency} property demonstrates a tight trade-off between block production speed and the system's security in terms of resisting adversarial attacks. This paper proposes a novel method, Ironclad, that improves blockchain consistency bound by assigning a different weight to randomly selected blocks. We apply our method to the original Nakamoto protocol and rigorously prove that such a combination can improve the consistency bound significantly by analyzing the fundamental consensus properties. Such an improvement enables a much faster block production rate than the original Nakamoto protocol under the same security guarantee with the same proportion of malicious mining power (see Figure 1).

cs.CR↗

arXiv2021

Decay of Fourier coefficients for Furstenberg measures

Let $ν$ be the Furstenberg measure associated with a non-elementary probability measure $μ$ on SL_2(R). We show that, when $μ$ has a finite second moment, the Fourier coefficients of $ν$ tend to zero at infinity. In other words, $ν$ is a Rajchman measure. This improves a recent result of Jialun Li.

math.PR↗

arXiv2021

Increase of barium ion-trap lifetime via photodissociation

The lifetime of Ba$^+$ ions confined in a Paul trap is found, under typical conditions, to be limited by chemical reactions with residual background gas. An integrated ion trap and time-of-flight mass spectrometer are used to analyze the reactions of the trapped Ba$^+$ ions with three common gases in an ultrahigh vacuum system (H$_2$, CO$_2$ and H$_2$O). It is found that the products of these reactions can all be photodissociated by a single ultraviolet laser at 225~nm, thereby allowing the recovery of the Ba$^+$ ions and leading to an increase of the effective trap lifetime. For a Coulomb crystal, the lifetime increased from roughly 6~hours to 2~days at room temperature. It is suggested that higher enhancement factors are possible in systems with stronger traps. In addition, photodissociation wavelengths for other common trapped ion systems are provided.

physics.atom-ph↗

arXiv2021

SynCoBERT: Syntax-Guided Multi-Modal Contrastive Pre-Training for Code Representation

Code representation learning, which aims to encode the semantics of source code into distributed vectors, plays an important role in recent deep-learning-based models for code intelligence. Recently, many pre-trained language models for source code (e.g., CuBERT and CodeBERT) have been proposed to model the context of code and serve as a basis for downstream code intelligence tasks such as code search, code clone detection, and program translation. Current approaches typically consider the source code as a plain sequence of tokens, or inject the structure information (e.g., AST and data-flow) into the sequential model pre-training. To further explore the properties of programming languages, this paper proposes SynCoBERT, a syntax-guided multi-modal contrastive pre-training approach for better code representations. Specially, we design two novel pre-training objectives originating from the symbolic and syntactic properties of source code, i.e., Identifier Prediction (IP) and AST Edge Prediction (TEP), which are designed to predict identifiers, and edges between two nodes of AST, respectively. Meanwhile, to exploit the complementary information in semantically equivalent modalities (i.e., code, comment, AST) of the code, we propose a multi-modal contrastive learning strategy to maximize the mutual information among different modalities. Extensive experiments on four downstream tasks related to code intelligence show that SynCoBERT advances the state-of-the-art with the same pre-training corpus and model size.

cs.CL↗

arXiv2021

Enabling variable high spatial resolution retrieval from a long pulse BOTDA sensor

In the field of Internet of Things, there is an urgent need for sensors with large-scale sensing capability for scenarios such as intelligent monitoring of production lines and urban infrastructure. Brillouin optical time domain analysis (BOTDA) sensors, which can monitor thousands of continuous points simultaneously, show great advantages in these applications. We propose a convolutional neural network (CNN) to process the data of conventional Brillouin optical time domain analysis (BOTDA) sensors, which achieves unprecedented performance improvement that allows to directly retrieve higher spatial resolution (SR) from the sensing system that use long pump pulses. By using the simulated Brillouin gain spectrums (BGSs) as the CNN input and the corresponding high SR BFS as the output target, the trained CNN is able to obtain a SR higher than the theoretical value determined by the pump pulse width. In the experiment, the CNN accurately retrieves 0.5-m hotspots from the measured BGS with pump pulses from 20 to 50 ns, and the acquired BFS is in great agreement with 45/40 ns differential pulse-width pair (DPP) measurement results. Compared with the DPP technique, the proposed CNN demonstrates a 2-fold improvement in BFS uncertainty with only half the measurement time. In addition, by changing the training datasets, the proposed CNN can obtain tunable high SR retrieval based on conventional BOTDA sensors that use long pulses without any requirement of hardware modifications. The proposed data post-processing approach paves the way to enable novel high spatial resolution BOTDA sensors, which brings substantial improvement over the state-of-the-art techniques in terms of system complexity, measurement time and reliability, etc.

eess.SP↗

arXiv2021

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a Gaussian random field with the Karhunen-Loève (KL) expansion structure and the target stochastic field, where the KL expansion coefficients and the invertible networks are trained by maximizing the sum of the log-likelihood on scattered measurements. This NFF model can be used to solve data-driven forward, inverse, and mixed forward/inverse stochastic partial differential equations in a unified framework. We demonstrate the capability of the proposed NFF model for learning Non Gaussian processes and different types of stochastic partial differential equations.

cs.LG↗

arXiv2021

The ByteDance Speaker Diarization System for the VoxCeleb Speaker Recognition Challenge 2021

This paper describes the ByteDance speaker diarization system for the fourth track of the VoxCeleb Speaker Recognition Challenge 2021 (VoxSRC-21). The VoxSRC-21 provides both the dev set and test set of VoxConverse for use in validation and a standalone test set for evaluation. We first collect the duration and signal-to-noise ratio (SNR) of all audio and find that the distribution of the VoxConverse's test set and the VoxSRC-21's test set is more closer. Our system consists of voice active detection (VAD), speaker embedding extraction, spectral clustering followed by a re-clustering step based on agglomerative hierarchical clustering (AHC) and overlapped speech detection and handling. Finally, we integrate systems with different time scales using DOVER-Lap. Our best system achieves 5.15\% of the diarization error rate (DER) on evaluation set, ranking the second at the diarization track of the challenge.

cs.SD↗