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## 备查：2021年国家自然科学基金申请代码大全——数理学部

2021年国科金申请正在进行时，数理学部的各类研究方向代码列表如下图，建议下载或在新窗口查看图片。

## 物理学：《高等量子力学》（孙昌璞讲授）在线课程

 量子物理的基本概念及相关研究 量子物理应用 1. 量子的概念 量子信息 原子 物质波 宏观量子态 1. 玻色-爱因斯坦凝聚 2. 经典与量子边界上的薛定谔猫 2. 量子绝热近似理论与Berry相因子 3. 量子力学测量问题与量子信息 3. 微腔量子电动力学的基本概念 4. 量子理论创建的科学启示 4. 宏观物体的退相干与量子宇宙的经典约化 5. 量子测量问题的研究及应用 5. 从参数“浸渐”的量子演化到热力学的绝热过程 6. 量子测量问题与量子力学诠释 6. 宏观人工原子相关的量子相干操纵 7. 量子力学若干基本问题研究的新进展 (I) (II) 7. 基于量子系综的准自旋波激发的量子存贮研究 8. 量子退相干问题 8. 量子态操纵的若干基础物理问题 9. 薜定愕猫与量子测量—兼谈量子信息的发展 9. 量子信息启发的固体系统量子态操纵的基本问题 10. 量子开系统理论及其应用 10. 量子信息启发的量子态操纵 11. 量子力学诠释问题 11. 信息处理的物理极限与量子热力学

## 物理学：Halbach array（海尔贝克阵列/哈尔贝克/哈尔巴赫阵列）

Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side of the array while cancelling the field to near zero on the other side.[1][2] This is achieved by having a spatially rotating pattern of magnetisation.

The rotating pattern of permanent magnets (on the front face; on the left, up, right, down) can be continued indefinitely and have the same effect. The effect of this arrangement is roughly similar to many horseshoe magnets placed adjacent to each other, with similar poles touching.

The principle was first invented by James (Jim) M. Winey of Magnepan in 1970, for the ideal case of continuously rotating magnetization, induced by a one-sided stripe-shaped coil.[3]

The effect was also discovered by John C. Mallinson in 1973, and these “one-sided flux” structures were initially described by him as a “curiosity”, although at the time he recognized from this discovery the potential for significant improvements in magnetic tape technology.[4]

Physicist Klaus Halbach, while at the Lawrence Berkeley National Laboratory during the 1980s, independently invented the Halbach array to focus particle accelerator beams.[5]

### Applications

The advantages of one-sided flux distributions are twofold:

• The field is twice as large on the side on which the flux is confined (in the idealized case).
• There is no stray field produced (in the ideal case) on the opposite side. This helps with field confinement, usually a problem in the design of magnetic structures.

Although one-sided flux distributions may seem somewhat abstract, they have a surprising number of applications ranging from the refrigerator magnet through industrial applications such as the brushless DC motorvoice coils,[7] magnetic drug targeting[8] to high-tech applications such as wiggler magnets used in particle accelerators and free-electron lasers.

This device is also a key component of the Inductrack Maglev train[9] and Inductrack rocket-launch system,[10] wherein the Halbach array repels loops of wire that form the track after the train has been accelerated to a speed able to lift.

The simplest example of a one-sided flux magnet is a refrigerator magnet. These are usually composed of powdered ferrite in a binder such as plastic or rubber. The extruded magnet is exposed to a rotating field giving the ferrite particles in the magnetic compound a magnetization resulting in a one-sided flux distribution. This distribution increases the holding force of the magnet when placed on a permeable surface, compared to the holding force from, say, a uniform magnetization of the magnetic compound.

Scaling up this design and adding a top sheet gives a wiggler magnet, used in synchrotrons and free-electron lasers. Wiggler magnets wiggle, or oscillate, an electron beam perpendicular to the magnetic field. As the electrons are undergoing acceleration, they radiate electromagnetic energy in their flight direction, and as they interact with the light already emitted, photons along its line are emitted in phase, resulting in a “laser-like” monochromatic and coherent beam.

The design shown above is usually known as a Halbach wiggler. The magnetization vectors in the magnetized sheets rotate in the opposite senses to each other; above, the top sheet\\’s magnetization vector rotates clockwise, and the bottom sheet\\’s magnetization vector rotates counter-clockwise. This design is chosen so that the x components of the magnetic fields from the sheets cancel, and the y components reinforce, so that the field is given by

where k is the wavenumber of the magnetic sheet given by the spacing between magnetic blocks with the same magnetization vector.

These cylindrical structures are used in devices such as brushless AC motors, magnetic couplings and high-field cylinders. Both brushless motors and coupling devices use multipole field arrangements:

• Brushless motors typically use cylindrical designs in which all the flux is confined to the centre of the bore (such as k = 4 above, a 6-pole rotor) with the AC coils also contained within the bore. Such self-shielding motors designs are more efficient and produce higher torque than conventional motor designs.
• Magnetic-coupling devices transmit torque through magnetically transparent barriers (that is, the barrier is non-magnetic or is magnetic but not affected by an applied magnetic field), for instance, between sealed containers or pressurised vessels. The optimal torque couplings consists of a pair of coaxially nested cylinders with opposite k and −k flux magnetization patterns, as this configuration is the only system for infinitely long cylinders that produces a torque.[14] In the lowest-energy state, the outer flux of the inner cylinder exactly matches the internal flux of the outer cylinder. Rotating one cylinder relative to the other from this state results in a restoring torque.

Klaus Halbach（左）在探讨永磁阵列模型。

海尔贝克阵列有哪些形式？

• 直线阵列

• 环形阵列

## 飞行：电磁悬浮四轴飞行（器）

Obviously this “quadcopter” is a demonstration device, showing how moving magnets over a conducting surface can generate levitation. It has not been optimized to minimize losses or be an efficient mode of transport. I still think it’s pretty cool. I’m used to seeing light things levitated by induced currents but not a 100+ lb machine.