vectorial field

简明释义

矢量场

英英释义

例句

1.In fluid dynamics, the velocity of the fluid creates a vectorial field 向量场 that can be visualized using streamlines.

在流体动力学中，流体的速度形成了一个 vectorial field 向量场，可以通过流线进行可视化。

2.In physics, a vectorial field 向量场 represents the distribution of a vector quantity across space.

在物理学中，vectorial field 向量场 表示一个向量量在空间中的分布。

3.The electric vectorial field 向量场 around a charged particle illustrates the direction and magnitude of the force on other charges.

带电粒子周围的电 vectorial field 向量场 说明了对其他电荷施加的力的方向和大小。

4.Mathematicians often use vectorial fields 向量场 to study differential equations and their solutions.

数学家常常使用 vectorial fields 向量场 来研究微分方程及其解。

5.The gravitational vectorial field 向量场 around a planet shows how the force of gravity varies with distance.

围绕一个行星的引力 vectorial field 向量场 显示了重力如何随距离变化。

作文

In the realm of mathematics and physics, the concept of a vectorial field plays a crucial role in understanding various phenomena. A vectorial field is essentially a function that assigns a vector to every point in a given space. This can be visualized as an array of arrows, where each arrow represents the direction and magnitude of a vector at a specific point. For instance, consider the wind blowing across a landscape. At every point in the area, the wind has a certain speed and direction, which can be represented as a vectorial field. One of the most common examples of a vectorial field is the gravitational field surrounding a mass. The gravitational force experienced by an object in this field can be described by vectors pointing towards the mass, indicating the direction of the force as well as its strength. The closer an object is to the mass, the stronger the gravitational force it experiences, which is why the vectorial field can vary in intensity throughout the space.In addition to gravity, electric fields are another example of vectorial fields. When charged particles are present, they create electric fields that exert forces on other charges within the vicinity. Similar to gravitational fields, electric fields can be represented as vectors, showing both the direction of the force on a positive test charge and its magnitude. Understanding these vectorial fields is essential for physicists and engineers when designing electrical circuits or analyzing forces acting on objects.The mathematical representation of a vectorial field often involves vector calculus. For example, if we have a vectorial field denoted as **F**, which depends on the position vector **r**, we can express it as **F(r) = (F1(r), F2(r), F3(r))**, where **F1**, **F2**, and **F3** are the components of the vector field in three-dimensional space. The study of vectorial fields leads to important concepts such as divergence and curl, which provide insights into the behavior of the field lines and their sources or sinks.Moreover, vectorial fields are not limited to physical applications; they also find their place in computer graphics, fluid dynamics, and even economics. In computer graphics, for instance, vectorial fields can be used to simulate fluid flow, allowing for realistic animations. By manipulating vectorial fields, artists and developers can create stunning visual effects that mimic real-world phenomena.In conclusion, the concept of a vectorial field is fundamental in various scientific and engineering disciplines. Whether it is analyzing forces in physics, simulating natural phenomena in computer graphics, or solving complex mathematical problems, understanding vectorial fields allows us to grasp the intricate relationships between different variables in a system. As we continue to explore the universe and develop new technologies, the significance of vectorial fields will undoubtedly grow, making them an essential topic for anyone interested in science and mathematics.

在数学和物理的领域中，向量场的概念在理解各种现象中起着至关重要的作用。向量场本质上是一个函数，它将一个向量分配给给定空间中的每个点。这可以被可视化为一系列箭头，其中每个箭头表示特定点处的向量的方向和大小。例如，考虑风在一个景观上吹动。在该区域的每个点，风都有一定的速度和方向，这可以表示为一个向量场。向量场最常见的例子之一是围绕质量的引力场。在这个场中，物体所经历的引力可以用指向质量的向量来描述，表明力的方向以及其强度。物体离质量越近，它所经历的引力就越强，这就是为什么向量场在整个空间中可以变化强度。除了重力，电场也是另一个向量场的例子。当带电粒子存在时，它们会产生电场，对周围的其他电荷施加力。与引力场类似，电场也可以用向量表示，显示对正测试电荷的力的方向及其大小。理解这些向量场对于物理学家和工程师在设计电路或分析作用于物体的力时至关重要。向量场的数学表示通常涉及向量微积分。例如，如果我们有一个标记为**F**的向量场，它依赖于位置向量**r**，我们可以将其表示为**F(r) = (F1(r), F2(r), F3(r))**，其中**F1**、**F2**和**F3**是三维空间中向量场的分量。对向量场的研究导致了重要概念，如散度和旋度，这些概念提供了关于场线行为及其源或汇的洞察。此外，向量场并不限于物理应用；它们还在计算机图形学、流体动力学甚至经济学中找到了自己的位置。例如，在计算机图形学中，向量场可以用来模拟流体流动，从而实现逼真的动画。通过操纵向量场，艺术家和开发者可以创造出模仿现实世界现象的惊人视觉效果。总之，向量场的概念在各种科学和工程学科中是基础性的。无论是分析物理中的力、在计算机图形学中模拟自然现象，还是解决复杂的数学问题，理解向量场使我们能够掌握系统中不同变量之间的复杂关系。随着我们继续探索宇宙并开发新技术，向量场的重要性无疑会增加，使其成为任何对科学和数学感兴趣的人必不可少的话题。