arXiv subjects

Pu Zhang

Publications and source records attributed to Pu Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2019

Multifunctional Liquid Metal Lattice Materials with Recoverable and Reconfigurable Behaviors

Multifunctional lattice materials are of great interest to modern engineering including aerospace, robotics, wave control, and sensing. In this work, we proposed and developed a new class of functional lattice materials called liquid metal lattice materials, which are composed of liquid metals and elastomer coatings organized in a co-axial way. This hybrid design enables the liquid metal lattice materials with a thermal-activated shape memory effect and hence a variety of intriguing functionalities including recoverable energy absorption, tunable shape and rigidity, deployable and reconfigurable behaviors. The fabrication of liquid metal lattice materials is realised by a hybrid manufacturing approach combining 3D printing, vacuum casting, and coating. The mechanical properties and functionalities of these liquid metal lattice materials are studied via experimental testing. We expect that this new class of lattice materials will greatly expand the current realm of lattice materials and lead to novel multifunctional applications.

cond-mat.mtrl-sci↗

arXiv2019

Exceptional cycles for perfect complexes over gentle algebras

Exceptional cycles in a triangulated category $\mathcal T$ with Serre duality, introduced by N. Broomhead, D. Pauksztello, and D. Ploog, have a notable impact on the global structure of $\mathcal T$. In this paper we show that if $\mathcal T$ is homotopy-like, then any exceptional $1$-cycle is indecomposable and at the mouth; and any object in an exceptional $n$-cycle with $n\ge 3$ is at the mouth. Let $A$ be an indecomposable gentle $k$-algebra with $A\ne k$. The Hom spaces between string complexes at the mouth are explicitly determined. The main result classifies "almost all" the exceptional cycles in $K^b(A\mbox{-}{\rm proj})$, using characteristic components and their AG-invariants, except those exceptional $1$-cycles which are band complexes. Namely, the mouth of a characteristic component $C$ of $K^b(A\mbox{-}{\rm proj})$ forms a unique exceptional cycle in $C$, up to an equivalent relation $\approx$; if the quiver of $A$ is not of type $A_3$, this gives all the exceptional $n$-cycle in $K^b(A\mbox{-}{\rm proj})$ with $n\ge 2$, up to $\approx$; and a string complex is an exceptional $1$-cycle if and only if it is at the mouth of a characteristic component with {\rm AG}-invariant $(1, m)$. However, a band complex at the mouth is possibly not an exceptional $1$-cycle.

math.RT↗

arXiv2019

Single-Molecule Doped Crystalline Nanosheets for Delicate Photophysics Studies and Directional Single-Photon Emitting Devices

Single molecules in solids have been considered as an attractive class of solid-state single quantum systems because they can be chemically synthesized at low cost to have stable narrow transitions at desired wavelengths. Here we report and demonstrate single dibenzoterrylene molecules in crystalline anthracene nanosheets as a robust and versatile solid-state platform for delicate photophysics studies and building blocks of single-photon devices. The high-quality nanosheet sample enables robust studies of delicate single-molecule photophysics at room temperature, including the first real-time observation of single molecule insertion site jump, quantitative measurements of the associated changes of dipole moment orientation and magnitude, unambiguous determination of excitation-power dependent intersystem crossing rate and triplet lifetime. Moreover, we demonstrate the flexible assembly of the nanosheets into a planar antenna device to achieve bright single-molecule emission with a Gaussian emission pattern. The thin thickness, good photostability and mechanical stability make the dibenzoterrylene-in-anthracene nanosheet system an excellent candidate of static quantum nodes in integrated photonic circuit.

physics.app-ph↗

arXiv2019

Quantum Photonic Node for On-Chip State Transfer

Integrated quantum photonics hold the promise to scale up the system size and form an on-chip quantum network with distributed information processing and simulation units. An outstanding need of such quantum network is to have high fidelity and efficiency on-chip state transfer between distant nodes. Although the nodes are naturally connected via waveguides, it is challenging to fulfill this need because stringent conditions such as spatial mode-matching configuration and time-reversal symmetry have to be satisfied. Here we report a type of quantum photonic nodes consisting of single quantum emitters and cascaded microring resonators for on-chip state transfer. By interfacing the node with a waveguide, we show that all the emission from the node can be funneled into the waveguide and its temporal profile can be synthesized to be time-reversal symmetric. We demonstrate theoretically on-chip quantum state transfer between two distant nodes with near-unity overall success rate can be achieved without any dynamic control. Moreover, we discuss the experimental implementation of our scheme with CMOS compatible integrated photonic platforms and solid-state quantum optics techniques.

quant-ph↗

arXiv2019

Gorenstein-projective and semi-Gorenstein-projective modules

An A-module M will be said to be semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. All Gorenstein-projective modules are semi-Gorenstein-projective and only few and quite complicated examples of semi-Gorenstein-projective modules which are not Gorenstein-projective have been known. The aim of the paper is to provide conditions on A such that all semi-Gorenstein-projective modules are Gorenstein-projective (we call such an algebra left weakly Gorenstein). In particular, we show that in case there are only finitely many isomorphism classes of indecomposable left modules which are both semi-Gorenstein-projective and torsionless, then A is left weakly Gorenstein. On the other hand, we exhibit a 6-dimensional algebra with a semi-Gorenstein-projective module M which is not torsionless (thus not Gorenstein-projective). Actually, also the dual module M* is semi-Gorenstein-projective module. In this way, we show the independence of the total reflexivity conditions of Avramov and Martsinkovsky, thus completing a partial proof by Jorgensen and Sega. Since all the syzygy-modules of M and M* are 3-dimensional, the example can be visualized quite easily.

math.RT↗

arXiv2019

Gorenstein-projective and semi-Gorenstein-projective modules. II

Let k be a field and q a non-zero element of k. In Part I, we have exhibited a 6-dimensional k-algebra A = A(q) and we have shown that if q has infinite multiplicative order, then A has a 3-dimensional local module which is semi-Gorenstein-projective, but not torsionless, thus not Gorenstein-projective. This Part II is devoted to a detailed study of all the 3-dimensional local A-modules for this particular algebra A. If q has infinite multiplicative order, we will encounter a whole family of 3-dimensional local modules which are semi-Gorenstein-projective, but not torsionless.

math.RT↗

arXiv2019

BLVD: Building A Large-scale 5D Semantics Benchmark for Autonomous Driving

In autonomous driving community, numerous benchmarks have been established to assist the tasks of 3D/2D object detection, stereo vision, semantic/instance segmentation. However, the more meaningful dynamic evolution of the surrounding objects of ego-vehicle is rarely exploited, and lacks a large-scale dataset platform. To address this, we introduce BLVD, a large-scale 5D semantics benchmark which does not concentrate on the static detection or semantic/instance segmentation tasks tackled adequately before. Instead, BLVD aims to provide a platform for the tasks of dynamic 4D (3D+temporal) tracking, 5D (4D+interactive) interactive event recognition and intention prediction. This benchmark will boost the deeper understanding of traffic scenes than ever before. We totally yield 249,129 3D annotations, 4,902 independent individuals for tracking with the length of overall 214,922 points, 6,004 valid fragments for 5D interactive event recognition, and 4,900 individuals for 5D intention prediction. These tasks are contained in four kinds of scenarios depending on the object density (low and high) and light conditions (daytime and nighttime). The benchmark can be downloaded from our project site https://github.com/VCCIV/BLVD/.

cs.CV↗

arXiv2019

SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction

In crowd scenarios, reliable trajectory prediction of pedestrians requires insightful understanding of their social behaviors. These behaviors have been well investigated by plenty of studies, while it is hard to be fully expressed by hand-craft rules. Recent studies based on LSTM networks have shown great ability to learn social behaviors. However, many of these methods rely on previous neighboring hidden states but ignore the important current intention of the neighbors. In order to address this issue, we propose a data-driven state refinement module for LSTM network (SR-LSTM), which activates the utilization of the current intention of neighbors, and jointly and iteratively refines the current states of all participants in the crowd through a message passing mechanism. To effectively extract the social effect of neighbors, we further introduce a social-aware information selection mechanism consisting of an element-wise motion gate and a pedestrian-wise attention to select useful message from neighboring pedestrians. Experimental results on two public datasets, i.e. ETH and UCY, demonstrate the effectiveness of our proposed SR-LSTM and we achieves state-of-the-art results.

cs.CV↗

arXiv2019

Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Let $0<α<n$ and $M_α$ be the fractional maximal function. The nonlinear commutator of $M_α$ and a locally integrable function $b$ is given by $[b,M_α](f)=bM_α(f)-M_α(bf)$. In this paper, we mainly give some necessary and sufficient conditions for the boundedness of $[b,M_α]$ on variable Lebesgue spaces when $b$ belongs to Lipschitz or $BMO(\rn)$ spaces, by which some new characterizations for certain subclasses of Lipschitz and $BMO(\rn)$ spaces are obtained.

math.CA↗

arXiv2018

On the Emission Pattern of Nanoscopic Emitters in Planar Anisotropic Matrix and Nanoantenna Structures

Single nanoscopic emitters embedded in crystalline matrix have become a valuable resource for emerging nanophotonic and quantum technologies. The generally anisotropic nature of the matrix strongly affects the emission properties of the quantum emitters, in particular, when the matrix is assembled in nanophotonic structures. We report on rigorous analysis and engineering of spontaneous emission from single emitters coupled to nanoantenna and planar anisotropic antenna structures. By developing a convenient theoretical method with efficient numerical implementation, we show that accurate modeling of the anisotropy is essential in predicting the emission pattern for many important systems, such as single molecules in solid-state matrix, isolated defects in 2D materials and so on. In particular, we illustrate the amplified effects of material anisotropy and geometrical anisotropy for emitters coupled to planar antenna and nanoantenna structures. We show that with proper design of the anisotropies strong enhancement of the emission rate and nearly collimated beam from single emitters can be simultaneously achieved.

physics.optics↗

arXiv2018

Symmetry and Degeneracy of Phonon Modes for Periodic Structures with Glide Symmetry

A large class of phononic crystals and mechanical metamaterials exhibit glide symmetry that dictates their functionality or exceptional performance. The glide symmetry gives rise to a number of intriguing phenomena like sticking-bands and degeneracy in the phononic band structures. Fully understanding of these phenomena demands analysis of the phonon modes' symmetry property, which is, however, a challenging task since it involves nonsymmorphic space group analysis and special treatment to the Brillouin zone boundary. Therefore, this work introduces a systematic group-theoretical procedure determining the symmetry of phonon modes for periodic structures with glide symmetry. By taking the p4g group as an example, the symmetry of phonon modes is discussed by deriving the small representations for high symmetry k-points, and different types of degeneracies are elucidated. This work provides insight into the role of glide symmetry on phononic band structures and guides the symmetry analysis to periodic structures of other types.

cond-mat.mtrl-sci↗

arXiv2018

Hyperelastic antiplane ground cloaking

Hyperelastic materials possess the appealing property that they may be employed as elastic wave manipulation devices and cloaks by imposing pre-deformation. They provide an alternative to microstructured metamaterials and can be used in a reconfigurable manner. Previous studies indicate that exact elastodynamic invariance to pre-deformation holds only for neo-Hookean solids in the antiplane wave scenario and the semi-linear material in the in-plane compressional/shear wave context. Furthermore, although ground cloaks have been considered in the acoustic context they have not yet been discussed for elastodynamics, either by employing microstructured cloaks or hyperelastic cloaks. This work therefore aims at exploring the possibility of employing a range of hyperelastic materials for use as antiplane ground cloaks (AGCs). The use of the popular incompressible Arruda-Boyce and Mooney-Rivlin nonlinear materials is explored. The scattering problem associated with the AGC is simulated via finite element analysis where the cloaked region is formed by an indentation of the surface. Results demonstrate that the neo-Hookean medium can be used to generate a perfect hyperelastic AGC as should be expected. Furthermore, although the AGC performance of the Mooney-Rivlin material is not particularly satisfactory, it is shown that the Arruda-Boyce medium is an excellent candidate material for this purpose.

physics.app-ph↗

arXiv2017

A Single-Emitter Gain Medium for Bright Coherent Radiation from a Plasmonic Nanoresonator

We theoretically demonstrate the generation and radiation of coherent nanoplasmons powered by a single three-level quantum emitter on a plasmonic nanoresonator. By pumping the three-level emitter in a Raman configuration, we show a pathway to achieve macroscopic accumulation of nanoplasmons due to stimulated emission in the nanoresonator despite their fast relaxation. Thanks to the antenna effect of the nanoresonator, the system acts as an efficient and bright nanoscopic coherent light source with a photon emission rate of hundreds of Terahertz and could be realized with solid-state emitters at room temperatures in pulse mode. We provide physical interpretations of the results and discuss their realization and implications for ultra-compact integration of optoelectronics.

physics.optics↗

arXiv2017

Bimodule monomorphism categories and RSS equivalences via cotilting modules

The monomorphism category $\mathscr{S}(A, M, B)$ induced by a bimodule $_AM_B$ is the subcategory of $Λ$-mod consisting of $\left[\begin{smallmatrix} X\\ Y\end{smallmatrix}\right]_ϕ$ such that $ϕ: M\otimes_B Y\rightarrow X$ is a monic $A$-map, where $Λ=\left[\begin{smallmatrix} A&M\\0&B \end{smallmatrix}\right]$. In general, it is not the monomorphism categories induced by quivers. It could describe the Gorenstein-projective $\m$-modules. This monomorphism category is a resolving subcategory of $\modcatΛ$ if and only if $M_B$ is projective. In this case, it has enough injective objects and Auslander-Reiten sequences, and can be also described as the left perpendicular category of a unique basic cotilting $Λ$-module. If $M$ satisfies the condition ${\rm (IP)}$, then the stable category of $\mathscr{S}(A, M, B)$ admits a recollement of additive categories, which is in fact a recollement of singularity categories if $\mathscr{S}(A, M, B)$ is a {\rm Frobenius} category. Ringel-Schmidmeier-Simson equivalence between $\mathscr{S}(A, M, B)$ and its dual is introduced. If $M$ is an exchangeable bimodule, then an {\rm RSS} equivalence is given by a $Λ$-$Λ$ bimodule which is a two-sided cotilting $Λ$-module with a special property; and the Nakayama functor $\mathcal N_\m$ gives an {\rm RSS} equivalence if and only if both $A$ and $B$ are Frobenius algebras.

math.RT↗

arXiv2017

Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of `bands-sticking-together' is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying pre-stretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with soft rubbers and unfavorable damping.

physics.app-ph↗

arXiv2017

Separated monic representations II: Frobenius subcategories and RSS equivalences

This paper aims at looking for Frobenius subcategories, via the separated monomorphism category ${\rm smon}(Q, I, \x)$, and on the other hand, to establish an {\rm RSS} equivalence from ${\rm smon}(Q, I, \x)$ to its dual ${\rm sepi}(Q, I, \x)$. For a bound quiver $(Q, I)$ and an algebra $A$, where $Q$ is acyclic and $I$ is generated by monomial relations, let $Λ=A\otimes_k kQ/I$. For any additive subcategory $\x$ of $A$-mod, we construct ${\rm smon}(Q, I, \x)$ combinatorially. This construction describe Gorenstein-projective $\m$-modules as $\mathcal {GP}(\m) = {\rm smon}(Q, I, \mathcal {GP}(A))$. It admits a homological interpretation, and enjoys a reciprocity ${\rm smon}(Q, I, \ ^\bot T)= \ ^\bot (T\otimes kQ/I)$ for a cotilting $A$-module $T$. As an application, ${\rm smon}(Q, I, \x)$ has Auslander-Reiten sequences if $\x$ is resolving and contravariantly finite with $\widehat{\x}=A$-mod. In particular, ${\rm smon}(Q, I, A)$ has Auslander-Reiten sequences. It also admits a filtration interpretation as ${\rm smon}(Q, I, \mathscr{X})={\rm Fil}(\mathscr{X}\otimes \mathcal P(kQ/I))$, provided that $\x$ is extension-closed. As an application, ${\rm smon}(Q, I, \x)$ is an extension-closed Frobenius subcategory if and only if so is $\x$. This gives "new" Frobenius subcategories of $\m$-mod in the sense that they are not $\mathcal{GP}(\m)$. Ringel-Schmidmeier-Simson equivalence ${\rm smon}(Q, I, \x)\cong{\rm sepi}(Q, I, \x)$ is introduced and the existence is proved for arbitrary extension-closed subcategories $\x$. In particular, the Nakayama functor $\mathcal N_\m$ gives an {\rm RSS} equivalence ${\rm smon}(Q, I, A)\cong{\rm sepi}(Q, I, A)$ if and only if $A$ is Frobenius. For a chain $Q$ with arbitrary $I$, an explicit formula of an {\rm RSS} equivalence is found for arbitrary additive subcategories $\x$.

math.RT↗

arXiv2017

Types of Serre subcategories of Grothendieck categories

Every Serre subcategory of an abelian category is assigned a unique type. The type of a Serre subcategory of a Grothendieck category is in the list: $$(0, 0), \ (0, -1), \ (1, -1), \ (0, -2), \ (1, -2), \ (2, -1), \ (+\infty, -\infty);$$ and for each $(m, -n)$ in this list, there exists a Serre subcategory such that its type is $(m, -n)$. This uses right (left) recollements of abelian categories, Tachikawa-Ohtake [TO] on strongly hereditary torsion pairs, and Geigle-Lenzing [GL] on localizing subcategories. If all the functors in a recollement of abelian categories are exact, then the recollement splits. Quite surprising, any left recollement of a Grothendieck category can be extended to a recollement; but this is not true for a right recollement. Thus, a colocalizing subcategory of a Grothendieck category is localizing; but the converse is not true. All these results do not hold in triangulated categories.

math.CT↗

arXiv2017

Characterization of Lipschitz functions in terms of variable exponent Lebesgue spaces

Our aim is to characterize the Lipschitz functions by variable exponent Lebesgue spaces. We give some characterizations of the boundedness of the maximal or nonlinear commutators of the Hardy-Littlewood maximal function and sharp maximal function in variable exponent Lebesgue spaces when the symbols $b$ belong to the Lipschitz spaces, by which some new characterizations of Lipschitz spaces and nonnegative Lipschitz functions are obtained. Some equivalent relations between the Lipschitz norm and the variable exponent Lebesgue norm are also given.

math.CA↗