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Hongjie Li

Publications and source records attributed to Hongjie Li.

At least 37 records · Page 2Linked to original sources

Autonomous Character-Scene Interaction Synthesis from Text Instruction

Synthesizing human motions in 3D environments, particularly those with complex activities such as locomotion, hand-reaching, and human-object interaction, presents substantial demands for user-defined waypoints and stage transitions. These requirements pose challenges for current models, leading to a notable gap in automating the animation of characters from simple human inputs. This paper addresses this challenge by introducing a comprehensive framework for synthesizing multi-stage scene-aware interaction motions directly from a single text instruction and goal location. Our approach employs an auto-regressive diffusion model to synthesize the next motion segment, along with an autonomous scheduler predicting the transition for each action stage. To ensure that the synthesized motions are seamlessly integrated within the environment, we propose a scene representation that considers the local perception both at the start and the goal location. We further enhance the coherence of the generated motion by integrating frame embeddings with language input. Additionally, to support model training, we present a comprehensive motion-captured dataset comprising 16 hours of motion sequences in 120 indoor scenes covering 40 types of motions, each annotated with precise language descriptions. Experimental results demonstrate the efficacy of our method in generating high-quality, multi-stage motions closely aligned with environmental and textual conditions.

cs.CV↗

Resonant modes of two hard inclusions within a soft elastic material and their stress estimate

In this paper, we are concerned with subwavelength resonant modes of two hard inclusions embedding in soft elastic materials to realize negative materials in elasticity. All the $12$ subwavelength resonant frequencies are derived explicitly for general convex resonators. In addition, the resonant modes are categorized into dipolar, quadrupolar, and hybrid groups, facilitating the effective realization of negative mass density, negative shear modulus and double-negative properties (both mass density and shear modulus) in elastic metamaterials. Moreover, we analyze the stress distribution between two hard inclusions when they are closely touching. We also precisely derive the sharp blow-up rates of the gradient estimates of the resonant modes. Our findings show that certain resonant modes have bounded stress estimates when the curvature of the hard inclusions is appropriately designed. These results provide valuable insights into the stability of the design and fabrication of elastic metamaterials. Lastly, we express the scattering wave fields explicitly in terms of resonant modes, offering a clear understanding of their impact on the overall scattering behavior.

math.AP↗

Scaling Up Dynamic Human-Scene Interaction Modeling

Confronting the challenges of data scarcity and advanced motion synthesis in human-scene interaction modeling, we introduce the TRUMANS dataset alongside a novel HSI motion synthesis method. TRUMANS stands as the most comprehensive motion-captured HSI dataset currently available, encompassing over 15 hours of human interactions across 100 indoor scenes. It intricately captures whole-body human motions and part-level object dynamics, focusing on the realism of contact. This dataset is further scaled up by transforming physical environments into exact virtual models and applying extensive augmentations to appearance and motion for both humans and objects while maintaining interaction fidelity. Utilizing TRUMANS, we devise a diffusion-based autoregressive model that efficiently generates HSI sequences of any length, taking into account both scene context and intended actions. In experiments, our approach shows remarkable zero-shot generalizability on a range of 3D scene datasets (e.g., PROX, Replica, ScanNet, ScanNet++), producing motions that closely mimic original motion-captured sequences, as confirmed by quantitative experiments and human studies.

cs.CV↗

Learning Deformable Hypothesis Sampling for Accurate PatchMatch Multi-View Stereo

This paper introduces a learnable Deformable Hypothesis Sampler (DeformSampler) to address the challenging issue of noisy depth estimation for accurate PatchMatch Multi-View Stereo (MVS). We observe that the heuristic depth hypothesis sampling modes employed by PatchMatch MVS solvers are insensitive to (i) the piece-wise smooth distribution of depths across the object surface, and (ii) the implicit multi-modal distribution of depth prediction probabilities along the ray direction on the surface points. Accordingly, we develop DeformSampler to learn distribution-sensitive sample spaces to (i) propagate depths consistent with the scene's geometry across the object surface, and (ii) fit a Laplace Mixture model that approaches the point-wise probabilities distribution of the actual depths along the ray direction. We integrate DeformSampler into a learnable PatchMatch MVS system to enhance depth estimation in challenging areas, such as piece-wise discontinuous surface boundaries and weakly-textured regions. Experimental results on DTU and Tanks \& Temples datasets demonstrate its superior performance and generalization capabilities compared to state-of-the-art competitors. Code is available at https://github.com/Geo-Tell/DS-PMNet.

cs.CV↗

A novel time-domain direct sampling approach for inverse scattering problems in acoustics

This work is concerned with an inverse scattering problem of determining unknown scatterers from time-dependent acoustic measurements. A novel time-domain direct sampling method is developed to efficiently determine both the locations and shapes of inhomogeneous media. In particular, our approach is very easy to implement since only cheap space-time integrations are involved in the evaluation of the imaging functionals. Based on the Fourier-Laplace transform, we establish an inherent connection between the time-domain and frequency-domain direct sampling method. Moreover, rigorous theoretical justifications and numerical experiments are provided to verify the validity and feasibility of the proposed method.

math.NA↗

Mathematical theory on dipolar resonances of hard inclusions within a soft elastic material

The current study is motivated by the paper [Z. Liu, et al., {\it Science}, 289(5485), 2000], which investigates the incorporation of hard inclusions within a soft elastic matrix (HISE). The objective is to attain a negative mass density, which is caused by sub-wavelength dipolar resonances. This paper offers a comprehensive and mathematically rigorous understanding of the dipolar resonances within the HISE structure. Firstly, the original formula for the resonant frequencies of arbitrarily shaped hard inclusions is derived explicitly for the first time. Additionally, we demonstrate that the resonances arise due to the high contrast in Lamé parameters between various materials, while the sub-wavelength characteristics of the resonances are attributed to the significant disparities in material densities. Furthermore, the dipolar characterization of the resonances is rigorously justified. To validate our findings, we investigate resonant phenomena within a spherical geometry, offering both an alternative method for calculating resonant frequencies and a confirmation of the results presented in this paper.

math.AP↗

Fano resonances in all-dielectric electromagnetic metasurfaces

We are interested in the resonant electromagnetic (EM) scattering by all-dielectric metasurfaces made of a two-dimensional lattice of nanoparticles with high refractive indices. In [Ammari et al., Trans. AMS, 376 (2023), 39-90], it has been shown that a single high-index nanoresonator can couple with the incident wave and exhibit a strong magnetic dipole response. Recent physics experiments reveal that when the particles are arranged in certain periodic configurations, they may have different anomalous scattering effects in the macroscopic scale, compared to the single-particle case. In this work, we shall develop a rigorous mathematical framework for analyzing the resonant behaviors of all-dielectric metasurfaces. We start with the characterization of subwavelength scattering resonances in such a periodic setting and their asymptotic expansions in terms of the refractive index of the nanoparticles. Then we show that real resonances always exist below the essential spectrum of the periodic Maxwell operator and that they are the simple poles of the scattering resolvent with the exponentially decaying resonant modes. By using group theory, we discuss the implications of the symmetry of the metasurface on the subwavelength band functions and their associated eigenfunctions. For the symmetric metasurfaces with the normal incidence, we use a variational method to show the existence of embedded eigenvalues (i.e., real subwavelength resonances embedded in the continuous radiation spectrum). Furthermore, we break the configuration symmetry either by introducing a small deformation of particles or by slightly deviating from the normal incidence and prove that Fano-type reflection and transmission anomalies can arise in both of these scenarios.

physics.optics↗

Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications

We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in this work which are new to the literature. First, under a mild condition on the medium parameters, we prove the existence of an acoustic-elastic transmission eigenvalue. Second, we establish a geometric rigidity result of the transmission eigenfunctions by showing that they tend to localize on the boundary of the underlying domain. Moreover, we also consider interesting implications of the obtained results to the effective construction of metamaterials by using bubbly elastic structures and to the inverse problem associated with the fluid-structure interaction.

math.AP↗

Invisibility enables super-visibility in electromagnetic imaging

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme.

math.AP↗

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Given the flexibility of choosing negative elastic parameters, we construct material structures that can induce two resonance phenomena, referred to as the elastodynamical resonances. They mimic the emerging plasmon/polariton resonance and anomalous localized resonance in optics for subwavelength particles. However, we study the peculiar resonance phenomena for linear elasticity beyond the subwavelength regime. It is shown that the resonance behaviours possess distinct characters, with some similar to the subwavelength resonances, but some sharply different due to the frequency effect. It is particularly noted that we construct a core-shell material structure that can induce anomalous localized resonance as well as cloaking phenomena beyond the quasi-static limit. The study is boiled down to analyzing the so-called elastic Neumann-Poincáre (N-P) operator in the frequency regime. We provide an in-depth analysis of the spectral properties of the N-P operator beyond the quasi-static approximation,and these results are of independent interest to the spectral theory of layer potential operators.

math-ph↗

Minnaert resonances for bubbles in soft elastic materials

Minnaert resonance is a well known physical phenomenon and it has many important applications, in particular in the effective realisation of acoustic metamaterials using bubbly mediums in recent years. In this paper, motived by the Minnaert resonance, we consider the low-frequency resonance for acoustic bubbles embedded in soft elastic materials. This is a hybrid physical process that couples the acoustic and elastic wave propagations. By delicately and subtly balancing the acoustic and elastic parameters as well as the geometry of the bubble, we show that Minnaert resonance can (approximately) occur for rather general constructions. Our study poses a great potential for the effective realisation of negative elastic materials by using bubbly elastic mediums.

math.AP↗

Spectral properties of Neumann-Poincare operator and anomalous localized resonance in elasticity beyond quasi-static limit

This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within the finite frequency regime beyond the quasi-static approximation. We first derive the complete spectral system of the Neumann-Poincaré operator associated with the elastic system within the finite frequency regime. Based on the obtained spectral results, we construct a broad class of elastic configurations that can induce polariton resonances beyond the quasi-static limit. As an application, the invisibility cloaking effect is achieved through constructing a class of core-shell-matrix metamaterial structures provided the source is located inside a critical radius. Moreover, if the source is located outside the critical radius, it is proved that there is no resonance.

math.AP↗

Analysis of electromagnetic scattering from plasmonic inclusions beyond the quasi-static approximation and applications

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the inclusions are allowed to be negative-valued. Using layer potential techniques for the full Maxwell system, the scattering problem is reformulated into a system of integral equations. We derive the complete eigensystem of the involved matrix-valued integral operator within spherical geometry. As applications, we construct two types of plasmonic structures such that one can induce surface plasmon resonances within finite frequencies and the other one can produce invisibility cloaking. It is particularly noted that the cloaking effect is a newly found phenomenon and is of different nature from those existing ones for plasmonic structures in the literature. The surface plasmon resonance result may find applications in electromagnetic imaging.

math.AP↗

Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions

This paper reports some novel and intriguing discoveries about the localization and geometrization phenomenon in plasmon resonances and the intrinsic geometric structures of Neumann-Poincaré eigenfunctions. It is known that plasmon resonance generically occurs in the quasi-static regime where the size of the plasmonic inclusion is sufficiently small compared to the wavelength. In this paper, we show that the global smallness condition on the plasmonic inclusion can be replaced by a local high-curvature condition, and the plasmon resonance occurs locally near the high-curvature point of the plasmonic inclusion. We provide partial theoretical explanation and link with the geometric structures of the Neumann- Poincaré (NP) eigenfunctions. The spectrum of the Neumann-Poincaré operator has received significant attentions in the literature. We show for the first time some intrinsic geometric structures of the Neumann-Poincaré eigenfunctions near high-curvature points.

math.AP↗

On anomalous localized resonance and plasmonic cloaking beyond the quasistatic limit

In this paper, we give the mathematical construction of novel core-shell plasmonic structures that can induce anomalous localized resonance and invisibility cloaking at certain finite frequencies beyond the quasistatic limit. The crucial ingredient in our study is that the plasmon constant and the loss parameter are constructed in a delicate way that are correlated and depend on the source and the size of the plasmonic structure. As a significant byproduct of this study, we also derive the complete spectrum of the Neumann-Poincáre operator associated to the Helmholtz equation with finite frequencies in the radial geometry. The spectral result is the first one in its type and is of significant mathematical interest for its own sake.

math.AP↗

Formation of the Abundance Boundaries of the Heavier Neutron-capture Elements in Metal-poor Stars

The abundance scatter of heavier r-process elements (Z > 56) relative to Fe ([r/Fe]) in metal-poor stars preserves excellent information of the star formation history and provides important insights into the various situations of the Galactic chemical enrichment. In this respect, the upper and lower boundaries of [r/Fe] could present useful clues for investigating the extreme situations of the star formation history and the early Galactic chemical evolution. In this paper, we investigate the formation of the upper and lower boundaries of [r/Fe] for the gas clouds. We find that, for a cloud from which metal-poor stars formed, the formation of the upper limits of [r/Fe] is mainly due to the pollution from a single main r-process event. For a cloud from which metal-poor stars formed, the formation of the lower limits of [r/Fe] is mainly due to the pollution from a single SN II event that ejects primary Fe.

astro-ph.SR↗

Analysis of surface polariton resonance for nanoparticles in elastic system

This paper is concerned with the analysis of surface polariton resonance for nanoparticles in linear elasticity. With the presence of nanoparticles, we first derive the perturbed displacement field associated to a given elastic source field. It is shown that the leading-order term of the perturbed elastic wave field is determined by the Neumann-Poincáre operator associated to the Lamé system. By analyzing the spectral properties of the aforesaid Neumann-Poincáre operator, we study the polariton resonance for the elastic system. The results may find applications in elastic wave imaging.

math.AP↗

Fourier method for identifying electromagnetic sources with multi-frequency far-field data

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse problem from far-field measurements. The method is based on recovering the Fourier coefficients of the unknown source. A key ingredient of the method is to establish the relationship between the Fourier coefficients and the multi-frequency far-field data. Uniqueness and stability results are established for the proposed reconstruction method. Numerical experiments are presented to illustrate the effectiveness and efficiency of the method.

math.AP↗