scaling law

简明释义

比例缩小规则

英英释义

例句

1.The researchers discovered a new scaling law that predicts how the energy consumption of cities increases with population size.

研究人员发现了一种新的缩放法则，可以预测城市的能耗如何随着人口规模的增加而增加。

2.The team applied the scaling law to optimize their algorithms for processing large datasets efficiently.

团队应用了缩放法则来优化他们的算法，以高效处理大数据集。

3.The scaling law for biological systems shows how metabolic rates change with body size across different species.

生物系统的缩放法则显示了不同物种之间代谢率如何随身体大小变化。

4.In machine learning, the scaling law indicates that larger models tend to perform better as more data is provided.

在机器学习中，缩放法则表明，随着提供更多数据，较大的模型往往表现更好。

5.Understanding the scaling law in physics can help engineers design better structures that withstand various forces.

理解物理中的缩放法则可以帮助工程师设计出能够承受各种力量的更好结构。

作文

In the field of science and engineering, the concept of scaling law (缩放定律) plays a crucial role in understanding how different systems behave as their size changes. Scaling laws provide a mathematical framework that allows researchers to predict how physical quantities will change when the dimensions of an object are altered. This is particularly important in disciplines such as physics, biology, and materials science, where the properties of materials and organisms can vary dramatically with size. For example, consider the scaling laws that govern the behavior of animals. The metabolic rate of an organism does not scale linearly with its mass; instead, it often follows a power law. This means that larger animals tend to have slower metabolisms per unit mass compared to smaller animals. This observation leads to the formulation of scaling law (缩放定律) equations that help biologists understand energy consumption, growth patterns, and ecological dynamics. Similarly, in engineering, the scaling law (缩放定律) is essential when designing structures or machines. Engineers must account for how various forces, such as gravity and pressure, will affect a structure as its size increases or decreases. For instance, if a bridge is scaled up, the materials used must be able to withstand greater loads, and the design must ensure stability under these new conditions. By applying scaling law (缩放定律), engineers can create models that accurately reflect how larger or smaller versions of a structure will perform, allowing for more efficient and safer designs. The implications of scaling law (缩放定律) extend beyond just physical objects. In the realm of computer science and data analysis, scaling laws can help in understanding algorithms' performance as the size of the input data increases. For instance, some algorithms exhibit linear scaling, meaning that doubling the input size will double the time required to process it. Others may show logarithmic or exponential scaling, indicating that performance can degrade significantly with larger datasets. Researchers can use these insights to optimize algorithms and improve computational efficiency. In conclusion, the concept of scaling law (缩放定律) is fundamental across various scientific and engineering disciplines. It provides a framework for understanding how changes in size can impact physical and biological systems. By applying these laws, scientists and engineers can make accurate predictions, design better structures, and develop more efficient algorithms. As we continue to explore the complexities of our world, the importance of scaling law (缩放定律) will only grow, highlighting the interconnectedness of size, structure, and function in nature and technology.

在科学和工程领域，缩放定律的概念在理解不同系统随着其大小变化而表现出的行为方面起着至关重要的作用。缩放定律提供了一个数学框架，使研究人员能够预测当物体的尺寸发生变化时，物理量将如何变化。这在物理学、生物学和材料科学等学科中尤为重要，因为材料和生物体的性质可能会随着大小的变化而显著不同。例如，考虑支配动物行为的缩放定律。生物体的代谢率并不与其质量线性缩放；相反，它通常遵循幂律。这意味着较大的动物相对于较小的动物，每单位质量的代谢率往往较慢。这一观察结果导致了缩放定律方程的制定，帮助生物学家理解能量消耗、成长模式和生态动态。同样，在工程学中，缩放定律在设计结构或机器时至关重要。工程师必须考虑各种力量，如重力和压力，如何影响结构在大小增加或减少时的表现。例如，如果一座桥被放大，则使用的材料必须能够承受更大的负荷，设计必须确保在这些新条件下的稳定性。通过应用缩放定律，工程师可以创建准确反映结构的较大或较小版本性能的模型，从而实现更高效和更安全的设计。缩放定律的影响不仅限于物理物体。在计算机科学和数据分析领域，缩放定律可以帮助理解算法在输入数据大小增加时的性能。例如，一些算法表现出线性缩放，这意味着输入大小翻倍将使处理所需时间翻倍。其他算法可能显示对数或指数缩放，表明随着数据集的增大，性能可能显著下降。研究人员可以利用这些见解来优化算法，提高计算效率。总之，缩放定律的概念在各个科学和工程学科中是基础性的。它提供了一个框架，用于理解大小变化如何影响物理和生物系统。通过应用这些定律，科学家和工程师可以做出准确的预测，设计更好的结构，并开发更高效的算法。随着我们继续探索世界的复杂性，缩放定律的重要性只会增加，突显出自然和技术中大小、结构与功能之间的相互联系。