Multiresolution finite element method based on a new locking-free rectangular Mindlin plate element

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic node shape function. The basic node shape function is constructed by extending the node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1404.1165, arXiv:1405.677

Impact of Temperature-Dependent Rattling Phonons on Lattice Dynamics and Thermal Transport in Ag6_{6}Ge10_{10}P12_{12}

Crystalline compounds exhibiting low-frequency rattling phonons constitute an important class of high-performance thermoelectrics owning to their intrinsically very low lattice thermal conductivity ($\kappa_{l}$). Theoretical approach that is capable of revealing the physical origin and accurately predicting $\kappa_{l}$ is of particular interest, which, however, still remains an outstanding challenge. In this study, we perform a case study of lattice dynamics and thermal transport properties of Ag$_{6}$Ge$_{10}$P$_{12}$, which has recently been identified as a high-performance thermoelectric phosphide due to low $\kappa_{l}$, arising from rattling vibrations associated with Ag$_{6}$ clusters. Analysis within a first-principles-based lattice-dynamics framework based on self-consistent phonon theory reveals a strong temperature dependence of rattling phonons due to high-order anharmonic interactions. Anharmonic hardening of the rattling optical modes has a strong effect on the lifetimes of heat-carrying acoustic phonons by decreasing the rate of three-phonon combination processes. This mechanism results in a significant increase in $\kappa_l$ and changes its temperature dependence to $1/T^{0.64}$

Generating Semantically Valid Adversarial Questions for TableQA

Adversarial attack on question answering systems over tabular data (TableQA) can help evaluate to what extent they can understand natural language questions and reason with tables. However, generating natural language adversarial questions is difficult, because even a single character swap could lead to huge semantic difference in human perception. In this paper, we propose SAGE (Semantically valid Adversarial GEnerator), a Wasserstein sequence-to-sequence model for TableQA white-box attack. To preserve meaning of original questions, we apply minimum risk training with SIMILE and entity delexicalization. We use Gumbel-Softmax to incorporate adversarial loss for end-to-end training. Our experiments show that SAGE outperforms existing local attack models on semantic validity and fluency while achieving a good attack success rate. Finally, we demonstrate that adversarial training with SAGE augmented data can improve performance and robustness of TableQA systems.Comment: AAAI 2021 Workshop on Towards Robust, Secure and Efficient Machine Learnin

Dynamics and flow-coupling in two-layer turbulent thermal convection

We present an experimental investigation of the dynamics and flow-coupling of convective turbulent flows in a cylindrical Rayleigh-Benard convection cell with two immiscible fluids, water and fluorinert FC-77 electronic liquid (FC77). It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by $\sim\pi$. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (flow directions of the two LSCs are opposite to each other at the fluid-fluid interface) and viscous coupling (flow directions of the two LSCs are the same at the fluid-fluid interface), are identified with the former one as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remained unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric.Comment: 13 pages, 8 figure

Microscopic Mechanisms of Glass-Like Lattice Thermal Transport in Cubic Cu12_{12}Sb4_{4}S13_{13} Tetrahedrites

Materials based on cubic tetrahedrites (Cu$_{12}$Sb$_{4}$S$_{13}$) are useful thermoelectrics with unusual thermal and electrical transport properties, such as very low and nearly temperature-independent lattice thermal conductivity ($\kappa_{L}$). We explain the microscopic origin of the glass-like $\kappa_{L}$ in Cu$_{12}$Sb$_{4}$S$_{13}$ by explicitly treating anharmonicity up to quartic terms for both phonon energies and phonon scattering rates. We show that the strongly unstable phonon modes associated with trigonally coordinated Cu atoms are anharmonically stabilized above approximately $100$ K and continue hardening with increasing temperature, in accord with experimental data. This temperature induced hardening effect reduces scattering of heat carrying acoustic modes by reducing the available phase space for three-phonon processes, thereby balancing the conventional $\propto T$ increase in scattering due to phonon population and yielding nearly temperature-independent $\kappa_{L}$. Furthermore, we find that very strong phonon broadening lead to a qualitative breakdown of the conventional phonon-gas model and modify the dominant heat transport mechanism from the particle-like phonon wave packet propagation to incoherent tunneling described by off-diagonal terms in the heat-flux operator, which are typically prevailing in glasses and disordered crystals. Our work paves the way to a deeper understanding of glass-like thermal conductivity in complex crystals with strong anharmonicity

Turbulent thermal convection over rough plates with varying roughness geometries

We present a systematic investigation of the effects of roughness geometry on turbulent Rayleigh-B\'enard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter $\lambda$ defined as the height of a roughness element over its base width, the heat transport, the flow dynamics and local temperatures are measured for the Rayleigh number range $7.50\times 10^{7} \leq Ra\leq 1.31\times 10^{11}$, and the Prandtl number $Pr$ from 3.57 to 23.34 at four values of $\lambda$. It is found that the heat transport scaling, i.e. $Nu\sim Ra^{\alpha}$ where $Nu$ is the Nusselt number, may be classified into three regimes. In Regime I, the system is in a dynamically smooth state. The heat transport scaling is the same as that in a smooth cell. In Regimes II and III, the heat transport enhances. When $\lambda$ is increased from 0.5 to 4.0, $\alpha$ increases from 0.36 to 0.59 in Regime II, and it increases from 0.30 to 0.50 in Regime III. The experiment demonstrates the heat transport scaling in turbulent RBC can be manipulated using $\lambda$. Previous studies suggest that the transition from Regime I to Regime II, occurs when the thermal boundary layer (BL) thickness becomes smaller than the roughness height $h$. Direct measurements of the viscous BL in the present study suggest that the transition from Regime II to Regime III is likely a result of the viscous BL thickness becoming smaller $h$. The scaling exponent of the Reynolds number $Re$ vs. $Ra$ changes from 0.471 to 0.551 when $\lambda$ is increased from 0.5 to 4.0. It is also found that increasing $\lambda$ increases the clustering of thermal plumes which effectively increases the plumes lifetime that are ultimately responsible for the enhanced heat transport.Comment: 27 pages, 19 figure

Anharmonic stabilization and lattice heat transport in rocksalt β\beta-GeTe

Peierls-Boltzmann transport equation, coupled with third-order anharmonic lattice dynamics calculations, has been widely used to model lattice thermal conductivity ($\kappa_{l}$) in bulk crystals. However, its application to materials with structural phase transition at relatively high temperature is fundamentally challenged by the presence of lattice instabilities (imaginary phonon modes). Additionally, its accuracy suffers from the absence of higher-than-third-order phonon scattering processes, which are important near/above the Debye temperature. In this letter, we present an effective scheme that combines temperature-induced anharmonic phonon renormalization and four-phonon scattering to resolve these two theoretical challenges. We apply this scheme to investigate the lattice dynamics and thermal transport properties of GeTe, which undergoes a second-order ferroelectric phase transition from rhombohedral $\alpha$-GeTe to rocksalt $\beta$-GeTe at about 700~K. Our results on the high-temperature phase $\beta$-GeTe at 800~K confirm the stabilization of $\beta$-GeTe by temperature effects. We find that considering only three-phonon scattering leads to significantly overestimated $\kappa_{l}$ of 3.8~W/mK at 800~K, whereas including four-phonon scattering reduces $\kappa_{l}$ to 1.7~W/mK, a value comparable with experiments. To explore the possibility to further suppress $\kappa_{l}$, we show that alloying $\beta$-GeTe with heavy cations such as Pb and Bi can effectively reduce $\kappa_{l}$ to about 1.0~W/mK, whereas sample size needs to be around 10nm through nanostructuring to achieve a comparable reduction of $\kappa_{l}$

Renormalized Lattice Dynamics and Thermal Transport in VO2_{2}

Vanadium dioxide (VO$_{2}$) undergoes a first-order metal-insulator transition (MIT) upon cooling near room temperature, concomitant with structural change from rutile to monoclinic. Accurate characterization of lattice vibrations is vital for elucidating the transition mechanism. To investigate the lattice dynamics and thermal transport properties of VO$_{2}$ across the MIT, we present a phonon renormalization scheme based on self-consistent phonon theory through iteratively refining vibrational free energy. Using this technique, we compute temperature-dependent phonon dispersion and lifetimes, and point out the importance of both magnetic and vibrational entropy in driving the MIT. The predicted phonon dispersion and lifetimes show quantitative agreement with experimental measurements. We demonstrate that lattice thermal conductivity of rutile VO$_{2}$ is nearly temperature independent as a result of strong intrinsic anharmonicity, while that of monoclinic VO$_{2}$ varies according to $1/T$. Due to phonon softening and enhanced scattering rates, the lattice thermal conductivity is deduced to be substantially lower in the rutile phase, suggesting that Wiedemann-Franz law might not be strongly violated in rutile VO$_{2}$

Distributed Space-Time Coding for Full-Duplex Asynchronous Cooperative Communications

In this paper, we propose two distributed linear convolutional space-time coding (DLC-STC) schemes for full-duplex (FD) asynchronous cooperative communications. The DLC-STC Scheme 1 is for the case of the complete loop channel cancellation, which achieves the full asynchronous cooperative diversity. The DLC-STC Scheme 2 is for the case of the partial loop channel cancellation and amplifying, where some loop signals are used as the self-coding instead of treated as interference to be directly cancelled. We show this scheme can achieve full asynchronous cooperative diversity. We then evaluate the performance of the two schemes when loop channel information is not accurate and present an amplifying factor control method for the DLC-STC Scheme 2 to improve its performance with inaccurate loop channel information. Simulation results show that the DLC-STC Scheme 1 outperforms the DLC-STC Scheme 2 and the delay diversity scheme if perfect or high quality loop channel information is available at the relay, while the DLC-STC Scheme 2 achieves better performance if the loop channel information is imperfect.Comment: 9 pages, 7 figure

A Family of Counter Examples to an Approach to Graph Isomorphism

We give a family of counter examples showing that the two sequences of polytopes $\Phi_{n,n}$ and $\Psi_{n,n}$ are different. These polytopes were defined recently by S. Friedland in an attempt at a polynomial time algorithm for graph isomorphism