arXiv subjects

Tian Lan

Publications and source records attributed to Tian Lan.

268 records · Page 15Linked to original sources

arXiv2015

Advanced Post-Processing Techniques of Molecular Dynamics Simulations in Studying Strong Anharmonic Thermodynamics of Solids

While the vibrational thermodynamics of materials with small anharmonicity at low temperatures has been understood well based on the harmonic phonons approximation; at high temperatures, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermal expansion, thermodynamic stability, heat capacity, optical properties, thermal transport and other nonlinear properties of materials. To date the anharmonic lattice dynamics is poorly understood despite its great importance, and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. With recent developement of computational models, the anharmonic information can be extracted from the atomic trajectories of molecular dynamics simulations. For example, the vibrational energy spectra, the effective potential energy surface and the phonon-phonon interaction channels can be derived from these trajectories which appear stochastic. These inter-dependent methods are adopted to successfully uncover the strong anharmonic phenomena while the traditional harmonic models fail dramatically, e.g., the negative thermal expansion of cuprite and the high temperature thermal stability of rutile.

cond-mat.mtrl-sci↗

arXiv2015

Action Recognition by Hierarchical Mid-level Action Elements

Realistic videos of human actions exhibit rich spatiotemporal structures at multiple levels of granularity: an action can always be decomposed into multiple finer-grained elements in both space and time. To capture this intuition, we propose to represent videos by a hierarchy of mid-level action elements (MAEs), where each MAE corresponds to an action-related spatiotemporal segment in the video. We introduce an unsupervised method to generate this representation from videos. Our method is capable of distinguishing action-related segments from background segments and representing actions at multiple spatiotemporal resolutions. Given a set of spatiotemporal segments generated from the training data, we introduce a discriminative clustering algorithm that automatically discovers MAEs at multiple levels of granularity. We develop structured models that capture a rich set of spatial, temporal and hierarchical relations among the segments, where the action label and multiple levels of MAE labels are jointly inferred. The proposed model achieves state-of-the-art performance in multiple action recognition benchmarks. Moreover, we demonstrate the effectiveness of our model in real-world applications such as action recognition in large-scale untrimmed videos and action parsing.

cs.CV↗

arXiv2015

A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries

We propose that, up to invertible topological orders, 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry $G$ are classified by non-degenerate unitary braided fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC describes a fermionic product state without symmetry or a fermionic/bosonic product state with symmetry $G$, and the UBFC has a modular extension. We developed a simplified theory of non-degenerate UBFC over a SFC based on the fusion coefficients $N^{ij}_k$ and spins $s_i$. This allows us to obtain a list that contains all 2+1D fermionic topological orders (without symmetry). We find explicit realizations for all the fermionic topological orders in the table. For example, we find that, up to invertible $p+\hspace{1pt}\mathrm{i}\hspace{1pt} p$ fermionic topological orders, there are only four fermionic topological orders with one non-trivial topological excitation: (1) the $K={\scriptsize \begin{pmatrix} -1&0\\0&2\end{pmatrix}}$ fractional quantum Hall state, (2) a Fibonacci bosonic topological order $2^B_{14/5}$ stacking with a fermionic product state, (3) the time-reversal conjugate of the previous one, (4) a primitive fermionic topological order that has a chiral central charge $c=\frac14$, whose only topological excitation has a non-abelian statistics with a spin $s=\frac14$ and a quantum dimension $d=1+\sqrt{2}$. We also proposed a categorical way to classify 2+1D invertible fermionic topological orders using modular extensions.

cond-mat.str-el↗

arXiv2015

Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile TiO$_2$

Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO$_2$ from 300 to 1373\,K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of $3d$ electrons of Ti and $2p$ electrons of O atoms. With thermal expansion, the energy variation in this "phonon-tracked hybridization" flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.

cond-mat.mtrl-sci↗

arXiv2014

Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models

String-net models allow us to systematically construct and classify 2+1D topologically ordered states which can have gapped boundaries. We can use a simple ideal string-net wavefunction, which is described by a set of F-matrices [or more precisely, a unitary fusion category (UFC)], to study all the universal properties of such a topological order. In this paper, we describe a finite computational method -- Q-algebra approach, that allows us to compute the non-Abelian statistics of the topological excitations [or more precisely, the unitary modular tensor category (UMTC)], from the string-net wavefunction (or the UFC). We discuss several examples, including the topological phases described by twisted gauge theory (i.e., twisted quantum double $D^α(G)$). Our result can also be viewed from an angle of holographic bulk-boundary relation. The 1+1D anomalous topological orders, that can appear as edges of 2+1D topological states, are classified by UFCs which describe the fusion of quasiparticles in 1+1D. The 1+1D anomalous edge topological order uniquely determines the 2+1D bulk topological order (which are classified by UMTC). Our method allows us to compute this bulk topological order (i.e., the UMTC) from the anomalous edge topological order (i.e., the UFC).

cond-mat.str-el↗

arXiv2014

Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.

cond-mat.str-el↗

arXiv2014

Joint Latency and Cost Optimization for Erasure-coded Data Center Storage

Modern distributed storage systems offer large capacity to satisfy the exponentially increasing need of storage space. They often use erasure codes to protect against disk and node failures to increase reliability, while trying to meet the latency requirements of the applications and clients. This paper provides an insightful upper bound on the average service delay of such erasure-coded storage with arbitrary service time distribution and consisting of multiple heterogeneous files. Not only does the result supersede known delay bounds that only work for a single file or homogeneous files, it also enables a novel problem of joint latency and storage cost minimization over three dimensions: selecting the erasure code, placement of encoded chunks, and optimizing scheduling policy. The problem is efficiently solved via the computation of a sequence of convex approximations with provable convergence. We further prototype our solution in an open-source, cloud storage deployment over three geographically distributed data centers. Experimental results validate our theoretical delay analysis and show significant latency reduction, providing valuable insights into the proposed latency-cost tradeoff in erasure-coded storage.

cs.DC↗

arXiv2014

Anharmonic lattice dynamics of Ag$_2$O studied by inelastic neutron scattering and first principles molecular dynamics simulations

Inelastic neutron scattering measurements on silver oxide (Ag$_2$O) with the cuprite structure were performed at temperatures from 40 to 400\,K, and Fourier transform far-infrared spectra were measured from 100 to 300\,K. The measured phonon densities of states and the infrared spectra showed unusually large energy shifts with temperature, and large linewidth broadenings. First principles molecular dynamics (MD) calculations were performed at various temperatures, successfully accounting for the negative thermal expansion (NTE) and local dynamics. Using the Fourier-transformed velocity autocorrelation method, the MD calculations reproduced the large anharmonic effects of Ag$_2$O, and were in excellent agreement with the neutron scattering data. The quasiharmonic approximation (QHA) was less successful in accounting for much of the phonon behavior. The QHA could account for some of the NTE below 250 K, although not at higher temperatures. Strong anharmonic effects were found for both phonons and for the NTE. The lifetime broadenings of Ag$_2$O were explained by anharmonic perturbation theory, which showed rich interactions between the Ag-dominated modes and the O-dominated modes in both up- and down-conversion processes.

cond-mat.mtrl-sci↗

arXiv2012

Cosmic Duality and Statefinder Diagnosis of Spinor Quintom

In this paper, we study the possible connections among different Spinor Quintom Dark Energy (DE) models by the aid of duality. Then we apply the statefinder diagnostic to these models. By this diagnostic pair {$\{r,s\}$}, we differentiate one Quintom DE model from the others in a model independent manner. A class of evolutionary trajectories of these Spinor Quintom models are presented in the statefinder parameter planes. We also obtain the current locations of the parameters $r$ and $s$, and these locations correspond to different models in statefinder parameter planes theoretically.

gr-qc↗

arXiv2011

Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data

This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age. Currently, there are two major methods of independent observational H(z) measurement, which we summarize as the "differential age method" and the "radial BAO size method". Starting with fundamental cosmological notions such as the spacetime coordinates in an expanding universe, we present the basic principles behind the two methods. We further review the two methods in greater detail, including the source of errors. We show how the observational H(z) data presents itself as a useful tool in the study of cosmological models and parameter constraint, and we also discuss several issues associated with their applications. Finally, we point the reader to a future prospect of upcoming observation programs that will lead to some major improvements in the quality of observational H(z) data.

astro-ph.CO↗

arXiv2010

Constraints on smoothness parameter and dark energy using observational $H(z)$ data

The universe, with large-scale homogeneity, is locally inhomogeneous, clustering into stars, galaxies and larger structures. Such property is described by the smoothness parameter $α$ which is defined as the proportion of matter in the form of intergalactic medium. If we take consideration of the inhomogeneities in small scale, there should be modifications of the cosmological distances compared to a homogenous model. Dyer and Roeder developed a second-order ordinary differential equation (D-R equation) that describes the angular diameter distance-redshift relation for inhomogeneous cosmological models. Furthermore, we may obtain the D-R equation for observational $H(z)$ data (OHD). The density-parameter $Ω_{\rm M}$, the state of dark energy $ω$, and the smoothness-parameter $α$ are constrained by a set of OHD in a spatially flat $Λ$CDM universe as well as a spatially flat XCDM universe. By using of $χ^2$ minimization method we get $α=0.81^{+0.19}_{-0.20}$ and $Ω_{\rm M}=0.32^{+0.12}_{-0.06}$ at $1σ$ confidence level. If we assume a Gaussian prior of $Ω_{\rm M}=0.26\pm0.1$, we get $α=0.93^{+0.07}_{-0.19}$ and $Ω_{\rm M}=0.31^{+0.06}_{-0.05}$. For XCDM model, $α$ is constrained to $α\geq0.80$ but $ω$ is weakly constrained around -1, where $ω$ describes the equation of the state of the dark energy ($p_{\rm X}=ωρ_{\rm X}$). We conclude that OHD constrains the smoothness parameter more effectively than the data of SNe Ia and compact radio sources.

astro-ph.CO↗

arXiv2010

Thermodynamical properties of the Undulant Universe

Recent observations show that our universe is accelerating by dark energy, so it is important to investigate the thermodynamical properties of it. The Undulant Universe is a model with equation of state $ω(a)=-\cos(b\ln a)$ for dark energy, where we show that there neither the event horizon nor the particle horizon exists. However, as a boundary of keeping thermodynamical properties, the apparent horizon is a good holographic screen. The Universe has a thermal equilibrium inside the apparent horizon, so the Unified First Law and the Generalized Second Law of thermodynamics are satisfied. As a thermodynamical whole, the evolution of the Undulant Universe behaves very well in the current phase. However, when considering the unification theory, the failure of conversation law at the epoch of the matter dominated or near singularity need some more consideration for the form of the Undulant Universe.

astro-ph↗

arXiv2010

Cosmological Constraints on the Undulant Universe

We use the redshift Hubble parameter $H(z)$ data derived from relative galaxy ages, distant type Ia supernovae (SNe Ia), the Baryonic Acoustic Oscillation (BAO) peak, and the Cosmic Microwave Background (CMB) shift parameter data, to constrain cosmological parameters in the Undulant Universe. We marginalize the likelihood functions over $h$ by integrating the probability density $P\propto e^{-χ^2/2}$. By using the Markov Chain Monte Carlo (MCMC) technique, we obtain the best fitting results and give the confidence regions on the $b-Ω_{\rm m0}$ plane. Then we compare their constraints. Our results show that the $H(z)$ data play a similar role with the SNe Ia data in cosmological study. By presenting the independent and joint constraints, we find that the BAO and CMB data play very important roles in breaking the degeneracy compared with the $H(z)$ and SNe Ia data alone. Combined with the BAO or CMB data, one can improve the constraints remarkably. The SNe Ia data sets constrain $Ω_{\rm m0}$ much tighter than the $H(z)$ data sets, but the $H(z)$ data sets constrain $b$ much tighter than the SNe Ia data sets. All these results show that the Undulant Universe approaches the $Λ\rm$CDM model. We expect more $H(z)$ data to constrain cosmological parameters in future.

astro-ph.CO↗

arXiv2009

An Axiomatic Theory of Fairness in Network Resource Allocation

We present a set of five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Well-known notions such as alpha-fairness, Jain's index, and entropy are shown to be special cases. Properties of fairness measures satisfying the axioms are proven, including Schur-concavity. Among the engineering implications is a generalized Jain's index that tunes the resolution of the fairness measure, a new understanding of alpha-fair utility functions, and an interpretation of "larger alpha is more fair". We also construct an alternative set of four axioms to capture efficiency objectives and feasibility constraints.

cs.NI↗

arXiv2009

Signatures of the Baryon Acoustic Oscillations on the Convergence Power Spectrum of Weak lensing by Large Scale Structure

We employ an analytical approach to investigate the signatures of Baryon Acoustic Oscillations (BAOs) on the convergence power spectrum of weak lensing by large scale structure. It is shown that the BAOs wiggles can be found in both of the linear and nonlinear convergence power spectra of weak lensing at about $40\le l\le600$, but they are weaker than that of matter power spectrum. Although the statistical error for LSST are greatly smaller than that of CFHT and SNAP survey especially at about $30<l<300$, they are still larger than the their maximum variations of BAOs wiggles. Thus, the detection of BAOs with the ongoing and upcoming surveys such as LSST, CFHT and SNAP survey confront a technical challenge.

astro-ph↗

arXiv2008

Dark energy and neutrino mass constraints from weak lensing, supernova, and relative galaxy ages

We use the current weak lensing data to constrain the equation of state of dark energy $w$ and the total mass of massive neutrinos $\sum m_ν$. The constraint on $w$ would be weak if only the current weak lensing data are used. With the addition of other observational data such as the type Ia supernovae, baryon acoustic oscillation, and the high redshift Hubble parameter data $H(z)$ derived from relative galaxy ages to break the degeneracy, the result is significantly improved. For the pure $w$CDM model without massive neutrinos, we find $w=-1.00^{+0.10}_{-0.12}$. For the $w$CDM model with the massive neutrino component, we show that the constraint on $w$ is almost unchanged, there is very little degeneracy between $w$ and $\sum m_ν$. After marginalizing over other parameters, we obtain the probability distribution function of $\sum m_ν$, and find that the upper limit is $\sum m_ν \leq 0.8$ eV at 95.5% confidence level for the combined data sets. Our constraints of $w$ and $\sum m_ν$ are both compatible and comparable with the constraints obtained from the WMAP 5-year data.

astro-ph↗