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Xu Yang

Publications and source records attributed to Xu Yang.

At least 379 records · Page 21Linked to original sources
arXiv2019

Spin-Dependent Electron Transmission Model for Chiral Molecules in Mesoscopic Devices

Various device-based experiments have indicated that electron transfer in certain chiral molecules may be spin-dependent, a phenomenon known as the Chiral Induced Spin Selectivity (CISS) effect. However, due to the complexity of these devices and a lack of theoretical understanding, it is not always clear to what extent the chiral character of the molecules actually contributes to the magnetic-field-dependent signals in these experiments. To address this issue, we report here an electron transmission model that evaluates the role of the CISS effect in two-terminal and multi-terminal linear-regime electron transport experiments. Our model reveals that for the CISS effect, the chirality-dependent spin transmission is accompanied by a spin-flip electron reflection process. Furthermore, we show that more than two terminals are required in order to probe the CISS effect in the linear regime. In addition, we propose two types of multi-terminal nonlocal transport measurements that can distinguish the CISS effect from other magnetic-field-dependent signals. Our model provides an effective tool to review and design CISS-related transport experiments, and to enlighten the mechanism of the CISS effect itself.

cond-mat.mes-hall↗
arXiv2018

Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene

Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. Similar to graphene which admits Dirac Fermions and topological edge states, photonic graphene supports novel and subtle propagating modes (edge modes) of electromagnetic waves. These modes have wide applications in many optical systems. In this paper, we propose a novel gradient recovery method based on Bloch theory for the computation of topological edge modes in the honeycomb structure. Compared to standard finite element methods, this method provides higher order accuracy with the help of gradient recovery technique. This high order accuracy is highly desired for constructing the propagating electromagnetic modes in applications. We analyze the accuracy and prove the superconvergence of this method. Numerical examples are presented to show the efficiency by computing the edge mode for the $\mathcal{P}$-symmetry and $\mathcal{C}$-symmetry breaking cases in honeycomb structures.

math.NA↗
arXiv2018

Auto-Encoding Scene Graphs for Image Captioning

We propose Scene Graph Auto-Encoder (SGAE) that incorporates the language inductive bias into the encoder-decoder image captioning framework for more human-like captions. Intuitively, we humans use the inductive bias to compose collocations and contextual inference in discourse. For example, when we see the relation `person on bike', it is natural to replace `on' with `ride' and infer `person riding bike on a road' even the `road' is not evident. Therefore, exploiting such bias as a language prior is expected to help the conventional encoder-decoder models less likely overfit to the dataset bias and focus on reasoning. Specifically, we use the scene graph --- a directed graph ($\mathcal{G}$) where an object node is connected by adjective nodes and relationship nodes --- to represent the complex structural layout of both image ($\mathcal{I}$) and sentence ($\mathcal{S}$). In the textual domain, we use SGAE to learn a dictionary ($\mathcal{D}$) that helps to reconstruct sentences in the $\mathcal{S}\rightarrow \mathcal{G} \rightarrow \mathcal{D} \rightarrow \mathcal{S}$ pipeline, where $\mathcal{D}$ encodes the desired language prior; in the vision-language domain, we use the shared $\mathcal{D}$ to guide the encoder-decoder in the $\mathcal{I}\rightarrow \mathcal{G}\rightarrow \mathcal{D} \rightarrow \mathcal{S}$ pipeline. Thanks to the scene graph representation and shared dictionary, the inductive bias is transferred across domains in principle. We validate the effectiveness of SGAE on the challenging MS-COCO image captioning benchmark, e.g., our SGAE-based single-model achieves a new state-of-the-art $127.8$ CIDEr-D on the Karpathy split, and a competitive $125.5$ CIDEr-D (c40) on the official server even compared to other ensemble models.

cs.CV↗
arXiv2018

Frozen Gaussian Approximation for 3-D Elastic Wave Equation and Seismic Tomography

The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P-wave). The main contribution of this paper consists of three aspects: 1. We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptotic expansion in the week sense (integral form) so that one is able to perform integration by parts. Compared to the FGA theory for acoustic wave equation, the calculations in the derivation are much more technically involved due to the existence of both P- and S-waves, and the coupling of the polarized directions for SH- and SV-waves. In particular, we obtain the diabatic coupling terms for SH- and SV-waves, with the form closely connecting to the concept of Berry phase that is intensively studied in quantum mechanics and topology (Chern number). The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method for 3-D elastic wave equation in homogeneous media; 2. We derive the interface conditions of FGA for 3-D elastic wave equation based on an Eulerian formulation and the Snell's law. We verify these conditions by simulating high-frequency elastic wave propagation in a 1-D layered Earth model. In this example, we also show that it is natural to apply the FGA algorithm to geometries with non-Cartesian coordinates; 3. We apply the developed FGA algorithm for 3-D seismic { wave-equation-based traveltime tomography and full waveform inversion, respectively

physics.geo-ph↗
arXiv2018

Bosonic SET to SPT Transition under Dyonic LSM Theorem

Employing large-scale quantum Monte Carlo simulatoins, we study the phase diagram of a quantum spin model which is subject to the recently developed dyonic Lieb-Shultz-Mattis (LSM) theorem. The theorem predicts there are symmetry enriched/protected topological (SET/SPT) phases in the phase diagram. Our numerical results reveal a first order quantum phase transition between SET and SPT phases, consistent with an anyon condensation mechanism that enforces SPT phase according to the theorem. Also there exists in the phase diagram a symmetry-breaking phase in the form of superfluid (SF). The transition between SET and SF is continuous and that between SPT and SF is first order. Interestingly, the SET, SPT and SF phases meet at a critical endpoint, whose presence can be universally explained via theory contains emergent gauge field coupled to vortex fields, and consequently reveals the exotic feature of our model even beyond the realm of dyonic LSM.

cond-mat.str-el↗
arXiv2018

A general continuous-state nonlinear branching process

In this paper we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process. \beqnn X_t \ar=\ar x+\int_0^tγ_0(X_s)\dd s+\int_0^t\int_0^{γ_1(X_{s-})} W(\dd s,\dd u)\cr \ar\ar\qquad+\int_0^t\int_{0}^\infty\int_0^{γ_2(X_{s-})} z\tilde{N}(\dd s, \dd z, \dd u), \eeqnn where $W(\dd t,\dd u) $ and $\tilde{N}(\dd s, \dd z, \dd u)$ denote a Gaussian white noise and an independent compensated spectrally positive Poisson random measure, respectively, and $γ_0,γ_1$ and $γ_2$ are functions on $\mbb{R}_+$ with both $γ_1$ and $γ_2$ taking nonnegative values. Intuitively, this process can be identified as a continuous-state branching process with population-size-dependent branching rates and with competition. Using martingale techniques we find rather sharp conditions on extinction, explosion and coming down from infinity behaviors of the process. Some Foster-Lyapunov type criteria are also developed for such a process. More explicit results are obtained when $γ_i, i=0, 1, 2$ are power functions.

math.PR↗
arXiv2018

Colossal Bulk Photovoltaic Effect in a Weyl Semimetal

Broadband, efficient and fast conversion of light to electricity is crucial for sensing and clean energy. Here we reveal the largest observed bulk photo-voltaic effect (BPVE), an intrinsic mechanism predicted to be ultrafast and exceed the Shockley-Quiesser limit. This discovery results from combining recent developments in the connection of BPVE to topology, Weyl semimetals and focused-ion beam fabrication. Our room temperature observation of the first BPVE in the mid-IR, is enabled by microscopic devices of the Weyl semimetal TaAs. Detailed symmetry analysis enables unambiguous separation of this response from competing photo-thermal effects. The size and wavelength range of the shift current offers new opportunities in optical detectors, clean energy, and topology, while directly demonstrating the utility of Weyl semimetals for applications.

cond-mat.mes-hall↗
arXiv2018

A time-space Hausdorff fractal model for non-Fickian transport in porous media

This paper presents a time-space Hausdorff derivative model for depicting solute transport in aquifers or water flow in heterogeneous porous media. In this model, the time and space Hausdorff derivatives are defined on non-Euclidean fractal metrics with power law scaling transform which, respectively, connect the temporal and spatial complexity during transport. The Hausdorff derivative model can be transformed to an advection-dispersion equation with time- and space-dependent dispersion and convection coefficients. This model is a fractal partial differential equation (PDE) defined on a fractal space and differs from the fractional PDE which is derived for non-local transport of particles on a non-fractal Euclidean space. As an example of applications of this model, an explicit solution with a constant diffusion coefficient and flow velocity subject to an instantaneous source is derived and fitted to the breakthrough curves of tritium as a tracer in porous media. These results are compared with those of a scale-dependent dispersion model and a time-scale dependent dispersion model. Overall, it is found that the fractal PDE based on the Hausdorff derivatives better captures the early arrival and heavy tail in the scaled breakthrough curves for variable transport distances. The estimated parameters in the fractal Hausrdorff model represent clear physical mechanisms such as linear relationships between the orders of Hausdorff derivatives and the transport distance. The mathematical formulation is applicable to both solute transport and water flow in porous media.

physics.flu-dyn↗
arXiv2018

Shuffle-Then-Assemble: Learning Object-Agnostic Visual Relationship Features

Due to the fact that it is prohibitively expensive to completely annotate visual relationships, i.e., the (obj1, rel, obj2) triplets, relationship models are inevitably biased to object classes of limited pairwise patterns, leading to poor generalization to rare or unseen object combinations. Therefore, we are interested in learning object-agnostic visual features for more generalizable relationship models. By "agnostic", we mean that the feature is less likely biased to the classes of paired objects. To alleviate the bias, we propose a novel \texttt{Shuffle-Then-Assemble} pre-training strategy. First, we discard all the triplet relationship annotations in an image, leaving two unpaired object domains without obj1-obj2 alignment. Then, our feature learning is to recover possible obj1-obj2 pairs. In particular, we design a cycle of residual transformations between the two domains, to capture shared but not object-specific visual patterns. Extensive experiments on two visual relationship benchmarks show that by using our pre-trained features, naive relationship models can be consistently improved and even outperform other state-of-the-art relationship models. Code has been made available at: \url{https://github.com/yangxuntu/vrd}.

cs.CV↗
arXiv2018

Impact of damping on superconducting gap oscillations induced by intense Terahertz pulses

We investigate the interplay between gap oscillations and damping in the dynamics of superconductors taken out of equilibrium by strong optical pulses with sub-gap Terahertz frequencies. A semi-phenomenological formalism is developed to include the damping within the electronic subsystem that arises from effects beyond BCS, such as interactions between Bogoliubov quasiparticles and decay of the Higgs mode. Such processes are conveniently expressed as $T_{1}$ and $T_{2}$ times in the standard pseudospin language for superconductors. Comparing with data on NbN that we report here, we argue that the superconducting dynamics in the picosecond time scale, after the pump is turned off, is governed by the $T_{2}$ process.

cond-mat.supr-con↗
arXiv2018

Divergent bulk photovoltaic effect in Weyl semimetals

Weyl semimetals (WSM) have been discovered in time-reversal symmetric materials, featuring monopoles of Berry's curvature in momentum space. WSM have been distinguished between Type-I and II where the velocity tilting of the cone in the later ensures a finite area Fermi surface. To date it has not been clear whether the two types results in any qualitatively new phenomena. Here we focus on the shift-current response ($σ_{shift}(ω)$), a second order optical effect generating photocurrents. Surprisingly we find that up to an order unity constant, $σ_{shift}(ω)\sim \frac{e^3}{h^2}\frac{1}ω$ in Type-II WSM, diverging in the low frequency $ω\rightarrow 0$ limit. This is in stark contrast to the vanishing behavior ($σ_{shift}(ω)\propto ω$) in Type-I WSM. In addition, in both Type-I and Type-II WSM, a nonzero chemical potential $μ$ relative to nodes leads to a large peak of shift-current response with a width $\sim |μ|/\hbar$ and a height $\sim \frac{e^3}{h}\frac{1}{|μ|}$, the latter diverging in the low doping limit. We show that the origin of these divergences is the singular Berry's connections and the Pauli-blocking mechanism. Similar results hold for the real part of the second harmonic generation, a closely related nonlinear optical response.

cond-mat.mes-hall↗
arXiv2017

The Calibration of Stochastic-Local Volatility Models - An Inverse Problem Perspective

We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers recently. More precisely, given a local volatility surface and a choice of stochastic volatility parameters, we calibrate the corresponding leverage function. Our approach makes use of regularization techniques from the inverse-problem theory, respecting the integrity of the data and thus avoiding data interpolation. The result is a stable and robust algorithm which is resilient to instabilities in the regions of low probability density of the spot price and of the instantaneous variance. We substantiate our claims with numerical experiments using simulated as well as real data.

q-fin.CP↗
arXiv2017

Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models

We consider 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin in the unit cell. We propose and prove a modified Lieb-Shultz Mattis (LSM) theorem in this setting, which applies even when the spin in the enlarged magnetic unit cell is integral. There are two nontrivial outcomes for gapped ground states that preserve all symmetries. In the first case, one necessarily obtains a symmetry protected topological (SPT) phase with protected edge states. This allows us to readily construct models of SPT states by decorating dimer models of Mott insulators to yield SPT phases, which should be useful in their physical realization. In the second case, exotic bulk excitations, i.e. topological order, is necessarily present. While both scenarios require fractional spin in the lattice unit cell, the second requires that the symmetries protecting the fractional spin is related to that involved in the magnetic translations. Our discussion encompasses the general notion of fractional spin (projective symmetry representations) and magnetic flux (magnetic translations tied to a symmetry generator). The resulting SPTs display a dyonic character in that they associate charge with symmetry flux, allowing the flux in the unit cell to screen the projective representation on the sites. We provide an explicit formula that encapsulates this physics, which identifies a specific set of allowed SPT phases.

cond-mat.str-el↗
arXiv2017

Gradient recovery for elliptic interface problem: III. Nitsche's method

This is the third paper on the study of gradient recovery for elliptic interface problem. In our previous works [H. Guo and X. Yang, 2016, arXiv:1607.05898 and {\it J. Comput. Phys.}, 338 (2017), 606--619], we developed {gradient recovery methods} for elliptic interface problem based on body-fitted meshes and immersed finite element methods. Despite the efficiency and accuracy that these methods bring to recover the gradient, there are still some cases in unfitted meshes where skinny triangles appear in the generated local body-fitted triangulation that destroy the accuracy of recovered gradient near the interface. In this paper, we propose a gradient recovery technique based on Nitsche's method for elliptic interface problem, which avoids the loss of accuracy of gradient near the interface caused by skinny triangles. We analyze the supercloseness between the gradient of the numerical solution by the Nitsche's method and the gradient of interpolation of the exact solution, which leads to the superconvergence of the proposed gradient recovery method. We also present several numerical examples to validate the theoretical results.

math.NA↗
arXiv2017

Superconvergence analysis of partially penalized immersed finite element method

The contribution of this paper contains two parts: first, we prove a supercloseness result for the partially penalized immersed finite element (PPIFE) method in [T. Lin, Y. Lin, and X. Zhang, SIAM J. Numer. Anal., 53 (2015), 1121--1144]; then based on the supercloseness result, we show that the gradient recovery method proposed in our previous work [H. Guo and X. Yang, arXiv: 1608.00063] can be applied to the PPIFE method and the recovered gradient converges to the exact gradient with a superconvergent rate $\mathcal{O}(h^{3/2})$. Hence, the gradient recovery method provides an asymptotically exact a posteriori error estimator for the PPIFE method. Several numerical examples are presented to verify our theoretical result.

math.NA↗
arXiv2016

Pathwise uniqueness for a SPDE with Hölder continuous coefficient driven by α-stable noise

In this paper we study the pathwise uniqueness of solution to the following stochastic partial differential equation (SPDE) with Hölder continuous coefficient: \begin{eqnarray*} \frac{\partial X_t(x)}{\partial t}=\frac{1}{2} ΔX_t(x) +G(X_t(x))+H(X_{t-}(x)) \dot{L}_t(x),~~~ t>0, ~x\in\mathbb{R}, \end{eqnarray*} where $\dot{L}$ denotes an $α$-stable white noise on $\mathbb{R}_+\times \mathbb{R}$ without negative jumps, $G$ satisfies the Lipschitz condition and $H$ is nondecreasing and $β$-Hölder continuous for $1<α<2$ and $0<β<1$. For $G\equiv0$ and $H(x)=x^β$, in Mytnik (2002) a weak solution to the above SPDE was constructedand the pathwise uniqueness of the solution was left as an open problem. In this paper we give an affirmative answer to this problem for certain values of $α$ and $β$. In particular, for $αβ=1$, where the solution to the above equation is the density of a super-Brownian motion with $α$-stable branching (see also Mytnik (2002)), our result leads to its pathwise uniqueness for $1<α<\sqrt{5}-1$. The local Hölder continuity of the solution is also obtained in this paper for fixed time $t>0$.

math.PR↗
arXiv2016

A distribution-function-valued SPDE and its applications

In this paper we further study the stochastic partial differential equation first proposed by Xiong (2013). Under localized conditions on the coefficients we show that the solution is in fact distribution-function-valued and we establish the pathwise uniqueness of the solution. As applications we obtain the well-posedness of the martingale problems for two classes of measure-valued diffusions: interacting super-Brownian motions and interacting Fleming-Viot processes. Properties of the two superprocesses such as the existence of density fields and the extinction behaviors are also studied.

math.PR↗