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密度函数理论和杜比宁方程可以用来研究活性炭纤维在多段充填过程中的吸附行为。
密度函数理论是一种分子统计力学理论，它建立在分子统计学和热力学的基础上，用来研究一种系统中分子的分布。
杜比宁方程是一种描述分子吸附行为的方程，它可以用来计算吸附层的厚度、吸附速率和吸附能量等参数。
在研究活性炭纤维多段充填过程中，可以使用密度函数理论和杜比宁方程来研究纤维表面的分子结构和吸附行为。
通过分析密度函数和杜比宁方程的解，可以得出纤维表面的分子结构以及纤维吸附的分子的种类、数量和能量。
这些信息有助于更好地理解活性炭纤维的多段充填机理。
在研究活性炭纤维的多段充填机理时，还可以使用其他理论和方法来帮助我们更好地了解这一过程。
例如，可以使用扫描电子显微镜(SEM)和透射电子显微镜(TEM)等技术来观察纤维表面的形貌和结构。
可以使用X射线衍射(XRD)和傅里叶变换红外光谱(FTIR)等技术来确定纤维表面的化学成分和结构。
还可以使用氮气吸附(BET)和旋转氧吸附(BJH)等技术来测量纤维表面的比表面积和孔结构。
通过综合运用密度函数理论、杜比宁方程和其他理论和方法，可以更全面地了解活性炭纤维的多段充填机理，从而更好地控制和优化多段充填的过程。
在研究活性炭纤维多段充填机理时，还可以使用温度敏感性测试方法来研究充填过程中纤维表面的动力学性质。
例如，可以使用动态氧吸附(DAC)或旋转杆氧吸附(ROTA)等技术来测量温度对纤维表面吸附性能的影响。
通过对比不同温度下纤维表面的吸附性能，可以更好地了解充填过程中纤维表面的动力学性质。
此外，还可以使用分子动力学模拟方法来研究纤维表面的吸附行为。
例如，可以使用拉曼光谱或红外光谱等技术来测量纤维表面的分子吸附构型。
然后，使用分子动力学模拟方法来模拟不同分子吸附构型下的纤维表面的动力学性质，帮助我们更好地了解活性炭纤维的多段充填机理。
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分子动力学中的非平衡态研究分子动力学是一种运用计算机模拟系统的方法，研究分子尺度上的物理运动规律的学科。
通过分子动力学模拟，可以更好地解释和预测分子的行为，有助于发展新型材料和探索新的生物医学领域。
然而，通常情况下分子在非平衡态下的运动规律并不容易研究。
非平衡态通常是指分子系统处于一个不稳定或动态变化的状态，例如外部施加强制、化学反应、热力学不平衡等等，这些不同的场景也会在不同的尺度上展示出不同的行为。
为了更好地研究分子在非平衡态下的运动规律，有学者针对不同场景提出了不同的分子动力学模拟方法。
以下将介绍几种常见的方法。
1. 基于广义热力学的非平衡分子动力学 (NAMD)非平衡分子动力学 (NAMD)，是一种基于广义热力学的非平衡分子动力学方法，由 John Eastwood 和 Peter Winn 于 2013 年首次提出并发表，旨在模拟非平衡状态下的分子运动。
该方法在传统分子动力学基础上加入了一些广义热力学理论，可以更准确地模拟能量交换，从而更好地研究分子在非平衡态下的行为。
2. 最大熵方法最大熵方法是另一种常见的非平衡态研究方法，起源于热力学中的最大熵原理。
该方法旨在从分子系统的部分坐标或其他限制条件中推导出整个分子系统的热力学性质，从而更好地描述非平衡态下的分子运动。
最大熵方法可用于模拟混合物、高粘度溶液和生物体系等复杂环境的非平衡态动力学行为。
在遇到高耗散能力或复杂协同机制的情况时，最大熵方法往往比传统方法更加准确。
3. 非平衡态界面动力学 (NIDS)非平衡态界面动力学 (NIDS) 是用于模拟非平衡态界面的分子动力学模拟方法。
在NIDS方法中，模拟系统通常包括两个或更多不同的相，例如气/液界面、液/液界面等等。
该方法可以模拟各种不同类型的非平衡态现象，如张力、相互作用能等，为化学、环境和物理领域中的大量系统提供了一种基本的分子动力学模拟方法。
总之，非平衡态分子动力学是一个快速发展的领域，其应用范围十分广泛。
自演化分子动力学蒙特卡罗方法自演化分子动力学蒙特卡罗方法（Self-Evolving Molecular Dynamics Monte Carlo，简称SEMDMC）是一种用于模拟复杂多体系统的计算方法。
该方法结合了分子动力学（MD）和蒙特卡罗（MC）方法的优势，能够在较低的计算成本下获得更准确的模拟结果。
一、SEMDMC方法的基本原理SEMDMC方法的基本原理是将模拟系统分为两部分：演化部分和非演化部分。
演化部分由一组有限数量的粒子组成，这些粒子相互作用并遵循牛顿运动定律。
非演化部分由系统的其余部分组成，被视为静态背景。
在模拟过程中，演化部分的粒子会根据牛顿运动定律进行运动。
同时，会使用MC方法对非演化部分进行采样。
通过不断迭代演化部分和非演化部分，可以获得系统的完整配置空间信息。
二、SEMDMC方法的优势SEMDMC方法具有以下优势：1．能够模拟复杂多体系统：SEMDMC方法可以模拟包含大量粒子的复杂系统，例如生物大分子、材料等。
2．计算效率高：SEMDMC方法结合了MD和MC方法的优势，在较低的计算成本下获得更准确的模拟结果。
3．具有良好的可扩展性：SEMDMC方法可以并行化，从而提高计算效率。
三、SEMDMC方法的应用SEMDMC方法已被广泛应用于材料科学、生物物理、化学等领域。
例如，SEMDMC方法已被用于模拟蛋白质折叠、纳米材料的结构和性能等。
四、以下是一些SEMDMC方法的应用实例：1．模拟蛋白质折叠：SEMDMC方法已被用于模拟蛋白质折叠过程。
通过模拟，可以获得蛋白质折叠的自由能景观，从而了解蛋白质折叠的机制。
2．模拟纳米材料的结构和性能：SEMDMC方法已被用于模拟纳米材料的结构和性能。
通过模拟，可以获得纳米材料的原子结构、电子结构、力学性能等信息。
五、总结SEMDMC方法是一种用于模拟复杂多体系统的计算方法。
该方法具有计算效率高、可扩展性好等优势，已被广泛应用于材料科学、生物物理、化学等领域。
Tomas MikolovGoogle Inc.Mountain View mikolov@Ilya SutskeverGoogle Inc.Mountain Viewilyasu@Kai ChenGoogle Inc.Mountain Viewkai@Greg CorradoGoogle Inc.Mountain View gcorrado@Jeffrey DeanGoogle Inc.Mountain View jeff@AbstractThe recently introduced continuous Skip-gram model is an efficient method forlearning high-quality distributed vector representations that capture a large num-ber of precise syntactic and semantic word relationships.In this paper we presentseveral extensions that improve both the quality of the vectors and the trainingspeed.By subsampling of the frequent words we obtain significant speedup andalso learn more regular word representations.We also describe a simple alterna-tive to the hierarchical softmax called negative sampling.An inherent limitation of word representations is their indifference to word orderand their inability to represent idiomatic phrases.For example,the meanings of“Canada”and“Air”cannot be easily combined to obtain“Air Canada”.Motivatedby this example,we present a simple method forfinding phrases in text,and showthat learning good vector representations for millions of phrases is possible.1IntroductionDistributed representations of words in a vector space help learning algorithms to achieve better performance in natural language processing tasks by grouping similar words.One of the earliest use of word representations dates back to1986due to Rumelhart,Hinton,and Williams[13].This idea has since been applied to statistical language modeling with considerable success[1].The follow up work includes applications to automatic speech recognition and machine translation[14,7],and a wide range of NLP tasks[2,20,15,3,18,19,9].Recently,Mikolov et al.[8]introduced the Skip-gram model,an efficient method for learning high-quality vector representations of words from large amounts of unstructured text data.Unlike most of the previously used neural network architectures for learning word vectors,training of the Skip-gram model(see Figure1)does not involve dense matrix multiplications.This makes the training extremely efficient:an optimized single-machine implementation can train on more than100billion words in one day.The word representations computed using neural networks are very interesting because the learned vectors explicitly encode many linguistic regularities and patterns.Somewhat surprisingly,many of these patterns can be represented as linear translations.For example,the result of a vector calcula-tion vec(“Madrid”)-vec(“Spain”)+vec(“France”)is closer to vec(“Paris”)than to any other word vector[9,8].Figure1:The Skip-gram vector representations that are good at predictingIn this paper we We show that sub-sampling of frequent(around2x-10x),and improves accuracy of we present a simpli-fied variant of Noise model that results in faster training and better vector representations for frequent words,compared to more complex hierarchical softmax that was used in the prior work[8].Word representations are limited by their inability to represent idiomatic phrases that are not com-positions of the individual words.For example,“Boston Globe”is a newspaper,and so it is not a natural combination of the meanings of“Boston”and“Globe”.Therefore,using vectors to repre-sent the whole phrases makes the Skip-gram model considerably more expressive.Other techniques that aim to represent meaning of sentences by composing the word vectors,such as the recursive autoencoders[15],would also benefit from using phrase vectors instead of the word vectors.The extension from word based to phrase based models is relatively simple.First we identify a large number of phrases using a data-driven approach,and then we treat the phrases as individual tokens during the training.To evaluate the quality of the phrase vectors,we developed a test set of analogi-cal reasoning tasks that contains both words and phrases.A typical analogy pair from our test set is “Montreal”:“Montreal Canadiens”::“Toronto”:“Toronto Maple Leafs”.It is considered to have been answered correctly if the nearest representation to vec(“Montreal Canadiens”)-vec(“Montreal”)+ vec(“Toronto”)is vec(“Toronto Maple Leafs”).Finally,we describe another interesting property of the Skip-gram model.We found that simple vector addition can often produce meaningful results.For example,vec(“Russia”)+vec(“river”)is close to vec(“V olga River”),and vec(“Germany”)+vec(“capital”)is close to vec(“Berlin”).This compositionality suggests that a non-obvious degree of language understanding can be obtained by using basic mathematical operations on the word vector representations.2The Skip-gram ModelThe training objective of the Skip-gram model is tofind word representations that are useful for predicting the surrounding words in a sentence or a document.More formally,given a sequence of training words w1,w2,w3,...,w T,the objective of the Skip-gram model is to maximize the average log probability1training time.The basic Skip-gram formulation defines p(w t+j|w t)using the softmax function:exp v′w O⊤v w Ip(w O|w I)=-2-1.5-1-0.5 0 0.511.5 2-2-1.5-1-0.5 0 0.5 1 1.5 2Country and Capital Vectors Projected by PCAChinaJapanFranceRussiaGermanyItalySpainGreece TurkeyBeijingParis Tokyo PolandMoscow Portugal Berlin Rome Athens MadridAnkara Warsaw LisbonFigure 2:Two-dimensional PCA projection of the 1000-dimensional Skip-gram vectors of countries and their capital cities.The figure illustrates ability of the model to automatically organize concepts and learn implicitly the relationships between them,as during the training we did not provide any supervised information about what a capital city means.which is used to replace every log P (w O |w I )term in the Skip-gram objective.Thus the task is to distinguish the target word w O from draws from the noise distribution P n (w )using logistic regres-sion,where there are k negative samples for each data sample.Our experiments indicate that values of k in the range 5–20are useful for small training datasets,while for large datasets the k can be as small as 2–5.The main difference between the Negative sampling and NCE is that NCE needs both samples and the numerical probabilities of the noise distribution,while Negative sampling uses only samples.And while NCE approximately maximizes the log probability of the softmax,this property is not important for our application.Both NCE and NEG have the noise distribution P n (w )as a free parameter.We investigated a number of choices for P n (w )and found that the unigram distribution U (w )raised to the 3/4rd power (i.e.,U (w )3/4/Z )outperformed significantly the unigram and the uniform distributions,for both NCE and NEG on every task we tried including language modeling (not reported here).2.3Subsampling of Frequent WordsIn very large corpora,the most frequent words can easily occur hundreds of millions of times (e.g.,“in”,“the”,and “a”).Such words usually provide less information value than the rare words.For example,while the Skip-gram model benefits from observing the co-occurrences of “France”and “Paris”,it benefits much less from observing the frequent co-occurrences of “France”and “the”,as nearly every word co-occurs frequently within a sentence with “the”.This idea can also be applied in the opposite direction;the vector representations of frequent words do not change significantly after training on several million examples.To counter the imbalance between the rare and frequent words,we used a simple subsampling ap-proach:each word w i in the training set is discarded with probability computed by the formulaP (w i )=1− f (w i )(5)Method Syntactic[%]Semantic[%]NEG-563549761 HS-Huffman53403853NEG-561583661 HS-Huffman5259/p/word2vec/source/browse/trunk/questions-words.txtNewspapersNHL TeamsNBA TeamsAirlinesCompany executives.(6)count(w i)×count(w j)Theδis used as a discounting coefficient and prevents too many phrases consisting of very infre-quent words to be formed.The bigrams with score above the chosen threshold are then used as phrases.Typically,we run2-4passes over the training data with decreasing threshold value,allow-ing longer phrases that consists of several words to be formed.We evaluate the quality of the phrase representations using a new analogical reasoning task that involves phrases.Table2shows examples of thefive categories of analogies used in this task.This dataset is publicly available on the web2.4.1Phrase Skip-Gram ResultsStarting with the same news data as in the previous experiments,wefirst constructed the phrase based training corpus and then we trained several Skip-gram models using different hyper-parameters.As before,we used vector dimensionality300and context size5.This setting already achieves good performance on the phrase dataset,and allowed us to quickly compare the Negative Sampling and the Hierarchical Softmax,both with and without subsampling of the frequent tokens. The results are summarized in Table3.The results show that while Negative Sampling achieves a respectable accuracy even with k=5, using k=15achieves considerably better performance.Surprisingly,while we found the Hierar-chical Softmax to achieve lower performance when trained without subsampling,it became the best performing method when we downsampled the frequent words.This shows that the subsampling can result in faster training and can also improve accuracy,at least in some cases.Dimensionality10−5subsampling[%]30027NEG-152730047Table3:Accuracies of the Skip-gram models on the phrase analogy dataset.The models were trained on approximately one billion words from the news dataset.HS with10−5subsamplingLingsugurGreat Rift ValleyRebbeca NaomiRuegenchess grandmasterVietnam+capital Russian+riverkoruna airline Lufthansa Juliette Binoche Check crown carrier Lufthansa Vanessa Paradis Polish zoltyflag carrier Lufthansa Charlotte Gainsbourg CTK Lufthansa Cecile De Table5:Vector compositionality using element-wise addition.Four closest tokens to the sum of two vectors are shown,using the best Skip-gram model.To maximize the accuracy on the phrase analogy task,we increased the amount of the training data by using a dataset with about33billion words.We used the hierarchical softmax,dimensionality of1000,and the entire sentence for the context.This resulted in a model that reached an accuracy of72%.We achieved lower accuracy66%when we reduced the size of the training dataset to6B words,which suggests that the large amount of the training data is crucial.To gain further insight into how different the representations learned by different models are,we did inspect manually the nearest neighbours of infrequent phrases using various models.In Table4,we show a sample of such comparison.Consistently with the previous results,it seems that the best representations of phrases are learned by a model with the hierarchical softmax and subsampling. 5Additive CompositionalityWe demonstrated that the word and phrase representations learned by the Skip-gram model exhibit a linear structure that makes it possible to perform precise analogical reasoning using simple vector arithmetics.Interestingly,we found that the Skip-gram representations exhibit another kind of linear structure that makes it possible to meaningfully combine words by an element-wise addition of their vector representations.This phenomenon is illustrated in Table5.The additive property of the vectors can be explained by inspecting the training objective.The word vectors are in a linear relationship with the inputs to the softmax nonlinearity.As the word vectors are trained to predict the surrounding words in the sentence,the vectors can be seen as representing the distribution of the context in which a word appears.These values are related logarithmically to the probabilities computed by the output layer,so the sum of two word vectors is related to the product of the two context distributions.The product works here as the AND function:words that are assigned high probabilities by both word vectors will have high probability,and the other words will have low probability.Thus,if“V olga River”appears frequently in the same sentence together with the words“Russian”and“river”,the sum of these two word vectors will result in such a feature vector that is close to the vector of“V olga River”.6Comparison to Published Word RepresentationsMany authors who previously worked on the neural network based representations of words have published their resulting models for further use and comparison:amongst the most well known au-thors are Collobert and Weston[2],Turian et al.[17],and Mnih and Hinton[10].We downloaded their word vectors from the web3.Mikolov et al.[8]have already evaluated these word representa-tions on the word analogy task,where the Skip-gram models achieved the best performance with a huge margin.Model Redmond ninjutsu capitulate (training time)Collobert(50d)conyers reiki abdicate (2months)lubbock kohona accedekeene karate rearmJewell gunfireArzu emotionOvitz impunityMnih(100d)Podhurst-Mavericks (7days)Harlang-planning Agarwal-hesitatedVaclav Havel spray paintpresident Vaclav Havel grafittiVelvet Revolution taggers/p/word2vecReferences[1]Yoshua Bengio,R´e jean Ducharme,Pascal Vincent,and Christian Janvin.A neural probabilistic languagemodel.The Journal of Machine Learning Research,3:1137–1155,2003.[2]Ronan Collobert and Jason Weston.A unified architecture for natural language processing:deep neu-ral networks with multitask learning.In Proceedings of the25th international conference on Machine learning,pages160–167.ACM,2008.[3]Xavier Glorot,Antoine Bordes,and Yoshua Bengio.Domain adaptation for large-scale sentiment classi-fication:A deep learning approach.In ICML,513–520,2011.[4]Michael U Gutmann and Aapo Hyv¨a rinen.Noise-contrastive estimation of unnormalized statistical mod-els,with applications to natural image statistics.The Journal of Machine Learning Research,13:307–361, 2012.[5]Tomas Mikolov,Stefan Kombrink,Lukas Burget,Jan Cernocky,and Sanjeev Khudanpur.Extensions ofrecurrent neural network language model.In Acoustics,Speech and Signal Processing(ICASSP),2011 IEEE International Conference on,pages5528–5531.IEEE,2011.[6]Tomas Mikolov,Anoop Deoras,Daniel Povey,Lukas Burget and Jan Cernocky.Strategies for TrainingLarge Scale Neural Network Language Models.In Proc.Automatic Speech Recognition and Understand-ing,2011.[7]Tomas Mikolov.Statistical Language Models Based on Neural Networks.PhD thesis,PhD Thesis,BrnoUniversity of Technology,2012.[8]Tomas Mikolov,Kai Chen,Greg Corrado,and Jeffrey Dean.Efficient estimation of word representationsin vector space.ICLR Workshop,2013.[9]Tomas Mikolov,Wen-tau Yih and Geoffrey Zweig.Linguistic Regularities in Continuous Space WordRepresentations.In Proceedings of NAACL HLT,2013.[10]Andriy Mnih and Geoffrey E Hinton.A scalable hierarchical distributed language model.Advances inneural information processing systems,21:1081–1088,2009.[11]Andriy Mnih and Yee Whye Teh.A fast and simple algorithm for training neural probabilistic languagemodels.arXiv preprint arXiv:1206.6426,2012.[12]Frederic Morin and Yoshua Bengio.Hierarchical probabilistic neural network language model.In Pro-ceedings of the international workshop on artificial intelligence and statistics,pages246–252,2005. [13]David E Rumelhart,Geoffrey E Hintont,and Ronald J Williams.Learning representations by back-propagating errors.Nature,323(6088):533–536,1986.[14]Holger Schwenk.Continuous space language puter Speech and Language,vol.21,2007.[15]Richard Socher,Cliff C.Lin,Andrew Y.Ng,and Christopher D.Manning.Parsing natural scenes andnatural language with recursive neural networks.In Proceedings of the26th International Conference on Machine Learning(ICML),volume2,2011.[16]Richard Socher,Brody Huval,Christopher D.Manning,and Andrew Y.Ng.Semantic CompositionalityThrough Recursive Matrix-Vector Spaces.In Proceedings of the2012Conference on Empirical Methods in Natural Language Processing(EMNLP),2012.[17]Joseph Turian,Lev Ratinov,and Yoshua Bengio.Word representations:a simple and general method forsemi-supervised learning.In Proceedings of the48th Annual Meeting of the Association for Computa-tional Linguistics,pages384–394.Association for Computational Linguistics,2010.[18]Peter D.Turney and Patrick Pantel.From frequency to meaning:Vector space models of semantics.InJournal of Artificial Intelligence Research,37:141-188,2010.[19]Peter D.Turney.Distributional semantics beyond words:Supervised learning of analogy and paraphrase.In Transactions of the Association for Computational Linguistics(TACL),353–366,2013.[20]Jason Weston,Samy Bengio,and Nicolas Usunier.Wsabie:Scaling up to large vocabulary image annota-tion.In Proceedings of the Twenty-Second international joint conference on Artificial Intelligence-Volume Volume Three,pages2764–2770.AAAI Press,2011.。
Maxwell-Chern-Simons模型拓扑解的存在性的开题报告1. 摘要Maxwell-Chern-Simons（MCS）模型是一种描述电磁波和规范场相互作用的场论模型。
该模型有许多有趣的数学性质，包括非平庸拓扑解的存在性。
本文将探讨MCS模型拓扑解的存在性问题，并针对该问题提出一些研究思路和方法。
2. 研究背景和意义MCS模型在凝聚态物理、高能物理和数学物理等领域有广泛的应用。
该模型可以用来描述拓扑绝缘体、拓扑序等物理现象，也可以用来研究拓扑场论的数学性质。
在这些研究中，拓扑解的存在性是一个关键问题。
拓扑解是指场论模型中的一类非平庸解，具有拓扑结构的性质。
例如，这类解可以被表示为曲率形式，也可以建立在拓扑内的不变量上。
拓扑解在物理学和数学中都有广泛的应用，它们可以解释许多复杂的物理现象和几何现象。
在MCS模型中，拓扑解是指具有非零拓扑荷的局域化解。
这些解可以被认为是拓扑缺陷或拓扑激发。
它们具有有趣的性质，并且在拓扑序和凝聚态物理中有广泛的应用。
目前，对于MCS模型拓扑解的存在性问题仍存在许多挑战。
本文将尝试探讨这一问题，并提出一些可能的研究思路和方法。
3. 研究内容和方法在本文中，我们将从以下几个方面研究MCS模型拓扑解的存在性问题：（1）理论分析。
我们将从场论的角度出发，探讨MCS模型的基本性质和数学结构。
通过理论推导，我们可以研究MCS模型中拓扑解的物理和数学性质，并探寻拓扑解的存在性条件。
（2）数值模拟。
我们将借助数值模拟的方法探究MCS模型中的拓扑解。
通过数值模拟，我们可以生成MCS模型的非平庸解，并分析它们的拓扑荷和局域性质。
（3）掺杂材料的制备和实验研究。
我们将尝试通过掺杂材料的制备和实验测量，验证MCS模型的拓扑解。
通过实验数据的分析，我们可以研究MCS模型中拓扑解的影响和性质。
4. 预期结果我们预期将会得到以下结果：（1）理论推导MCS模型拓扑解的存在性条件，并分析拓扑解的拓扑荷和局域性质。
