arXiv subjects
Publications and source records attributed to Kun Wang.
In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.
Using atomistic simulations, dislocation dynamics modeling, and continuum elastic-plastic stress-wave theory, we present a systematic investigation on shock-induced plasticity in semi-coherent CuNi multilayers. The features of stress wave evolutions in the multilayers, including wave-front stress attenuation and strong interfacial discontinuities, are revealed by atomistic simulations. Continuum models are proposed to explain the shockwave propagation features. The simulations provide insight into microplasticity behaviors including interactions between lattice and misfit dislocations. The formation of hybrid Lomer-Cottrell locks through the attraction and combination of lattice and misfit dislocations is a major mechanism for trapping gliding lattice dislocations at interfaces. The relationship between dislocation activity and dynamic stress wave evolution history is explored. The hybrid Lomer-Cottrell locks can dissociate under shock compression or reverse yielding. This dissociation facilitates slip transmission. The influence of coherent stress causes direction dependency in the slip transmission: a lattice dislocation is transmitted more smoothly across an interface from Ni to Cu than from Cu to Ni. The interaction forces between lattice and misfit dislocations are calculated using dislocation dynamics code. Lattice dislocation nucleation from semi-coherent interfaces under shock compression is also reported.
In this paper, we investigate the problem of minimizing the long-term total cost (i.e., the sum of energy cost and thermal discomfort cost) associated with a Heating, Ventilation, and Air Conditioning (HVAC) system of a multizone commercial building under smart grid environment. To be specific, we first formulate a stochastic program to minimize the time average expected total cost with the consideration of uncertainties in electricity price, outdoor temperature, the most comfortable temperature level, and external thermal disturbance. Due to the existence of temporally and spatially coupled constraints as well as unknown information about the future system parameters, it is very challenging to solve the formulated problem. To this end, we propose a realtime HVAC control algorithm based on the framework of Lyapunov optimization techniques without the need to predict any system parameters and know their stochastic information. The key idea of the proposed algorithm is to construct and stabilize virtual queues associated with indoor temperatures of all zones. Moreover, we provide a distributed implementation of the proposed realtime algorithm with the aim of protecting user privacy and enhancing algorithmic scalability. Extensive simulation results based on real-world traces show that the proposed algorithm could reduce energy cost effectively with small sacrifice in thermal comfort.
Object detection, scene graph generation and region captioning, which are three scene understanding tasks at different semantic levels, are tied together: scene graphs are generated on top of objects detected in an image with their pairwise relationship predicted, while region captioning gives a language description of the objects, their attributes, relations, and other context information. In this work, to leverage the mutual connections across semantic levels, we propose a novel neural network model, termed as Multi-level Scene Description Network (denoted as MSDN), to solve the three vision tasks jointly in an end-to-end manner. Objects, phrases, and caption regions are first aligned with a dynamic graph based on their spatial and semantic connections. Then a feature refining structure is used to pass messages across the three levels of semantic tasks through the graph. We benchmark the learned model on three tasks, and show the joint learning across three tasks with our proposed method can bring mutual improvements over previous models. Particularly, on the scene graph generation task, our proposed method outperforms the state-of-art method with more than 3% margin.
We study the Cuntz semigroup for non-simple $\text{C}^*$-algebras in this paper. In particular, we use the extended Elliott invariant to characterize the Cuntz comparison for $\text{C}^*$-algebras with the projection property which have only one ideal.
Ultrasound computed tomography (USCT) holds great promise for breast cancer screening. Waveform inversion-based image reconstruction methods account for higher order diffraction effects and can produce high-resolution USCT images, but are computationally demanding. Recently, a source encoding technique was combined with stochastic gradient descent to greatly reduce image reconstruction times. However, this method bundles the stochastic data fidelity term with the deterministic regularization term. This limitation can be overcome by replacing stochastic gradient descent (SGD) with a structured optimization method, such as the regularized dual averaging (RDA) method, that exploits knowledge of the composition of the cost function. In this work, the dual averaging method is combined with source encoding techniques to improve the effectiveness of regularization while maintaining the reduced reconstruction times afforded by source encoding. It is demonstrated that each iteration can be decomposed into a gradient descent step based on the data fidelity term and a proximal update step corresponding to the regularization term. Furthermore, the regularization term is never explicitly differentiated, allowing non-smooth regularization penalties to be naturally incorporated. The wave equation is solved by use of a time-domain method. The effectiveness of this approach is demonstrated through computer-simulation and experimental studies. The results suggest that the dual averaging method can produce images with less noise and comparable resolution to those obtained by use of stochastic gradient descent.
The goal of load balancing (grid partitioning) is to minimize overall computations and communications, and to make sure that all processors have a similar workload. Geometric methods divide a grid by using a location of a cell while topological methods work with connectivity of cells, which is generally described as a graph. This paper introduces a Hilbert space-filling curve method. A space-filling curve is a continuous curve and defines a map between a one-dimensional space and a multi-dimensional space. A Hilbert space-filling curve is one special space-filling curve discovered by Hilbert and has many useful characteristics, such as good locality, which means that two objects that are close to each other in a multi-dimensional space are also close to each other in a one dimensional space. This property can model communications in grid-based parallel applications. The idea of the Hilbert space-filling curve method is to map a computational domain into a one-dimensional space, partition the one-dimensional space to certain intervals, and assign all cells in a same interval to a MPI. To implement a load balancing method, a mapping kernel is required to convert high-dimensional coordinates to a scalar value and an efficient one-dimensional partitioning module that divides a one-dimensional space and makes sure that all intervals have a similar workload. The Hilbert space-filling curve method is compared with ParMETIS, a famous graph partitioning package. The results show that our Hilbert space-filling curve method has good partition quality. It has been applied to grids with billions of cells, and linear scalability has been obtained on IBM Blue Gene/Q.
Strain-based theory on elastic instabilities is being widely employed for studying onset of plasticity, phase transition or melting in crystals. And size effects, observed in nano-materials or solids under dynamic loadings, needs to account for contributions from strain gradient. However, the strain gradient based higher order elastic theories on the elastic instabilities are not well established to enable one to predict high order instabilities of solids directly at atom level. In present work, a general continuum theory for higher order elastic instabilities is established and justified by developing an equivalent description at atom level. Our results show that mechanical instability of solids, triggered by either strain or strain gradient, is determined by a simple stability condition consisting of strain or strain gradient related elastic constants. With the atom-level description of the higher order elasticity, the strain-gradient elastic constants could be directly obtained by a molecular statics procedure and then serve as inputs of the stability condition. In this way, mechanical instabilities of three metals, i.e., copper, aluminum and iron, are predicted. Alternatively, ramp compression technique by nonequilibrium molecular dynamics (NEMD) simulations is employed to study the higher order instabilities of the three metals. The predicted critical strains at onset of instabilities agree well with the results from the NEMD simulations for all the metals. Since the only inputs for the established higher order elastic theory are the same as atomic simulations, i.e., atomic potentials and structures of solids, the established theory is completely equivalent to empirical-potential based atomic simulations methods, at least, for crystals.
Under high pressures, phase transition, as well as deformation twins, are constantly reported in many BCC metals, whose interactions are of fundamental importance to understand strengthen mechanism of these metals under extreme conditions. However, the interactions between twins and phase transition in BCC metals are remain largely unexplored. In this work, interactions between coherent twin boundaries and $α\to ε$ phase transition of iron are investigated using both non- equilibrium molecular dynamics simulations and nudge elastic band method. Mechanisms of both twin-assisted phase transition and reverse phase transition are studied and orientation relationships between BCC and HCP phase are found to be <11-1>BCC || <-12-10>HCP and <1-10>BCC || <0001>HCP for both cases. The twin boundary corresponds to after the phase transition. It is amazing that the reverse transition seems to be able to "memory" and recover the initial BCC twins. The memory would partly loss when plastic slips take place in the HCP phase before the reverse transition. In the recovered initial BCC twins, three major twin spacing are observed, which are well explained in terms of energy barriers of the transition from HCP phase to BCC twin. Besides, variant selection rule of the twin assisted phase transition is also discussed. The results of present work could be expected to give some clues for producing ultra-fine grain structure in materials exhibiting martensitic phase transition.
A lattice in the Euclidean space is standard if it has a basis consisting vectors whose norms equal to the length in its successive minima. In this paper, it is shown that with the $L^2$ norm all lattices of dimension $n$ are standard if and only if $n\leqslant 4$. It is also proved that with an arbitrary norm, every lattice of dimensions 1 and 2 is standard. An example of non-standard lattice of dimension $n\geqslant 3$ is given when the lattice is with the $L^1$ norm.
In this paper, we consider $\text{C}^*$-algebras with the ideal property (the ideal property unifies the simple and real rank zero cases). We define two categories related the invariants of the $\text{C}^*$-algebras with the ideal property. And we showed that these two categories are in fact isomorphic. As a consequence, the Elliott's Invariant and the Stevens' Invariant are isomorphic for $\text{C}^*$-algebras with the ideal property.
In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of $u'(t)$ with the kernel $(t_n-t)^{-α}$. In the fast algorithm, the interval $[0,t_{n-1}]$ is split into nonuniform subintervals. The number of the subintervals is in the order of $\log n$ at the $n$-th time step. The fractional kernel function is approximated by a polynomial function of $K$-th degree with a uniform absolute error on each subinterval. We save $K+1$ integrals on each subinterval, which can be written as a convolution of $u'(t)$ with a polynomial base function. As compared with the direct method, the proposed fast algorithm reduces the storage requirement and computational cost from $O(n)$ to $O((K+1)\log n)$ at the $n$-th time step. We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order direct method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples.
Phase transition of iron, as a prototype of martensite phase transition under dynamic loadings, exhibits huge diverges in its TP among experiments with different pressure medium and loading rates, even in the same initial samples. Great achievements are made in understanding strain or stress dependence of the TP under dynamic loadings. However, present understandings on the strain rate dependence of the TP are far from clear, even a virgin for extreme high strain rates. In this work, large scale NEMD simulations are conducted to study the effects of strain rates on the phase transition of iron-based single crystals. Our results show that the phase transition is preceded by lattice instabilities under ramp compressions, but present theory, represented by modified Born criteria, cannot correctly predict observed onsets of the instability. Through considering both strain and strain gradient disturbances, new instability criteria are proposed, which could be generally applied for studying instabilities under either static or dynamic loadings. For the ramp with a strain rate smaller than about 1010s-1, the observed onset of instabilities is indeed equal to the one predicted by the new instability criteria under small gradient disturbances. The observed onsets deviates from the predicted one at lager strain rates because of finite strain gradient effect. Interestingly, the strain rate dependence of the TP also exhibits an obvious change at the same strain rate, i.e., 1010 s-1. When 1010 s-1, a certain power law is obeyed, but it is not applicable at larger strain rates. This strain rate effect on the TP is well interpreted with nucleation time and the finite strain gradient effect. According to these basic understandings, the roles of strain rates on nucleation and growth of the phase transition are studied.
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are investigated. A multi-stage preconditioner for two-phase flow is applied and advanced matrix processing strategies are studied. A local reordering method is developed to speed the solution of linear systems. Numerical experiments show that these computational methods are effective and scalable, and are capable of computing large-scale reservoir simulation problems using thousands of CPU cores on parallel computers. The nonlinear techniques, preconditioner and matrix processing strategies can also be applied to three-phase black oil, compositional and thermal models.
In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $τ$ self-loops. We derive an analytic expression for the localization probability of the walker at the origin after infinite steps, and obtain the peak velocities of the walker. We also calculate rigorously the wave function of the walker starting from the origin and obtain a long time approximation for the entire probability density function. As an application of the density function, we prove that lackadaisical quantum walks spread ballistically for arbitrary $τ$, and give an analytic solution for the variance of the walker's probability distribution.
We present systematic investigations on the shock responses of nanoporous aluminum (np-Al) by nonequilibrium molecular dynamics simulations. The dislocation nucleation sites are found to concentrate in low latitude region near the equator of the spherical void surfaces. We propose a continuum wave reflection theory and a resolved shear stress model to explain the distribution of dislocation nucleation sites. The simulations reveals two mechanisms of void collapse: the plasticity mechanism and the internal jetting mechanism. The plasticity mechanism, which leads to transverse collapse of voids, prevails under relatively weaker shocks; while the internal jetting mechanism, which leads to longitudinal filling of the void vacuum, plays more significant role as the shock intensity increases. In addition, an abnormal thermodynamic phenomenon (i.e., arising of temperature with pressure dropping) in shocked np-Al is discovered. This phenomenon is incompatible with the conventional Rankine-Hugoniot theory, and is explained by the nonequilibrium processes involved in void collapse. The influences of void collapse on spall fracture of np-Al is studied. Under the same loading velocity, the spall strength of np-Al is found to be lower than that of single-crystal Al; but the spall resistance is higher in np-Al than in single-crystal Al. This is explained by the combined influences of thermal dissipation and stress attenuation during shock wave propagation in np-Al.
The visual cues from multiple support regions of different sizes and resolutions are complementary in classifying a candidate box in object detection. Effective integration of local and contextual visual cues from these regions has become a fundamental problem in object detection. In this paper, we propose a gated bi-directional CNN (GBD-Net) to pass messages among features from different support regions during both feature learning and feature extraction. Such message passing can be implemented through convolution between neighboring support regions in two directions and can be conducted in various layers. Therefore, local and contextual visual patterns can validate the existence of each other by learning their nonlinear relationships and their close interactions are modeled in a more complex way. It is also shown that message passing is not always helpful but dependent on individual samples. Gated functions are therefore needed to control message transmission, whose on-or-offs are controlled by extra visual evidence from the input sample. The effectiveness of GBD-Net is shown through experiments on three object detection datasets, ImageNet, Pascal VOC2007 and Microsoft COCO. This paper also shows the details of our approach in wining the ImageNet object detection challenge of 2016, with source code provided on \url{https://github.com/craftGBD/craftGBD}.
A parallel reservoir simulator has been developed, which is designed for large-scale black oil simulations. It handles three phases, including water, oil and gas, and three components, including water, oil and gas. This simulator can calculate traditional reservoir models and naturally fractured models. Various well operations are supported, such as water flooding, gas flooding and polymer flooding. The operation constraints can be fixed bottom-hole pressure, a fixed fluid rate, and combinations of them. The simulator is based on our in-house platform, which provides grids, cell-centred data, linear solvers, preconditioners and well modeling. The simulator and the platform use MPI for communications among computation nodes. Our simulator is capable of simulating giant reservoir models with hundreds of millions of grid cells. Numerical simulations show that our simulator matches with commercial simulators and it has excellent scalability.