...Chaos: A short Introduction Scientists have been coming up with theories for thousands of years now. The theories have been tried and tested have been altered and improved to better understand why certain things happen in and out of this world. Many of these theories are still in the works and our not fully comprehendible and scientists have been working hard to achieve breakthroughs in these areas. One such theory has achieved several breakthroughs within the past couple of years and that theory is called Chaos Theory. This theory first started out mainly as a sort of fictitious happening only read about in novels until lately when scientist have discovered that this theory may have more effect than previously deliberated. In Leonard Smith’s book, “Chaos: A Very Short Introduction” he gives an understandable account of what the Chaos Theory is and how it affects the environment around us. Leonard explains to the reader how the Chaos Theory works through mathematical diagrams, models, and simulations to show the possible results the theory could claim on the environment around us. The book is for the most part easy to understand and gives the reader a sufficient understanding even if the reader does not have a background in mathematics or science. Chaos theory first came about when scientist decided they wanted to be able to predict the future more accurately of certain events happening. The theory takes a look at the initial beginning of a system and tries to determine...
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...INTRODUCTION TO CHAOS THEORY BY T.R.RAMAMOHAN C-MMACS BANGALORE -560037 SOME INTERESTING QUOTATIONS * “PERHAPS THE NEXT GREAT ERA OF UNDERSTANDING WILL BE DETERMINING THE QUALITATIVE CONTENT OF EQUATIONS; TODAY WE DO NOT KNOW WHETHER THE EQUATIONS OF FLUID FLOW CONTAIN THE BARBER POLE STRUCTURE OF TURBULENCE; TODAY WE DO NOT KNOW WHETHER THE SCHRODINGER EQUATION CONTAINS FROGS, MUSICAL COMPOSERS OR MORALITY OR WHETHER SOMETHING BEYOND IT LIKE GOD IS NEEDED OR NOT “ PARAPHRASED FROM R.P.FEYNMAN * “ONLY A CORNER OF THE VEIL HAS BEEN LIFTED, BUT PERHAPS WE HAVE STARTED ON THE ABOVE JOURNEY ” PARAPHRASED FROM FLORIS TAKENS WHAT IS CHAOS THEORY? * CHAOS THEORY IS BASED ON THE OBSERVATION THAT SIMPLE RULES WHEN ITERATED CAN GIVE RISE TO APPARENTLY COMPLEX BEHAVIOR. * EG. LET US CONSIDER X0 RULE X1 X2 RULE | | | | X1 XN RULE X N+1 THE BASIC OBSERVATION IS ; IF IN THE IMPLEMENTATION OF THE ABOVE RULE X 0 IS CHANGED BY A SMALL AMOUNT, THE RESULTING SEQUENCE WILL BE VERY DIFFERENT. AFTER SOME ITERATIONS MATHEMATICIANS HAVE STILL NOT AGREED ON A DEFINITION OF CHAOS THAT IS ACCEPTABLE TO ALL HOW EVER AN OPERATIONAL (MEANING ONE THAT CAPTURES MOST ESSENTIAL FEATURES) DEFINITION OF A CHAOTIC SYSTEM IS ; 1) THE SOLUTION MUST BE APERIODIC 2) THE SOLUTION MUST BE BOUNDED 3) THE SOLUTION MUST BE EXPONENTIALLY SENSITIVE TO INITIAL CONDITIONS THE RULE THAT GOVERNS A CHAOTIC SYSTEM MUST SATISFY CERTAIN PROPERTIES 1) THE RULE MUST BE NONLINEAR 2) IN THE...
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...Film Analysis 1 Fine Arts Film- Spring 2014 Order and Chaos in Jurassic Park First time watching Jurassic Park the theme that stands out most is Man vs. Nature but this is not the best fit. The true theme is almost shown straight forward during the helicopter ride to the island when Dr. Malcolm states, “John doesn't subscribe to Chaos, particularly what it has to say about his little science project!” (Koepp 19) pitting him against Hammond. These two are the most obvious players in the chaos game, but Dr. Sattler against Dr. Grant and the Tyrannosaurus Rex (T. rex) against the Velociraptors (Raptors) are also players. The other characters do not have as defined roles but still play into the game. They all have a common theme: Chaos vs. Order. Most of the main characters arrive on the island on the same helicopter. The first view inside shows Hammond, Dr. Sattler, and Dr. Grant on the right with Dr. Malcolm and Gennaro on the left. This scene shows who is on which side of the line, but Hammond’s and Dr. Malcolm’s conflict with each other is most prevalent. Hammond is wearing all white while Dr. Malcolm is, “dressed all in black” (Koepp 18) adding visual representation of the polar difference between chaos and order. Chaos and order is the root topic during the Velociraptor birth and lunch scene. Dr. Sattler and Dr. Grant debate which will win in the end but Dr. Malcolm and Hammond have already made up their minds. Chaos is thrown its first blow when Dr. Malcolm is hurt by the...
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...Shifting Paradigms: From Newton to Chaos In the article “Shifting Paradigms: From Newton to Chaos”, Toby Tetenbaum argues that Chaos theory, a term used to describe nonlinear complex systems and organizations, can be used to study change in organizations. Unlike Newtonian scientists who believed that “…relationships between cause and effect are simple, clear and linear.” , Tetenbaum argues that due to the information era organizations are more complex with employees working anytime from dispersed locations. The increasing speed of communications and the demand for knowledge sharing has also contributed to more of a self managed model. Consequently, Tetenbaum says that the 21st century manager’s role must consist of 5 critical skills. He/she must be able to: 1) Manage the Transition, 2) Build Resilience, 3) Destabilize the System, 4) Manage Order and Disorder, the Present and the Future, and 5) Create and maintain a Learning Organization. In the first role, “Managing the Transition”, Tetenbaum explains that organizations are moving from the industrial to the information era. Both employees and managers have to change their attitudes towards how work is done and how problems are solved. In the industrial era workers take orders from upper management and follow instructions to ensure the expected results. Their knowledge and practices are based on proven skills and experiences previously tested. Transitioning to an information era would mean letting go of what is...
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...Learning Outcome 1 - Know the range of different businesses and their ownership Assessment Criteria P1 Describe the type of business, purpose and ownership of two contrasting organisations Activities or scenario: You work as a business liaison officer with a local government council. This is an important role as it is involved with promoting the area as a good place to do business. The council is keen to encourage new businesses to relocate to, or start up in the local area, thus creating more jobs for local people. Your task is to investigate some organisations already operating in the area, to find out about how successful they are and how they operate, so that this information can be used at future planning meetings. Your research should be written up in the form of a well-structured report about them. You are to focus your work on ‘two contrasting organisations’. This task assesses P1 Describe the type of business, purpose and ownership of two contrasting organisations Your task is to investigate some organisations already operating in the area, to find out about how successful they are and how they operate, so that this information can be used at future planning meetings. Task 1 |Introduce the range of different businesses and their ownership. Include a summary of the following; | |Range of different businesses: local;...
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...CHAPTER 9 INTEGRATION Focus on Exam 9 1 ∫ 3 + sin x dx = cos2 x ∫cos 3 2 x + sin2 x dx cos x = ∫[3 sec2 x + (cos x)−2 sin x] dx = ∫[3 sec2 x − (cos x)−2 (−sin x)] dx (cos x)−1 = 3 tan x − +c −1 = 3 tan x + 1 + c cos x 2 ∫sin2 x cos2 x dx = ∫(sin x cos x)2 dx = = = = 1 ∫2 sin 2x 2 dx sin 2x = 2 sin x cos x 1 sin x cos x = sin 2x 2 ∫ 4 sin 1 4 1 2 2x dx ∫ 1 − cos 4x dx 2 cos 4x = 1 − 2 sin2 2x sin2 2x 1 − cos 4x = 2 ∫ 1 1 = x − sin 4x + c 8 4 3 1 (1 − cos 4x) dx 8 ∫ du x 2 dx = 1 − u2 1 − x4 ∫ = = = 1 du 1 − u2 2 ∫ u = x2 du = 2x dx du x dx = 2 1 1 1+u × ln +c 2 2 1−u 1 1 + x2 ln +c 1 − x2 4 ∫ a − x = − 2a dx 1 2 2 ln a − x + c © Oxford Fajar Sdn. Bhd. (008974-T) 2012 a+x 2 ACE AHEAD Mathematics (T) Second Term 4 Let x = sin θ dx = cos θ dθ dx = cos θ dθ ∫x 2 dx cos θ dθ = 2 2 1−x sin θ 1 − sin2 θ ∫ = = ∫ sin θ ∫ sin dθ 2 cos θ dθ 2 cos2 θ θ q 1 x = ∫cosec2 θ dθ = − cot θ + c 1 − x2 =− x +c 5 Let u = ln x du 1 = dx x dx = du x dx 1 dx ∫ x ln x = ∫ x ln x = 1 − x2 [Shown] ∫u du = ln |u| + c = ln |ln x| + c 6 d (tan3 x) = 3 tan2 x sec2 x dx = 3(sec2 x − 1) sec2 x = (3 sec2 x − 3) sec2 x = 3 sec4 x − 3 sec2 x 4 2 3 [Shown] ∫(3 sec x − 3 sec x) dx = tan x + c ∫3 sec4 x dx − ∫3 sec2 x dx = tan3 x + c ∫3 sec4 x dx = ∫3 sec2 x dx + tan3 x + c = 3 tan x + tan3 x + c 1 c ∫ sec4...
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...Chaos Report The Standish Group is a widely known source of independent primary research and analysis of IT project performance. In 1995, the Standish Group published the CHAOS Report, an often-quoted analysis that focuses on the failure of IT projects to better improve overall IT project performance. The CHAOS Report had documented monetary loss on software developments for unsuccessful projects. The Standish Group comprised such data using focus groups, in depth surveys and executive interviews discussing project performance of completed IT projects. The CHAOS Report provides data on the failure rate of IT projects and also details common explanations for such failure. The authors of the CHAOS Report describe the advantageous process of building bridges to accentuate the lack thereof in software development; Alfred Spector had used such a comparison originally in his article, a computer science perspective of bridge design. The concept is that an error, which resulted in the collapse in a bridge, can be so great in its severity that investigations were subsequently done, allowing those involved in the building process to learn from their mistakes. Differentially, the computer industry allegedly covers up, ignores and/or rationalizes the errors or shortcomings that led up to the failure. The Standish Group contends that project failures will decrease if the following is focused on following a project failure: the scope of software project failure, main factors that cause...
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...A Constitutional chaos. On September 17th, 1787, The Constitution of the United states of America was signed by the delegates on the conclusion of the Constitutional Convention in Philadelphia. Weeks later after many arguments between the same delegates about other rights of American citizens, the Bill of Rights was written to solidify all of the basic individual freedoms of the people. It was on this document that several laws were written and many great freedoms given. But because these amendments didn't give a specific definition of these freedoms and rights problems ranging from wars being fought because of conflicting ideals in people to poor moral choices being unjustified because there is no line drawn to decide how far things will go; and the vague rules that allow and cause these things to happen need to rewritten . To learn where it all this mess starts is easy; it starts almost immediately after the signing of the Constitution. The document states that there will be freedom of speech, assembly, the right to bear arms, and other freedoms. The cause of one of the first issues that plagued America was not whether the rules are fair and good or not, but who the rules and freedoms are meant for. This was cause of the continuation of slavery in America even after men were supposed to be free because the Bill of rights did not state that a man, either black or white or red or green, has these freedoms. It just simply says that the citizens of America have these rights...
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...Chaos and Fractals Chaos is a fairly new science. The definition of chaos is complete confusion and disorder, but more generalized to everyday speech it means a random pattern that can occur. (Mirriam - Webster) For scientist this can be a good thing. Henry Adams is quoted as saying "Chaos often breeds life as order breeds habit." (STSCI) Fractals simply put, is a repeat design that as you zoom in is repeated indefinitely. Above is the Sierpenski Triangle, as you zoom in you see three more of the triangle, and in each of those is three more triangle, and as you zoom in you see three more triangles. I imagine that on a big enough scale, or with a strong enough computer there is no end to the number of triangles you can put in the Sierpenski Triangle. (STSCI) If you break a straight line into an equal number N than the equation to describe those parts would be r=1/N(1/d) In the case of the Sierpenski Triangle, a self repeating object, the equation is D = log (N) / log (1/r) (STSCI) The Koch Snowflake is designed by: * divide a line segment into three equal parts * remove the middle segment (= 1/3 of the original line segment) * replace the middle segment with two segments of the same length (= 1/3 the original line segment) such that they all connect (i.e. 3 connecting segments of length 1/3 become 4 connecting segments of length 1/3.) The top row of shapes is the pattern to make the snowflake with a triangle, the bottom shape is a blowup of the edge...
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...Mayhem- Danielle Hamilton Chaos- Melissa Mayhem’s Victim- Crystal Chaos’ Victim- Whitney K. Hass & May Hemm, Attys. At Law Commercial Mayhem- I’m the face of your ex-boyfriend’s new girlfriend that you just can’t stop thinking about and the more you drink that tequila the harder it is to forget me. But go ahead, try one more. Maybe I’ll go away then. (Crystal is sitting at a table obviously intoxicated looking sad and mad crying and so on.) Chaos- O my god! Don’t you just love me! I’m the new ipod and wow I love this song too! Let’s get jiggy with it! Oh no! What’s happening? I’m stuck. I’m stuck. I’m stuck. (Whitney is pretending to drive jamming on her ipod when something goes wrong causing her to take her eyes off the road and focus on her device) At the same time Crystal gets up to leave and drive home. Swaying as she walks she says: Crystal- “I’m fine…I’mmmm fine I shay….” (While driving Whitney knocks over a street sign for a one way road but she is too focused on her ipod to even notice) Chaos- Weeeeeeee!!!! Allright! Let’s get the jams going again!!!! Now in her car Crystal is driving and attempting to watch the road. Mayhem- I’m still here. And the longer you focus on me instead of the road with your double vision glasses on the madder you become… and forget where to turn. Yup, this looks good. (Crystal turns onto the one way road and runs into the...
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...Chaos and Fractals What is a Fractal A fractal is a never ending pattern. Fractals are never ending complex patterns that are self-similar across different scales. They are created by by being repeated over and over in a feedback loop. Fractals are everywhere. They can be found in nature, algebra, and math. Nature Algebra Geometry Mandelbrot Set This was created in 1980 shortly after the first personal computer in order to calculate numbers thousands and sometimes millions of times. Equation (old)Z=(new)Z2+C We start by plugging a value for the variable C into the simple equation below. Each complex number is actually a point in a 2-dimensional plane. The equation gives an answer, Znew . We plug this back into the equation, as Zold and calculate it again. We are interested in what happens for different starting values of C. When you square a number it gets bigger. Then you square the answer and it get even bigger.. Eventually, it goes to infinity. This is the fate of most starting values of C. Some values of C do not get bigger, but get smaller, or alternate between a set of fixed values. These are the points inside the Mandelbrot Set, which we color black. Outside the Set, all the values of C cause the equation to go to infinity, and the colors are proportional to the speed at which they expand. Ju Fractals in Nature Natural fractals can be found anywhere in nature. Even in our body. It can be the blood vessels in our arms, or...
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...BORDERING ON CHAOS The book "Bordering on Chaos" tells an important stage in the history of Mexico. Everything happened just as Mexico enjoyed great success for growth and economic development in1994 when was recently signed the North American Free Trade Agreement and the president Salinas enjoyed and celebrated the economic growth of the country. The Mexicans had finally found a leader in which they could trust. Foreign investment in Mexico had grown by 98 Percent in 1993 and the streets were full of Mexican foreign brands and stores, such as Mcdonals, Dominos pizza, Pizza hut outlets,etc.. Mexico was about to be accepted as a full member of the OECD, the Organization for Economic Co-operation and Development. The whole world was surprised by the rapid growth of Mexico and its citizens were proud of it. “Polls showed that Mexican people were more optimistic about the future than they had been in years”(12).Everything seemed too good to be true, until this happiness and celebration did not last long for Mexican people. Just when everything was going perfectly well, one night in1994 when the president Carlos Salinas de Gortari was celebrating the New year with his family and friends, it was reported that there had just been a guerrilla uprising in the southern state of Chiapas remote, “More than two thousand Mayan Indians, carrying everything from machetes to AK47 riffles, had taken the city of St Cristobal de las Casas shortly after midnight and were reported to have also seized...
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...astronomer Michele Henon.[2] [5] [pic] Fig. 1 Henon map with parameters a = 1.4 and b = 0.3. The chaotic behavior of the attractor has many physical applications. Such as: ▪ Application to the transverse betatron motion in cyclic accelerators ▪ Application of the Henon Chaotic Model on to design of low density parity ▪ Application to Financial Markets ▪ Application on area-conserving ▪ Deterministic chaos in financial time series by recurrence plots ▪ Application to the motion of stars Application in air bubble formation Introduction Below the explanation of how the Henon attractor effects a real life application is presented, which is based on the bubble formation. This experiment took place in order to detect the chaotic dynamics that give the bubble shape and motion. By using the methodology that is described below, observations using topological characterization, a chaotic region where some reconstructed attractors resemble Henon-like attractors, which visualize a possible route to chaos in bubbling dynamics. The formation of air bubbles was studied submerging nozzle in a water/glycerol solution inside a...
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...Divorce Chaos Rebecca H. Fischer, Esq. Howard Chusid, Ed.D, NCC, LMHC The scenario is one that is known to many. Your spouse and you are continually arguing. You can’t agree on anything. Everything, be it little or large, becomes an argument. The children hear it, your friends hear it in your voice, and your parents hear it in your interactions with them. You decide to visit a counselor, together and individually, but it doesn’t help. You still are not getting along and are left with few options. So, your friends tell you of a great attorney who has done great for many. You visit with the attorney and are told that you need a $5000 retainer but you have no idea where that is going to come from. The attorney also tells you that the cost for the divorce will be in the $50,000 – $80,000 range by the time you get through. You don’t have that kind of money to throw away on attorneys’ fees. If you are feeling this way, there is a high probability your spouse is feeling the exact same way. The exclusion of happiness is always felt by both partners. Problems and irritations are not just a unitary function of a marriage; both partners experience it, usually at the same time. Moreover, we should not forget the kids because they always know what is going on. There are three models of way to get through a divorce: the litigated model, collaborative model and the mediation option. The last two are similar in ideology but are different in approach. The litigated model is the one discussed...
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...CHAOS THEORY It is a field of study in mathematics, with applications in several disciplines including, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect. Chaotic behavior can be observed in many natural systems, such as weather and climate. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincare maps. This latter idea is known as sensitive dependence on initial conditions , a circumstance discovered by Edward Lorenz (who is generally credited as the first experimenter in the area of chaos) in the early 1960s. DEFINITION: It is the study of non linear dynamics, in which seemingly random events are actually predictable from simple deterministic equation. Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic systems are predictable for a while and then appear to become random. The amount of time for which the behavior of a chaotic system can be effectively predicted depends on three things: * How much uncertainty we are willing to tolerate in the forecast? * How accurately we are able to measure its current state? * Which time scale is depending on the dynamics of the system? The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying...
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