Quantum algorithm for neighborhood preserving embedding

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.     

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.     

全局优化问题的一个新的无参数填充函数

求全局最优化问题的填充函数算法被提出以来，参数的选取和调整一直是制约算法有效性的因素。如何在实际的计算过程中选取合适的参数，直接影响和决定了运算速度和效率。因此，构造不含参数的填充函数就显得极为重要。提出一个新的无参数的填充函数，对其理论性质进行了分析，并给出相应的填充函数算法，数值计算验证了算法的有效性。     

Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid

This letter studies the problem of minimizing increasing set functions, equivalently, maximizing decreasing set functions, over the base matroid. This setting has received great interest, since it generalizes several applied problems including actuator and sensor placement problems in control, task allocation problems, video summarization, and many others. We study two greedy heuristics, namely, the forward and reverse greedy. We provide two novel performance guarantees for the approximate solutions obtained by them depending on both submodularity ratio and curvature.     

石墨基液流电池复合双极板

液流电池是一种安全性高、使用寿命长、可扩展的大规模储能系统,可以协助电网调峰储能,提高能源利用率,发展前景广阔。双极板是液流电池的重要组成部分。功能上起到了分隔、串联电池、传导电流、为电堆提供结构支撑等作用。从成本构成角度看,双极板的价格占电堆成本的比重也较大。开发高性能、低成本的双极板对加快液流电池的商业化应用具有重要意义,也是目前业界的迫切需求。虽然文献上报道了许多针对液流电池双极板开发的工作,但是目前高性能、低成本的液流电池双极板产品仍无法充分满足市场需求。本文着重介绍了石墨基复合双极板的研究现状,介绍了材料选择、工艺流程对关键性能的影响,对相关工作进行了评述,并为液流电池双极板的开发提出了建议。     

Hybrid continuum–coarse-grained modeling of erythrocytes

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE–POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum–coarse-grained model for the study of RBCs in fluid flows.     

Pullback exponential attractors for the non-autonomous micropolar fluid flows

This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.     

基于Caputo导数的分数阶非线性振动系统响应计算

研究了含分数阶Caputo导数的非线性振动系统响应的数值计算方法。首先，由Caputo分数阶导数算子的叠加关系，得到含分数阶导数项非线性振动系统状态方程的标准形式。其次，基于Caputo导数与Riemann-Liouville导数和Grunwald-Letnikov导数间的关系，推导计算了Caputo导数的一般数值迭代格式。本文方法不要求状态方程中各分数阶导数阶数相等，弱化了已有算法中对分数阶导数阶数的限制，并可推广到多自由度的情形。随后，选择若干有解析解的算例验证了本文方法的正确性。最后，以多吸引子共存的分数阶Duffing振子系统为例，比较Caputo和GL两种算法所得结果，说明了用GL算法求解存在的问题。     

Particle manipulation via integration of electroosmotic flow of power-law fluids with standing surface acoustic waves (SSAW)

Standing surface acoustic wave (SSAW) based microfluidic devices have shown great promise toward fluid and particle manipulation applications in medicine, chemistry, and biotechnology. In this article, we present an analytical model for investigating continuous manipulation of particles (both synthetic and biological) within electroosmotic flow of non-Newtonian bio-fluids in a microfluidic channel under the influence of standing surface acoustic waves (SSAW). The particles are injected along the center of channel into the electroosmotically driven flow of power-law fluids, wherein their transport through the SSAW region is dictated by the hydrodynamic, electrophoretic, and acoustic forces. We first present a mathematical model to analyze the characteristics of electroosmotic flow of non-Newtonian power-law fluids in a hydrophobic slit microchannel. Next, we investigate the trajectories of particles in the flow field due to the combined effect of electroosmotic, electrophoretic, and acoustophoretic forcing mechanisms. The effect of key parameters such as particle size, their physical properties, input power, flow rate, and flow behavior index on the particle trajectories is examined while including the effect of the channel walls. The presented model delineates the methodologies of improving SSAW-based particle separation technology by considering the fluid rheology as well as the surface properties of the channel walls. Therefore, we believe that this model can serve as an efficient tool for device design and quick optimizations to explore novel applications concerning the integration of electroosmotic flows with acoustofluidic technologies.