A PARTON MODEL FOR DIFFRACTIVE PROCESSES IN DEEP INELASTIC SCATTERING
- 格式:pdf
- 大小:120.24 KB
- 文档页数:11
英文回答:The stabilization of proliferation processes is an important task for modelling and studying the proliferation of substances under different conditions. The process includes three key steps of preparation, modelling and analysis of results. Preparatory work is needed to determine the nature of the substance, the nature of the medium and the time and spatial scope of the simulation. Modelling is done usingputer simulation methods to obtain numerical simulations of the diffusion process and to produce relevant proliferation patterns and distribution maps. An in—depth analysis of the simulation results,parison of proliferation patterns under different conditions, assessment of proliferation stability and trends, and an important reference for further research routes and policies. This work is important for better understanding and understanding of patterns of proliferation behaviour and for promoting development in related areas.稳定扩散流程是一项用于模拟和研究物质在不同条件下扩散行为的重要工作。
diffusion model简书(中英文实用版)Title: A Brief Introduction to Diffusion Models标题:扩散模型简述Diffusion models have gained immense popularity in the field of machine learning, particularly in the generation of images, text, and audio.扩散模型在机器学习领域变得非常流行,尤其是在图像、文本和音频的生成方面。
The core concept of diffusion models lies in simulating the process of data distribution evolving from a noisy state to a clean, high-quality state.扩散模型的核心概念是模拟数据分布从噪声状态演变为干净、高质量状态的过程。
These models are trained to reverse this process, effectively generating new, high-quality data from random noise.这些模型被训练来逆转这一过程,有效地从随机噪声生成新的、高质量的数据。
One of the key advantages of diffusion models is their ability to generate data with high fidelity and diversity, making them highly suitable for various applications such as image synthesis, text generation, and audio processing.扩散模型的一大优势是它们能够生成高保真度和多样性的数据,使它们非常适合各种应用,如图像合成、文本生成和音频处理。
variational diffusion models详解Variational Diffusion Models (VDMs) are a class of generative models that are used for modeling images and videos. VDMs are based on the concept of diffusion processes and leverage variational inference techniques to learn the underlying probability distribution of the data.Here is a detailed explanation of variational diffusion models:1. Diffusion Processes:Diffusion processes model the evolution of probability distributions over time. It starts with an initial distribution and gradually transforms it into the desired target distribution through a series of diffusion steps. Each diffusion step introduces a small amount of noise into the current distribution, pushing it closer to the target distribution. Diffusion processes are commonly used in physics and other fields to describe the spread of particles or heat.2. Generative Modeling:VDMs use diffusion processes for generative modeling of images and videos. Instead of directly modeling the target distribution, VDMs learn a series of diffusion steps that transform a simple initial distribution, suchas a Gaussian distribution, into the target distribution. By iteratively applying these diffusion steps, VDMs generate samples from the target distribution.3. Variational Inference:VDMs employ variational inference techniques to learn the diffusion steps. Variational inference is a framework for approximating complex probability distributions by optimizing a lower bound on the log-likelihood of the data. In VDMs, the diffusion steps are represented by a neural network, known as the diffusion model or encoder. The encoder takes an input sample and performs a series of transformations to generate a latent representation.4. Reverse Diffusion:During training, VDMs use a reverse diffusion process to estimate the likelihood of the data. This involves starting from a sample drawn from the target distribution and iteratively applying reverse diffusion steps to recover the initial distribution. The goal is to maximize the likelihood of the data under the reverse diffusion process, which indirectly maximizes the likelihood under the forward diffusion process.5. Applications:VDMs have found applications in various areas, including image and video generation, denoising, inpainting, and super-resolution. By learning the underlying probability distribution of the data, VDMs can generate high-quality samples and perform tasks like image interpolation and manipulation.In summary, variational diffusion models combine diffusion processes and variational inference to learn the underlying probability distribution of images or videos. By iteratively applying diffusion steps, VDMs generate samples from the target distribution and can be used for various generative modeling tasks.If you have any further questions, feel free to ask!。
1、Chapter 11.1 What is Software Engineering? Software engineering is the application of engineering principles and techniques to the development, operation, and maintenance of software systems. It is a discipline that involves the application of scientific and mathematical principles to the design, development, and maintenance of software products. Software engineering focuses on the development of efficient, reliable, and maintainable software systems thatmeet the needs of their users.1.2 What is the Software Life Cycle? The software life cycle is the set of stages that a software product goes through from its conception to its retirement. It typically consists of the following stages: Requirements Analysis, Design, Implementation, Testing, Deployment, Maintenance, and Retirement. Requirements Analysis involves gathering information from stakeholders and users to determine the needs of the software. Design involves creating a plan for the software thatmeets the requirements identified during Requirements Analysis. Implementation involves coding the software according to the plan created during Design. Testing involves verifying that the software works as expected. Deployment involves making the software available to its users. Maintenance involves making changes to the software to fix any bugs or to add new features. Retirement involves removing the software from use and archiving any important data or documents associated with it.1.3 What is the Difference Between Software Engineering and Computer Science?Software engineering and computer science are related disciplines, but they are not the same. Software engineering focuses on the development of software products, while computer science focuses on the study of computers and computing. Software engineering involves the design, development, and maintenance of software systems, while computer science involves the study of algorithms, data structures, and programming languages. Softwareengineering focuses on the practical application of engineering principles and techniques to the development of software products, while computer science focuses on the theoretical aspects of computing.2、Chapter 22.1 What is the System Development Life Cycle?The system development life cycle (SDLC) is a process used by software engineers to develop software products. The SDLC consists of six stages: planning, analysis, design, implementation, testing, andmaintenance. During the planning stage, the software engineer collects information from stakeholders and users to determine the scope and requirements of the software product. During the analysis stage, the software engineer analyzes the gathered information to determine the user’s needs and the software’s requirements. During the design stage, the software engineer creates a plan for the software product. During the implementation stage, the software engineer codes the software according to the plan created during the design stage. During thetesting stage, the software engineer verifies that the software works as expected. During the maintenance stage, the software engineer makes changes to the software to fix any bugs or to add new features.2.2 What is the Waterfall Model?The waterfall model is a software development process that follows a linear approach. It is a sequential process where each stage must be completed before the next stage can begin. The stages of the waterfall model are: requirements analysis, design,implementation, testing, deployment, and maintenance. During the requirements analysis stage, the software engineer collects information from stakeholders and users to determine the scope and requirements of the software product. During the design stage, the software engineer creates a plan for the software product. During the implementation stage, the software engineer codes the software according to the plan created during the design stage. During the testing stage, the software engineer verifies that the software works as expected. During thedeployment stage, the software engineer makes the software available to its users. During the maintenance stage, the software engineer makes changes to the software to fix any bugs or to add new features.2.3 What is the Spiral Model?The spiral model is a software development process that follows a cyclical approach. It is an iterative process where each stage is repeated multiple times until the desired result is achieved. The stages of the spiral model are: requirements analysis, design,implementation, testing, deployment, and maintenance. During the requirements analysis stage, the software engineer collects information from stakeholders and users to determine the scope and requirements of the software product. During the design stage, the software engineer creates a plan for the software product. During the implementation stage, the software engineer codes the software according to the plan created during the design stage. During the testing stage, the software engineer verifies that the software works as expected. During the软件工程第四版齐治昌课后答案deployment stage, the software engineer makes the software available to its users. During the maintenance stage, the software engineer makes changes to the software to fix any bugs or to add new features. The spiral model allows the software engineer to quickly make changes and adjustments to the software product as needed.。
2025年全国大学英语CET四级考试模拟试卷及答案指导一、写作(15分)Writing (30 points)Part A (10 points)Directions: For this part, you are allowed 30 minutes to write an essay on the topic “The Impact of Technology on Education”. You should write at least 120 words and base your essay on the outline given below:1.Briefly describe the role of technology in modern education.2.Discuss the positive effects of technology on education.3.Present some challenges faced by technology in education.4.Give your own opinion on how to effectively integrate technology into education.Example:The Impact of Technology on EducationIn the 21st century, technology has become an indispensable part of our lives, and its influence on education is no exception. Technology has transformed the way we learn and teach, bringing both benefits and challenges.Firstly, technology has significantly enhanced the role of education. Withthe advent of the internet, students can access a vast amount of information from all over the world, which broadens their horizons and deepens their understanding of various subjects. Moreover, educational technology tools, such as online learning platforms, virtual classrooms, and interactive software, have made learning more engaging and personalized.The positive effects of technology on education are numerous. For one, it allows for flexibility in learning, as students can study at their own pace and schedule. Additionally, technology can help students with special needs, such as those with disabilities, by providing customized learning materials and resources.However, technology in education also poses challenges. One major concern is the digital divide, where students from low-income families may not have access to the necessary technology. Another challenge is the potential for technology to distract students from their studies, leading to decreased focus and productivity.In my opinion, to effectively integrate technology into education, schools should ensure that all students have equal access to technology resources. Moreover, teachers should be trained to use technology appropriately to enhance learning outcomes. Additionally, parents and students should be educated on the responsible use of technology to avoid its negative consequences.Part B (20 points)Directions: For this part, you are allowed 30 minutes to write a letter.Suppose you are Zhang Wei, a student of English at a university. You have just won a scholarship to study in the UK for one year. Write a letter to your friend Li Hua, who is planning to apply for the same scholarship. In your letter, you should:1.Congratulate Li Hua on his success in the application.2.Share your experiences and advice for applying for the scholarship.3.Express your hopes for Li Hua’s success in the future.Example:Dear Li Hua,I hope this letter finds you well. I am writing to share some exciting news with you. I have just won a scholarship to study in the UK for one year, and I couldn’t be more thrilled!I want to start by congratulating you on your success in the application process. It’s fantastic to see that you have achieved such a commendable goal.I am sure that your hard work and dedication have paid off.Now, I would like to share some of my experiences and advice for applying for the scholarship. Firstly, it’s essential to thoroughly research the scholarship program and ensure that your application meets all the requirements. Secondly, make sure to highlight your achievements, skills, and experiences that are relevant to the scholarship. Thirdly, be prepared for the interview process, as it is often a crucial step in securing the scholarship.I am confident that you will do exceptionally well in your application. Yourpassion for learning and your determination to excel make you a perfect candidate for this opportunity. I hope that you will follow in my footsteps and achieve great success.Lastly, I wish you all the best in your future endeavors. I am looking forward to hearing about your success story soon.Best regards,Zhang Wei二、听力理解-短篇新闻(选择题,共7分)第一题新闻内容:A new study conducted by the National Institute of Health has found that regular exercise can significantly improve the cognitive function of elderly individuals. The study involved 1,500 participants aged 60 or over, who were divided into two groups. The first group was asked to engage in at least 30 minutes of moderate-intensity aerobic exercise, such as walking or cycling, three times a week. The second group was asked to maintain their current lifestyle with no additional exercise. After one year, the study found that the group participating in regular exercise showed a 30% improvement in their cognitive scores, compared to the group that did not exercise.The researcher, Dr. John Smith, explained that the improvement was particularly noticeable in areas such as memory and problem-solving skills. Headded that the benefits were consistent regardless of the type of exercise performed, as long as the participants adhered to a regular routine.题目:1、What was the main finding of the study conducted by the National Institute of Health?A)Regular exercise can improve the cognitive function of elderly individuals.B)Walking and cycling have different effects on cognitive function.C)The benefits of regular exercise are only seen in people under 60.答案:1、A) Regular exercise can improve the cognitive function of elderly individuals.第二题News Item OneThe popular cartoon character, Tom and Jerry, might soon become a major player in the movie industry. According to a recent report, a new live-action film adaptation of the classic cartoon series is in the works. The movie is expected to be a blend of animated and live-action sequences, with well-known actors set to voice the iconic characters. The producers announced that they have s ecured a major deal with a top Hollywood studio to finance the film’s production. The film is scheduled for release in the fall of 2023.Questions:1、Who will voice the iconic characters in the upcoming live-action film adaptation of Tom and Jerry?A) Unknown actorsB) Well-known actorsC) Famous singersD) Rising stars2、What will the new live-action Tom and Jerry film be a blend of?A) Live-action and animated sequencesB) entirely live-action sequencesC) entirely animated sequencesD) live-action and silent sequences3、When is the movie set for release?A) winter of 2023B) summer of 2023C) fall of 2023D) spring of 2024Answers:1.B2.A3.C三、听力理解-长对话(选择题,共8分)第一题听力原文:M: Hi, Linda, how was your vacation in Beijing?W: It was fantastic! I visited the Forbidden City, the Great Wall, and the Summer Palace. The architecture was amazing.M: Really? I’ve heard the Great Wall is a must-see. Did you go there?W: Yes, I did. It was quite an experience. The wall is so long and the scenery along the way is stunning.M: Did you take any photos?W: Of course. I took a lot of photos, but the best one was the view of the wall from a distance.M: That sounds great. I hope to visit Beijing one day. It’s such a historic city.W: You sh ould definitely go. It’s a place you won’t forget.选择题:1、What is the main topic of the conversation?A) The woman’s vacation in BeijingB) The woman’s favorite place in BeijingC) The man’s plan to visit BeijingD) The architecture of Beijing2、Which place did the woman visit first during her vacation?A) The Forbidden CityB) The Great WallC) The Summer PalaceD) The man’s house3、How did the woman feel about the Great Wall?A) She was boredB) She was disappointedC) She was amazedD) She was afraid4、W hat does the woman suggest about the man’s plan to visit Beijing?A) He should wait until next yearB) He should bring a cameraC) He should go on a guided tourD) He should not expect it to be as memorable as the woman’s trip答案:1、A2、A3、C4、D第二题Directions:In this section, you will hear six dialogues. Each dialogue will be spoken only once. After each dialogue, you will be asked a question about what was said. The dialogues and questions will be spoken two times. Choose the best answer from the four choices marked A, B, C and D.DialogueWoman: Hi, Tom. Do you like the new restaurant we went to last night? Man: Yes, I do. The food was great and the atmosphere was perfect. Woman: Did you see the girl at the corner table with long curly hair? Man: Yes, I did. She was very attractive, wasn’t she?Woman: Yes, what a nice dress she was wearing!Man: And I think her date was a bit rough around the edges.Woman: Poor guy. I heard he works in IT, but he seems to have a rough disposition. Man: Hey, what time is it? I have to catch the last train back to our college. Woman: It’s a quarter to ten. We have plenty of time, don’t worry.Questions1、What activity were they discussing?A、A new store opening in the area.B、A movie they watched together.C、A meal they had at a restaurant.D、A book they read recently.2、What can we learn about the girl from the dialogue?A、She came with a friend who had a difficult personality.B、She arrived late and missed the train.C、She worked in IT.D、She preferred to sit at the corner table.3、What is the man’s concern?A、They need to finish their homework.B、They have limited time to meet their friends.C、They need to get back to their college.D、They need to buy something for a party.4、What does the woman imply about the man?A、He has a strong will.B、He is quite friendly.C、He is a bit rushed.D、He is considerate.Answers1、C、2、A、3、C、4、C、四、听力理解-听力篇章(选择题,共20分)第一题Title: The Story of the Great Wall of ChinaIntroduction:The Great Wall of China is one of the most remarkable architectural achievements in human history. Stretching over 21,196 kilometers, it was built to protect the Chinese empire from invasions. Its construction began over 2,200 years agoand was completed over a period of several centuries.Text:In the 7th century B.C., warlords built the initial wall to safeguard their kingdoms. However, it was Emperor Qin Shi Huang who initiated the expansion of the wall into the grand structure it is today. Over two million workers, including soldiers, convicts, and local people, contributed to its construction. The wall is made up of bricks, tamped earth, and wood, depending on the region. It is equipped with watchtowers, camps, and signal stations to allow for communication and quick military response.Despite its defensive purpose, the Great Wall has also been a symbol of strength and unity for China. Over the centuries, it has faced numerous challenges, including natural erosion, human vandalism, and relentless weathering by wind and rain.Questions:1、What is the primary purpose of the Great Wall of China?A. It served as a toll road.B. It was constructed for military protection.C. It was built as a monument to the emperor.D. It served as a trade corridor.2、Who initiated the expansion of the wall into the grand structure it is today?A. The warlords of the 7th centuryB.C.B. Emperor Qin Shi HuangC. Local peopleD. Soldiers3、According to the passage, what material primary composed the Great Wall?A. StoneB. Brick, tamped earth, and woodC. Iron and steelD. Wood and leatherAnswers:1、B. It was constructed for military protection.2、B. Emperor Qin Shi Huang3、B. Brick, tamped earth, and wood第二题Passage OneYou probably know that the Great Wall of China is the most famous ancient architectural wonder in the world. It is also one of the longest man-made structures ever built. The Great Wall was built over a period of more than 2,000 years. It was originally constructed to protect the Chinese Empire from invasions by various nomadic groups from the north.The construction of the Great Wall began in the 7th century BC, during the Warring States period. It was mainly built of earth and stone. Over time, different dynasties added their own sections to the wall, which resulted in thevarious styles and designs we see today.1、What was the primary purpose of building the Great Wall?A) To serve as a tourist attraction.B) To protect the Chinese Empire from invasions.C) To expand the territory of the Chinese Empire.D) To store food and water for the soldiers.2、When did the construction of the Great Wall begin?A) During the Han Dynasty.B) During the Warring States period.C) During the Tang Dynasty.D) During the Qing Dynasty.3、What materials were mainly used in the construction of the Great Wall?A) Iron and wood.B) Marble and glass.C) Earth and stone.D) Concrete and steel.Answers:1、B) To protect the Chinese Empire from invasions.2、B) During the Warring States period.3、C) Earth and stone.第三题Listening Comprehension - PassagePassage: During the early years of World War II, a British civilian, named John Smith, found himself stationed in a British base in the Middle East. He was assigned to a group tasked with providing support to soldiers. One day, he heard about an opportunity to provide intelligence support to Allied forces by secretly gathering and delivering intelligence to allied bases. Initially, John was skeptical about the proposal, but when he learned that the information could significantly impact the war effort, he decided to take a risk. John was given a cipher machine and instructed to deliver intelligence to a nearby allied camp located in a remote area. The camp was known to be under constant surveillance, making the mission dangerous. Despite the risks, John felt a strong sense of duty and embarked on his mission.1、Why did John Smith initially hesitate to take the opportunity to provide intelligence support?A)He was unsure about the safety of the mission.B)He thought the information was not useful.C)He was concerned about the complexity of the cipher machine.D)He was skeptical about the proposal.Answer: D2、What was the primary motivation for John Smith to accept the mission?A)He wanted to prove his bravery.B)He thought it would bring him fame.C)He was afraid of being assigned to a menial task.D)He felt a strong sense of duty.Answer: D3、What made John Smith’s mission to the allied camp particularly dangerous?A)The remote location of the camp.B)The constant surveillance of the camp.C)The high level of security at the British base.D)The complexity of the cipher machine.Answer: B五、阅读理解-词汇理解(填空题,共5分)第一题Reading PassageThe modern office environment is a product of the Industrial Revolution. With the advent of machines, employees were no longer required to perform manual labor. They were now expected to multitask, communicating with colleagues, managing emails, and using a variety of technologies. This shift in the nature of work required employees to develop new skills and adapt to a more dynamic work environment. As a result, companies began to emphasize the importance of education and training for their employees. Today, the office environment is characterized by the presence of diverse technology, increasing workloads, and the need for continuous professional development.Vocabulary Understanding1、The shift in the nature of work required employees to_________to a moredynamic work environment.a.adhere tob.adapt2、The Industrial Revolution led to the_________of machines, which changed the way employees worked.a.manifestationb.development3、Employees in the modern office environment are expected to_________multiple tasks, such as communicating and using technology.a.reflectb.multitask4、One of the reasons companies began to emphasize education and training is because they wanted their employees to_________the new skills required in the modern work environment.a.acquireb.maintain5、The office environment today is characterized by the presenceof_________technology, diverse workloads, and the need for professional development.a.variedb.advanced第二题The following passage is followed by some questions or unfinished statements, each with four suggested answers. Choose the one that fits best according tothe passage.The Internet has become an integral part of our daily lives. From shopping and banking to communication and entertainment, we rely on it for a variety of purposes. However, along with its benefits, the Internet also brings along some challenges that we need to be aware of.1、( ) 1. The word “integral” in the first se ntence can be best replaced by:a) indispensableb) occasionalc) occasionald) occasional2、( ) 2. The phrase “a variety of purposes” in the second sentence can be replaced by:a) many different usesb) limited usesc) common usesd) single use3、( ) 3. T he word “challenges” in the second paragraph can be defined as:a) opportunitiesb) problemsc) benefitsd) solutions4、( ) 4. The sentence “However, along with its benefits, the Internet also brings along some challenges” suggests that:a) the Internet has no negative aspectsb) the Internet is purely beneficialc) the Internet has both positive and negative aspectsd) the Internet is a source of frustration5、( ) 5. The word “aware” in the last sentence can be best replaced by:a) knowledgeableb) indifferentc) unawared) uninterestedAnswers:1、a) indispensable2、a) many different uses3、b) problems4、c) the Internet has both positive and negative aspects5、a) knowledgeable六、阅读理解-长篇阅读(选择题,共10分)First QuestionReading PassageMachine Learning: Tackling the Big Data DilemmaWith the rapid growth of data generation due to the increasing use of smartphones, the Internet of Things (IoT), and social media, industries face a major challenge in managing and analyzing this Big Data. Traditional data processing methods are no longer sufficient to handle the sheer volume of data being generated. Machine learning (ML) provides a solution by allowing computers to learn from data without explicit programming, enabling them to make predictions, recognize patterns, and improve their performance over time.One of the most prevalent applications of ML is in recommendation systems, used by social media platforms and e-commerce websites to suggest content or products to users. This system analyzes user behavior and preferences, then recommends items that might be of interest. Another application is in healthcare, where ML can be used to predict patient outcomes and identify potential health issues before they become serious.However, ML also has its challenges. One of the major issues is the need for large amounts of high-quality data, which can be time-consuming and expensive to gather. Additionally, ML models are often opaque, making it difficult for users to understand how their data is being used and what insights are being extracted from it. Ethical concerns also arise, such as the potential for biased predictions based on flawed or biased training data.1、Which of the following is the main idea of the passage?1、The role and challenges of machine learning in data analysis2、The importance of data quality in machine learning3、The ethical concerns surrounding machine learning4、The applications of machine learning in various industriesAnswer: 1、2、What is one of the major challenges of using machine learning in data analysis?2、The need for high-quality data3、Lack of transparency in the decision-making process4、Ethical concerns5、The cost of data storageAnswer: 2、3、Which application of machine learning is mentioned in the passage?3、Recommendation systems4、Image recognition5、Fraud detection6、Speech recognitionAnswer: 3、4、What is a potential problem with machine learning models as described in the passage?4、They require large amounts of data5、They are difficult to develop6、They are too transparent7、They are ineffective in large datasetsAnswer: 4、5、What does the passage suggest as a key challenge for using machine learning in healthcare?5、The need to predict patient outcomes6、The potential for biased predictions7、The difficulty in gathering patient data8、The complexity of healthcare dataAnswer: 6第二题Many factors contribute to the high rate of childhood obesity in the United States. One significant factor is the environment in which children live and grow. This passage discusses various aspects of the environment that contribute to childhood obesity and proposes some solutions.Structured neighborhoods without sidewalks, playgrounds, or safe routes to school discourage physical activity and increase the likelihood of obesity. Children spend more time sitting in front of screens, playing video games or watching television, rather than engaging in active play. Access to fast food restaurants is abundant, making it easy for families to choose high-calorie, low-nutrition m eals. Finally, parental involvement in children’s activities has decreased, leading to a lack of guidance and监督 in healthy lifestyles.Solutions to address childhood obesity involve a multi-faceted approach.For example, communities could redesign their neighborhoods to include more parks and playgrounds, sidewalks, and safe walking routes to schools. School districts could promote physical education and after-school sports programs to encourage children to be active. Additionally, parents can be involved in creating healthy eating environments by planning family meals, setting a healthy menu, and limiting screen time.Reading the passage, answer the questions below:1、What is one of the factors contributing to childhood obesity according to the passage?A、Lack of physical activityB、Excessive screen timeC、Parental involvementD、High-calorie fast food2、How does the environment in which children live contribute to obesity?A、It encourages physical activity and leads to healthier lifestyles.B、It discourages physical activity and increases the likelihood of obesity.C、It provides access to healthy food and exercise facilities.D、It promotes healthy eating and physical exercise through community programs.3、What is one solution proposed to address childhood obesity?A、Designing neighborhoods with more parks and playgrounds.B、Reducing the number of fast food restaurants.C、Increasing parental involvement in children’s activities.D、Strengthening physical education programs in schools.4、What is the author’s view on the role of parents in their children’s healthy lifestyles?A、Parents have no influence on their children’s lifestyle choices.B、Parents should strictly regulate their children’s screen time.C、Parents play a crucial role in creating and maintaining a healthy home environment.D、Parents should prioritize physical education over other extracurricular activities.5、Which of the following statements is NOT mentioned in the passage as a factor contributing to childhood obesity?A、Lack of physical activityB、Increased screen timeC、Healthy school meal programsD、Reduced parental involvementAnswer Key:1、A2、B3、A4、C5、C七、阅读理解-仔细阅读(选择题,共20分)第一题Reading Passage 1Questions 1 to 5 are based on the following passage.In the United States, the four-year college degree is the most common form of higher education. However, in recent years, there has been a growing interest in alternative forms of higher education. One of these alternatives is the two-year community college, which provides a less expensive and more flexible option for students.Community colleges offer a variety of courses, from basic academic subjects to vocational training. Many students choose to attend community colleges because they are less expensive than four-year institutions. Additionally, community colleges often have more flexible schedules, which allow students to work or take care of family responsibilities while pursuing their education.Despite the benefits of community colleges, there are some challenges associated with them. One of the main challenges is the lack of resources compared to four-year colleges. For example, community colleges may have fewer faculty members, smaller libraries, and less advanced technology. This can make it difficult for students to receive the level of education they desire.Another challenge is the perception that community colleges are less prestigious than four-year colleges. This perception can make it difficult for students to transfer to four-year institutions after completing their two-yearprograms. However, many community colleges have agreements with four-year colleges that allow students to transfer easily and continue their education.The following questions are based on the above passage.1、What is the main topic of the passage?A. The importance of a four-year college degreeB. The growing interest in alternative forms of higher educationC. The challenges faced by students attending community collegesD. The benefits of attending a community college2、Why do many students choose to attend community colleges?A. They offer advanced technologyB. They provide a less expensive and more flexible optionC. They have prestigious faculty membersD. They have larger libraries3、Which of the following is a challenge associated with community colleges?A. They have more faculty members than four-year collegesB. They offer vocational trainingC. They have fewer resources than four-year collegesD. They have more flexible schedules4、What is one way community colleges are trying to overcome the perception of being less prestigious?A. They are increasing their tuition feesB. They are improving their technologyC. They are entering into agreements with four-year collegesD. They are offering more academic courses5、What can be inferred about the future of community colleges from the passage?A. They will become more expensive and less flexibleB. They will become less common and more prestigiousC. They will continue to grow in popularity and importanceD. They will merge with four-year collegesAnswers:1、B2、B3、C4、C5、C第二题PassageThe world of technology is rapidly evolving, and artificial intelligence (AI) is at the forefront of this change. AI has a wide range of applications in different fields, including healthcare, finance, manufacturing, and transportation. One of the most significant areas of AI development is natural language processing (NLP), which allows machines to understand and process human language in a more sophisticated and nuanced way. This has led to the creationof virtual assistants, chatbots, and language translators that can assist businesses and individuals in diverse ways. However, with the rapid development of AI, concerns about ethics and privacy have also risen.1、Which of the following fields is NOT mentioned as an application area of AI in the passage?A、HealthcareB、FinanceC、ManufacturingD、EducationAnswer: D2、What does NLP allow machines to do?A、Understand and process human language in a sophisticated and nuanced way.B、Create visual images.C、Perform physical tasks.D、Drive autonomous vehicles.Answer: A3、What kind of assistance can virtual assistants and chatbots provide?A、Technical support for computer problems.B、Assistance in diverse ways for businesses and individuals.C、Financial management.D、Medical diagnosis.Answer: B。
a rXiv:c ond-ma t/978100v114Aug1997A Growth Model for Porous Sedimentary Rocks Sujata Tarafdar and Shashwati Roy 1Condensed Matter Physics Research Centre Physics Department Jadavpur University Calcutta-700032,INDIA.Abstract A growth model for porous sedimentary rocks is proposed,using a simple com-puter simulation algorithm.We generate the structure by ballistic deposition of particles with a bimodal size distribution.Porosity and specific surface area are calculated varying the proportion of small and larger particles.Permeability and it’s variation with porosity are studied.The fractal nature of the pore space is also discussed.PACS Nos –61.43.Bn,91.65.+p,47.55.Mh,47.53.+n1IntroductionStudy of natural growth processes through models and computer simulation is useful and instructive.Successful computer models give an insight into how a simple sequence of steps governed by stochastic or other algorithms may generate a structure with very specific characteristics.The computer generated system can then be used to study other properties of interest.A striking example is the diffusion limited aggregation or DLA model.DLA and it’s variation-the diffusion limited cluster-cluster aggregation(DLCA)can be used to generate patterns resembling growth of colloidal aggregates,bacterial colonies,corals,dielectric breakdown and many similar systems[1].Anotherfield where such growth models have been applied is the formation of rough surfaces [2].An area where such studies are lacking is the formation process of porous sed-imentary rocks.The study of sedimentary rocks is a very importantfield due to application in oil exploration,ground waterflow problems,spread of pollutants and other such cases.The structure of sedimentary rocks show certain character-istic features which make them distinct from other porous materials-such as foams or aerogel[3].However,there is still no simple model which simulates the growth process of sedimentary rocks.The present work is an attempt in this direction.We use a simple ballistic deposition model on a square or cubic lattice with a bimodal particle size distri-bution.This generates a realistic rock structure with porosity varying according to the particle size distribution.The paper is organised as follows;in the next section we briefly discuss the principal characteristics of sedimentary rock structure.In section3our model is presented and the details of the computer simulation are given in section4.In the5th section we present the results of our study andfinally discuss the success and drawbacks of our approach.2Sedimentary rocks:Structure and properties The sedimentary rocks originate from accumulation of small grains of sand or clay often together with organic material[4,5].Sedimentation takes place through the action of wind or water,and leads to a highly porous(50-80%)unconsolidated agglomerate.The sedimentation process is followed by compaction and diagenesis causing the unconsolidated mass to become a consolidated rock byflow of pore fillingfluids accompanied by cementation,dissolution and other chemical pro-cesses.The resulting secondary porosity is usually less,but sometimes greater than the primary porosity.Sedimentary rocks are divided into classes such as sandstones or limstones depending upon their composition.Our model has been developed with the sand-stone structure in mind,however,it is quite general.The principal characteristics2of sedimentary rocks are as follows;1.The solid phase and pore phase are both connected. 2.Porosities are usually in the range(5-25%).3.Many studies re-port a fractal structure of the pore phase[3].Adsorption studies report that the pore-solid interface is fractal,but this method gives no information whether the system is a volume fractal as well.But several scattering experiments indicate that the pore space is a volume fractal. 4.the electrical conductivity of brine filled porous sedimentary rocks and their permeability are found to follow two well known emperical laws,referred to as respectively Archie’s law and Darcy’s law[6].Archie’s law isσ∝σ0.φm eff(1) Hereσis the effective conductivity of the electrolytefilled rock,σ0is the con-ductivity of the electrolyte,m is a constant called the cementation exponent. Usually m has values between1.3and4.0.For consolidated sandstones the value lies between1.8and2.0.Normallyφeff means porosity of the connected pore space,i.e.excluding the isolated pores,however some authors give it a more restricted definition.The permeability is defined by Darcy’s lawJ=(K/µ)∇P(2) Here J is the volumetricflow rate,K the permeability,µthe viscosity of thefluid flowing through the porous medium and∇P the pressure gradient.The permeability depends not only on the porosity,but also on other details of the pore structure[7].Obviously,while a rock with no porosity will have zero permeability,two samples with same porosity may have very different perme-abilities.Other relevant parameters characterising the permeability have been suggested as-the specific surface area,tortuosity and connectedness of the pore space.Definitions of the last two quantities are not very clear.It is expected that a realistic model of a sedimentary rock will give a satisfac-tory description of the above properties.3The ModelOur work has two objectives–the proposed model should simulate the process of rock formation in a realistic way,and thefinal structure formed should be representative of a natural sedimentary rock.The model has been developed in both two and three dimensional versions on a squre and cubic lattice respectively with unit spacing.Sand particles are dropped onto a substrate from a definite height from a random horizontal position.If all particles are squares of unit size(or cubes in3dimension),obviously the whole space isfilled up after a sufficient number of particles are allowed to deposit.The upper boundary may be highly uneven.If however,the particles to be deposited3include a fraction of particles of size larger than unity,we get a structure with voids left randomly.The rough upper boundary is cut off.Wefind that a fraction F∼0.01of larger particles can generate a significant porosity(about8%),and the porosity increases with F.For F=1,we get the maximum porosity permissible for a specific size and shape of the larger particle. The variation in porosity with F gives a quite good logarithmicfit.Let us discuss the two dimensional systemfirst.For the larger sized particle we tried out squares of dimension2×2and alternatively rectangles of dimension 2×1with qualitatively similar results.Finally we confined our attention to the elongated larger grain version only,because real sand grains are reported to be ellipsoidal with the long axis approximately twice the shortest[5,4].The random structure generated is shown in thefigures1(a)-(c).We show three different porosity ranges for three values of F.In the3-dimensional version we choose X-Y plane horizontal,and the Z-axis to be vertical.The smaller grains are cubes of unit side,and the larger are rods with dimension2×1×1.Here the larger particles are allowed to settle ballistically with long axis parallel to either X-or Y-axis,with equal probability.A modified version allowing preferred orientation is also being tried.This simple model simulates the action of gravity through vertical ballistic deposition.For the present we have not included the effects of drift or diffusion in the horizontal direction but this may be introduced in future work.We have studied the following features of the porous structure generated:-1.The variation of average porosity with F(the fraction of large particles).and the variation of porosity with sample size for a particular F.2.The specific surface area of the pore-solid interface.3.The fractal nature of the pore space generated and Archie’s law.4.The permeability variation with porosity and specific surface area has beencalculated using the Kozeny relation[8].In the following section we give details of the computer simulation and the results obtained.4Computer SimulationIn our work the two-dimensional system has been generated upto size600×600 and the three dimensional upto150×150×150.Wefirst generate a linear(or square for three-dimensions)array of side N x which is solid i.e.all sites are occupied.An uneven layer is generated on top of this,byfilling up certain sites randomly,other being left vacant.These two layers constitute the substrate.4Now the growth process by deposition starts.The site for deposition is chosen randomly at a height N z above the substrate(N z=N x+10).The particle to be dropped is of size I(small)or II(elongated)with a probability1−F or F. Whether the particle is of size I or II is decided by a random number generator. The particle descends as long as the sites immediately below it are empty.It stops on encountering afilled site.Then the next particle drops.the process is continued until a square(or cube)of side N x is saturated,i.e.the porosity does not change further on adding more particles.The structure generated in two-dimension is shown infigs1(a-c).We repeat the whole process for a large number of times N av.We have averaged over200-500 runs in two and50-100runs in three dimension.4.1Porosity and Fractal NatureAfter generating the system of the largest possible size,the average porosity is calculated as(the number of pores)/(total number of sites)in boxes of gradually increasing size.A typical porosity variation with size is shown infigure2,here F is con-stant.A constant porosity indicates a homogenous structure without any fractal characteristics.Wefind however,that the porosityfirst stabilises to an almost constant value for N x∼200in two and N x∼100in three dimensions.But for still larger sizes there is a slow but definite decrease in porosity.This shows that though the structure is homogenous for small sizes a fractality appears above a certain cutoffscale.This effect is more prominent for low porosities(i.e.small F).Our boxes are always smaller than N x to eliminate any end effects in the structure generated.In the subsequent discussion P means the constant value of the porosity obtained,before it starts to fall.We have estimated the fractal dimension using the relationM(N)∼N d f(3) Here M is the number of pores in a box of size N and d f is the fractal dimension of pore space.Wefind d f≥1.99in two and2.99in three dimensions initially but it deviates towards d f≈1.90in two and2.89in three dimensions as system size increases.The value of d f is lower for low porosities.Due to limited availability of computer facility we have not yet been able to generate larger sizes so as to give a converging value of the fractal dimension.Porosity variation with F is shown infigures3in three dimension.The curve obtained gives a good logarithmicfit.The maximum value of P(for F=1) is0.50in two and0.63in three dimensions.Figure-4shows logM(N)plotted against logN for F=0.005.54.2Specific Surface AreaPore dependent Properties of porous rocks depend not only on porosity but also on other chacteristics of the pore structure,the easiest to calculate is the specific surface area–the interface area per unit mass(or volume).We have calculated S–the average pore-solid interface area per unit volume, in the structure generated.S plays a crucial role in permeability of the rock.The variation of S with P from our model is shown in Figure5.As expected Sfirst increases with P upto P≈0.6,after that the pores become so large that many of the vacant sites do not contribute to the interface and S decreases.To get an idea of the connectivity of the pore structure we calculate I=S/P this gives the average number of interfaces exposed per each pore site.For completely isolated pores the maximum value I can have is4in two and6in three dimension. I≤4is a necessary but not sufficient condition for connectedness in three dimen-sion.We have calculated I only in three-dimension andfind that I remains close to3,even for porosities near4%.This indicates a high connectivity of the pore space.The variation of I with P is shown infigure-6.At P≈0.2%I approaches 6,so pores definitely become isolated.The very sharp fall in I between P=14% to P=6%seems to indicate that the connectivity threshold is in this region,but this must be verified.5Results and DiscussionWe now discuss the results obtained and their relevance to the features of rock structures discussed earlier.P for a given F is taken as the constant value obtained for intermediate sizes(200in two and100in three dimensions).In two dimension the maximum porosity for F=1is0.50.This is the per-colation threshold for a square lattice in the random percolation(RP)problem [9].It is instructive to compare our model with RP.Here we have ensured the connectivity of the solid phase through our growth algorithm and obviously it is not possible to have both the pore and solid phases connected in two dimen-sions.But the diagrams generated in two dimensionfigs1show that a high degree of connectivity in pore space is present for large F,particularly in the vertical direction,i.e.pores are not isolated.There is an anisotropy in the struc-ture generated in our model with pores elongated in the vertical direction.This shows up more clearly in the low porosity case.There is in fact some evidence of pores having higher aspect ratio in case of low porosity[10].There is also evidence of anisotropy of sedimentary rock structures,though there appears to be no systematic study[11].The three dimensional structure our model generates,cannot be shown in a two-dimensionalfigure,and it is not possible to see the connectivity directly.We have plans to make a complete study of the threshold porosity for connectedness and the pore size distribution.The percolation threshold for RP in three dimen-6sions is found to be P c≈25−30%,and for porosities in the range P c to(1−P c) both pore and solid phases are connected.it will be of interest to see whether we get a connected pore space here for lower porosities.Real rock structures are seen to be connected for very small porosities,in fact some authors speak of a zero percolation threshold[3].At present we have calculated the porosity,specific surface area and permeabilty with interesting results.5.1PermeabilityThe permeability is an important property of a porous rock.It depends in a complicated manner on the structure of the pore space.P and S may be consid-ered as the simplest parameters characterizing a pore space.To our knowledge no exact theory connecting the permeability with P and S or any other such parameter exists,for the case of such complicated multiply connected pore space as in our model.We may however get a qualitative idea of permeability(K)behavior using the oversimplified Kozeny relation[8]which gives K asK∼P3/S2(4) In the case of a pore space consisting of a bundle of unconnected tubes.Usually application of the Kozeny relation considers P and S as separate independently varying parameters.In our model,however,they are related both being obtained simultaneously as a function of F.We omit the tortuosity factor appearing in Kozeny relation as a proportion-ality constant and consider only relative values of K for different F and plot it as a function of P.The results are shown infigure-7.Wefind a very good exponentialfit.This implies thatlog(K)∝PA large body of data for real rocks do show such a variation[5].For sandstones from different sources log(K)vs porosity shows on the average a quite clear linear variation.There is of course a considerable spread in the data for real rocks.This may indicate that even in the case of such a complicated pore space,the Kozeny picture is not a very bad approximation as far as averageflow properties are concerned.In determination of K the values of S and P play more crucial roles than the connectivity,which is missing in Kozeny relation.5.2ConductivityIt has been shown that Archie’s law(eq1)connecting the conductivity of brine-filled rocks with their porosity is valid for fractal pore spaces[12,13,14].Though7we have not been able to conclusively demonstrate the fractal nature of the pore space generated by our model,we can make some conjectures from the results we have obtained.For a fractal pore space,the cementation exponent depends on d f–the fractal dimension of the pore space and d w–the dimension of a random walk through the pore space as followsm=1+(2−d w)/(d f−d)(5) For d f close to3in three dimension,say2.85–2.90as indicated by our simulation we may assume a value of d w slightly larger than2,say2.1–2.2.With these values we get a range of m as1.66to3,which is very realistic.However,this results should be substantiated by an exact determination of d w.Work on this problem is in progress.In comparison to[12]and[14],where the rock is modelled as a deterministic fractal,the present model is more realistic being a statistical model.6Conclusions and Directions for Future Work Let us review how far our growth model represents actual formation of sandstones. Thefirst simplification is the assumption of cubic grains.In sanstones the grains do in fact have somewhat angular form[4],so this assumption is not worse than the more usual approximation of spherical grains.A consequence of the grains being cubic in our model is that the intergrain contact areas are large andflat, whereas the sandstones are reported to have tangential point contact between grains.This,however may take care partially of the compaction after deposition in our model,which we have otherwise ignored.We have not considered the effect of restructuring of the pore space,after de-position through diagenesis.This may be taken up in future work.The elongated structure of the larger grains,which we have assumed,is realistic as mentioned earlier.We have also checked that squareflat grains produce a higher porosity than P max in our3-dimensional model.One point to note is that the porosity we have calculated from our model is the total pore space per unit volume,not the effective porosity,which only considers the connected pore space.Calculation of the effective porosity is much more complicated,and we assume for the present that since the pore space is substantially connected the difference is not too much.In Archie’s law,some authors use the total porosity,and others the effective porosity.Our calculation of pore space may also be modified by taking second nearest neighbor pores as connected.This would give a picture of pores connected by narow throats as modelled by some authors[15].The structure produced by our simulation algorithm has an anisotropy in the vertical direction.Pores are seen to elongated in the vertical direction,specially8for low porosities.We could notfind any systematic data on anisotropy of pore structure in real rocks,but it is expected that due to the action of gravity an anisotropy should be present.The permeability data of some rocks show a marked anisotropy[7],which indicates anisotropy in the pore structure.The Kozeny the-ory does not take anisotropy into account since porosity and specific surface area are independent of direction.Experimental data shows the hprizontal conduc-tivity to be larger than the vertical in most cases,but the opposite trend is also seen sometimes.In our model,connectivity appears to be larger in the vertical direction,inclu-sion of diagenesis in some form may increase the horizontal connectivity through flow offluids.Further modifications of this model are possible by including a horizontal drift or diffusion to simulate the effect of wind or water currents on the sedimentation process,in addition to the effect of gravity.Comparing our model with the ballistic deposition model for surface growth [2],we note that our model introduces correlation between the adjacent growing columns,through incorporation of the larger sized particle.In conclusion,we think the present model is a convenient starting point for study of the growth and structure of sedimentary rocks through simulation.Suit-able modifications and further study of certain aspects of the present model are necessary,some of this work is already in progress.7AcknowledgementS Roy is grateful to the State Govt.,West Bengal forfinancial assistance.9References[1]T.Vicsek,Fractal Growth Phenomena,(World Scientific,Singapore),1992.[2]A Barabasi and H.E.Stanley,Fractal Concepts in Surface Growth,(WorldScientific,Singapore),1992.[3]M.Sahimi,Rev.Mod.Phys.,65,1393,1993.[4]F.J.Pettijohn,Sedimentary Rocks(CBS Publ.,Delhi),1984.[5]G.V.Chillingarian,Compactional Diaganesis,pg.57,in Sediment Diagene-sis,ed.A.Parker and B.W.Sellwood,NATO ASI series C:115,(D.Reidel p.,Dordrecht),1981.[6]P.Wong,Physics Today,24,December1988.[7]A.Scheidegger,The Physics of Flow Through Porous Media,(University ofToronto Press,Toronto),1974.[8]J.Kozeny,S.-Ber,Wiener Akad.Abst.,IIa,136,271,1927.[9]D.Stauffer and A.Aharony,Introduction to Percolation Theory,2nded.,(Taylor and Francis,London),1992.M.Sahimi,Applications of Per-colation Theory,(Taylor and Francis,London),1994.[10]M.H.Cohen and M.P.Anderson in The Chemistry and Physics of PorousMedia,ed.M.Tomkiewietz and P.N.Sen,(Pennington,New Jersey,The Electrochem Soc.),1985.[11]S.N.Davis,Porosity and Permeability of Natural Materials)pg.53,in FlowThrough Porous Media,ed.R.J.M.De Wiest(Acad.,New York),1969.[12]S.Roy and S.Tarafdar,to be published in Phys.Rev.B,1997.[13]A.H.Thompson,A,J.Katz and C.E.Krohn,Adv.Phys.36,625,(1987).[14]J.F.Thovert,F.Wary and P.M.Adler,J.Appl.Phys.,68,3872,1990.[15]J.Koplik and sseter,Soc.Model.Petr,Engg.,p.89,Feb198510Figure CaptionsFigure1(a)–(c):Pore structure generated in2-dimensions with(a)–F=0.2,(b)–F=0.4,and(c)–F=1.0.Open squares represent pore sites.Figure2(a):Porosity variation with sample size in3-dimensional structure,for F=0.10.Figure2(b):Porosity variation with sample size in3-dimensions for F=0.01.Figure3:Porosity variation with F in3-dimensions.Solid line shows logarithmicfit,and broken line shows simulation results.Figure4:Log[M(N)]plotted against Log[N],the slope deviates from 3for large N.Figure5:Specific surface area versus porosity in3-dimensions. Figure6:(Surface area)/(no.of pore sites)versus porosity.Figure7:Relative permeability(K)versus porosity.Solid line shows exponentialfit,points are simulation results.11。
决策过程模型在发展中的应用英语作文As an AI language model, I do not have personal opinions or prompt. However, I can provide a sample essay about the application of decision-making process models in development.The decision-making process model is a useful tool for individuals and organizations to make informed and rational decisions. It involves a series of steps that help identify the problem, gather information, evaluate alternatives, and select the best course of action. In recent years, the decision-making process model has been widely adopted in various fields, including business, healthcare, and public policy.In business, decision-making process models are commonly used to make strategic and operational decisions. For example, a company may use a decision-making process model to evaluate different marketing strategies and choose the one that is most effective. The model helps the company to consider all relevant factors, such as cost, target audience, and expected outcome, and to make a data-driven decision.在商业领域,决策过程模型被广泛用于制定战略和操作性决策。
a r X i v :h e p -p h /9504374v 1 24 A p r 1995DESY 95-077ISSN 0418-9833April 1995A Parton Model for Diffractive Processes in Deep Inelastic Scattering W.Buchm¨u ller and A.Hebecker Deutsches Elektronen-Synchrotron DESY,22603Hamburg,Germany Abstract We demonstrate that the global properties of the “rapidity gap”events,observedat HERA,can be understood based on electron-gluon scattering as the underlying partonic ing the measured inclusive structure function F 2to determinethe parameters of the parton model,the diffractive structure function F D 2is pre-dicted.The ratio of diffractive and inclusive cross sections,R D =σD /σincl ≃1/9,is determined by the probability of the produced quark-antiquark pair to evolve into a colour singlet state.This colour singlet cluster may fragment into hadrons independently of the proton remnant,yielding the observed gap in rapidity.In the“rapidity gap”events,observed in deep inelastic scattering at HERA[1]-[3], the detected hadronicfinal state has small invariant mass,and it is separated by a gap in rapidity from the proton beam direction.The absence of a hadronic energyflow between proton remnant and current fragment suggests that in the scattering process a colour neutral part of the proton is stripped offwhich fragments independently of the proton. In analogy to hadronic processes of similar kind the“rapidity gap”events are also called “diffractive”events.The measured“diffractive”cross section is not suppressed at large values of the momentum transfer Q2relative to the inclusive cross section.Such a“leading twist”behaviour is usually regarded as evidence for scattering on point-like constituents.This interpretation,however,appears to be in conflict with the fact that quarks and gluons, the constituents of the proton,carry colour.Hence,one expects the formation of jets in thefinal state with a hadronic energyflow familiar from ordinary deep inelastic scattering events without a rapidity gap.In the following we shall demonstrate that this puzzle can be resolved by taking non-perturbative fragmentation effects into account.We start from the production of a quark-antiquark pair in electron-gluon scattering as basic partonic process.Immediately after their production quark and antiquark propagate in the colourfield of the proton.With a certain probability,approximated by a statistical weight factor,the quark-antiquark pair evolves into a colour singlet parton cluster which can escape from the proton and fragment independently into hadrons.The cross section for diffractive events can then be calculated in terms of the statistical weight factor,the quark-antiquark production cross section and the gluon density which we determine in terms of the inclusive structure function F2.Our approach is related to previous work on“aligned jet models”[4]-[6]and “wee parton lumps”in deep inelastic scattering[7,8].Quark-antiquark pairs are produced in electron-gluon scattering.The relevant kine-matic variables are(cf.fig.1)s=(P+k)2,Q2=−q2=xys,x=Q2Q2+M2≃xThe differential cross section for the inclusive production of quark-antiquark pairs is given by [9]dσ(ep→e (q ¯q )X )πxQ 2g (ξ) 1−y +y 22σL .(4)Here g (ξ)is the gluon density,and the cross section σT (L )is obtained by integrating the differential parton cross section over the momentum transfer t =(q −l ′)2(cf.fig.1)from t min =−Q 2/βto t max =−m 2g /β,σT (L )= t max t mindσT (L )dt =πααst +t tu (t +u +Q 2)−Q 2m 2g 1t 2 ,(6)dσLQ 4 q e 2q β3(1−β),(7)where the sum extends over all quarks whose mass is small compared to Q .From eqs.(4)and (5)one obtains the contribution to the inclusive structure function F 2(x,Q 2),∆(g )F 2(x,Q 2)=x αsξg (ξ) (β2+(1−β)2)ln Q 2ξ(S q (ξ)+S ¯q (ξ))(δ(1−β)+O (αs ))+∆(g )F 2(x,Q 2).(9)Here S q and S ¯q are quark density and antiquark density,respectively.At small values of ξone has,S q (ξ),S ¯q (ξ)≪g (ξ).(10)For simplicity,we shall neglect in the following the quark contribution to F2.In this approximation we shall obtain a parameter free prediction for the diffractive structure function.Note,that S q(ξ)is different from S q(ξ,Q2),the quark density at scale Q2. Neglecting S q(ξ)in eq.(9)essentially amounts to calculating S q(ξ,Q2)in terms of an “intrinsic”gluon density g(ξ),corresponding to a scale m g=O(1GeV2).A more com-plete analysis keeping the contribution from S q(ξ)would require information about the longitudinal structure function F L in order to predict the diffractive structure function.For the gluon density at small values ofξwe use the usual parameterization,g(ξ)=A gξ−1−λ,(11)where A g is a constant.Inserting eq.(11)into eq.(8)we can now evaluate the inclusive structure function F2,F2(x,Q2)=αsm2gβ2−2+6β(1−β) .(12)A simple approximation for F2,valid at small x,is obtained by choosing x=0as lower limit of integration,and by settingλ=0in the integrand.This yields(x≪1),F2(x,Q2)≃αs3+lnQ2spin of quark and antiquark,the probabilities should simply be given by the statistical weight factor accounting for the possible states of the quark-antiquark pair,i.e.,P1≃19.(14)Similar ideas concerning the rotation of quarks in colour space have been discussed by Nachtmann and Reiter[10]in connection with QCD-vacuum effects on hadron-hadron scattering.In analogy with the usual inclusive structure functions,the diffractive structure func-tions are defined as,dσDxQ4 1−y+y22F D L(x,Q2,ξ) .(15)The structure function F D2is easily obtained from eq.(8).With x=βξ,and including the statistical weight factor(14),one obtainsF D2(x,Q2,ξ)≃12π q e2q g(ξ)¯F D2(β,Q2),(16)where¯F D2(β,Q2)=β (β2+(1−β)2)ln Q2F2(x,Q2)≃1The function ¯F D 2(β,Q 2)is plotted in fig.2for three different values of Q 2.For intermediate values of βbetween 0.2and 0.6this function is rather flat.Approximating ¯F D 2(β,Q 2)in this interval by ¯F D 2(0.4,Q 2),a comparison of eqs.(9)and (16)yieldsthescalingrelation [8]F D 2(x,Q 2,ξ)≃D2ln ξ(1−β)u +m 2g βdydQ 2dξdη=dt dydQ 2dξdt =dt 9α2 dσTdt −y 2dt .(22)The total diffractive cross section for a maximum rapidity ηmax can now be obtained by integrating over a specified kinematic domain,where the rapidity of the antiquark is larger than the rapidity of the quark.The reverse configurations yield the same contri-bution,resulting in a factor of 2.Hence,one obtainsdσDdydQ 2dξdη,(23)where ξmax =min {1,x +exp 2ηmax }.Using the kinematic boundaries 0.03<y <0.7and7.5GeV 2<Q 2<70GeV 2[3]one obtains the distribution shown in fig.3.Note,thatthe approximation m 2g ≪Q 2has been used throughout the calculation.Above ηmax ∼2the diffractive cross section is clearly negligible.Assuming that the final state hadronsare produced in the rapidity interval spanned by the quark-antiquark pair,one obtains the observed rapidity gap.In summary,we have demonstrated that electron-gluon scattering can account for the global properties of the“rapidity gap”events observed at HERA provided the following two hypotheses concerning the formation of thefinal state are correct:First,the initially produced quark-antiquark pair evolves with a probability,given by a statistical weight factor,into a colour singlet parton cluster which fragments independently of the proton remnant;second,the rapidity range of the diffractive hadronicfinal state is essentially given by the rapidity interval spanned by the produced quark-antiquark pair.This simple picture appears to provide a rather accurate description of the observed diffractive events,including the total rate,theξ-dependence and the Q2-dependence.This agreement with experimental data may appear fortuitous,since a number of theoretical issues still remain to be settled.These include the non-perturbative formation of the colour singlet cluster and the role of the infrared cutoff.Our results indicate,that an appropriate starting point for the evaluation of the inclusive as well as the diffractive structure functions at small values of x may be a semiclassical approach where“wee partons”are treated as a classical colourfield.We expect that such a framework will lead to results very similar to the ones described above.We would like to thank G.Ingelman,H.-G.Kohrs,M.Kr¨a mer,M.L¨u scher and P.Zerwas for valuable discussions.References[1]ZEUS collaboration,M.Derrick et al.,Phys.Lett.B315(1993)481;B332(1994)228[2]H1collaboration,T.Ahmed et al.,Nucl.Phys.B429(1994)477[3]H1collaboration,T.Ahmed at al.,preprint DESY95-036(1995)[4]J.D.Bjorken and J.Kogut,Phys.Rev.D8(1973)1341[5]L.Frankfurt and M.Strikman,Phys.Rep.160(1988)235;H.Abramowicz,L.Frankfurt and M.Strikman,preprint DESY95-047(1995)[6]N.N.Nikolaev and B.G.Zakharov,Z.Phys.C53(1992)331;M.Genovese,N.N.Nikolaev and B.G.Zakharov,preprint DFTT42/94(1994)[7]W.Buchm¨u ller,Phys.Lett.B335(1994)479[8]W.Buchm¨u ller,preprint DESY95-065(1995)[9]R.D.Field,Applications of Perturbative QCD,Addison Wesley,New York,1989[10]O.Nachtmann and A.Reiter,Z.Phys.C24(1984)283[11]H1collaboration,preprint DESY95-006(1995)[12]G.Ingelman and P.Schlein,Phys.Lett.152B(1985)256[13]A.Donnachie and ndshoff,Phys.Lett.191B(1987)309;Nucl.Phys.B303(1988)634[14]G.Ingelman and K.Prytz,Z.Phys.C58(1993)285[15]B.A.Kniehl,H.-G.Kohrs and G.Kramer,Z.Phys.C65(1995)657[16]T.Gehrmann and W.J.Stirling,preprint DTP/95/26(1995)[17]K.Golec-Biernat and J.Kwieci´n ski,INP report no.1670/PH(1995)Figure captionsFig.1Quark-antiquark pair production in electron-gluon scattering.Fig.2Dependence of the diffractive structure function onβand Q2.Fig.3Distribution of the maximal rapidity in theγ∗p-rest frame defined by the most forward quark or antiquark.lFig. 1。