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作者｜yubr编辑｜TraderJoe's1 引言微分方程是描述一个系统的状态随时间和空间演化的最基本的数学工具之一，其在物理、经济、工程、社会等各方面都有及其重要的应用。然而，只有很少的微分方程可以解析求解，尤其对于偏微分方程，能解析...

微分 Python

赞同0  1088浏览  0评论 yubr 2022-05-24 22:29

Giacomo 回复了问题 2022-05-23 19:58 物理: 问答广义相对论里曲率张量该如何理解？

Giacomo :有一个概念叫截面曲率（sectional curvature），是说在黎曼流形里面一点截取一个二维的子切空间，对应一个实数。这个概念是经典微分几何里面的高斯曲率的拓展; 赞同5 反对 0人感谢 0评论 1回复

阿兰那行 回复了问题 2022-05-17 19:37 物理: 问答从微观角度，如何解释物体产生的磁性？

$U = -\mathbf{m}\cdot\mathbf{B}\\ \mathbf{F} = \nabla(\mathbf{m}\cdot \mathbf{B})?w=100$

$\mathcal{H} = \sum_{ij} -J^F_{ij}(\mathbf{S}_i\cdot\mathbf{S}_j + \frac{1}{4}n_in_j) , \quad J_{ij}^F>0?w=100$

阿兰那行 : 本回答之后会更新更多细节，先提供一个框架和大图景。本回答分三个方面：为什么磁性物体表现宏观的磁力；量子层面上由于电子关联而涌现的磁性“序”；解释铁磁、顺磁、反铁磁之类通俗来讲，磁性其实应该理解为物质在磁场下的响应性质，而定量上这个响应由“磁化强度（磁矩）”“磁化率（响应函数）”来描述。磁化率先...; 赞同5 反对 1人感谢 0评论 4回复

林威 回复了问题 2022-05-23 01:20 天文黑洞: 问答事件视界望远镜（EHT）公布的银河系中心黑洞照片，和M87黑洞有什么区别？

林威 :以下回答总结于Core的描述：严格上说这并不能算是黑洞的照片，而是黑洞的事件视界附近的物质的照片。照片于黑洞本身更相关的信息是：阴影区域的大小，限制了黑洞事件视界的尺度。即便拍了黑洞照片，对于黑洞科普来说并没有加什么新料。这次发布，更有价值的事情，应该是EHT望远镜观测技术和数据到图像的处理过程。处...; 赞同0 反对 0人感谢 0评论 1回复

文章运动的分解为啥这样干？

“典例问答”栏目将不定期剖析典型问题，把最本质的方法与规律呈现给读者。欢迎大家关注“因物悦理”，我将持续分享高中物理的干货哟。问：如图，速度的分解为啥一定得这样干？相信读者不用想就能正确写出上图的速度分解的关系式：。不过我也确信总有人会疑惑...

高中物理 中学物理

赞同2  830浏览  0评论 music 2022-05-23 00:16

文章如何理解麦克斯韦方程中的不对称性

物理 麦克斯韦方程组

赞同1  960浏览  0评论 yubr 2022-05-23 00:01

文章科学哲学入门

我们准备探讨科学哲学的基础命题，世界观、真理、事实、推理、可证伪性以及工具主义和现实主义。（华南师范大学本科生）1 世界观世界观没有标准定义，但我们可以这样描述它：“世界观”是一个观点体系，其中不同观点如同拼图的一块块拼板一样相互联结。也就...

科学哲学

赞同1  904浏览  0评论 Xiey 2022-05-22 23:40

林威 回复了问题 2022-05-22 23:05 人工智能: 问答如何获得一个客服机器人？

林威 :如果是微信公众号的话，可以使用企业微信自带的企业微信客服功能。直接可以配置常用回复语。缺点在于是没有自动AI，如果客户问题超出知识库，就要转人工。具体效果可以看“悟理wuphys”公众号，用户服务-客服。如果是像野生旺财的AI效果，就比较复杂了。涉及软件和硬件，10个步骤以上。所以我建议大部分普通人...; 赞同0 反对 0人感谢 0评论 1回复

林威 回复了问题 2022-05-13 19:15 站务: 问答请问：网站的专栏和话题有什么不同？

林威 :其实，在悟理wuphys中，“专栏”和“话题”两个名词概念，和当前网络上通俗的概念是相同的。话题就相当于“标签”，每个问题、文章在发起时，都必须添加话题。话题可以是已经有的老话题，也可以由发起者自行添加新话题。回答是依附于问题的，因此回答不能添加话题。有了话题，每个问题或文章，就有了一个比较宽泛的标...; 赞同1 反对 0人感谢 0评论 1回复

林威 回复了问题 2022-05-20 00:06 流形 激发态 光化学: 问答如何通俗地理解分子激发态动力学中所谓的“流形”（manifold）

林威 : Manifold日语翻译：多样体。这是比较符合原意的。Mani-多，fold-折叠。中文译法为啥叫“流形”，当年的翻译者江泽涵老先生并没有给出明确答案。但我们也不能说这词很有逼格。见江泽涵，《我国数学名词的早期工作》，载《数学通报》，1980年，第12期，第23-24...; 赞同0 反对 0人感谢 0评论 2回复

文章简谐振动的运动学方程是怎么来的？

简谐振动是最简单最基本的振动，它的典型例子是弹簧振子。水平弹簧振子什么是弹簧振子呢？一个不考虑质量的弹簧连接一个有质量的小球或物块，然后把它沿着弹簧的方向压缩或者拉伸一定的距离（不要拉得太狠，悠着点儿）后松手，那么物块就会只在弹簧弹力的作用...

振动 牛顿力学

赞同3  807浏览  1评论 小熊君 2022-05-18 16:02

文章动能定理和机械能守恒定律到底该怎么用？

问：动能定理和机械能守恒定律到底该怎么用？从使用条件上来说，动能定理要比机械能守恒定律要广，无论物体受到什么力、运动过程有多么复杂，动能定理都可以使用。但是机械能守恒定律必须满足只有系统重力或者弹力做功这个条件时才能使用。所以从这个...

机械能守恒 中学物理

赞同3  824浏览  0评论 music 2022-05-18 15:08

文章中学生能理解最小作用量原理吗？

最小作用量原理被称为物理中的“第一性原理”，其地位可见一斑。我出于对物理规律普适性的向往，折腾了三个多月写出这篇三万七千字的长文，终于了却了自己的这个心愿。目录02 并不可怕的微积分04 初识变分06 横空出世的拉格朗日方程08 最小作...

拉格朗日函数 最速降线 理论力学 物理科普 最小作用量原理 中学物理

赞同2  716浏览  0评论 music 2022-05-18 14:38

文章普朗克尺度和普朗克时间

1. 引言1899年，德国物理学家、量子理论的开山鼻祖马克斯·普朗克 (Max Planck) 提出了一套特殊的单位制。他试图通过三个我们宇宙中的基本物理学常数：光速，约化普朗克常数和牛顿引力常数来构建长度、时间、质量、能量等基本...

量子力学 物理

赞同4  936浏览  0评论 yubr 2022-05-18 00:26

文章统计物理的基本思想

统计物理的基本思想作者 | yubr2. 经典统计在统计物理中，我们常用的系综有三类：微正则系综，正则系综和巨正则系综，下面分别加以介绍。 2.1 微正则系综（）微正则系综是最简单的系综，它所包含的系统是孤立系统，且具有确定...

统计物理

赞同0  787浏览  0评论 yubr 2022-05-17 23:36

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CONNECT:[ UseTime:0.000420s ] mysql:host=127.0.0.1;port=3306;dbname=wuphysthink;charset=utf8mb4
SHOW FULL COLUMNS FROM `aws_hook_plugins` [ RunTime:0.000542s ]
SELECT `hook`,`plugins` FROM `aws_hook_plugins` WHERE `status` = 1 ORDER BY `sort` DESC [ RunTime:0.000301s ]
SHOW FULL COLUMNS FROM `aws_config` [ RunTime:0.000524s ]
SELECT * FROM `aws_config` [ RunTime:0.000408s ]
SHOW FULL COLUMNS FROM `aws_forbidden_ip` [ RunTime:0.000459s ]
SELECT `ip` FROM `aws_forbidden_ip` [ RunTime:0.000166s ]
SHOW FULL COLUMNS FROM `aws_admin_group` [ RunTime:0.000390s ]
SELECT `permission` FROM `aws_admin_group` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000244s ]
SHOW FULL COLUMNS FROM `aws_users_online` [ RunTime:0.000428s ]
DELETE FROM `aws_users_online` WHERE `last_login_time` < 1746284813 [ RunTime:0.004187s ]
SHOW FULL COLUMNS FROM `aws_menu_rule` [ RunTime:0.000546s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'nav' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000381s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'footer' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000372s ]
SHOW FULL COLUMNS FROM `aws_links` [ RunTime:0.000529s ]
SELECT * FROM `aws_links` WHERE `status` = 1 [ RunTime:0.000313s ]
SHOW FULL COLUMNS FROM `aws_post_relation` [ RunTime:0.000561s ]
SELECT COUNT(*) AS think_count FROM `aws_post_relation` WHERE `status` = 1 AND `item_type` IN ('question','article','') LIMIT 1 [ RunTime:0.000432s ]
SELECT `id`,`item_id`,`item_type`,`uid` FROM `aws_post_relation` WHERE `status` = 1 AND `item_type` IN ('question','article','') ORDER BY `set_top_time` DESC,`update_time` DESC,`create_time` DESC LIMIT 75,15 [ RunTime:0.000492s ]
SHOW FULL COLUMNS FROM `aws_question` [ RunTime:0.000603s ]
SELECT `last_answer` FROM `aws_question` WHERE `id` IN (9,1,5,2,6,8) AND `status` = 1 [ RunTime:0.000374s ]
SHOW FULL COLUMNS FROM `aws_answer` [ RunTime:0.000550s ]
SELECT * FROM `aws_answer` WHERE `status` = 1 AND `id` IN (6,10,11,5,9,12) [ RunTime:0.000619s ]
SHOW FULL COLUMNS FROM `aws_topic_relation` [ RunTime:0.000487s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (9,1,5,2,6,8) AND `item_type` = 'question' [ RunTime:0.000452s ]
SHOW FULL COLUMNS FROM `aws_topic` [ RunTime:0.000532s ]
SELECT * FROM `aws_topic` WHERE `id` IN (2,8,24,25,5,47,48,49) [ RunTime:0.000408s ]
SELECT * FROM `aws_question` WHERE `status` = 1 AND `id` IN (9,1,5,2,6,8) [ RunTime:0.000656s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (35,34,33,32,31,29,28,27,26) AND `item_type` = 'article' [ RunTime:0.000710s ]
SELECT * FROM `aws_topic` WHERE `id` IN (36,41,26,42,23,43,44,45,46,40,27,2,29,20,50,51,52) [ RunTime:0.000659s ]
SHOW FULL COLUMNS FROM `aws_article` [ RunTime:0.000767s ]
SELECT * FROM `aws_article` WHERE `status` = 1 AND `id` IN (35,34,33,32,31,29,28,27,26) [ RunTime:0.014906s ]
SHOW FULL COLUMNS FROM `aws_users` [ RunTime:0.002603s ]
SELECT `uid`,`nick_name`,`user_name`,`salt`,`email`,`mobile`,`sex`,`is_first_login`,`inbox_unread`,`notify_unread`,`fans_count`,`friend_count`,`available_invite_count`,`is_valid_email`,`is_valid_mobile`,`integral`,`reputation`,`reputation_update_time`,`avatar`,`signature`,`verified`,`group_id`,`integral_group_id`,`reputation_group_id`,`last_login_time`,`last_login_ip`,`reg_ip`,`money`,`frozen_money`,`deal_password`,`birthday`,`url_token`,`views_count`,`agree_count`,`question_count`,`answer_count`,`article_count`,`draft_count`,`topic_focus_count`,`column_count`,`extend`,`status`,`theme`,`create_time`,`update_time` FROM `aws_users` WHERE `status` = 1 AND `uid` IN (55,42,1,65,6,2,46,12,10,33,35) [ RunTime:0.000558s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000288s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000226s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 2 LIMIT 1 [ RunTime:0.000215s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 2 LIMIT 1 [ RunTime:0.000195s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 6 LIMIT 1 [ RunTime:0.000210s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 6 LIMIT 1 [ RunTime:0.000189s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 10 LIMIT 1 [ RunTime:0.000213s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 10 LIMIT 1 [ RunTime:0.000221s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000211s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000194s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 33 LIMIT 1 [ RunTime:0.000196s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 33 LIMIT 1 [ RunTime:0.000225s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000208s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000225s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000246s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000203s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 46 LIMIT 1 [ RunTime:0.000215s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 46 LIMIT 1 [ RunTime:0.000208s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000252s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000193s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000226s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000197s ]
SHOW FULL COLUMNS FROM `aws_article_vote` [ RunTime:0.000440s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 35 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000296s ]
SHOW FULL COLUMNS FROM `aws_question_vote` [ RunTime:0.000389s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 12 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000272s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 9 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000242s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 6 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000232s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 1 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000240s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 11 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000230s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 5 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000237s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 34 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000251s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 33 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000297s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 32 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000274s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 10 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000240s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 2 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000229s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 5 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000234s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 6 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000229s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 9 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000255s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 8 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000231s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 31 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000255s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 29 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000259s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 28 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000311s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 27 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000265s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 26 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000262s ]
SHOW FULL COLUMNS FROM `aws_announce` [ RunTime:0.000484s ]
SELECT * FROM `aws_announce` WHERE `status` = 1 ORDER BY `set_top_time` DESC,`sort` DESC LIMIT 0,3 [ RunTime:0.000295s ]
SELECT COUNT(*) AS think_count FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 LIMIT 1 [ RunTime:0.000370s ]
SELECT * FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 ORDER BY RAND(),`top` DESC,`focus` DESC,`discuss_month` DESC LIMIT 0,5 [ RunTime:0.000678s ]
SHOW FULL COLUMNS FROM `aws_topic_focus` [ RunTime:0.000388s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 65 LIMIT 1 [ RunTime:0.000244s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 11 LIMIT 1 [ RunTime:0.000225s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 23 LIMIT 1 [ RunTime:0.000231s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 82 LIMIT 1 [ RunTime:0.000212s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 64 LIMIT 1 [ RunTime:0.000211s ]
SHOW FULL COLUMNS FROM `aws_column` [ RunTime:0.000442s ]
SELECT * FROM `aws_column` WHERE `verify` = 1 ORDER BY RAND(),`view_count` DESC LIMIT 0,5 [ RunTime:0.000417s ]
SELECT * FROM `aws_users` WHERE `uid` <> 0 AND `status` = 1 AND `reputation` > 0 ORDER BY RAND(),`reputation` DESC,`answer_count` DESC LIMIT 5 [ RunTime:0.000987s ]
SHOW FULL COLUMNS FROM `aws_users_follow` [ RunTime:0.000405s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 12 LIMIT 1 [ RunTime:0.000233s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 33 LIMIT 1 [ RunTime:0.000217s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 1 LIMIT 1 [ RunTime:0.000209s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000204s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 90 LIMIT 1 [ RunTime:0.000217s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 87 LIMIT 1 [ RunTime:0.000218s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 87 LIMIT 1 [ RunTime:0.000204s ]

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