We show that the solution of the free-boundary incompressible ideal magnetohydrodynamic (MHD) equations with surface tension converges to that of the free-boundary incompressible ideal MHD equations without surface tension given the Rayleigh-Taylor s
ign condition holds true initially. This result is a continuation of the authors previous works [13,27,12]. Our proof is based on the combination of the techniques developed in our previous works [13,27,12], Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.
In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler equations describing the motion of a liquid in an unbounded initial domain with moving boundary. The liquid is under the influence of gravity but without surface tens
ion, and it is not assumed to be irrotational. We apply the tangential smoothing method introduced in [9,10] to construct the approximation system with energy estimates uniform in the smooth parameter. It should be emphasized that, when doing the nonlinear a priori estimates, we need neither the higher order wave equation of the pressure and delicate elliptic estimates, nor the higher regularity on the flow-map or initial vorticity. Instead, we adapt the Alinhacs good unknowns to the estimates of full spatial derivatives.
The interlayer coupling in van der Waals heterostructures governs a variety of optical and electronic properties. The intrinsic dipole moment of Janus transition metal dichalcogenides (TMDs) offers a simple and versatile approach to tune the interlay
er interactions. In this work, we demonstrate how the van der Waals interlayer coupling and charge transfer of Janus MoSSe/MoS2 heterobilayers can be tuned by the twist angle and interface composition. Specifically, the Janus heterostructures with a sulfur/sulfur (S/S) interface display stronger interlayer coupling than the heterostructures with a selenium/sulfur (Se/S) interface as shown by the low-frequency Raman modes. The differences in interlayer interactions are explained by the interlayer distance computed by density-functional theory (DFT). More intriguingly, the built-in electric field contributed by the charge density redistribution and interlayer coupling also play important roles in the interfacial charge transfer. Namely, the S/S and Se/S interfaces exhibit different levels of PL quenching of MoS2 A exciton, suggesting the enhanced and reduced charge transfer at the S/S and Se/S interface, respectively. Our work demonstrates how the asymmetry of Janus TMDs can be used to tailor the interfacial interactions in van der Waals heterostructures.
Recovering high-quality 3D human motion in complex scenes from monocular videos is important for many applications, ranging from AR/VR to robotics. However, capturing realistic human-scene interactions, while dealing with occlusions and partial views
, is challenging; current approaches are still far from achieving compelling results. We address this problem by proposing LEMO: LEarning human MOtion priors for 4D human body capture. By leveraging the large-scale motion capture dataset AMASS, we introduce a novel motion smoothness prior, which strongly reduces the jitters exhibited by poses recovered over a sequence. Furthermore, to handle contacts and occlusions occurring frequently in body-scene interactions, we design a contact friction term and a contact-aware motion infiller obtained via per-instance self-supervised training. To prove the effectiveness of the proposed motion priors, we combine them into a novel pipeline for 4D human body capture in 3D scenes. With our pipeline, we demonstrate high-quality 4D human body capture, reconstructing smooth motions and physically plausible body-scene interactions. The code and data are available at https://sanweiliti.github.io/LEMO/LEMO.html.
This paper describes a novel design of a neural network-based speech generation model for learning prosodic representation.The problem of representation learning is formulated according to the information bottleneck (IB) principle. A modified VQ-VAE
quantized layer is incorporated in the speech generation model to control the IB capacity and adjust the balance between reconstruction power and disentangle capability of the learned representation. The proposed model is able to learn word-level prosodic representations from speech data. With an optimized IB capacity, the learned representations not only are adequate to reconstruct the original speech but also can be used to transfer the prosody onto different textual content. Extensive results of the objective and subjective evaluation are presented to demonstrate the effect of IB capacity control, the effectiveness, and potential usage of the learned prosodic representation in controllable neural speech generation.
Dynamic objects in the environment, such as people and other agents, lead to challenges for existing simultaneous localization and mapping (SLAM) approaches. To deal with dynamic environments, computer vision researchers usually apply some learning-b
ased object detectors to remove these dynamic objects. However, these object detectors are computationally too expensive for mobile robot on-board processing. In practical applications, these objects output noisy sounds that can be effectively detected by on-board sound source localization. The directional information of the sound source object can be efficiently obtained by direction of sound arrival (DoA) estimation, but depth estimation is difficult. Therefore, in this paper, we propose a novel audio-visual fusion approach that fuses sound source direction into the RGB-D image and thus removes the effect of dynamic obstacles on the multi-robot SLAM system. Experimental results of multi-robot SLAM in different dynamic environments show that the proposed method uses very small computational resources to obtain very stable self-localization results.
Dynamic environments that include unstructured moving objects pose a hard problem for Simultaneous Localization and Mapping (SLAM) performance. The motion of rigid objects can be typically tracked by exploiting their texture and geometric features. H
owever, humans moving in the scene are often one of the most important, interactive targets - they are very hard to track and reconstruct robustly due to non-rigid shapes. In this work, we present a fast, learning-based human object detector to isolate the dynamic human objects and realise a real-time dense background reconstruction framework. We go further by estimating and reconstructing the human pose and shape. The final output environment maps not only provide the dense static backgrounds but also contain the dynamic human meshes and their trajectories. Our Dynamic SLAM system runs at around 26 frames per second (fps) on GPUs, while additionally turning on accurate human pose estimation can be executed at up to 10 fps.
In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among more that tw
o variables, which may also involve conditional independence. Here I am particularly interested in visualizing Markov chains which have the well known memoryless property. I am not talking about drawing the transition graph, instead, I will draw all events of the Markov process in a single plot. Here, to simplify the question, this work will only consider dichotomous variables, but all the methods actually can be generalized to arbitrary set of discrete variables.
We consider 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. It describes the motion of a free-surface perfect conducting fluid in an electro-magnetic field. The local well-posedness was r
ecently proved by Trakhinin and Wang [66] by using Nash-Moser iteration. In this paper, we prove the a priori estimates without loss of regularity for the free-boundary compressible MHD system in Lagrangian coordinates in anisotropic Sobolev space, with more regularity tangential to the boundary than in the normal direction. It is based on modified Alinhac good unknowns, which take into account the covariance under the change of coordinates to avoid the derivative loss; full utilization of the cancellation structures of MHD system, to turn normal derivatives into tangential ones; and delicate analysis in anisotropic Sobolev spaces. Our method is also completely applicable to compressible Euler equations and thus yields an alternative estimate for compressible Euler equations without the analysis of div-curl decomposition or the wave equation in Lindblad-Luo [42], that do not work for compressible MHD. To the best of our knowledge, we establish the first result on the energy estimates without loss of regularity for the free-boundary problem of compressible ideal MHD.
For tunable control of asymmetric light reflection, we propose a Rydberg atomic system of the optical response varying in space induced by the long-range position-dependent Rydberg dipole-dipole interaction either in the type of self-van der Waals di
pole-dipole interaction or the cross F{o}rster-like dipole-dipole exchange interaction. In such a one-dimensional system consisting of a control atomic driven upon the Rydberg state and a homogeneous target atomic ensemble, the non-localized action from the control atom on the target atoms gradually decreases with the distance between the control and target atoms. Our scheme yields a nonlinear correspondence from a finite spectra range to a finite spatial range of susceptibility via the nonlinear characteristics of Rydberg interaction relative to the position. Therefore, the asymmetric reflection can be induced via the spatial modulation on the target ensemble. In particular, the reflection from one direction can be completely suppressed when the absorption and dispersion parts of the susceptibility are modulated to satisfy the spatial Kramers-Kronig relation in an infinite spectral range. The opposite reflection exhibits a band of a small nonzero reflectivity due to the realistic restriction of the cold atomic density of a relatively small value. Thus, via trapping the target atoms in the optical lattice for the Bragg scattering, we enhance the nonzero reflection obviously and retain the directional reflectionlessness.
