on Self-organization, Scale and Stability in a Spatial Predator–Prey Interaction
1.
I NTRODUCTION
Simple predator–prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity—a phenomenon often called the paradox of enrichment (Rosenzweig, 1971; Gilpin, 1972) because such depression is more likely in nutrient rich systems. Instability in such models usually takes the form of limit-cycle oscillations, whose amplitude is often sufficient to imply the extinction of one or both players. Although the behaviour of some laboratory systems [e.g., Gause (1934); Huffaker (1958)] apparently conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator, accompanied by random fluctuations or small amplitude oscillations [e.g., McCauley and Murdoch (1987, 1990)]. Considerable effort has consequently been expended on constructing more elaborate models incorporating a variety of potential stabilizing mechanisms. Murdoch et al. (1998) give a wide-ranging survey of these possibilities, together with tests of some of them in the context of the interaction between Daphnia and its
Bulletin of Mathematical Biology (2000) 62, 61–86 Article No. bulm.1999.0130 Available online at on
Self-organization, Scale and Stability in a Spatial Predator–Prey Interaction
WILLIAM S. C. GURNEY AND A. ROY VEITCH Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, Scotland, U.K.
Simple predator–prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity. Although the behaviour of some laboratory systems conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator. Prominent among the possible causes of this discrepancy are the effects of spatial heterogeneity. In this paper we show that both discrete and continuous representations of the spatial Rosenzweig–McArthur model with immobile prey can be stabilized by selforganized prey heterogeneity. This concordance of behaviour closely parallels that which we have previously established in the context of invasion waves. We use the continuous model variant to calculate the characteristic spatial scales of the selforganized structures. The discrete variant forms the basis of a simulation study demonstrating the variety of stable structures and elucidating their relation to the history of the system. We note that all stable prey distributions take the form of a network of occupied patches separated by prey-free regions, and liken the process which generates such assemblages to the formation of a landscape mozaic. c 2000 Society for Mathematical Biology
0092-8240/00/010061 + 26 $35.00/0 c 2000 Society for Mathematical Biology
62
ቤተ መጻሕፍቲ ባይዱ
W. S. C. Gurney and A. R. Veitch
algal food. They conclude that many of the most straightforward mechanisms can readily be shown to be incompatible with currently available evidence, but prominent among those which cannot be so falsified is spatial heterogeneity. It has long been known that environmental heterogeneity can stabilize population processes. Gurney and Nisbet (1975) showed that non-linear dispersal can stabilize a population growing uncontrollably in a finite geographical region surrounded by territory where it suffers net mortality. Gurney and Nisbet (1976) demonstrated that donor-regulated populations exhibit spatial distributions in which some of the scales present in the resource distribution are amplified—an effect which McLaughlin and Roughgarden (1991, 1992) have shown to stabilize the spatial Lotka–Volterra predator–prey model, which is invariably neutrally stable in a homogeneous environment. The possibility that spatial predator–prey interactions might exhibit self-organization capable of producing stabilizing heterogeneities in prey distribution was first suggested by the work of Jansen (1994, 1995), who considered a model with two patches, each with unstable Rosenzweig–McArthur dynamics, linked by diffusive dispersal. This model has several equilibria, among which is one with identical prey (and predator) populations in the two patches. When this homogeneous equilibrium is unstable, the model can exhibit large amplitude limit cycles with the patch populations fluctuating in synchrony. Jansen (1994) showed that this homogeneous limit-cycle can become unstable, whereupon the system is attracted to a smaller amplitude limit-cycle in which the patch populations fluctuate about an equilibrium with low prey in one patch and high prey in its neighbour. Subsequent work (Jansen and de Roos, 1998) has shown that similar effects occur in arbitrary sized linear arrays of patches provided that the prey are significantly less mobile than the predator. A related effect has been reported by McCauley et al. (1996) in an individualbased simulation model with Rosenzweig–McArthur dynamics and a separate juvenile stage. They found that where prey mobility is low, systems with parameters implying large amplitude oscillations in a non-spatial model, can be stabilized by a mechanism intimately connected to the formation of a persistent, small-scale heterogeneous structure in the prey distribution. De Roos et al. (1998) have studied a related continuous time patch dynamic model with logistic local prey dynamics and predators with a type II functional response, whose searching covers an area which is large compared to the distance over which the prey can diffuse in a generation. They found that when the homogeneous equilibrium of this system is unstable, most trajectories other than those starting from an exactly homogeneous initial condition are attracted to a stable spatially heterogeneous steady state. The work of Jansen (1995), McCauley et al. (1996) and De Roos et al. (1998) suggests that a saturating predator functional response plays a key role in the selforganization of stabilizing structures in the spatial distribution of prey. Although such structures have, as yet, only been observed in individual-based and patch-
英语作文如何更好的进行自我管理
英语作文如何更好的进行自我管理Captivating the essence of self-management in English composition is akin to mastering the art of orchestration, where each word is a note in a symphony of expression. Toexcel in this craft, one must first embrace the discipline of time management, ensuring that ample time is allocated to brainstorming, drafting, revising, and polishing the piece. The use of a structured outline serves as a compass, guiding the writer through the labyrinth of ideas, ensuring acoherent flow and logical progression of thoughts.Moreover, the cultivation of a rich vocabulary is paramount; it's the paint on the writer's palette. Reading extensively across genres and engaging with diverselinguistic expressions not only broadens the lexicon but also refines the writer's sensitivity to the nuances of language. Active learning, such as taking notes and creating flashcards, further solidifies the grasp of new words and phrases.In the realm of grammar, precision is key. A firm graspof English grammar rules acts as the skeleton that supportsthe flesh of the narrative. Regular practice and immediate correction of errors through peer review or the use of language tools can significantly enhance grammatical accuracy.Furthermore, embracing a critical mindset is essentialfor self-improvement. Self-editing with a discerning eye can unearth areas for improvement, allowing the writer to refinethe composition to a higher standard. Seeking feedback from mentors or peers can provide valuable perspectives and insights, acting as a mirror to reflect on one's writing style.Lastly, the practice of writing regularly is thelifeblood of any writer. It is through the consistent act of writing that one hones their craft, experiments withdifferent styles, and ultimately finds their unique voice. By integrating these elements into the writing process, one can elevate their English composition skills to new heights, crafting pieces that are not only well-managed but also rich in content and style.。
self-control self-management 高中英语阅读
self-control self-management 高中英语阅读The Art of Self-Control and Self-ManagementIn today's fast-paced world, the ability to control oneself and manage time and resources effectively has become increasingly important. These skills, known as self-control and self-management, are crucial for success in both academic and professional environments.Self-control refers to the ability to resist impulses and desires, and to act in accordance with one's goals and values. It involves regulating one's emotions, thoughts, and behaviors in the face of challenges and temptations. For example, a student with good self-control will be able to resist the urge to procrastinate and instead focus on completing their homework or studying for an exam.On the other hand, self-management involves effectively managing one's time, energy, and resources to achieve specific goals. It requires planning, prioritizing, and making conscious decisions about how to allocate one's resources. For instance, a self-managed student might create a study schedule that balances their schoolwork, extracurricular activities, and personal time.Both self-control and self-management are essential for academic success. Students who possess these skills are better able to focus on their studies, avoid distractions, and complete tasks efficiently. They are also more likely to develop good habits, such as regular exercise andhealthy eating, which further contribute to their overall well-being and productivity.Moreover, self-control and self-management are transferrable skills that can be applied to various aspects of life. Whether it's managing a budget, maintaining a work-life balance, or achieving personal goals, these skills can help individuals navigate the challenges of adulthood with greater ease and success.In conclusion, the art of self-control and self-management is a valuable asset for students to cultivate. By developing these skills, they can enhance their academic performance, improve their overall well-being, and set themselves up for success in future endeavors. As such, it is important for educators and parents to encourage and support the development of self-control and self-management in young people.阅读理解问题：What is the main idea of this article?A. The importance of self-control and self-management in academic success.B. How to balance schoolwork, extracurricular activities, and personal time.C. The challenges of adulthood and how to overcome them.D. The difference between self-control and self-management.Which of the following is an example of self-control?A. Creating a study schedule.B. Managing a budget.C. Resisting the urge to procrastinate.D. Prioritizing tasks.How can self-control and self-management contribute to a student's overall well-being?A. By helping them develop good habits.B. By allowing them to avoid all challenges and temptations.C. By ensuring they always get perfect grades.D. By making them more popular with their peers.Why is it important for educators and parents to encourage the development of self-control and self-management in young people?A. Because it helps them become more obedient.B. Because it sets them up for success in the future.C. Because it makes them happier.D. Because it allows them to have more free time.Which statement best reflects the transferability of self-control and self-management skills?A. Self-control and self-management are only important for students.B. Self-control and self-management can be applied to different areas of life.C. Self-control and self-management are easy to learn.D. Self-control and self-management have nothing to do with adulthood.答案：A. The importance of self-control and self-management in academic success.文章主要讲述了自我控制和自我管理在学业成功中的重要性。
榜样的力量英语作文
The power of role models is a profound and influential force in our lives.They serve as beacons of inspiration,guiding us towards our aspirations and shaping our values. Heres an exploration of the impact role models can have on individuals and society as a whole.Inspirational Figures:Role models can be anyone who embodies the qualities we admire and aspire to.They are often individuals who have achieved great success in their respective fields,such as scientists,athletes,artists,or leaders.Their accomplishments serve as a testament to the heights one can reach with dedication and perseverance.Setting Goals and Aspirations:One of the primary ways role models influence us is by setting a standard for what we can achieve.By observing their hard work and success,we are motivated to set our own goals and strive for excellence.This can lead to personal growth and the development of a strong work ethic.Moral and Ethical Guidance:Role models also provide moral and ethical guidance.They demonstrate the importance of integrity,honesty,and compassion.By emulating these traits,we learn to navigate the complexities of life with a strong moral compass.Cultural Representation:In a diverse society,role models from various backgrounds can inspire individuals from different cultures and communities.They show that success is attainable regardless of ones origins,fostering a sense of belonging and pride in ones heritage. Overcoming Adversity:Many role models have overcome significant challenges or adversity in their lives.Their stories of resilience and triumph can be incredibly motivating,teaching us that obstacles can be overcome with determination and courage.Encouraging Innovation and Creativity:Role models in fields such as technology,arts,and sciences often push the boundaries of what is possible.Their innovative thinking and creative solutions inspire us to think outside the box and explore new ideas.Social Change and Activism:Some role models are known for their activism and contributions to social change.They inspire us to take action on issues that matter to us,promoting a sense of socialresponsibility and the desire to make a positive impact on the world.Personal Development:On a personal level,role models can influence our selfesteem and selfworth.By seeing someone who looks like us or shares similar experiences succeed,we are encouraged to believe in our own abilities and potential.Conclusion:In conclusion,the power of role models is multifaceted and farreaching.They inspire us to dream big,work hard,and believe in ourselves.By setting an example,they help us to develop into wellrounded individuals who contribute positively to society.It is important to choose role models wisely,selecting those who align with our values and aspirations, and who can guide us towards becoming the best versions of ourselves.。
Practicing Self-Acceptance
Practicing Self-AcceptanceSelf-acceptance is an essential aspect of one's personal growth and development. It is the ability to acknowledge and embrace who we are, including our strengths, weaknesses, and imperfections. Practicing self-acceptance can be challenging, especially in a world that often values perfection and conformity. However, it is a crucial step towards achieving inner peace, happiness, and fulfillment. In this response, I will discuss the importance of self-acceptance from multiple perspectives and provide some practical tips for practicing it.From a psychological perspective, self-acceptance is a critical component of mental health and well-being. It involves accepting ourselves for who we are, including our flaws and limitations. When we practice self-acceptance, we are less likely to experience negative emotions such as shame, guilt, and self-criticism. Instead, we can cultivate a sense of self-compassion and self-love, which can lead to increased resilience and emotional stability. Moreover, self-acceptance can improve our relationships with others since we are more likely to be authentic and vulnerable when we accept ourselves fully.From a spiritual perspective, self-acceptance is essential for personal growth and spiritual development. It involves recognizing that we are all unique and valuable, regardless of our external circumstances or achievements. When we practice self-acceptance, we can let go of our ego and connect with our inner selves, which can lead to a deeper sense of purpose and fulfillment. Moreover, self-acceptance can help us cultivate gratitude and compassion towards ourselves and others, which are essential qualities in many spiritual traditions.From a social perspective, self-acceptance is crucial for building healthy relationships and contributing to society. When we practice self-acceptance, we are less likely to judge and criticize others, which can lead to more harmonious and compassionate relationships. Moreover, self-acceptance can help us cultivate empathy and understanding towards others, which are essential qualities for effective communication and conflict resolution. Furthermore, when we accept ourselves, we are more likely to pursue our passions and contribute to society in meaningful ways, which can lead to a sense of purpose and fulfillment.Practicing self-acceptance can be challenging, especially if we have internalized negative beliefs and messages from our upbringing or society. However, there are some practical tips that can help us cultivate self-acceptance:1. Practice self-compassion: When we make mistakes or face challenges, it is essential to treat ourselves with kindness and understanding. We can talk to ourselves as we would to a good friend, offering support and encouragement rather than criticism and judgment.2. Embrace imperfection: Perfectionism can be a significant barrier to self-acceptance. Instead, we can recognize that we are all imperfect and make mistakes. We can focus on progress rather than perfection, celebrating our successes and learning from our failures.3. Challenge negative self-talk: When we hear negative self-talk, such as \"I'm not good enough\" or \"I'm a failure,\" we can challenge these thoughts by asking ourselves if they are true and if there is evidence to support them. We can then replace these thoughts with more positive and realistic ones.4. Focus on our strengths: Instead of dwelling on our weaknesses, we can focus on our strengths and positive qualities. We can make a list of our strengths and accomplishments and remind ourselves of them regularly.5. Surround ourselves with positive influences: It is essential to surround ourselves with people who support and encourage us. We can seek out friends, family, or mentors who accept us for who we are and offer positive feedback and support.6. Practice mindfulness: Mindfulness can help us cultivate self-awareness and self-acceptance. We can practice mindfulness meditation, yoga, or other mindful activities to connect with our inner selves and cultivate a sense of acceptance and compassion towards ourselves.In conclusion, practicing self-acceptance is essential for personal growth, spiritual development, and social harmony. It involves acknowledging and embracing who we are,including our strengths, weaknesses, and imperfections. While it can be challenging to practice self-acceptance, there are some practical tips that can help us cultivate it, such as practicing self-compassion, embracing imperfection, challenging negative self-talk, focusing on our strengths, surrounding ourselves with positive influences, and practicing mindfulness. By practicing self-acceptance, we can cultivate a sense of inner peace, happiness, and fulfillment, and contribute to a more compassionate and harmonious society.。
领导者的自尊和自我效能感对其主观幸福感的影响
Advances in Psychology 心理学进展, 2016, 6(10), 1083-1092Published Online October 2016 in Hans. /journal/ap /10.12677/ap.2016.610138文章引用: 唐梓轩, 潘孝富(2016). 领导者的自尊和自我效能感对其主观幸福感的影响. 心理学进展, 6(10), 1083-1092.The Influence of Leadership’s Self-Esteem and Self-Efficacy on Their Subjective Well-BeingZixuan Tang, Xiaofu Pan *School of Culture and Social Development, Southwest University, ChongqingReceived: Oct. 10th , 2016; accepted: Oct. 25th , 2016; published: Oct. 28th , 2016Copyright © 2016 by authors and Hans Publishers Inc.This work is licensed under the Creative Commons Attribution International License (CC BY)./licenses/by/4.0/AbstractQuestionnaire survey is used to examine the influence of leadership’s self-esteem and self-efficacy on their subjective well-being. This survey covers 237 leaders from government offices, public se-curity department, procurator organs and people’s courts of different administrative levels in Chongqing. Statistics collected are studied by multi-level regression analysis, mediating effect examination and advantage analysis. The result shows that leadership’s self-esteem and self-effi- cacy work as forward prediction variables of subjective well-being and that self-efficacy has a sig-nificant part of the mediating effect on leadership’s self-esteem and subjective well-being. Contri-bution of the role of self-esteem is significantly greater than the role of self-efficacy in the influ-ence of leadership’s subjective well-being. Enhancement of leadership’s self-esteem and self-effi- cacy is helpful to promote their subjective well-being.KeywordsSelf-Esteem, Self-Efficacy, Subjective Well-Being, Leadership领导者的自尊和自我效能感对其 主观幸福感的影响唐梓轩，潘孝富∗*通讯作者。
建议减肥的英语作文
When it comes to writing an essay on weight loss,there are several key points to consider.Heres a detailed guide on how to approach this topic:Title:Effective Strategies for Weight LossIntroduction:Begin with a hook that captures the readers attention.You might start with a startling statistic about obesity rates or a quote from a wellknown health expert.Briefly introduce the importance of the topic and the purpose of your essay.Paragraph1:Understanding the ProblemDefine obesity and overweight issues.Discuss the health risks associated with being overweight,such as diabetes,heart disease, and certain types of cancer.Mention the psychological impact of being overweight,including selfesteem and body image issues.Paragraph2:The Role of DietEmphasize the importance of a balanced diet in weight loss.Suggest specific dietary changes,such as reducing sugar and processed food intake, increasing fruit and vegetable consumption,and choosing lean proteins.Discuss portion control and mindful eating as strategies to manage calorie intake.Paragraph3:The Significance of ExerciseExplain how regular physical activity contributes to weight loss and overall health. Recommend different types of exercises,such as aerobic activities,strength training,and flexibility exercises.Highlight the benefits of finding an enjoyable form of exercise to maintain motivation.Paragraph4:Lifestyle ChangesDiscuss the importance of making sustainable lifestyle changes rather than temporary diets.Suggest strategies such as getting enough sleep,reducing stress,and creating a supportive environment for weight loss.Mention the role of social support and accountability in maintaining weight loss efforts.Paragraph5:Psychological AspectsAddress the mental challenges of weight loss,such as dealing with setbacks and maintaining motivation.Discuss the importance of setting realistic goals and celebrating small victories.Introduce the concept of selfcompassion and the avoidance of negative selftalk.Paragraph6:Medical Assistance and SupportMention the role of healthcare professionals in weight loss journeys,including doctors, nutritionists,and personal trainers.Discuss the potential use of medical interventions for weight loss,such as prescription medications or weight loss surgery,when appropriate.Highlight the importance of a personalized approach to weight loss plans.Conclusion:Summarize the main points of your essay.Reiterate the importance of a holistic approach to weight loss,combining diet,exercise, lifestyle changes,and psychological support.End with a call to action,encouraging readers to take the first steps towards a healthier lifestyle.Word of Caution:Ensure that your essay is respectful and nonjudgmental.Avoid using stigmatizing language or promoting unhealthy weight loss methods.Use reputable sources to back up any claims or statistics you include in your essay.Remember,the goal of your essay is to inform and inspire,not to dictate.Encourage readers to make informed decisions about their health and wellbeing.。
self regulatory focus theory and leadership
Self-Regulatory Focus Theory (SRFT) is a psychologicalSelf-Regulatory Focus Theory (SRFT) is a psychological theory that explains how individuals approach goals and make decisions. It suggests that people have two different mindsets when it comes to achieving their goals: promotion focus and prevention focus.Promotion focus is characterized by a desire to achieve positive outcomes and gain advantages. People with a promotion focus are motivated by the possibility of success and tend to engage in actions that will help them achieve their goals. They are more likely to take risks and seek out new opportunities.Prevention focus, on the other hand, is characterized by a desire to avoid negative outcomes and losses. People with a prevention focus are motivated by the possibility of failure and tend to engage in actions that will help them avoid mistakes or problems. They are more likely to play it safe and stick to familiar routines.In terms of leadership, SRFT suggests that leaders who have a strong promotion focus may be more effective at inspiring and motivating their team members to achieve ambitious goals. They may be more willing to take risks and embrace change, which can help their team members grow and develop.However, leaders who have a strong prevention focus may be more effective at avoiding problems and minimizing risks. They may be more cautious and detail-oriented, which can help ensure that their team members are following best practices and avoiding costly mistakes.Ultimately, the most effective leaders are those who are able to balance promotion and prevention focus, depending on the situation and the needs of their team. By understanding the strengths and weaknesses of each mindset, leaders can make better decisions and guide their team members towards success.。
怎样自力更生英语作文
怎样自力更生英语作文Self-reliance is the key to success。
Self-reliance is the ability to depend on one's own capabilities and resources rather than relying on others.It is an important trait that can lead to success in all aspects of life. When we are self-reliant, we are able to overcome challenges and achieve our goals without depending on others for help.One of the key benefits of self-reliance is that it builds confidence and independence. When we are able torely on ourselves to solve problems and achieve our goals, we become more self-assured and independent. This confidence can help us to take on new challenges and opportunities with a positive attitude, knowing that we have the skills and resources to succeed.Self-reliance also fosters a sense of responsibility and accountability. When we are self-reliant, we takeownership of our actions and decisions, knowing that we are ultimately responsible for our own success or failure. This sense of responsibility can motivate us to work harder and strive for excellence in everything we do.Furthermore, self-reliance can lead to greatercreativity and innovation. When we are not reliant onothers for help or guidance, we are forced to think outside the box and come up with creative solutions to our problems. This can lead to new ideas and innovations that can help us to achieve our goals more effectively.In conclusion, self-reliance is an important trait that can lead to success in all aspects of life. By developing our own capabilities and resources, we can build confidence, independence, responsibility, and creativity. Thesequalities can help us to overcome challenges, achieve our goals, and ultimately lead to a more fulfilling and successful life.。
新人教版英语必修二_Unit 1 综合能力提升练(解析版)
Ⅰ.根据语境及首字母提示完成句子1．I was disappointed by the q________ of the wine.2．I gave the letter to our local press and they q________ from it.3．The force of the water washed him back into the c________.4．My students have learnt to p________ difficult English sentences.5．T________ the process, children develop good habits for life.6．(牛津高阶)They wanted the store to have a folksy small-town i________.7．Within a few years the whole country will switch over to d________ television.8．(剑桥高阶)Eventually, the government will have to take notice of public o________.9．She had to face the fact that her life had changed f________.10．The h________ feeling of the town makes it a pleasant place to base oneself for summer vacations.答案：1.quality 2.quoted 3.cave 4.paraphrase 5.Throughout 6.image 7.digital 8.opinion 9.forever 10.historic二、单句语法填空1．(2020·江苏高考)For in-person humor, ________ (质量) isn't as important as you might think. 2．(2020·天津高考)Detective Ashley Jones works at a police ________ (部) in England. 3．(2020·全国卷Ⅰ)He picked up the case and walked towards the ________ (出口)．4．(2020·全国卷Ⅰ)Many stations have wheelchair access from the car park or ________ (入口) to the station platforms.5．(柯林斯词典)This gave me a ________ (线索) as to the source of the problem.6．(牛津高阶)We contributed ￡5,000 to the earthquake ________ (基金).7．(剑桥高阶)He's only been playing football as a ________ (职业选手) for two years.8．(牛津高阶)These ancient buildings are part of the national ________ (遗产).9．(牛津高阶)Address your ________ (申请) to the Personnel Manager.10．(柯林斯词典)They fanned out and carefully combed the ________ (庙) grounds.11．(2020·天津高考)The genius tends to get things done ________ (creative).12．(2020·江苏高考)I can, from my computer at home, pull up satellite ________ (image) of Juan's village.13．(2019·江苏高考)There are species (物种) that are ________ (disappear) every day. 14．(2019·江苏高考)People should be encouraged to make more ________ (donate).15．(剑桥高阶)How you choose ________ (conduct) your private life is your own business! 16．(牛津高阶)A group of ________ (protest) gathered outside the firm's office.17．(剑桥高阶)The committee is evenly ________ (balance), with six members from each party. 18．(朗文当代)Weather conditions prevented them from ________ (attempt) the jump.19．(柯林斯词典)He ordered an ________ (investigate) into the affair.20．(柯林斯词典)Now we live ________ (far) away from the city centre.21．Our products are ________ high quality.22．Most of the computers we are using are ________ (digitally) computers.23．You should not identify wealth ________ happiness.24．________ an archaeologist explained, these caves could date back to Han Dynasty.25．It is a ________ (traditional) to eat mooncakes during the Mid-Autumn Festival.26．________ her opinion, Tom will fail in the exam.27．We expect to see ________ (far) improvement over the coming year.28．Martin L uther King delivered a ________ (history) speech known as the “I Have a Dream”. 29．People all over ________ world eat eggs.30．People always ________ (comparison) life to a journey.答案：1.quality 2.department 3.exit 4.entrance 5.clue 6.fund 7.professional 8.heritage 9.application 10.temple 11.creatively 12.images 13.disappearing 14.donations 15.to conduct 16.protesters 17.balanced 18.attempting 19.investigation 20.further/farther 21.of 22.digital 23.with 24.As 25.tradition 26.In 27.further 28.historic 29.the pare三、阅读(共15小题；每小题2.5分，满分37.5分)阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项.A(2022·山东省济南市高三检则(B))Explore the National Gallery of Art Sculpture Garden, which offers a relaxing setting for you to enjoy works of modern sculpture.Chair Transformation Number 20B, made in 1996—by Lucas SamarasHere, Samaras explores the double meaning of “flight”，referring to both the starlike form created by the stacked chairs, and the movement of a single chair moving through space. From different viewpoints, the sculpture appears to be upright, leaning back, or springing forward. From the side, it even appears like a zigzagging (之字形的) line.Type w riter Eraser, Scale X, made in 1998—by Coosje van BruggenThe artist chose the typewriter eraser as his model for this work based upon childhood memories of playing with the object in his father's office. Here the brush arcs (作弧形运动) back, conveying a sense of motion, as if the wheel-like eraser were rolling down the hill and making its way towards the gate of the garden.Moondog, model 1974, made in 19981999—by Tony SmithThe title itself comes from two sources: Moondog was the name of a blind poet and folk musician who lived in New York City, and Smith has also compared this sculpture to Dog Barking at the Moon, a painting by Joan Miro. He first created Moondog in 1974 as a 33-inch cardboard model and cast it in bronze as a garden sculpture in 1980. This version was designed by Smith, but it was not completed until after his death.Che v al Rouge (Red Horse), made in 1964—by Alexander CalderDuring the last two decades of his life, Alexander Calder devoted his greatest efforts to large-scale mobiles and stabiles (立式抽象派雕塑), many of which have become popular public landmarks in cities around the world. Here the silky legs and tensile (张力的) upthrust “neck” re call the power of a horse. This stabile reflects Calder's statement: “I want to make things that are fun to look at.”1．Which was based on its creator's early life?A．Moondog.B．Che v al Rouge (Red Horse)．C．Type w riter Eraser, Scale X.D．Chair Transformation Number 20B.2．What can we learn about the sculpture Moondog?A．It was originally intended for a garden.B．It was the only work of its creator.C．It was inspired by a modern painter.D．It wasn't completed by its designer.3．Whose work was created the earliest?A．Tony Smith's.B．Lucas Samaras'.C．Alexander Calder's.D．Coosje van Bruggen's.篇章导读：本文是一篇应用文。
The emergence of design in pedestrian dynamics
Available online at Physics of Life Reviews10(2013)168–190/locate/plrevReviewThe emergence of design in pedestrian dynamics:Locomotion, self-organization,walking paths and constructal lawAntonio F.Miguel a,b,∗a Department of Physics,Evora University,Rua Romão Ramalho59,7000-671Evora,Portugalb Geophysics Center of Evora(CGE),PO Box84,7002-554Evora,PortugalReceived25February2013;accepted7March2013Available online26March2013Communicated by J.FontanariAbstractGait is inherent to human life and hence its importance is often overlooked.But walking remains the most basic form of transportation and almost all journeys begin and end with a walk,regardless of the modes used in-between.Gaining a good under-standing of pedestrian’s dynamics is thus a crucial step in meeting the mobility and accessibility needs of people by providing safe and quick walkingflows.This paper presents a critical and integrative review of research on pedestrian’s dynamics and associated topics.The review focuses on comprehensive theories and models,with an emphasis on the advances made possible by the application of the con-structal law.Constructal law points out that the emergence and evolution of design in pedestrian dynamics is analogous to that of animateflow systems.Most importantly,it also highlights that the basic features of pedestrian dynamics and supportive walking infrastructures can be optimally envisaged with the help of a few fundamental physics laws.©2013Elsevier B.V.All rights reserved.Keywords:Human gait;Walk–run transition speed;Fundamental pedestrian diagram;Self-organization;Walking paths;Constructal law1.IntroductionAlthough there are over250species of primates,only one moves primarily on two legs.Bipedalism developed approximately4–5million years ago and it was thefirst major adaptation that separated hominids from other primates [1–4].Human anatomy is built on a body planned for bipedal locomotion.The two distinct gait modes of humans are walking and running,which make use of strikingly different mechanics and energetics.Currently,the fastest human being on Earth,Usain Bolt,is able to run at a speed greater than10.44m/s.Regular pedestrians,however,tend to walk rather than run,and do this mainly at a comfort walking speed of around1.3m/s[5,6].The different speeds at which humans walk or run translate themselves into varying energy costs.Keeping energy spending low is highly desirable and leads to greater mobility,given that humans must carry their energy supply with them[7,8].*Correspondence to:Department of Physics,Evora University,Rua Romão Ramalho59,7000-671Evora,Portugal.Tel.:+351266745372;fax: +351266745394.E-mail address:afm@uevora.pt.1571-0645/$–see front matter©2013Elsevier B.V.All rights reserved./10.1016/j.plrev.2013.03.007A.F.Miguel/Physics of Life Reviews10(2013)168–190169Since the middle of last century,the study of the pedestrian dynamics has become an active subject of research in science[5–8].Pedestrian dynamics has theoretical importance and a multitude of practical applications.Primary questions such as why and how human walks,or how crowd dynamics occurs based on individual interactions,along with some more practical aspects like the design of pedestrian optimized facilities,have puzzled many researchers.In-situ observational studies and time-lapsefilms,together with the modeling have revealed important quantitative details and have led to a unique understanding of pedestrian dynamics with important practical implications[5,6].Despite the considerable progress in understanding various aspects of pedestrian dynamics,there has been no systematic attempt to integrate what remain disconnected,because of the wide scope of the subject.Fitting the“pieces”together will contributes decisively to a unified view of the topic.This paper starts with a brief description of basic mechanics of human locomotion and its energetic cost.Factor such as gender,age and environment are important in the walking speed choice.Pedestrians react to other pedestrians and obstacles,and can only move freely when there is enough free space in front of them.Then,the relation between spatial headway(distance to the predecessor)and speed of pedestrians is analyzed.Empirical data(i.e.,the fundamental diagram)available in the literature is presented and models of pedestrian interactions are introduced.The calibration and the validation of the models using empirical data are also discussed.Finally,I turn the attention to the Constructal law which constitutes the thermodynamics law of nonequilibrium (flow)systems with configuration.For these systems,this law provides new physical insights,and a unified view on domains apparently foreign to each other.The Constructal law is introduced and,then,the Constructal view of pedestrian dynamics is presented and discussed.Furthermore,the design of improved pedestrian facilities,using the Constructal law,is also addressed.The objective of this Constructal section is to forge a more structured and unified view that engage a set of issues which are addressed under different frameworks and disciplinary spaces.2.Modern human anatomy and locomotion:mechanics,energetics and gait speedBipedal locomotion is the sole form of locomotion in all healthy modern humans and it sets them apart from all other living primates[1–4].A large number of anatomical features are functionally related to this type of locomotion. The human pelvis is pronouncedly bowl-shaped,with an adapted musculature which allows the thighs to be angled in, the lower limbs are lengthened and have an enlarged joint surface area to properly support body weight,the vertebral column is shortened and S-shaped,for rigidity and balance,lining up head and trunk vertically above the feet,the hole through which the column cord enters the skull is situated near the center of the cranium which allows the head to balance easily atop the column,the feet have an arched shape with the enlarged great toe brought in line with the other toes,to absorb shock and a more efficient walk,are among other important evolutionary features[9,10].From an evolutionary perspective,the global impression of the human anatomy is that of a bio-cylinder shape[7,10].Although bipedalism is not the most stable and fast way of locomotion,it must clearly represent an evolutionary advantage to humans,because we still walk on two legs.Some of the advantages associated to bipedalism include the ability to carry things over longer distances,the freeing of arms and hands for other tasks(foraging and protection,for instance),the acquisition of improved long-distance perception and the improvement of body thermoregulation[1,9, 11–13].It is not uncommon to see apes such as chimpanzees walking on two legs in order to carry things.Octopuses have been also documented walking bipedally in order to camouflage themselves from predators[14].Placing six limbs close to their head,the octopus assumes the shape of a drifting plant,and then uses its two remaining limbs to walk away from predators.Another possible explanation for bipedalism is its lower energetic cost compared to other forms of locomotion. In a study by Taylor and Rowntree[15],chimpanzees(Pan troglodytes)and capuchin monkeys(Cebus capucinus) were trained to run on a treadmill on either two or four legs.Results showed that the energy spent by the animals on this exercise was fairly independent of the mode of locomotion they adopted.Fedak and Seeherman[16]also reported negligible differences of the scaling of energy requirements for locomotion between bipedal and quadrupedal behavior. On the other hand,Alexander[7]stated that gait of humans is distinct from the occasional bipedalism of apes because the patterns of force exerted on the ground are different,due to biomechanical differences in anatomy mentioned above.Therefore,the trajectory of the center of mass is completely different for gaits in humans and other animals [7,17].Sockol et al.[18]reported that the energy expended in human walking is approximately75%less than that expend in both quadrupedal and bipedal walking in chimpanzees.The study of Carrier et al.[8]also supported the170 A.F.Miguel/Physics of Life Reviews10(2013)168–190idea that humans are more economical when they walk.Besides,Alexander[7]stated that while the walk spends less energy than the gait pattern of quadrupedal mammals of the same body mass,running actually spends more.2.1.Forms of human gait:walking and runningPeople move across the Earth’s surface(are not be attached to one site),and this capability is called locomotion. Walking and running are the two most common forms of human gait.The increase of speed intuitively triggers the switch from a walk to a run.Walking gait is characterized by two distinct phases[19]:the stance phase,when the leg is on the ground,and the swing phase,when it is off the ground.The stance phase begins with heel-strike,as the foot strikes the ground.Most of the time just one foot is on the ground,with brief periods where both feet come in contact with the walking surface.The body vaults up and over each stiff leg in an arc.This gait pattern can be well approximated by a linear“inverted pendulum”[7,17,19,20].An ideal inverted pendulum system exhibits an optimal conversion of gravitational potential energy to kinetic energy.The energy converted by such an“inverted pendulum”mechanism can reduce the mechanical work required from the muscular system by up to70%[17].Running,in contrast,involves longer aerial phases,in which neither foot is in contact with the ground.In this case,the pendulum mechanism that characterizes gait switches to a spring-mass system,where bent legs bounce up between aerial phases [20].As feet hit the ground in a run,the leg springs compress,as a result of jointflexion,and the mass moves downwards.At the middle of the stance phase,the leg is maximally compressed,and the mass reaches its lowest point.The plantigrade foot posture of a runner is also very distinct of that of a walker[21],with its center of mass reaching the lowest point at the middle of the stance phase.In contrast,the center of mass of walkers is at its highest point precisely at the middle of the stance phase.Moreover,the stance limb sweeps through a larger angle during walking(∼30◦)than during running(∼19◦)[17].Finally,running involves a decrease of approximately35%in time of foot–ground contact and an increase of the peak ground reaction force by about50%,when compared to walking[17].Humans prefer changing their gait from walking to running and from running to walking at increasing and decreas-ing speeds.This switch occurs at a Froude number of0.5[22,23].For adults,it corresponds to a walking speed of about2m/s[24].Both walking and running are related to several demands that must be processed simultaneously:the propulsion of the body in the horizontal plane,the maintenance of a stable equilibrium(coordination between posture and move-ment),and a continuous and instantaneous adaptation to environmental requirements[25,26].This demands the use of the central and peripheral nervous system,the regulation of the skeletal segments and the contraction of mus-cles[27].Gait speed is therefore tightly linked to neurological development/degeneration,balance control,changes in limb length,and maturation.Studies performed by several authors[28,29]suggest that the gait speed is a quick, inexpensive,reliable measure of functional capacity.Recent studies also reported a significant association between walking speed and life span in seniors[30,31].Others[32],finally,presented evidence that successive step durations during walking actually present a typical structure over time,one that is characterized by a long-range dependence (i.e.,a scaling relationship).It is suggested that this dependence plays an important role in the adaptability and the flexibility of locomotion,since it disappears in individuals with neurodegenerative pathologies.2.2.Least energy-consuming gaitHumans carry their energy supply with them,and they are limited by the rate of production of metabolic energy in their bodies,that depends of the capacity of the cardiovascular system to absorb and distribute oxygen throughout the body.The slower energy is consumed,the less energy must be carried and greater mobility is achieved.A number of experimental studies have shown that the average metabolic energy consumption per unit distance traveled,E x,may be expressed by[33]E x=0.533M bu+0.3M b u(1)Here M b is the body mass and u is the gait speed.This equation has a minimum at a speed of∼1.33m/s,which is within the walking speed range(i.e.,below the average transition speed of∼2m/s between walking and run-ning[24]).This average speed is recurrently mentioned in the literature as the comfortable walking speed or desired walking speed[5,6,34].A.F.Miguel/Physics of Life Reviews10(2013)168–190171Fig.1.The comfortable walking speed versus decade of age:!female,"male(experimental data obtained from Bohannon[35]).Fig.2.The comfortable walking speed versus the body mass:!female,"male(experimental data obtained from[6]and[35]).Several studies[6,35]report the effect of gender and age on the comfortable walking speed of healthy humans (Fig.1).Speed is also expected to increase with the body mass due to fundamental structural reasons[36,37].The effect of the body mass on the comfortable walking speed is illustrated in Fig.2.From thisfigure,one can conclude that the comfortable walking speed scales sublinearly with body mass.Indeed,the power exponents depicted for females and males are0.182and0.156,respectively.3.Pedestrian’s guided locomotionPedestrians are attentive to details of the walking environment,especially those that are very close to them[38]. They feel uncomfortable if they get too close to other pedestrians(territorial effect or private“sphere”),as well as to physical obstacles.The vision(the eye)provides information about the environment,which is then cognitively interpreted and helps shape the way pedestrians evolve in space[39,40].This enables the selection of safer and straighter paths,and the circumvention of other pedestrians and obstacles.This guided behavior constitutes a primary and an essential feature in the perfecting of locomotion.To avoid other pedestrians or obstacles,pedestrians may adjust their comfortable speed to a lower self-selected speed.A number of researchers have studied the influence of pedestrian density(or interpersonal distances1)on1The concept“interpersonal distance”was introduced by Thompson and Marchant[41].The average interpersonal distance is obtained from the inverse of square root of pedestrians’density.172 A.F.Miguel/Physics of Life Reviews10(2013)168–190Fig.3.Experimental fundamental diagram of pedestrian movement:walking speed vs.pedestrian density(or interpersonal distance).Fig.4.Pedestrian density domains in the fundamental diagram of pedestrian movement.pedestrian speed[41–44].Several experimental studies have shown that pedestrians are able to walk at their com-fortable walking speed at densities up to0.2–0.8persons/m2.Beyond such values,an increase of pedestrian density leads to a pronounced reduction of walking speed.The walking speed–pedestrian density diagram depicted in Fig.3is known as the fundamental diagram of pedestrian movement[45–48].Seyfried et al.[45]suggested that this diagram can be divided into5density-domains.In alternative,Miguel[46]proposed that the array of points in this diagram may be divided into two major density-domains,as indicated in Fig.4:(i)Density-domain I:The interpersonal distance between the pedestrians is large enough(or the density of pedes-trians is small enough)and pedestrians are able to walk at their comfortable walking speed(0 δ δfs,whereδfs is the smaller interpersonal distance between the pedestrians that corresponds to the free walking speed).(ii)Density-domain II:Due to the reduction of the free available space,pedestrians adjust their speed,due to a natural desire of avoiding or reducing contact with other pedestrians.In this domain two sub-domains are identified which exhibit curves with different slopes:(a)the interpersonal distance between the pedestrians is not enough to walk at their comfortable walking speed,but is large enough to avoid contacts between them by a small reduction of walking speed;and(b)a more pronounced reduction in walking speed is required,since the space around each pedestrian is very small,and contacts with other pedestrians may hardly be avoided.A.F .Miguel /Physics of Life Reviews 10(2013)168–190173These pedestrian interactions can be cast into mathematical equations.Accordingly,pedestrians dynamics can be well approached within the framework of a Langevin-like equation of motion [49,50].The Langevin formulation is used to describe the Brownian particle’s motion as an Ornstein–Uhlenbeck process [51],and its position as the time integral of its velocity.Illustrative examples of this formulation for pedestrians are the social force and centrifugal force models.In the social force model [52,53],pedestrians’movement toward a destination results of the acceleration towards the desired walking speed,and the repulsive/attractive interactions with other pedestrians and obstacles.This model includes the concept of territorial effect (the private sphere)that leads to repulsive forces between pedestrians,as first suggested by Gipps and Marksjös [54].In the centrifugal force model [55,56],pedestrian movement results from the driving and repulsive forces acting on each pedestrian,with the repulsive forces being described similarly to centrifugal forces.Both models are able to capture and describe important features of pedestrian movement,such the formation of lanes in counter-flow,clogging at exit doors,oscillations at bottlenecks,among others [56].ngevin-like model for the pedestrian dynamicsA simple Langevin-like model can be derived from the above-present concept of density-domain II [46].At den-sity sub-domain IIa,pedestrians’interpersonal distances are still large enough,hence the deviation from the desired walking speed results from the necessary deceleration to adjust own speed to the speed of neighboring pedestrians.Therefore,M b d 2r dt=M b τ dr dt −dr ∗dt ,δrp δ δfs (2)and after integration of this equation,the walking speed within this domain,u IIa ,can be expressed asu IIa =u 0+1τ(δ−δfs ),δrp δ δfs (3)Here r is the position of the pedestrian,τis a relaxation time,(dr/dt −dr ∗/dt )is the mean relative speed to the pedestrians situated around,u 0is the free walking speed,δrt is the interpersonal distance that corresponds to the start of sub-domain IIb,and δfs is the smaller interpersonal distance between the pedestrians for whom free walking speed is still available.Pedestrians get too close to others at sub-domain IIb.The decrease of pedestrians’interpersonal distances leads to the presence of repulsive forces between them.These forces depend not only on the relative velocity of pedestrians,but also on the distance between them.Within this domain,M b d 2r dt=M b γ(r −r ∗) dr dt −dr ∗dt ,δmin <δ δrp (4)Integration of this equation yields the following walking speed,u IIb ,u IIb =u rp +γln δδrp ,δmin <δ δrp (5)where γis a coefficient,r −r ∗(=δ)is the mean interpersonal distance between the pedestrians,u rp is the walking speed corresponding to the minimum interpersonal distance where “repulsive forces”start to occur,and δmin is the smallest interpersonal distance possible between pedestrians in the domain.The average interpersonal distance and the pedestrians’density are related through the equation [41]δ=1√ρ(6)Substituting Eq.(6)into Eqs.(3)and (5)gives [46]u IIa =u 0−1τ √ρ−√ρfs √ρfs ρ ,ρfs ρ ρrp (7)u IIb =u rp +γ2ln ρrp ρ ,ρrp <ρ<ρmax (8)174 A.F.Miguel/Physics of Life Reviews10(2013)168–190Empirical data available in the literature can befitted with Eqs.(7)and(8),and the corresponding empirical coeffi-cients obtained.Pedestrian traffic may be unidirectional or multidirectional by nature.An examination of the results presented in prior studies indicates that both unidirectional and multidirectional streams are consistent with these two sub-domains, but that the interpersonal distance that corresponds to the start of“repulsive”forces is different[57].Therefore, a separate analysis must be performed,which yields the following coefficients[46,57]:–For unidirectional streams:τ=3.77s,u0=1.36m/s(0.3 ρ 1.4persons/m2);andγ=1.17m/s and u rp=0.995m/s(1.5 ρ 4.1persons/m2).–For multidirectional streams:τ=5.56s,u0=1.35m/s(0.14 ρ 0.88persons/m2);γ=1.10m/s and u rp=1.03m/s(0.89 ρ 5.2persons/m2).Although these results clearly support the existence of similar velocity–density domains for unidirectional and mul-tidirectional streams,the density range corresponding to each domain is actually different.Notice that neitherγnor u rp are significantly different between both streams,because these are quantities measured in the domain with less space available to pedestrians.On the other hand,the relaxation time is higher for the multidirectional streams.As the interpersonal distances between pedestrians in this domain are still large,the existence of multidirectional stream requires that pedestrians are more attentive,and more time to adjust their motion is needed.3.2.Diffusion coefficient model for the pedestrian dynamicsEinstein’s perspective of the Langevin’s approach of motion(i.e.a Wiener process)describes the penetrants mo-bility through a diffusion coefficient[58,59]and may be approached by a single coefficient.By analogy with kinetic theory,the pedestrian diffusion coefficient is related to mean walking speed and mean free interpersonal distance via the Einstein–Smoluchowski equation.The experimental data available in the literature is bestfitted by taking[57] (a)For unidirectional streams:D=1.512δ−0.588,0.47<δ 4.47m(9) (b)For multidirectional streams:D=1.498δ−0.593,0.43<δ 4.47m(10)These results also provide direct evidence supporting the differences between uni-and multidirectionalflows of pedestrians.Additionally,these coefficients are valid for the entire range of domain II.In summary,the models based on Langevin’s and Einstein’s pioneering studies in1905and1908[49,58],respec-tively,are able tofit well experimental data that relates walking speed to pedestrian density.The analysis of pedestrian dynamics as an Ornstein–Uhlenbeck type process,however,produces more insight into the“forces”that drive pedes-trian motion,and delivers different approaches according to pedestrian density sub-ranges(Eqs.(7)and(8)).On the other hand,a Wiener-type process,which is based on a single coefficient(Eqs.(9)and(10)),provides a more compact and simples approach of pedestrian motion.Despite their different mathematical formulation,all of these approaches are physically equivalent.Gillespie[60]presents a review of the arguments that lead to the conclusion that any diffusion coefficient may be linked with quantities such asτandγ.4.Constructal theory of pedestrian dynamics4.1.A new thermodynamics insight into dissipativeflow systemsSince Anaximenes of Miletus(585–528B.C.),laws are considered operative throughout Nature[61].This consti-tutes a magnificent triumph of reason and observation:laws tell us how things operate and can guide us in the quest for news knowledge.The invariance provides a structure and coherence to the laws just as the laws provide a structure and coherence to the set of natural events.A.F .Miguel /Physics of Life Reviews 10(2013)168–190175Thermodynamics is one of the bedrocks of modern science,and is firmly grounded into laws.Different laws provide us a view of natural phenomena.The zeroth law defines a useful property “temperature”(and proposes the equality of temperature as necessary and sufficient condition for thermal equilibrium).The first law defines useful extensive property “energy”(and asserts that energy is conserved).Since it is possible to take the same amount of internal energy “forward”and “backward”,the first law expresses symmetry.Although all processes must take place in accordance to the first law,the principle of conservation of energy is,by itself,insufficient to describe preferred directions of action in time.Both the reverse flow (hot to cold and cold to hot)and the immutability of configuration are not in violation of the first law [61].The second law of thermodynamics asserts the existence of extensive property entropy and states that this property in an adiabatically isolated system never decreases in time.The entropy is a Lyapunov function of the dynamical system and the “backward”process is not allowed [61].There is a “time asymmetry“or a “direction of time”or an “arrow of time”of the state of the system.The third law defines a state known as “absolute zero”(and relates the entropy of a system to its absolute temperature).Most real systems are however not isolated and may exhibit distinct characteristics.If two mixable liquids are let to mix in a vase,diffusion takes place spontaneously and a progressive decrease of initial individual concentrations will occur with a corresponding increase of entropy.But living organisms are able to maintain the differences of liq-uid concentrations in time (by chemical reactions and active transport).Prigogine named these systems ‘dissipative structures’because they cannot exist independently of their environment [62,63].These “structures”make an effort to avoid a transition into thermodynamic equilibrium by a continuous exchange of materials and energy with the en-vironment.Therefore,they are also able to self-organize through instabilities that lead to irreversible bifurcations and new stable system states [62,63].Another of Prigogine’s contributions was the minimum entropy production principle (or Prigogine theorem),which applies to open linear nonequilibrium systems in the stationary (or approaching the stationary)state.At every instant,currents of fluid,heat,mass,or information are flowing through animate and inanimate,dissipative open systems.This involves a state of organizational structure intimately coupled with nodes and channels of supply and distribution.The ubiquitous generation of configuration (design,organization)in these nonequilibrium systems is covered by the constructal law of Adrian Bejan,which states that “For a finite-size flow system to persist in time (to live )it must evolve such that it provides greater and greater access to the currents that flow through it ”[64–70].This new law asserts that for any flow system there is a property “configuration”and relates the generation of configuration to its greater access to flow.2This is possible because systems have the freedom to morph (i.e.,freedom to change the configuration in time)to achieve their purpose of higher global performance under constraints.Flows occur against resistances (imperfections)that constantly cause energy dissipation and try to slow them down.Therefore,the emergence of configuration (organization)with a purpose,defined by the constructal law,also requires that entropy changes.For the sake of simplicity,let us consider a linear pressure–flow relation (or potential–current relation).In this case,the resistance,R ,is related with the time rate of entropy generation,d ˙S g ,by R =1T V 2d ˙Sg and R =T d ˙S g 2,where V is the potential (or pressure difference),I is the current (or flow),and T is the absolute temperature.Minimization of resistance in morphing configurations under constant I and constant V (constraints)corresponds not only to a minimization of the entropy generation rate but to a maximization of the entropy generation,respectively.In summary,configuration emerges in systems that have a purpose and are far from equilibrium,and the emergence of this organization requires that entropy changes.The constructal law is not only connected to the entropy generation rate,but it also provides the reasons for why and how design occurs in nonequilibrium systems.4.2.Constructal view of human gaitEngines (man-made,animal,geophysical)use energy to produce the work required for driving movement.In order to induce movement,they should be able to overcome internal and external resistances (i.e.,energy input is matched by energy loss).Such thermodynamic “imperfections”cannot be avoided,and the constructal improvement of functions implies the generation of a design that distributes imperfections optimally to fill the flow space.Therefore,the constructal law is about both the necessity and the evolution of design to occur.2“Maximum flow access”corresponds to minimum travel time or minimum transfer time [67].Therefore,“for a finite-size flow system to persist in time it must evolve such that it provides a minimum travel time to currents that flow through it”.。