arXiv subjects

X. Xie

Publications and source records attributed to X. Xie.

28 records · Page 2Linked to original sources

arXiv2017

Data-Driven Filtered Reduced Order Modeling Of Fluid Flows

We propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps: (i) In the first step, we use explicit ROM spatial filtering of the nonlinear PDE to construct a filtered ROM. This filtered ROM is low-dimensional, but is not closed (because of the nonlinearity in the given PDE). (ii) In the second step, we use data-driven modeling to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes. To this end, we use a quadratic ansatz to model this interaction and close the filtered ROM. To find the new coefficients in the closed filtered ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz. We emphasize that the new DDF-ROM is built on general ideas of spatial filtering and optimization and is independent of (restrictive) phenomenological arguments. We investigate the DDF-ROM in the numerical simulation of a 2D channel flow past a circular cylinder at Reynolds number $Re=100$. The DDF-ROM is significantly more accurate than the standard projection ROM. Furthermore, the computational costs of the DDF-ROM and the standard projection ROM are similar, both costs being orders of magnitude lower than the computational cost of the full order model. We also compare the new DDF-ROM with modern ROM closure models in the numerical simulation of the 1D Burgers equation. The DDF-ROM is more accurate and significantly more efficient than these ROM closure models.

physics.flu-dyn↗

arXiv2017

Spatial Filtering for Reduced Order Modeling

Spatial filtering has been central in the development of large eddy simulation reduced order models (LES-ROMs) and regularized reduced order models (Reg-ROMs), In this paper, we perform a numerical investigation of spatial filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM (L-ROM), which uses ROM spatial filtering to smooth the flow variables and decreases the amount of energy aliased to the lower index ROM basis functions. We also propose a new form of ROM differential filter and use it as a spatial filter for the L-ROM. We investigate the performance of this new form of ROM differential filter in the numerical simulation of a flow past a circular cylinder at a Reynolds number $Re=760$.

math.NA↗

arXiv2017

Calibrated Filtered Reduced Order Modeling

We propose a calibrated filtered reduced order model (CF-ROM) framework for the numerical simulation of general nonlinear PDEs that are amenable to reduced order modeling. The novel CF-ROM framework consists of two steps: (i) In the first step, we use explicit ROM spatial filtering of the nonlinear PDE to construct a filtered ROM. This filtered ROM is low-dimensional, but is not closed (because of the nonlinearity in the given PDE). (ii) In the second step, we use a calibration procedure to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes. To this end, we use a linear or quadratic ansatz to model this interaction and close the filtered ROM. To find the new coefficients in the closed filtered ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz. Although we use a fluid dynamics setting to illustrate how to construct and use the CF-ROM framework, we emphasize that it is built on general ideas of spatial filtering and optimization and is independent of (restrictive) phenomenological arguments. Thus, the CF-ROM framework can be applied to a wide variety of PDEs.

math.NA↗

arXiv2015

Few-photon imaging at 1550 nm using a low-timing-jitter superconducting nanowire single-photon detector

We demonstrated a laser depth imaging system based on the time-correlated single-photon counting technique, which was incorporated with a low-jitter superconducting nanowire single-photon detector (SNSPD), operated at the wavelength of 1550 nm. A sub-picosecond time-bin width was chosen for photon counting, resulting in a discrete noise of less than one/two counts for each time bin under indoor/outdoor daylight conditions, with a collection time of 50 ms. Because of the low-jitter SNSPD, the target signal histogram was significantly distinguishable, even for a fairly low retro-reflected photon flux. The depth information was determined directly by the highest bin counts, instead of using any data fitting combined with complex algorithms. Millimeter resolution depth imaging of a low-signature object was obtained, and more accurate data than that produced by the traditional Gaussian fitting method was generated. Combined with the intensity of the return photons, three-dimensional reconstruction overlaid with reflectivity data was realized.

physics.optics↗

arXiv2015

Expected number of real zeros for random linear combinations of orthogonal polynomials

We study the expected number of real zeros for random linear combinations of orthogonal polynomials. It is well known that Kac polynomials, spanned by monomials with i.i.d. Gaussian coefficients, have only $(2/π+ o(1))\log{n}$ expected real zeros in terms of the degree $n$. On the other hand, if the basis is given by Legendre (or more generally by Jacobi) polynomials, then random linear combinations have $n/\sqrt{3} + o(n)$ expected real zeros. We prove that the latter asymptotic relation holds universally for a large class of random orthogonal polynomials on the real line, and also give more general local results on the expected number of real zeros.

math.PR↗

arXiv2013

The Stokes-Einstein Relation at Moderate Schmidt Number

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently-developed minimally-resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The numerical data is in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

cond-mat.soft↗

arXiv2013

Enhanced superconductivity and evidence for novel pairing in single-layer FeSe on SrTiO3 thin film under large tensile strain

Single-layer FeSe films with extremely expanded in-plane lattice constant of 3.99A are fabricated by epitaxially growing FeSe/Nb:SrTiO3/KTaO3 heterostructures, and studied by in situ angle-resolved photoemission spectroscopy. Two elliptical electron pockets at the Brillion zone corner are resolved with negligible hybridization between them, indicating the symmetry of the low energy electronic structure remains intact as a free-standing single-layer FeSe, although it is on a substrate. The superconducting gap closes at a record high temperature of 70K for the iron based superconductors. Intriguingly, the superconducting gap distribution is anisotropic but nodeless around the electron pockets, with minima at the crossings of the two pockets. Our results put strong constraints on the current theories, and support the coexistence of both even and odd parity spin-singlet pairing channels as classified by the lattice symmetry.

cond-mat.supr-con↗

arXiv2013

The origin of the dead-layer at the La0.67Sr0.33MnO3/SrTiO3 interface and dead-layer reduction via interfacial engineering

Transition metal oxide hetero-structure has great potential for multifunctional devices. However, the degraded physical properties at interface, known as dead-layer behavior, present a main obstacle for device applications. Here we present the systematic study of the dead-layer behavior in La0.67Sr0.33MnO3 thin film grown on SrTiO3 substrate with ozone assisted molecular beam epitaxy. We found that the evolution of electric and magnetic properties as a function of thickness shows a remarkable resemblance to the phase diagram as a function of doping for bulk materials, providing compelling evidences of the hole depletion in near interface layers that causes dead-layer. Detailed electronic and surface structure studies indicate that the hole depletion is due to the intrinsic oxygen vacancy formation. Furthermore, we show that oxygen vacancies are partly caused by interfacial electric dipolar field, and thus by doping-engineering at the single-atomic-layer level, we demonstrate the dead-layer reduction in films with higher interfacial hole concentration.

cond-mat.mtrl-sci↗

arXiv2013

Interface-induced superconductivity and strain-dependent spin density wave in FeSe/SrTiO3 thin films

The record of superconducting transition temperature(Tc) has long been 56K for the iron-based high temperature superconductors(Fe-HTS's). Recently, in single layer FeSe films grown on SrTiO3 substrate, signs for a new 65K Tc record are reported. Here with in-situ photoemission measurements, we substantiate the presence of the spin density wave(SDW) in FeSe films, a key ingredient of Fe-HTS that was missed in FeSe before, which weakens with increased thickness or reduced strain. We demonstrate that the superconductivity occurs when the electrons transferred from the oxygen-vacant substrate suppress the otherwise most pronounced SDW in single layer FeSe. Besides providing a comprehensive understanding of FeSe films and directions to further enhance its Tc, we establish the phase diagram of FeSe vs. lattice constant that contains all the essential physics of Fe-HTS's. With the simplest structure, cleanest composition and single tuning parameter, it is ideal for testing theories of Fe-HTS's.

cond-mat.supr-con↗

arXiv1999

Modeling Pressure-Ionization of Hydrogen in the Context of Astrophysics

The recent development of techniques for laser-driven shock compression of hydrogen has opened the door to the experimental determination of its behavior under conditions characteristic of stellar and planetary interiors. The new data probe the equation of state (EOS) of dense hydrogen in the complex regime of pressure ionization. The structure and evolution of dense astrophysical bodies depend on whether the pressure ionization of hydrogen occurs continuously or through a ``plasma phase transition'' (PPT) between a molecular state and a plasma state. For the first time, the new experiments constrain predictions for the PPT. We show here that the EOS model developed by Saumon and Chabrier can successfully account for the data, and we propose an experiment that should provide a definitive test of the predicted PPT of hydrogen. The usefulness of the chemical picture for computing astrophysical EOS and in modeling pressure ionization is discussed.

astro-ph↗