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相关概念视频

Stress Concentrations01:24

Stress Concentrations

271
Stress concentration is when stress intensifies near discontinuities such as holes or abrupt cross-sectional changes in a structural member. This localized stress can often surpass the average stress within the member. The stress distribution in flat bars, either with a circular hole or varying widths connected by fillets, can be determined experimentally using a photoelastic method. The results are based on ratios of geometric parameters like the ratio of the hole's radius to the smaller...
271
Group Design02:01

Group Design

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The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except for one difference— experimental manipulation. The experimental group gets the experimental manipulation—that is, the treatment or variable being tested—and the control group does not. Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between...
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State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
162
General State of Stress01:21

General State of Stress

168
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
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Randomized Experiments01:13

Randomized Experiments

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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
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Inertia Tensor01:24

Inertia Tensor

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The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...
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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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随机张量网络的反集中和状态设计

Guglielmo Lami1, Jacopo De Nardis1, Xhek Turkeshi2

  • 1Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France.

Physical review letters
|February 6, 2025
PubMed
概括
此摘要是机器生成的。

量子随机张量网络表现出哈尔随机行为,当键尺寸与系统大小多项式扩展时. 这适用于一维和二维系统,显示对单元设计的趋同.

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科学领域:

  • 量子信息理论 量子信息理论
  • 凝聚物质物理学 凝聚物质物理学
  • 多体物理多体物理

背景情况:

  • 张量网络状态对于模拟量子多体系统至关重要.
  • 了解随机张量网络的特性是它们在量子信息中的应用的关键.
  • 随机矩阵产物状态 (RMPS) 和预测纠对状态 (PEPS) 是张量网络的重要类别.

研究的目的:

  • 为了研究量子随机张量网络状态的脱局属性.
  • 在随机矩阵产品状态 (RMPS) 中导出逆参与率 (IPR) 的分析表达式.
  • 确定随机张量网络对哈尔随机行为和单元设计的收.

主要方法:

  • 导出RMPS的逆参与比率 (IPR) 的确切分析表达式.
  • 对不同债券尺寸的重叠概率分布的分析.
  • 数值计算的潜力,以测量距离哈尔集团的距离.
  • 将分析扩展到二维系统,使用随机预测纠对状态 (PEPS).

主要成果:

  • 对于开放和封闭边界条件来说,RMPS的IPR的确切分析表达式得到了推导.
  • 对于债券尺寸 χ∼γN,随着 γ 的增加,重叠概率分布与波特-托马斯分布趋同.
  • 数字证据显示随机的MPS和PEPS近似哈尔状行为和单位设计的 χ≫sqrt[N].
  • 这些属性不管空间维度如何,都保持不变.

结论:

  • 具有多项式缩放键维度的随机张量网络完全是Haar反集中的.
  • 这些状态接近单元设计,这对于量子信息处理来说是一个重要的发现.
  • 该研究提供了对随机张量网络的统计性质的全面理解.