...March 28, 2008 22:40 Applicable Analysis ArticleApplAnalHomogVolChoquetMikeliclast Applicable Analysis Vol. 00, No. 00, March 2008, 1{22 RESEARCH ARTICLE Laplace transform approach to the rigorous upscaling of the in¯nite adsorption rate reactive °ow under dominant Peclet number through a pore z Catherine Choquet a and Andro Mikeli¶c b ¤ aUniversit¶e P. C¶ezanne, LATP UMR 6632, Facult¶e des Sciences et Techniques de Saint-J¶er^ome, 13397 Marseille Cedex 20, FRANCE bUniversit¶e de Lyon, Lyon, F-69003, FRANCE; Universit¶e Lyon 1, Institut Camille Jordan, UFR Math¶ematiques, Site de Gerland, B^at. A, 50, avenue Tony Garnier 69367 Lyon Cedex 07, FRANCE (submitted on March 31, 2008) In this paper we undertake a rigorous derivation of the upscaled model for reactive °ow through a narrow and long two-dimensional pore. The transported and di®used solute par- ticles undergo the in¯nite adsorption rate reactions at the lateral tube boundary. At the inlet boundary we suppose Danckwerts' boundary conditions. The transport and reaction pa- rameters are such that we have dominant Peclet number. Our analysis uses the anisotropic singular perturbation technique, the small characteristic parameter " being the ratio between the thickness and the longitudinal observation length. Our goal is to obtain error estimates for the approximation of the physical solution by the upscaled one. They are presented in the energy norm. They give the approximation error as a power of...
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...MATH 364A: Ordinary Differential Equations (Midterm 1) Name: Student ID: Signature: Question 1 (40 points) Solve the following initial value problems. (a) y + t3 y = t3 y(0) = 0. (b) y = − (1+x) y y(−1) = 1. Question 2 (40 points) Solve the second-order initial value problem 2y − 3y − 5y = 0 y(0) = 0 2 y (0) = 1. Question 3 (40 points) For each equation below, first determine whether the equation is exact or not exact. If the equation is exact, find the solution. (a) cos(y) + (2y − x sin(y)) dy = 0. dx (b) 3xy 2 + (y 3 + 3x2 ) 3 dy = 0. dx Question 4 (40 points) Consider the following first-order differential equation y = (y 2 − 1)(4 − y 2 ). Find all critical (equilibrium) solutions and classify their stability. 4 Question 5 (40 points) (True/False) In each of the following, determine whether the given function solves the given differential equation or initial value problem. (a) If k > 0 denotes any real constant, then the function y(t) = e−kt solves the initial value problem y = −ky y(0) = 1. (b) The function y(t) = (1 − t)−1 = 1/(1 − t) solves the initial value problem y = y2 y(0) = 1. (c) The function y(t) = e2t solves the second-order initial value problem y = 2y y(0) = 1 y (0) = 2. (d) Any function y(x) defined by the implicit equation x4 + 2x2 y 2 + y 4 = C solves the differential equation x3 + xy 2 + (x2 y + y 3 )y = 0. 5 Question 6 (Extra Credit, 10 points) An object with mass...
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...Preface During the past century, the impact of mathematics on humanity has been more tremendous than ever since Galileo's agonizing fight against the old establishment and the revolution which physics experienced after Newton's subsequent synthesis. At the beginning of the last century, mathematical ideas and techniques were spread to theoretical and applied physics by the influence of two of the greatest mathematicians of all times, D. Hilbert and H. Poincar6, being then at the zenith of their careers. Their ability to establish very deep at first glance often hidden connections between a priori separated branches of science convinced physicists to adopt and work with the most powerful existing mathematical tools. Whereas the 20th century really was the century of physics, mathematics enjoyed a well deserved reputation from its very beginning, so facilitating the huge impact it had subsequently on humanity. This reputation has been crucial for the tremendous development of science and technology. Although mathematics supported the development of weapons of mass destruction, it simultaneously promoted the advancement of computers and high technology, without which the substantial improvement of the living conditions humanity as a whole has experienced, could not have been realized. In no previous time the world has seen such a spectacular growth of scientific knowledge as during the last century, with mathematics playing a central role in most scientific and...
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...| Lab 1: 1D Cellular Automaton | ECE 5760 | | Lucas Ackerman (lba36) Weiqing Li (wl336) | 9/16/2011 | Introduction The purpose of this lab was to design a hardware implementation of an elementary cellular automaton and display the evolving state of that automaton on a VGA screen (with a minimum resolution of 320x240). In the implementation, there was to be a way for the user to set the evolution rule which defined how each new generation formed from the previous generation. Additionally, the user should be able to press a button and display another screen with the next set of evolved states. The initial condition was to be selectable and either a single white cell in the center of the first generation or a random cellular automaton. In the proceeding sections we will discuss our implementation, the results, comparisons with natural phenomena and possible improvements to the design. Design and Testing Overview As mentioned above, the implementation of the 1D cellular automaton was completed in hardware and no software was designed. We used the Altera DE2 development board and the Cyclone II E2C35 FPGA. Since each cell of a new generation of the 1D cellular automaton is calculated by three cells from the previous generation and we wanted to generate the cellular automaton with hardware, a state machine running at 27Mhz was implemented to read from the memory, generate the new cell and store it back into memory. We also implemented a separate VGA interface...
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...ME3291 NATIONAL UNIVERSITY OF SINGAPORE ME3291 – NUMERICAL METHODS IN ENGINEERING (Semester 2 : AY2013/2014) Time Allowed : 2 Hours INSTRUCTIONS TO STUDENTS: 1. Please write your Student Number only. Do not write your name. 2. This assessment paper contains FOUR (4) questions and comprises FOUR (4) printed pages. 3. Students are required to answer ALL FOUR (4) questions. 4. Students should write the answers for each question on a new page. 5. This is a CLOSED-BOOK ASSESSMENT with authorized materials. Students are allowed to bring two A4 size sheets of notes/formulae written on both sides. 6. All questions carry equal marks. PAGE 2 ME3291 QUESTION 1 The heat conduction equation in 1D is given by T/ t = b 2 T/ x2. Here T is the temperature and b is the thermal conductivity. You are interested to use the DuFort & Frankel discretization scheme to obtain the finite difference equation of the governing equation because you have heard of its inherent stable properties. The DuFort & Frankel scheme is given as: (Tpq+1 - Tpq-1)/(2 t) = (b / ( x)2) [Tp+1q – (Tpq-1 + Tpq+1) + Tp-1q]. where Tpq = T (p x, q t) is the finite difference representation. You are interested to use the von Neumann (Fourier) stability analysis to determine if it is inherently stable or otherwise. If otherwise, then you show the criterion for the limit of stability. You may assume that Tpq = q ei ph where is the amplification factor,...
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...Introduction to Finite Element Analysis (FEA) or Finite Element Method (FEM) Finite Element Analysis (FEA) or Finite Element Method (FEM) The Finite Element Analysis (FEA) is a numerical method for solving problems of engineering and mathematical physics. Useful for problems with complicated geometries, loadings, and material properties where analytical solutions can not be obtained. The Purpose of FEA Analytical Solution • • Stress analysis for trusses, beams, and other simple structures are carried out based on dramatic simplification and idealization: – mass concentrated at the center of gravity – beam simplified as a line segment (same cross-section) Design is based on the calculation results of the idealized structure & a large safety factor (1.5-3) given by experience. FEA • Design geometry is a lot more complex; and the accuracy requirement is a lot higher. We need – To understand the physical behaviors of a complex object (strength, heat transfer capability, fluid flow, etc.) – To predict the performance and behavior of the design; to calculate the safety margin; and to identify the weakness of the design accurately; and – To identify the optimal design with confidence Brief History Grew out of aerospace industry Post-WW II jets, missiles, space flight Need for light weight structures Required accurate stress analysis Paralleled growth of computers Common FEA Applications Mechanical/Aerospace/Civil/Automotive ...
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...are related to one another. Comparison of the senses of Ethics and Engineering Ethics Ethics 1. Ethics is an activity which concerns with making investigations and knowing about moral values, finding solutions to moral issues and justifying moral issues and justifying moral judgments. 2. Ethics is a means of contrasting moral questions from non-moral problems. 3. Ethics is also used as a means of describing the beliefs, attitudes and habits related to an individual’s or group’s morality. Eg. : Ethics given in the Bhagavat Gita or the Bible or the Quran. 4. As per the definition of dictionaries – ‘moral principles’ is about the actions and principles of conduct of the people. i.e. ethical or unethical. Engineering Ethics 1. Like the ethics, engineering ethics also aims at knowing moral values related to engineering, finding accurate solutions to the moral problems in engineering and justifying moral judgments of engineering. 2. Engineering Ethics gives a total view of the moral problems and how to solve these issues specifically related to engineering field. 3. Engineering ethics is also using some currently accepted codes and standards which are to be followed by group of engineers and engineering societies. 4. Engineering ethics also concerns with discovering moral principles such as obligation, rights and ideals in engineering and by applying them to take a correct decision. From these senses of Engineering ethics, one can realize that it is...
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...reading assignments. Each response should be at least one half of one page in length and utilize APA format. 1. What is the difference between a moral judgment and an aesthetic judgment? · The difference between moral judgment and an aesthetic judgment is that moral judgment determines what is considered right or wrong based on one’s feelings, which is influenced mainly by religious beliefs and upbringing. Aesthetic judgment, on the other hand, judges the beauty and status of objects. 2. Define cultural relativism. · Cultural relativism is a theory that knowledge is related to the limited nature of mind and conditions of knowing. It focuses on what is considered right or wrong as judged by different cultures, and also focuses on the differences involving social mores, customs, religions, practices, moral codes, traditions, and attitudes from one culture to another. 3. Describe the problems with cultural relativism. In light of its problems, are there any valuable insights the theory brings to moral theorizing? · One problem with cultural relativism is that it may support intolerance for one’s culture, even though it is thought of being able to teach tolerance for other cultures. However, in light of its problems, cultural relativism can teach having respect for cultural values. 4. What is a moral saint? · A moral saint is defined as a person who is always, or almost always acting to improve the well-beings of others and society. They seek to...
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...Importance of Value Education in Modern time Beena Indrani* Everyone knows that life is precious – that life is important. We all protect our life because we care for it more than anything else. If life is so important, the values of life are even more important. Values are guiding principles, or standards of behaviour which are regarded desirable, important and held in high esteem by a particular society in which a person lives. "The Importance of Values and Morals are the code we live by in a civil and just society. They are what we use to guide our interactions with others, with our friends and family, in our businesses and professional behaviour. Our values and morals are a reflection of our spirituality; our character. They are what we hope to model for our children and the children around us, because children do watch us as they develop their own sense of right and wrong. Value education means inculcating in the children sense humanism, a deep concern for the wellbeing of others and the nation. This can be accomplished only when we instill in the children a deep feeling of commitment to values that would build this country and bring back to the people pride in work that brings order, security and assured progress. A person with proper values will not be afraid to face problems. He or she will expect and accept them as part of life. He or she will not give un necessary importance to anything that happens in life. He or she will have complete faith in God. Such a person...
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...Cruz, Laguna Experimental Psychology “Cheating and its effects on the Moral Sensibility” Of Criminology and Education Students In Union College Submitted by: Submitted to: Carable, Cris Madel Mrs. Bituin Gracia Z. Almonte Blanca, Jan Marinie Padua, Carla May Statements of the Problem: This study aimed to compare the effects of cheating on the moral sensibility of criminology and education students in Union College. Introduction: Moral Sensibility as define refers to our response towards what is right or wrong. Because man is believed—by nature is good but morally weak, he endures all the temptations through his life. Cheating is considered as one of those as one of those which lower the moral sensibility of students, it is also a serious problem that has negative educational, social, and psychological effects. Educationally, cheating is contrary to the spirit if higher education, especially in developing and promoting moral values and attitudes. Socially, cheating is unacceptable behavior to get something with no right. Cheating is also not only affects students who cheated but also other students as it forces them to live in an unfair system. The good thing is that by learning the consequences of this action, students learn to value fairness and honesty even more. Psychologically, cheating may cause an instability in a student’s values, potentially resulting in serious psychological problems, such as feelings of being guilty and with shame but in our culture Filipino...
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...1. Clearly Define the ethical problem. The ethical problem is that there is a security issue in the Communications and Electronics Section of the new unit in which I am assigned, and whether or not I should be honest and report this issue. 2. Employ applicable laws and regulations. To employ applicable laws and regulations I would need to research Army regulations and the unit's local Standard Operating Procedure to determine proper disposal of "Secret" documents. 3. Reflect on the ethical values and their ramifications. There are seven Army values. Some may believe that all seven Army values may not be involved in every ethical problem. In my opinion all seven Army values are in some way involved in every ethical problem. Here is how I believe all seven Army values are involved in this situation. "Loyalty" Would it be disloyal to the unit to not report this security violation? "Duty" Duty is to fulfill my obligations. In this situation my obligation would be to report this violation of security. "Respect" To treat others as they should be treated would be to report this situation. If they made the wrong ethical decision, reporting the violation would be how they should be treated. If they made an honest mistake, reporting the violation would still be how they should be treated and they could learn from the mistake for their future situations. "Selfless Service" To put the welfare of the Nation and the Army above my own would mean to report this situation...
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...In his essay Existentialism is Humanism Sartre develops an atheistic moral system. In this paper, I will examine the moral system that Sartre presents. I will attempt to provide the most plausible interpretation of this morality and determine if this moral system can work in a society. I will conclude that there are several problems with Sartre’s account of morality that make it inadequate. And I will try to provide a possible solution to these problems. In order to understand Sartre’s account of morality we should first examine the basis upon which it is developed. Sartre develops his account of morality from a perspective of what he calls a “consistently atheistic” existentialism. The “consistently atheistic” existentialism maintains that God does not exist. This means that there can be no universal moral values, but it also means, and this is very important for Sartre’s account that man’s existence comes before man’s essence. If God does not exist then there can be no universal moral values because such values, at least in the European morality, come from the “commandments of God”. We use these commandments to define good and evil, and upon these two opposing concepts we base our morality. Furthermore if God does not exist then man was not created according to a divine plan, his essence was not defined a priori, and therefore there is no such a thing as “Human nature”. Sartre defines his phrase “existence precedes essence” as applied to man...
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...Nash equilibrium = a pair of strategies (strategy is a best response against the other) When players act rationally, optimally, and in their own self-interest, it’s possible to compute the likely outcomes (equilibria) of G. By studying G, we learn: Strategies are likely to take us and how to modify the rules of the game to our own advantage. SEQUENTIAL G (players take turns moving) are influenced by who moves first (a potential first-mover advantage, or disadvantage), and who can commit to a future course of action. Credible commitments (threats) are difficult to make because they require players to commit to a course of action against their self-interest. Thus, the best threat is one you never have to use. SIMULTANEOUS-move G, players move at the same time. In the prisoners’ dilemma, convict and cooperation are in tension—self-interest leads to outcomes that reduce both players’ payoffs. Cooperation can improve both players’ payoffs. Rules of thumb: • Be nice: No rest strikes. • Be easily provoked: Respond immediately to rivals. • Be forgiving: Don’t try to punish competitors too much. • Don’t be envious: Focus on your own slice of the port pie, not on your competitor’s. • Be clear: Make sure your competitors can easily interpret your actions. Strategic: model as either a simultaneous-move or sequential-move game. Focusing on how the outcome of bargaining games depends on who moves first and who can commit to a bargaining position, as well as whether...
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...Assess sociological explanations of the role of the mass media in creating moral panics about crime and deviance: A moral panic is the process of arousing social concern over an issue, this is often an exaggerated over-reaction by society to a perceived problem, which is usually driven or inspired by the media. In this situation the reaction ends up amplifying the problem out of proportion to its real seriousness. This creates anxiety amongst the general population, and this therefore puts pressure on the agents of social control to deal with the problem, who then act accordingly to the group responsible for the panic. There is a strong relationship between mass media and crime. On average, around 30% of newspaper content is dedicated to crime, however it can be debated whether this news is true because the media exaggerate the truth in order to publish a newsworthy story. The mass media are heavily involved in creating moral panics about crime and deviance in society. According to Cohen, the mass media play a vital role in the societal reaction to crime and deviance. He suggests that moral panics have a number of stages, in which the media label certain groups, in order to maximise profit. Firstly, the media use exaggerated language and headlines when reporting on a particular event that has occurred and use follow-up articles, in which they identify this event as a social problem. Whereby ‘folk devils’ are created (Goode and Ben-Yehuda: 1994). Folk devils are over simplified...
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...professional people acting in the context of a business organization. Business organizations or organizations as such do have a formal structure in which responsibility ultimately lies with a director or the board of directors. A business organization forms a context for a great variety of decisions. In a juridical perspective the organization is the bearer of numerous transactions. Inside organizations one may find remarkable opportunities for just or unjust behaviour, for moral or immoral behaviour, for situations of equality or inequality which deserve to be evaluated ethically. As FEWEB is a school for the study of economics and business administration in an economic perspective we focus on so-called “economic decisions” which are decisions being taken with some form of economic calculus. In this course we will spend time on questioning whether the economic or financial outcomes of these decisions are morally neutral or deserve some further moral investigation. Now, this course trains its participants what moral investigation is all about. We do so, for example, by questioning whether such decisions or the expected outcome of such decisions may contribute to something as an increased income for some parties involves, or to our common good, or to the durability or continuity of the organization as such, or some other goal or objective. A good objective...
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