arXiv subjects

Weili Zhang

Publications and source records attributed to Weili Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Random periodic solutions of non-autonomous stochastic differential equations

In this paper, we study the existence of random periodic solutions for nonlinear stochastic differential equations with additive white noise. We extend the input-to-state characteristic operator of the system to the non-autonomous stochastic differential equation via the pull-back of the discretised stochastic differential equation. We then use the completeness of the measurable function space which we construct skillfully and the Banach fixed point theorem to prove the existence of a fixed point of the gain operator. And we prove that the image for the input-to-state characteristic operator at this fixed point is a random periodic solution for the forward stochastic flow generated by the non-autonomous stochastic differential equation. Finally, we present some examples.

math.DS↗

arXiv2019

Random Almost Periodic Solutions of Random Dynamical Systems

In this paper, we first give the definition of random almost periodic solutions of random dynamical systems and give some examples. Then, we prove the existence of such random almost periodic solutions. Further, we introduce the definition of random almost periodic measure. Finally, we discuss the relationship between random almost periodic solutions and almost periodic measures.

math.DS↗

arXiv2018

Resilience-based performance modeling and decision optimization for transportation network

This research presented a novel resilience-based framework to support resilience planning regarding pre-disaster mitigation and post-disaster recovery. First, the author proposes a new performance metric for transportation network, weighted number of independent pathways (WIPW), integrating the network topology, redundancy level, traffic patterns, structural reliability of network components, and functionality of the network during community's post-disaster recovery in a systematical way. To the best of our knowledge, WIPW is the only performance metric that permits risk mitigation alternatives for improving transportation network resilience to be compared on a common basis. Based on the WIPW, a decision methodology of prioritizing transportation network retrofit projects is developed. Second, our studies extend from pre-disaster mitigation to post-hazard recovery, in which this research presents two metrics to evaluate the restoration over the horizon after disasters . That is, total recovery time and the skew of the recovery trajectory. Both metrics are involved in the multi-objective stochastic optimization problem of restoration scheduling. The metrics provided a new dimension to evaluate the relative efficiency of alternative network recovery strategies. The author then develops a restoration scheduling methodology for network post-disaster recovery that minimizes the overall network recovery time and optimizes the recovery trajectory, which ultimately will reduce economic losses due to network service disruption.

physics.soc-ph↗

arXiv2018

A Stage-wise Decision Framework for Transportation Network Resilience Planning

This study introduces a comprehensive stage-wise decision framework to support resilience planning for roadway networks regarding pre-disaster mitigation (Stage I), post-disaster emergency response (Stage II) and long-term recovery (Stage III). Three decision metrics are first defined, each based on a derivation of the number of independent pathways (IPW) within a roadway system, to measure the performance of a network in term of its robustness, redundancy, and recoverability, respectively. Using the three IPW-based decision metrics, a stage-wise decision process is then formulated as a stochastic multi-objective optimization problem, which includes a project ranking mechanism to identify pre-disaster network retrofit projects in Phase I, a prioritization approach for temporary repairs to facilitate immediate post-disaster emergency responses in Phase II, and a methodology for scheduling network-wide repairs during the long-term recovery of the roadway system in Phase III. Finally, this stage-wise decision framework is applied to the roadway network of Shelby County, TN, USA subjected to seismic hazards, to illustrate its implementation in supporting community network resilience planning.

physics.soc-ph↗

arXiv2018

Objective Scaling Ensemble Approach for Integer Linear Programming

The objective scaling ensemble approach is a novel two-phase heuristic for integer linear programming problems shown to be effective on a wide variety of integer linear programming problems. The technique identifies and aggregates multiple partial solutions to modify the problem formulation and significantly reduce the search space. An empirical analysis on publicly available benchmark problems demonstrate the efficacy of our approach by outperforming standard solution strategies implemented in modern optimization software.

math.OC↗

arXiv2018

Empirical analysis of metaheuristic search techniques for the parameterized dynamic slope scaling procedure

The dynamic slope scaling procedure is an approximation method successfully which solves the fixed charge network flow (FCNF) problem by iteratively linearizing the fixed cost. The parameterized dynamic slope scaling procedure adds an additional $ψ$ parameter to the procedure which can significantly improve the solution quality. Finding the optimal value of $ψ$ for a given problem is non-trivial. This paper employs multiple metaheuristic techniques, including simulated annealing, tabu search, and particle swarm optimization, to guide the search for good parameter values. In rigorous testing, we examine the search results, compare the improvement efficiencies among the techniques, and evaluate the final solution quality of the FCNF problem. The experiments show that the solution improvement is robust with respect to these metaheuristics and the complexity of FCNF problem.

math.OC↗

arXiv2018

Optimal flow analysis, prediction and application

This thesis employs statistical learning technique to analyze, predict and solve the fixed charge network flow (FCNF) problem, which is common encountered in many real-world network problems. The cost structure for flows in the FCNF involves both fixed and variable costs. The FCNF problem is modeled mixed binary linear programs and can be solved with standard commercial solvers, which use branch and bound algorithm. This problem is important for its widely applications and solving challenges. There does not exist a efficient algorithm to solve this problem optimally due to lacking tight bounds. To the best of our knowledge, this is the first work that employs statistical learning technique to analyze the optimal flow of the FCNF problem. Most algorithms developed to solve the FCNF problem are based on the cost structure, relaxation, etc. We start from the network characteristics and explore the relationship between properties of nodes, arcs and networks and the optimal flow. This is a bi-direction approach and the findings can be used to locate the features that affect the optimal flow most significantly, predict the optimal arcs and provide information to solve the FCNF problem. In particular, we define 33 features based on the network characteristics, from which using step wise regression, we identify 26 statistical significant predictors for logistic regression to predict which arcs will have positive flow in the optimal solutions. The predictive model achieves 88% accuracy and the area under receiver operating characteristic curve is 0.95. Two applications are investigated. Firstly, the predictive results can be used directly as component critical index. The failure of arcs with higher critical index result in more cost increase over the entire network.

cs.SI↗

arXiv2017

Electro-optic routing of photons from single quantum dots in photonic integrated circuits

Recent breakthroughs in solid-state photonic quantum technologies enable generating and detecting single photons with near-unity efficiency as required for a range of photonic quantum technologies. The lack of methods to simultaneously generate and control photons within the same chip, however, has formed a main obstacle to achieving efficient multi-qubit gates and to harness the advantages of chip-scale quantum photonics. Here we propose and demonstrate an integrated voltage-controlled phase shifter based on the electro-optic effect in suspended photonic waveguides with embedded quantum emitters. The phase control allows building a compact Mach-Zehnder interferometer with two orthogonal arms, taking advantage of the anisotropic electro-optic response in gallium arsenide. Photons emitted by single self-assembled quantum dots can be actively routed into the two outputs of the interferometer. These results, together with the observed sub-microsecond response time, constitute a significant step towards chip-scale single-photon-source de-multiplexing, fiber-loop boson sampling, and linear optical quantum computing.

quant-ph↗

arXiv2016

Pancharatnam-Berry phase induced spin-selective transmission in herringbone dielectric metamaterials

Manipulating the polarisation of light is crucial for sensing and imaging applications. One such aspect in particular is selective transmission of one circular polarisation (spin) when light is transmitted through a medium or a device. However, most present methods of achieving this have relatively low efficiency and selectivity, whilst high selectivity examples rely on lossy and complex three-dimensional helical or multilayer structures. Here, we propose a dielectric metamaterial approach for achieving spin-selective transmission of electromagnetic waves, utilizing spin-controlled constructive or destructive interference between two Pancharatnam-Berry (PB) phases in conjunction with propagative dynamic phase. The dielectric metamaterial, consisting of monolithic silicon herringbone structures, exhibits a broadband operation in the terahertz regime whilst obtaining a spin-selective efficiency upwards of 60%. Such a device is robust and is not easily degraded by errors in fabrication.

physics.optics↗

arXiv2016

Coherent control of optical spin-to-orbital angular momentum conversion in metasurface

We propose and experimentally demonstrate that a metasurface consisting of Pancharatnam-Berry phase optical elements can enable the full control of optical spin-to-orbital angular momentum conversion. Our approach relies on the critical interference between the transmission and reflection upon the metasurfaceto create actively tunable and controllable conversion with a high output via coherent control of the two incident beams. The introduced control methodology is general and could be an important step toward the development of functional optical devices for practical applications.

physics.optics↗

arXiv2015

Polarization-controlled anisotropic coding metamaterials at terahertz frequencies

Metamaterials based on effective media have achieved a lot of unusual physics (e.g. negative refraction and invisibility cloaking) owing to their abilities to tailor the effective medium parameters that do not exist in nature. Recently, coding metamaterials have been suggested to control electromagnetic waves by designing the coding sequences of digital elements '0' and '1', which possess opposite phase responses. Here, we propose the concept of anisotropic coding metamaterial at terahertz frequencies, in which coding behaviors in different directions are dependent on the polarization status of terahertz waves. We experimentally demonstrate an ultrathin and flexible polarization-controlled anisotropic coding metasurface functioning in the terahertz regime using specially- designed coding elements. By encoding the elements with elaborately-designed digital sequences (in both 1 bit and 2 bits), the x- and y-polarized reflected waves can be deflected or diffused independently in three dimensions. The simulated far-field scattering patterns as well as near-electric-field distributions are given to illustrate the bifunctional performance of the encoded metasurface, which show good agreement to the measurement results. We further demonstrate the abilities of anisotropic coding metasurface to generate beam splitter and realize anomalous reflection and polarization conversion simultaneously, providing powerful controls of differently-polarized terahertz waves. The proposed method enables versatile beam behaviors under orthogonal polarizations using a single metasurface, and hence will promise interesting terahertz devices.

physics.optics↗

arXiv2015

Tailoring the slow light behavior in terahertz metasurfaces

We experimentally study the effect of near field coupling on the transmission of light in terahertz metasurfaces, possessing slightly distinctive SRR resonances. Our results show that the interplay between the strengths of electric and magnetic dipoles, modulates the amplitude of resulting electromagnetically induced transmission, probed under different types of asymmetries in the coupled system. We employ a two-particle model to theoretically study the influence of the near field coupling between bright and quasi-dark modes on the transmission properties of the coupled system and we find an excellent agreement with our observed results. Adding to the enhanced transmission characteristics, our results provide a deeper insight into the metamaterial analogues of atomic electromagnetically induced transparency and offer an approach to engineer slow light devices, broadband filters and attenuators at terahertz frequencies.

physics.optics↗

arXiv2014

Ultrasensitive THz sensing with high-Q Fano resonances in metasurfaces

High quality factor resonances are extremely promising for designing ultra-sensitive refractive index label-free sensors since it allows intense interaction between electromagnetic waves and the analyte material. Metamaterial and plasmonic sensing has recently attracted a lot of attention due to subwavelength confinement of electromagnetic fields in the resonant structures. However, the excitation of high quality factor resonances in these systems has been a challenge. We excite an order of magnitude higher quality factor resonances in planar terahertz metamaterials that we exploit for ultrasensitive sensing. The low-loss quadrupole and Fano resonances with extremely narrow linewidths enable us to measure the minute spectral shift caused due to the smallest change in the refractive index of the surrounding media. We achieve sensitivity levels of 7.75 x 10^3 nm/ RIU with quadrupole and 5.7 x 10^4 nm/ RIU with the Fano resonances which could be further enhanced by using thinner substrates. These findings would facilitate the design of ultrasensitive real time chemical and biomolecular sensors in the fingerprint region of the terahertz regime.

physics.optics↗

arXiv2011

Robust large dimension terahertz cloaking

Invisibility cloaking not only catches the human imagination, but also promises fascinating applications in optics and photonics. By manipulating electromagnetic waves with metamaterials, researchers have been able to realize electromagnetic cloaking in the microwave, terahertz and optical regimes. Nevertheless, the complex design and fabrication process, narrow bandwidth, and high intrinsic losses in the metamaterial-based cloaks have imposed intractable limitations on their realistic applications. Seeking new approaches to overcome these perceived disadvantages is in progress. Here by using uniform sapphire crystal, we demonstrate the first homogenous invisibility cloak functioning at terahertz frequencies. The terahertz invisibility device features a large concealed volume, low loss, and broad bandwidth. In particular, it is capable of hiding objects with a dimension nearly an order of magnitude larger than that of its lithographic counterpart, but without involving complex and time-consuming cleanroom processing. Such homogenous invisibility cloaks may lead to novel terahertz photonic devices potentially used in medicine, radars, and communications.

physics.optics↗

arXiv2011

Hiding a Realistic Object Using a Broadband Terahertz Invisibility Cloak

The invisibility cloak has been a long-standing dream for many researchers over the decades. The introduction of transformational optics has revitalized this field by providing a general method to design material distributions to hide the subject from detection. By transforming space and light propagation, a three-dimensional (3D) object is perceived as having a reduced number of dimensions, in the form of points, lines, and thin sheets, making it "undetectable" judging from the scattered field. Although a variety of cloaking devices have been reported at microwave and optical frequencies, the spectroscopically important Terahertz (THz) domain remains unexplored. Moreover, due to the difficulties in fabricating cloaking devices that are optically large in all three dimensions, hiding realistic 3D objects has yet to be demonstrated. Here, we report the first experimental demonstration of a 3D THz cloaking device fabricated using a scalable Projection Microstereolithography process. The cloak operates at a broad frequency range between 0.3 and 0.6 THz, and is placed over an α- lactose monohydrate absorber with rectangular shape. Characterized using angularresolved reflection THz time-domain spectroscopy (THz-TDS), the results indicate that the THz invisibility cloak has successfully concealed both the geometrical and spectroscopic signatures of the absorber, making it undetectable to the observer.

physics.optics↗

arXiv2010

Controlling metamaterial resonances via dielectric and aspect ratio effects

We study ways to enhance the sensitivity and dynamic tuning range of the fundamental inductor-capacitor (LC) resonance in split ring resonators (SRRs) by controlling the aspect ratio of the SRRs and their substrate thickness. We conclude that both factors can significantly affect the LC resonance. We show that metafilms consisting of low height SRRs on a thin substrate are most sensitive to changes in their dielectric environment and thus show excellent potential for sensing applications.

physics.optics↗

arXiv2010

Strong influence of packing density in terahertz metamaterials

We investigate the response of terahertz metamaterials made of split-ring resonators depending on the unit cell density. It is shown that the fundamental resonance has its highest Q factor for a period of one-third the resonance wavelength. Increasing or decreasing the period from that optimal period reduces the Q factor. All observations are explained by understanding radiative coupling as the dominant loss mechanism at low densities, whereas the strong inter SRR coupling enhances non-radiative losses at high densities. Our results allow designing metamaterials with adjustable Q factors and possibly suggesting that an optimal package density exists to induce the strongest dispersion.

physics.optics↗

arXiv2010

Asymmetric planar terahertz metamaterials

We report an experimental observation of three distinct resonances in split ring resonators (SRRs) for both vertical and horizontal electric field polarizations at normal incidence by use of terahertz time domain spectroscopy. Breaking the symmetry in SRRs by gradually displacing the capacitive gap from the center towards the corner of the ring allows for an 85% modulation of the fundamental inductive-capacitive resonance. Increasing asymmetry leads to the evolution of an otherwise inaccessible high quality factor electric quadrupole resonance that can be exploited for bio-sensing applications in the terahertz region.

physics.optics↗