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Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
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Continuous Charge Distributions01:17

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Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
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The German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that confirmed the existence of electromagnetic waves and verified that they travel at the speed of light. Hertz used an alternating-current RLC (resistor-inductor-capacitor) circuit that resonated at a known frequency and connected it to a loop of wire. High voltages induced across the gap in...
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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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The average temperature of Earth is the subject of much current discussion. Earth is in radiative contact with both the Sun and dark space; it receives almost all its energy from the radiation of the Sun and reflects some of it into outer space. Dark space is very cold, about 3 K, so Earth radiates energy into it. For instance, heat transfer occurs from soil and grasses, the rate of which can be so rapid that frost can occur on clear summer evenings, even in warm latitudes.
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相关实验视频

Updated: Jan 15, 2026

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies
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一种多源特征驱动的深度学习方法,用于生成质子治疗的线性能量转移分布.

Qian Liu1, Shangyan Wei1, Huijuan Peng1

  • 1National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China.

Medical physics
|October 9, 2025
PubMed
概括

这项研究开发了一种快速深度学习模型,用于预测鼻癌的质子疗法中剂量平均线性能量转移 (LETd). 结合剂量和CT成像数据提供了最准确和可靠的LETd预测.

关键词:
深度学习是一种深度学习.线性能量转移是线性的.多个来源的功能.质子疗法是一种质子疗法.

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科学领域:

  • 医学物理 医学物理
  • 辐射疗法 辐射疗法
  • 计算生物学 计算生物学

背景情况:

  • 蒙特卡洛 (MC) 模拟在质子疗法中提供准确的剂量平均线性能量转移 (LETd) 估计,但在计算上是密集的.
  • 深度学习 (DL) 模型提供更快的替代方案,但很少有针对多源输入进行优化或在复杂的瘤如鼻癌 (NPC) 上得到验证.

研究的目的:

  • 开发和评估一个多源DL框架用于NPC的质子疗法中的voxel级LETd预测.
  • 确定DL模型的最佳输入配置,并评估预测准确性和临床可靠性.

主要方法:

  • 分析了100名NPC患者 (500个质子疗法领域),使用基于GPU的MC模拟的基准真相LETd地图.
  • 训练了一个DL模型,使用剂量分布,CT图像,光束罩和放射深度进行八种配置.
  • 使用MAE,PSNR,NCC,SSIM和3D马分析评估性能;与3D U-Net基线进行比较.

主要成果:

  • 与3D U-Net基线 (MAE 0.38 ± 0.52 keV/μm) 相比,Mdose+ct DL模型实现了更高的性能 (MAE 0.21 ± 0.03 keV/μm).
  • 模型解释性 (Grad-CAM) 证实了对相关地区的关注,不确定性地图确定了高变化区域.
  • 每个案例的DL模型预测在7秒内生成,比MC模拟 (~30秒) 快得多.

结论:

  • 多源DL框架使NPC质子疗法能够快速准确地预测voxel级LETd.
  • 结合剂量和CT数据被证明是最可靠的输入配置.
  • 可解释性和不确定性分析提高了该框架适用于生物指导质子疗法规划的适用性.