limiting gradient

简明释义

限制坡度

英英释义

例句

1.The engineer calculated the limiting gradient to ensure the stability of the slope.

工程师计算了极限梯度以确保坡道的稳定性。

2.Understanding the limiting gradient helps in designing safer roadways.

理解极限梯度有助于设计更安全的道路。

3.The architect specified a limiting gradient for the roof to facilitate drainage.

建筑师为屋顶指定了一个极限梯度以促进排水。

4.The project was delayed due to the need to reassess the limiting gradient for the construction site.

由于需要重新评估施工现场的极限梯度，项目被延迟。

5.In geology, the limiting gradient indicates the maximum angle of repose for materials.

在地质学中，极限梯度表示材料的最大静止角度。

作文

In the study of physics and engineering, the concept of a limiting gradient plays a crucial role in understanding the behavior of various systems. The term refers to the maximum rate of change of a variable with respect to another variable, often under specific conditions. To illustrate this concept, let’s consider the example of a car driving up a hill. As the car ascends, it encounters an increasing incline that affects its speed and acceleration. The limiting gradient in this scenario would be the steepest angle at which the car can maintain a constant speed without rolling back down. Beyond this gradient, the car would either accelerate uncontrollably or come to a halt.Understanding the limiting gradient is essential for engineers when designing roads and vehicles. If they know the limiting gradient for certain types of vehicles, they can create safer and more efficient transportation systems. For instance, highways often have specified maximum grades to ensure that vehicles can travel safely without losing control.Moreover, the concept extends beyond simple mechanics. In thermodynamics, the limiting gradient can describe how temperature changes with respect to pressure in a given system. Engineers must account for these gradients when designing systems that involve heat exchange, such as engines or HVAC systems. A proper understanding of the limiting gradient helps in optimizing performance and ensuring safety in these systems.The significance of the limiting gradient also resonates in environmental science. For example, when analyzing soil erosion, scientists may look at the limiting gradient of a slope to determine how much vegetation is needed to stabilize the soil. If the slope exceeds the limiting gradient, it becomes susceptible to erosion, leading to detrimental effects on the ecosystem.In mathematics, the limiting gradient can be represented through calculus, particularly in the study of functions and their derivatives. The derivative at any point gives the instantaneous rate of change, but the limiting gradient provides insight into the overall trend of the function as it approaches certain limits. This mathematical perspective is invaluable in fields like economics, where understanding rates of change can inform better decision-making.In conclusion, the limiting gradient is a multifaceted concept that finds application across various disciplines. Whether in engineering, environmental science, or mathematics, recognizing the importance of the limiting gradient allows professionals to make informed decisions that enhance safety, efficiency, and sustainability. As technology continues to evolve, the relevance of understanding gradients will only grow, highlighting the need for ongoing education and research in this area.

在物理和工程学的研究中，limiting gradient（极限梯度）这一概念在理解各种系统的行为方面发挥着至关重要的作用。这个术语指的是在特定条件下，一个变量相对于另一个变量的最大变化率。为了说明这一概念，我们可以考虑一辆汽车上坡的例子。当汽车上升时，它会遇到越来越大的倾斜，这会影响它的速度和加速度。在这种情况下，limiting gradient将是汽车能够保持恒定速度而不向下滑的最陡角度。超过这个梯度，汽车要么会失控加速，要么会停下来。理解limiting gradient对工程师在设计道路和车辆时至关重要。如果他们知道某些类型车辆的limiting gradient，就可以创造出更安全、更高效的交通系统。例如，高速公路通常规定了最大坡度，以确保车辆能够安全行驶而不失控。此外，这个概念不仅限于简单的力学。在热力学中，limiting gradient可以描述在给定系统中温度与压力的变化关系。工程师在设计涉及热交换的系统（如发动机或暖通空调系统）时，必须考虑这些梯度。对limiting gradient的恰当理解有助于优化性能并确保这些系统的安全。limiting gradient的重要性在环境科学中也得到了体现。例如，在分析土壤侵蚀时，科学家可能会查看坡度的limiting gradient来确定需要多少植被来稳定土壤。如果坡度超过limiting gradient，则土壤容易受到侵蚀，从而对生态系统造成不利影响。在数学中，limiting gradient可以通过微积分表示，特别是在函数及其导数的研究中。任何点的导数给出了瞬时变化率，但limiting gradient提供了关于函数在接近某些极限时的整体趋势的见解。这种数学视角在经济学等领域是非常宝贵的，因为理解变化率可以帮助做出更好的决策。总之，limiting gradient是一个多方面的概念，广泛应用于各个学科。无论是在工程、环境科学还是数学中，认识到limiting gradient的重要性使专业人士能够做出明智的决策，从而提高安全性、效率和可持续性。随着技术的不断发展，理解梯度的相关性只会增加，这突显了在这一领域持续教育和研究的必要性。