isotropic distribution

简明释义

蛤同性分布

英英释义

例句

1.When modeling random walks, the steps can be assumed to follow an isotropic distribution, allowing for equal probability of movement in any direction.

在建模随机游走时，可以假设步伐遵循各向同性分布，允许在任何方向上有相等的移动概率。

2.In statistical mechanics, an ideal gas is often modeled with an isotropic distribution of molecular velocities, meaning that the velocities are uniformly distributed in all directions.

在统计力学中，理想气体通常被建模为分子速度的各向同性分布，这意味着速度在所有方向上均匀分布。

3.In computer graphics, light sources are often assumed to emit light in an isotropic distribution, providing uniform illumination across surfaces.

在计算机图形学中，光源通常被假设以各向同性分布发出光线，从而在表面上提供均匀的照明。

4.The isotropic distribution of points in a three-dimensional space can be visualized as a sphere where every point on the surface is equally likely to be chosen.

在三维空间中，点的各向同性分布可以被可视化为一个球体，其中表面上的每个点被选择的可能性是相等的。

5.The isotropic distribution of errors in a measurement system can indicate that the errors are random and do not favor any particular direction.

测量系统中误差的各向同性分布可以表明这些误差是随机的，不偏向任何特定方向。

作文

In the field of physics and mathematics, the concept of isotropic distribution refers to a situation where properties are uniform in all directions. This idea is crucial for various applications, particularly in the study of materials and the behavior of particles. To understand this concept better, let’s explore its implications in different contexts.Firstly, consider the example of a gas in a closed container. When the gas molecules are evenly distributed throughout the container, they exhibit an isotropic distribution of velocities. This means that if we were to measure the speed and direction of the molecules, we would find no preferential direction; the molecules move equally in all directions. This uniformity simplifies many calculations in thermodynamics and statistical mechanics, as it allows scientists to apply the laws of probability more easily.Moreover, in the realm of cosmology, the universe is often assumed to have an isotropic distribution of matter and energy on large scales. This assumption is fundamental to the widely accepted cosmological principle, which states that the universe is homogeneous and isotropic when viewed at a sufficiently large scale. This principle helps astronomers and physicists develop models of the universe's expansion and evolution, leading to insights about its origins and ultimate fate.In addition to physics, the concept of isotropic distribution can also be found in fields such as statistics and data analysis. For instance, when analyzing data points in a two-dimensional space, if the points are spread out evenly around a central point, they display an isotropic distribution. This characteristic is essential for certain statistical methods, such as those used in machine learning algorithms, where the assumption of isotropy can lead to more robust predictions and analyses.Furthermore, in engineering, particularly in materials science, understanding the isotropic distribution of stress within a material is vital for ensuring structural integrity. For example, when a material is subjected to forces, an isotropic material will respond uniformly regardless of the direction of the applied force. This property is critical in designing safe and reliable structures, as it allows engineers to predict how materials will behave under various loads.However, it is important to note that not all systems exhibit isotropic distribution. Anisotropic materials, for example, have properties that vary depending on the direction of measurement. In these cases, the analysis becomes more complex, requiring specialized approaches to account for the directional dependence of properties. Understanding the difference between isotropic and anisotropic distributions is crucial for scientists and engineers alike, as it influences their approach to problem-solving.In conclusion, the concept of isotropic distribution plays a significant role across various scientific disciplines. Whether in physics, cosmology, statistics, or engineering, recognizing when a system exhibits isotropy can greatly enhance our understanding and ability to model complex phenomena. As we continue to explore the universe and the materials within it, the principles of isotropy will undoubtedly remain a cornerstone of scientific inquiry, guiding researchers in their quest for knowledge and innovation. The study of isotropic distribution not only deepens our understanding of the natural world but also paves the way for advancements in technology and industry.

在物理和数学领域，isotropic distribution（各向同性分布）的概念指的是性质在所有方向上都是均匀的情况。这个思想对于各种应用至关重要，特别是在材料研究和粒子行为的研究中。为了更好地理解这一概念，让我们探讨其在不同背景下的影响。首先，考虑一个封闭容器中的气体的例子。当气体分子均匀分布在整个容器中时，它们表现出速度的isotropic distribution（各向同性分布）。这意味着如果我们测量这些分子的速度和方向，我们会发现没有优先方向；分子均匀地向所有方向移动。这种均匀性简化了热力学和统计力学中的许多计算，因为它允许科学家更容易地应用概率法则。此外，在宇宙学领域，宇宙在大尺度上常常被假设具有isotropic distribution（各向同性分布）的物质和能量。这一假设是广泛接受的宇宙学原理的基础，该原理指出，当从足够大的尺度观察时，宇宙是均匀和各向同性的。这个原理帮助天文学家和物理学家建立宇宙扩张和演化的模型，从而获得关于宇宙起源和最终命运的见解。除了物理学，isotropic distribution（各向同性分布）的概念还可以在统计学和数据分析等领域找到。例如，在分析二维空间中的数据点时，如果这些点均匀地围绕一个中心点分布，它们表现出isotropic distribution（各向同性分布）。这一特征对于某些统计方法至关重要，例如用于机器学习算法的方法，其中各向同性的假设可以导致更稳健的预测和分析。此外，在工程学，特别是材料科学中，理解材料内部应力的isotropic distribution（各向同性分布）对于确保结构完整性至关重要。例如，当材料受到力的作用时，各向同性材料将无论施加力的方向如何都以均匀的方式响应。这一特性在设计安全可靠的结构时至关重要，因为它允许工程师预测材料在各种载荷下的行为。然而，重要的是要注意，并非所有系统都表现出isotropic distribution（各向同性分布）。例如，各向异性材料的性质会根据测量方向的不同而变化。在这些情况下，分析变得更加复杂，需要采用专业的方法来考虑性质的方向依赖性。理解各向同性和各向异性分布之间的区别对于科学家和工程师来说至关重要，因为这会影响他们解决问题的方法。总之，isotropic distribution（各向同性分布）的概念在各个科学学科中扮演着重要角色。无论是在物理学、宇宙学、统计学还是工程学，识别一个系统何时表现出各向同性可以极大地增强我们对复杂现象的理解和建模能力。随着我们继续探索宇宙及其内的材料，各向同性的原则无疑将继续成为科学探究的基石，引导研究人员在追求知识和创新的过程中。对isotropic distribution（各向同性分布）的研究不仅加深了我们对自然世界的理解，也为技术和工业的进步铺平了道路。