arXiv subjects

Wei Fang

Publications and source records attributed to Wei Fang.

At least 109 records · Page 6Linked to original sources

arXiv2017

Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift: Part II, infinite time interval

This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of the ergodic SDEs with a drift which is not globally Lipschitz over an infinite time interval. If the timestep is bounded appropriately, we show not only the stability of the numerical solution and the standard strong convergence order, but also that the bound for moments and strong error of the numerical solution are uniform in T, which allow us to introduce the adaptive multilevel Monte Carlo. Numerical experiments support our analysis.

math.NA↗

arXiv2017

Monolithic integration of a high-quality factor lithium niobate microresonator with a free-standing membrane waveguide using femtosecond laser assisted ion beam writing (FLAIBW)

We demonstrate integrating a high quality factor lithium niobate microdisk resonator with a free-standing membrane waveguide. Our technique is based on femtosecond laser direct writing which produces the pre-structure, followed by focused ion beam milling which reduces the surface roughness of sidewall of the fabricated structure to nanometer scale. Efficient light coupling between the integrated waveguide and microdisk was achieved, and the quality factor of the microresonator was measured as high as 1.67*10^5.

physics.optics↗

arXiv2017

Hierarchical Attention Model for Improved Machine Comprehension of Spoken Content

Multimedia or spoken content presents more attractive information than plain text content, but the former is more difficult to display on a screen and be selected by a user. As a result, accessing large collections of the former is much more difficult and time-consuming than the latter for humans. It's therefore highly attractive to develop machines which can automatically understand spoken content and summarize the key information for humans to browse over. In this endeavor, a new task of machine comprehension of spoken content was proposed recently. The initial goal was defined as the listening comprehension test of TOEFL, a challenging academic English examination for English learners whose native languages are not English. An Attention-based Multi-hop Recurrent Neural Network (AMRNN) architecture was also proposed for this task, which considered only the sequential relationship within the speech utterances. In this paper, we propose a new Hierarchical Attention Model (HAM), which constructs multi-hopped attention mechanism over tree-structured rather than sequential representations for the utterances. Improved comprehension performance robust with respect to ASR errors were obtained.

cs.CL↗

arXiv2016

Stability of Complex Biomolecular Structures: Vander Waals, Hydrogen Bond Cooperativity, and Nuclear Quantum Effects

Biomolecules are complex systems stabilized by a delicate balance of weak interactions, making it important to assess all energetic contributions in an accurate manner. However, it is a priori unclear which contributions make more of an impact. Here, we examine stacked polyglutamine (polyQ) strands, a peptide repeat often found in amyloid aggregates. We investigate the role of hydrogen bond (HB) cooperativity, van der Waals (vdW) dispersion interactions, and quantum contributions to free energies, including anharmonicities through density functional theory and ab initio path integral simulations. Of these various factors, we find that the largest impact on structural stabilization comes from vdW interactions. HB cooperativity is the second largest contribution as the size of the stacked chain grows. Competing nuclear quantum effects make the net quantum contribution small but very sensitive to anharmonicities, vdW, and the number of HBs. Our results suggest that a reliable treatment of these systems can only be attained by considering all of these components.

physics.chem-ph↗

arXiv2016

Inverse Temperature Dependence of Nuclear Quantum Effects in DNA Base Pairs

Despite the inherently quantum mechanical nature of hydrogen bonding, it is unclear how nuclear quantum effects (NQEs) alter the strengths of hydrogen bonds. With this in mind, we use ab initio path integral molecular dynamics to determine the absolute contribution of NQEs to the binding in DNA base pair complexes, arguably the most important hydrogen-bonded systems of all. We find that depending on the temperature, NQEs can either strengthen or weaken the binding within the hydrogen-bonded complexes. As a somewhat counterintuitive consequence, NQEs can have a smaller impact on hydrogen bond strengths at cryogenic temperatures than at room temperature. We rationalize this in terms of a competition of NQEs between low-frequency and high-frequency vibrational modes. Extending this idea, we also propose a simple model to predict the temperature dependence of NQEs on hydrogen bond strengths in general.

physics.chem-ph↗

arXiv2016

On-chip electro-optic tuning of a lithium niobate microresonator with integrated in-plane microelectrodes

We demonstrate electro-optic tuning of an on-chip lithium niobate microresonator with integrated in-plane microelectrodes. First two metallic microelectrodes on the substrate were formed via femtosecond laser process. Then a high-Q lithium niobate microresonator located between the microelectrodes was fabricated by femtosecond laser direct writing accompanied by focused ion beam milling. Due to the efficient structure designing, high electro-optical tuning coefficient of 3.41 pm/V was observed.

physics.optics↗

arXiv2016

Adaptive Euler-Maruyama Method for SDEs with Non-globally Lipschitz Drift: Part I, Finite Time Interval

This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with a drift which is not globally Lipschitz. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Furthermore, the order of strong convergence is the same as usual, i.e. order one-half for SDEs with a non-uniform globally Lipschitz volatility, and order one for Langevin SDEs with unit volatility and a drift with sufficient smoothness. The analysis is supported by numerical experiments for a variety of SDEs.

math.NA↗

arXiv2016

Collective dynamics and entanglement of two atoms embedded into negative index material

We study the dynamics of two two-level atoms embedded near to the interface of paired meta-material slabs, one of negative permeability and the other of negative permittivity. The interface behaves as a plasmonic waveguide composed of surface-plasmon polariton modes. It is found that significantly different dynamics occur for the resonant and an off-resonant couplings of the plasma field to the atoms. In the case of the resonant coupling, the plasma field does not appear as a dissipative reservoir to the atoms. We adopt the image method and show that the dynamics of the two atoms are completely equivalent to those of a four-atom system. Moreover, two threshold coupling strengths exist, one corresponding to the strength of coupling of the plasma field to the symmetric and the other the antisymmetric mode of the two-atom system. The thresholds distinguish between the non-Markovian (memory preserving) and Markovian (memoryless) regimes of the evolutions that different time scales of the evolution of the memory effects and entanglement can be observed. The Markovian regime is characterized by exponentially decaying whereas the non-Markovian regime by sinusoidally oscillating contributions to the evolution of the probability amplitudes. The solutions predict a large and long living entanglement mediated by the plasma field in both Markovian and non-Markovian regimes of the evolution. We also show that a simultaneous Markovian and non-Markovian regime of the evolution may occur in which the memory effects exist over a finite evolution time. In the case of an off-resonant coupling of the atoms to the plasma field, the atoms interact with each other by exchanging virtual photons which results in the dynamics corresponding to those of two atoms coupled to a common reservoir. In addition, the entanglement is significantly enhanced under the off-resonant coupling.

quant-ph↗

arXiv2016

Dynamical System of Scalar Field from 2-Dimension to 3-D and its Cosmological Implication

We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models, change the dynamical variables from variables $(x, y, λ)$ to observable related variables $(w_ϕ, Ω_ϕ, λ)$, and show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that, it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in $(w_ϕ, Ω_ϕ, λ)$ instead of variables $(x, y, λ)$ and to investigate the dynamical system in 3-Dimension instead of 2-Dimension. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter.

gr-qc↗

arXiv2016

Optical analogy to quantum Fourier transform based on pseudorandom phase ensemble

In this paper, we introduce an optical analogy to quantum Fourier tanformation based on a pseudorandom phase ensemble. The optical analogy also brings about exponential speedup over classical Fourier tanformation. Using the analogy, we demonstrate three classcial fields to realize Fourier transform similar to three quantum particles.

quant-ph↗

arXiv2016

Constraining $f(R)$ Gravity Theory Using Weak Lensing Peak Statistics from the Canada-France-Hawaii-Telescope Lensing Survey

In this Letter, we report the observational constraints on the Hu-Sawicki $f(R)$ theory derived from weak lensing peak abundances, which are closely related to the mass function of massive halos. In comparison with studies using optical or x-ray clusters of galaxies, weak lensing peak analyses have the advantages of not relying on mass-baryonic observable calibrations. With observations from the Canada-France-Hawaii-Telescope Lensing Survey, our peak analyses give rise to a tight constraint on the model parameter $|f_{R0}|$ for $n=1$. The $95\%$ CL limit is $\log_{10}|f_{R0}| < -4.82$ given WMAP9 priors on $(Ω_{\rm m}, A_{\rm s})$. With Planck15 priors, the corresponding result is $\log_{10}|f_{R0}| < -5.16$.

astro-ph.CO↗

arXiv2015

Phase matched second harmonic generation in an on-chip lithium niobate microresonator fabricated by femtosecond laser

Nonlinear optical processes in whispering gallery mode (WGM) microresonators have attracted much attention. Owing to the strong confinement of light in a small volume, a WGM microresonator can dramatically boost the strength of light field, thereby promoting the nonlinear interaction between the light and the resonator material. However, realization of efficient nonlinear parametric process in microresonators is a challenging issue. The major difficulty is to simultaneously ensure the phase matching condition and a coherent multiple resonance condition for all the waves participating in the nonlinear conversion process. Here, we demonstrate highly efficient second harmonic generation (SHG) in an on-chip lithium niobate microresonator fabricated by femtosecond laser direct writing. We overcome the difficulty of double resonance for the phase matched pump and second harmonic waves by selectively exciting high order modes in the fabricated thin-disk microresonator. Our technique opens opportunities for integrated classical and quantum photonic applications.

physics.optics↗

arXiv2014

Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining

We report on fabrication of high Q lithium niobate (LN) whispering-gallery-mode (WGM) microresonators suspended on silica pedestals by femtosecond laser microfabrication. The micrometer-scale (diameter ~82 μm) LN resonator possesses a Q factor of 2.5x10^5 around 1550 nm wavelength range. Moreover, second harmonic generation with a continuous-wave tunable single-longitudinal-mode pump laser in the on-chip LN microresonator is demonstrated in the on-chip LN microresonator. A fiber taper is employed to couple the pump laser into the microresonator, showing a normalized conversion efficiency of 1.35x10^-5/mW.

physics.optics↗

arXiv2014

Full Investigation on the Dynamics of Power-Law Kinetic Quintessence

We give a full investigation on the dynamics of power-law kinetic quintessence $L(X, ϕ)=V(ϕ)(-X+X^2)$ by considering the potential related parameter $Γ$($=\frac{V V''}{V'^2}$) as a function of another potential parameter $λ$($=\frac{V'}{κV^{3/2}}$), which correspondingly extends the analysis of the dynamical system of our universe from two-dimension to three-dimension. Beside the critical points found in previous papers, we find a new de-Sitter-like dominant attractor(\textit{cp$6$}) and give its stable condition using the center manifold theorem. For the dark energy dominant solution(\textit{cp$6$} and \textit{cp$7$}), it could be distinguished from canonical quintessence and tachyon models since the sound speed $c_s^2=0$ or $c_s^2\ll 1$. For the scaling solution (\textit{cp$8$}), it is very interesting that the sound speed $c_s^2=1/5$ while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on cold dark matter power spectrum and cosmic microwave background both at early time when this scalar field is an early dark energy with $Ω_ϕ$ being non-negligible at high redshift and at late time when it drives the accelerating expansion. We even do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future.

gr-qc↗

arXiv2014

Fabrication of three-dimensional microdisk resonators in calcium fluoride by femtosecond laser micromachining

We report on fabrication of on-chip calcium fluoride (CaF2) microdisk resonators using water-assisted femtosecond laser micromachining. Focused ion beam (FIB) milling is used to create ultra-smooth sidewalls. The quality (Q)-factors of the fabricated microresonators are measured to be 4.2x10^4 at wavelengths near 1550 nm. The Q factor is mainly limited by the scattering from the bottom surface of the disk whose roughness remains high due to the femtosecond laser micromachining process. This technique facilitates formation of on-chip microresonators on various kinds of bulk crystalline materials, which can benefit a wide range of applications such as nonlinear optics, quantum optics, and chip-level integration of photonic devices.

physics.optics↗

arXiv2013

Generation of correlated photon pairs in micro/nano-fibers

We study the generation of correlated photon pairs via spontaneous four wave mixing in a 15 cm long micro/nano-fiber (MNF). The MNF is properly fabricated to satisfy the phase matching condition for generating the signal and idler photon pairs at the wavelengths of about 1310 and 851 nm, respectively. Photon counting measurements yield a coincidence-to-accidental ratio of 530 for a photon production rate of about 0.002 (0.0005) per pulse in the signal (idler) band. We also analyze the spectral information of the signal photons originated from the spontaneous four wave mixing and Raman scattering. In addition to discovering some unique feature of Raman scattering, we find the bandwidth of the individual signal photons is much greater than the calculated value for the MNF with homogeneous structure. Our investigations indicate the MNF is a promising candidate for developing the sources of nonclassical light and the spectral property of photon pairs can be used to non-invasively test the diameter and homogeneity of the MNF.

quant-ph↗

arXiv2013

Random Drift Particle Swarm Optimization

The random drift particle swarm optimization (RDPSO) algorithm, inspired by the free electron model in metal conductors placed in an external electric field, is presented, systematically analyzed and empirically studied in this paper. The free electron model considers that electrons have both a thermal and a drift motion in a conductor that is placed in an external electric field. The motivation of the RDPSO algorithm is described first, and the velocity equation of the particle is designed by simulating the thermal motion as well as the drift motion of the electrons, both of which lead the electrons to a location with minimum potential energy in the external electric field. Then, a comprehensive analysis of the algorithm is made, in order to provide a deep insight into how the RDPSO algorithm works. It involves a theoretical analysis and the simulation of the stochastic dynamical behavior of a single particle in the RDPSO algorithm. The search behavior of the algorithm itself is also investigated in detail, by analyzing the interaction between the particles. Some variants of the RDPSO algorithm are proposed by incorporating different random velocity components with different neighborhood topologies. Finally, empirical studies on the RDPSO algorithm are performed by using a set of benchmark functions from the CEC2005 benchmark suite. Based on the theoretical analysis of the particle's behavior, two methods of controlling the algorithmic parameters are employed, followed by an experimental analysis on how to select the parameter values, in order to obtain a good overall performance of the RDPSO algorithm and its variants in real-world applications. A further performance comparison between the RDPSO algorithms and other variants of PSO is made to prove the efficiency of the RDPSO algorithms.

cs.AI↗

arXiv2013

Low-threshold whispering-gallery-mode microlasers fabricated in a Nd: glass substrate by three-dimensional femtosecond laser micromachining

We report on fabrication of whispering-gallery-mode microlasers in a Nd:glass chip by femtosecond laser three-dimensional (3D) micromachining. Main fabrication procedures include the fabrication of freestanding microdisks supported by thin pillars by femtosecond laser ablation of the glass substrate immersed in water, followed by CO2 laser annealing for surface smoothing. Lasing is observed at a pump threshold as low as ~69 μW at room temperature with a continuous-wave laser diode operating at 780nm. This technique allows for fabrication of microcavities of high quality factors in various dielectric materials such as glasses and crystals.

physics.optics↗