The Giver by Louis Lowry free essay sample

The Giver by Louis Lowry Chapter 1-2 1. What did the word frightened mean, according to Jonas? The word frightened meaning according to Jonas was a deep, sickening feeling of something terrible about to happen. 2. About what were Jonas and the other children taught to be careful? Jonas and the other children were taught to be careful about language. 3. How did Jonas decide he felt? What was causing this feeling? Jonas felt apprehensive. The Ceremony of Twelve was causing Jonas’s apprehensive feelings. 4. What were the two occasions when release was not punishment? The twp occasions when release was not a punishment was the release of the elderly and release of a newchild. 5. Why was the Ceremony of Twelve so important? The Ceremony of Twelve’s is where a child turning twelve would get their adult job and was the end of their childhood and start of their adult life. Chapters 3-5 1. We will write a custom essay sample on The Giver by Louis Lowry or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page What was unusual about Jonas and the new child? Jonas and the new child had pale eyes while the community members had dark eyes. 2. Describe the Assignment of Birthmother. What did Lilys parents say about it? They said the assignment did not have much honor and the birthmothers had only three children also they were not allowed to see the children and were given jobs as laborers for the rest of their lives. 3. What happened to the apple while Jonas was playing with it? The apple changed for an instance when Jonas was playing with it. 4. Describe the of Celebration Release of Roberto. The release of Roberto started with him talking about his life. Then people cheered, and chanted the anthem. After that Roberto made a good-bye speech then he bowed and walked through a special door in the releasing room. 5. Did Larissa know where Roberto or anyone else went when they were released? Larissa did not know where Roberto or anyone else went when they were released. 6. About what was Jonass dream? What did his mother and father say about it? Jonas had a dreamt that he wanted Fiona to take off her clothes and get in a bathtub. His parents said it was the stirrings and his mother gave him a pill that would stop them. She said he would have to take one every day until he entered the house of the old. Chapters 6-7 1. Describe the jacket that the Fours, Fives, and Sixes wore and the reason it was designed the way it was. Also describe the jacket the Sevens wore and what it symbolized. The jacket the Fours, Fives, and Sixes wore buttoned down the back so that the other children would have to help each other dress and learn interdependence. The jacket the Sevens wore had buttons in the front, which symbolized independence and growing up. 2. Describe the Ceremony. Tell what happened at the Naming and the other age levels. During the ceremony they were newborns received their names and parents. The eights received new jackets with smaller buttons and pockets. The Nines got their bicycles. The Tens had their long hair cut off. The female Elevens got new undergarments. The male Elevens got longer trousers with a special pocket for their school calculator. 3. What Assignment did Asher get? He was assigned assistant director of recreation. 4. What happened when Jonas’ number should have been called? What did Jonas think? When Jonas’ number should have been called the Chief Elder did not call his number. Jonas had thought he had done something wrong then taught he had skipped his number at the end. Chapters 8-10 1. What was Jonas Assignment? Why was it important and unusual? Jonas was assign to become the new Receiver of Memory for the Community. It was unusual and important because the Community only had one Receiver and he chose his successor and being the receiver was the most important job in the community. 2. What were the four qualities the Chief Elder said the Receiver of Memory must have? The four qualities the Chief Elder said the Receiver of Memory must have are intelligence, integrity, courage, and wisdom. 3. What happened when Jonas was looking out at the crowd? When Jonas was looking out at the crowd they changed the way the apple had changed. 4. Did Jonas agree or disagree with the committees choice of him as the new Receiver? Jonas agreed with it. 5. What happened the last time a new Receiver had been chosen? The last time the girl was not successful and no one knew what had happened. 6. From what rules was Jonas exempted? Jonas was exempted from rules of lying, rudeness and ask anyone any question and he would receive an answer. 7. What was Jonas prohibited from doing? Jonas was prohibited from telling his dreams. 8. What was he allowed to do that he had not been allowed to do before? He was allowed to lie. 9. What memories did the Receiver of Memory say he had to transmit to Jonas? The receiver said it was the memories of the whole world. 10. What was the first memory the Receiver said he would give to Jonas? He said he would give the memory of snow. Short Answer A. Compare and contrast Jonas from the beginning of the novel to the end. At the beginning of the novel Jonas was a normal member of the community. He obeyed all the rules and didnt do anything wrong. But all this changed when he started to receive the memories from the Giver. The changes were not imminent but he grew into them. Jonas started to lie to his parents and soon his friends. This was one of the major changes in Jonas in the novel. Jonas learned his happy community was not so happy. This was due to the fact that no one had feelings except him and the Giver. Jonas started to see the colors which was a major change because all his life he saw in the grayscale. He soon figured out that everything was fake in their community and the rules against lying were fake too because his father lied many times about the release of a newborn. Also Jonas receives wisdom from the Giver. In the end Jonas leaves the community just to make people feel, see and hear. B. Would you recommend The Giver to a friend to read? Why? Yes, I would recommend this novel to a friend to read because it is its an amazing book and really sad to read. Also this novel uses great vivid languages to help the reader understand the feel of the memories that the Giver gives to Jonas.

Rosa Parks Essays - Montgomery Bus Boycott, Community Organizing

Rosa Parks Essays - Montgomery Bus Boycott, Community Organizing Rosa Parks Who is Rosa Parks? Rosa Parks is someone who grew up believing people should be judged by the respect they have for themselves and others. (Le Blanc, 190) Rosa Parks is mostly known for standing up for herself and for other all other African Americans when she refused to go to the back of the bus to give up her seat for a white man. (Le Blanc, 190) When Rosa took a stand, she didn?t do it to make her name go down in history. She did it because she believed in herself and she stood up for an injustice she thought was wrong. Rosa Parks is a courageous and very remarkable person. Rosa Parks was born in Tuskagee, Alabama. When she was a young child her parents separated. After her parents got divorced, she moved to Montgomery with her mom. (Le Blanc, 189) She grew up with an extended family that consisted of her maternal grandparents and Sylvester, her younger brother. (Le Blanc, 189) Rosa?s mother was a school teacher and she was taught by her until age 11. (Celsi, 1) At age 11 she went to Montgomery Industrial School for Girls. It was an all black school. Everything in Montgomery was either ?blacks only? or ?whites only.? Though she found it humiliating, Parks became used to obeying segregation laws. (Celsi, 1) ?With her mother?s help, Rosa was able to grow up proud of herself and other black people.? (Contemporary Black Biography, 190) By the time she reached the midpoint of her life, Rosa was no longer a stranger to white intimidation. (Le Blanc, 190) At the age of 20, Rosa married Raymond Parks, who was a barber. Rosa and Raymond had to keep steady jobs to support themselves. (Le Blanc, 190) Rosa hated the way of life. She had always dreamed of equality and freedom. (Stewart, 1) Although Rosa grew up with segregation, she turned out to be a very well rounded unique person many people can look up to. She was just a normal person with a normal life, but she did something that not many black people back then had the courage to do?she stood up for herself. In Rosa?s spare time, she became active in the NAACP. She was also active in the Montgomery Voters League. (Le Blanc, 190) The Montgomery Voters League was a group that helped black people pass a special test so they could register to vote. (Le Blanc, 190) Rosa had been silently protesting segregation in her own quiet way over the years. For example, instead of riding up an elevator that said ?blacks only? she would take the stairs. (Le Blanc, 190) The most well known boycott is the Montgomery Bus Boycott. This was a boycott that took place in response to Rosa?s arrest. Her arrest caused black people throughout Montgomery to refuse to ride buses. (Church, 393) The success of the Montgomery Bus Boycott encouraged a wave of massive demonstrations that swept across the South. (Church, 394) Rosa Parks has succeeded in establishing herself in history by what she did. She is one of the most honored and distinguished African Americans in our history. (Asante, 71) Rosa Parks stood didn?t only stand up for herself, she stood up for racism. It must have been hard for her because not only was she an African American, she was also a woman, and back then things were much more difficult for women. Even though Rosa did something very courageous, some might say she isn?t the best leader. Many leaders give speeches, lead demonstrations and write petitions. Rosa Parks didn?t do any of these things. Other people were motivated to do these things because of her standing up for herself. (Asante, 71) The most important incident that happened in Rosa?s life occurred on December 1, 1955 Rosa Parks was riding the bus home from work like she did every day. But that day had been especially tiring. (Le Blanc, 190) The bus was a constant irritation to black people. The front four rows were reserved for whites (and remained empty even when there were not enough white passengers to fill them). The back section, which was always very crowded, was for black passengers. In between

Talking about Age in the Media

Talking about Age in the Media Talking about Age in the Media Talking about Age in the Media By Maeve Maddox Everyone wants to live longer, but no one wants to be old. –Harry Moody, director of academic affairs for AARP (2012). To me old age is always ten years older than I am. –Bernard Baruch, American financier (1870-1965). About forty-two million Americans are 65 years or older. Advertisers, politicians, and researchers often need to refer to this group, but finding a term that will not insult its members is not easy. Various terms have been suggested with varying degrees of success. Elder, elderly, senior, and retiree are the most common. In Canada, according to what I’ve read in forums, the term elder has connotations of venerable age and wisdom; in the United States, however, people tend to associate elder with disapproving church elders or the word elderly. The decline of the acceptability of the word elder is illustrated by the name change of a travel organization established in 1975 for active Americans 60 and older. The parent organization is still called Elderhostel, but in advertising, the program is now known agelessly as â€Å"Road Scholar.† Even the word retiree is heavy with the connotations of age. These days, the American Association of Retired People (founded 1958) goes by its initials only: AARP. When politicians talk about â€Å"our seniors† in the same breath as â€Å"our children,† mature adults understandably bristle. An article in The Senior Times says that the term â€Å"senior citizen† was coined in 1938 during a political campaign. Its use soars on the Ngram Viewer beginning in the 1940s. According to National Public Radio reporter Ina Jaffe, â€Å"senior citizen† is a term that â€Å"seems to annoy just about everyone.† Recognizing the minefield of age and terms relating to it, The AP Stylebook has this entry for the word elderly: Use this word carefully and sparingly. Do not refer to a person as elderly unless it is clearly relevant to the story. It is appropriate in generic phrases that do not refer to specific individuals: concern for the elderly, a home for the elderly, etc. If the intent is to show that an individual’s faculties have deteriorated, cite a graphic example and give attribution for it. Use age when available and appropriate. Apply the same principle to terms such as senior citizen. Age is one of the realities of life that our culture prefers to deny. It’s unlikely that any term can be found to refer to old people that would not be offensive to someone because in our culture, old age itself is seen as offensive. Perhaps the safest course is to refer to the intended age group in numeric terms: between the ages of 65 and 75 above the age of 65 septuagenarian octogenarian nonagenarian centenarian Colloquial synonyms for â€Å"old person† range from friendly to deliberately hurtful, for example: old-timer oldster codger dotard crone coot Although the word codger (like coot) usually has a negative connotation, this review about Dick Van Dyke in the Chicago Tribune (1992) makes a kind of compliment of it: The wonderfully funny Dick Van Dyke, insufficiently honored in his prime, has now passed into the lovable-old-codger stage. His comic gifts are sharper than ever, and he still dances with grace, style and a naughty insouciance. He is much too good for the quirky-old-coot roles that are his lot nowadays. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Vocabulary category, check our popular posts, or choose a related post below:70 Idioms with Heart50 Idioms About Arms, Hands, and FingersComma Before Too?

Problem-solving proposals Essay Example | Topics and Well Written Essays - 1000 words

Problem-solving proposals - Essay Example These problems can be attributed to the actions and strategies instituted by all the previous CEOs (â€Å"Worst of 2012†). This topic is interesting as it gives an outlook on some of the important management issues relating to the business operations in the current business environment. Businesses need to make the relevant management changes to cope with the challenges in the internal environment including employee motivation and external environment such as increasing competition and dynamic customer demands. It is clear that there is lack of stability in the leadership, and this has made it complex for the company to maintain consistency in the company. It has been noted that each CEO has instituted more dramatic strategies than their predecessors, which have led to substantial changes in the company’s direction. The HP case study is one of a kind and has valuable lessons to managers and business students worldwide. Statement of the Problem Over the past few years, HP has lost approximately three quarters of their value, and this can be observed from its performance in the stock market (â€Å"Worst of 2012†). Any efforts to turn around the company’s deteriorating performance have proven to be futile. In the past ten years, the company has made efforts to transform its leadership and has lurched from one approach to another and recruited highly skilled leaders to amend the daunting problem of poor management. In 1999, the company brought on board Carly Fiorina whose main strategy focused on repositioning the company by taking the customers’ needs into account (â€Å"Worst of 2012†). It was under her leadership that the company made one of the most detrimental moves by entering into a merger with one of HP’s archrivals, Compaq. This was aimed at improving speed in preparation for the advent of the Internet era’ however, the strategy failed to meet the set objectives. HP then recruited Mark Hurd in 2005 to deal with the issue of decreasing profitably (â€Å"Worst of 2012†). The company experienced immense growth and increased revenues under the leadership of Mark Hurd. However, this was short lived in 2010 when he was suddenly suspended over sexual harassment allegations (â€Å"Worst of 2012†). This led to an upfront challenge to his predecessor as he would have to live up to Hurd’s exemplary reputation. The company then outsourced Leo Apotheker who worked at a Germany-based software company. Apotheker focused too much on software development and worked at the company for a short time (â€Å"Worst of 2012†). Currently, the company is under the leadership of Meg Whitman who is working tirelessly to solve the problems at HP. The third quarter earnings reveal that the company is not doing so well; however, Meg Whitman retorts that there are a lot of areas that need fixing. She claims that the company is at the initial stages of its take-off. Conversely, financ ial analysts are skeptical about this and argue that it could be a repeat of what has happened with predecessors. She states that HP is facing three major challenges including execution of proposed strategies, industry trends as well as macroeconomic problems. Presently, the company has a market capitalization of 46.92 B, revenue of 115.57 B, EPS – 6. 85 and from the PE ratio we can conclude that the

Learning Diary Essay Example | Topics and Well Written Essays - 2000 words

Learning Diary - Essay Example When I was growing up, one of my favourite quotes was byAlexander Graham Bell who said: â€Å" A man, as a general rule, owes a very little to what he is born with – a man is what he makes of himself†. I have made it a habit of writing down my goals and dreams and keep track of my achievements or failures in life, and hence when we were asked to keep a learning diary or log of experiences and activities undertaken during the MSc year I was even happier because this was now officially a part of my course. Body: When I look at my life right now, I am excited at what lies ahead of me. I have always been an optimist and the future seems bright and filled with possibilities. I presently work at a bank and love my job, and am well on the way to becoming a manager for the bank in the near future. Completing my Master’s degree in Business Management will add to my advantage of securing this position, which I consider to be prestigious and filled with challenges. However when I started working with the Bank, it was a whole new experience and because of the hard work and my extra effort put into my job over a period of time, I have managed to earn the respect of my colleague’s and more important get noted by the senior management and win the trust of my customers. I had put down quite a few goals which I wanted to achieve at the Bank into my Learning Diary and would review it every fortnight to personally rate my performance at work. Goals give you a sense of meaning and purpose. Goals give you a sense of direction. As you move toward your goals and you feel happier and stronger, you feel more energized and effective. You feel more competent and confident in yourself and your abilities. Every step you take toward your goals increases your belief that you can set and achieve even bigger goals in the future. My personal achievements at work can be categorised under three main headings. Respect from my Colleagues: My colleagues are the greatest in the world, simply because they appreciate and respect me so much for all the hard work that I have put in, the extra hours and the fact that I am always available to help them out when they ask, even if it means I have to stay back late. My skill and knowledge acquired in the Banking sector has increased and they often come to me for advice or a solution to a problem they are facing. Trust from my Customers: Edgar Watson Howe once said " The greatest humiliation in life is to work hard on something from which you expect great appreciation, and then fail to get it". Thank God, that doesn't apply to me. The customers more often that not pay compliments or sometimes go a step further and put in a personal word or send across an email to my Manager's and let them know I am doing a good job. Recognition from my Manager's: The good thing about the job is that there is a

Density Functional Theory (DFT): Literature Review

Density Functional Theory (DFT): Literature Review Theoretical Background and Literature Review 2.1 Density Functional Theory This section covers basics about Density Functional Theory (DFT), which is the theoretical method behind our investigations. For those who are interested in a much more deep knowledge about the DFT we refer to textbooks such as [29] and [30]. 2.1.1 History of Density Functional Theory To get precise and accurate results from both theoretical and computational methods, the scale of physical phenomena must be well defined. In physics and material science the relevant scales of matter are time and size. In computational material science, for the multiscale understanding in both time and size scale the smallest relevant scale of atomic interactions are best described by ab initio techniques. These techniques are based on the determination of electronic structure of the considered materials and an intelligent transfer of its characteristics to higher-order scales using multidisciplinary schemes. More specifically, if the interaction of electrons is solely described using universal principles such as the fundamental laws of quantum mechanics condensed in the Schrodinger equation, these simulations are called firstprinciples, or ab initio methods. One can also separate those methods as Hartree-Fock and post-HF techniques that mainly uses by quantum chemistry field and De nsity Functional Theory (DFT) which is typically used in of material science. Ab initio simulations are becoming remarkably popular in scientific research fields. For example in DFT case, in a simple search at Web Of Science [31] or any other publication search tool, one can easily see that number of publications that include †Density Functional Theory† in their title or abstract is over 15000 in 2013. Therefore, it can be concluded that, ab initio based research already an important third discipline that makes the connection between experimental approaches and theoretical knowledge. Figure 2.1: Usage trend of DFT over years Within ab initio simulations quantum mechanical equations for any system that may be ordered or disordered are solved. That actually gives one drawback which is, solving that kind of equations is generally only possible for simple systems, because of the expensive electron-electron interaction term. So, in general, the ab initio simulations are restricted to 150-200 atoms calculations with most powerful computer clusters. Due to the that severe limitation, better techniques and methods are developed and implemented to bring the real materials into realm of ab initio simulations. The major development of ab initio methods with practical applications took place when many electron interactions in a system was possible to be approximated using a set of one electron equations (Hartree-Fock method) or using density functional theory In 1927, Thomas [32] and Fermi [33] introduce a statistical model to compute the energy of atoms by approximate the distribution of electrons in an atom. Their concept was quite similar to modern DFT but less rigorous because of the crucial manybody electronic interaction was not taken into account. The idea of the Thomas and Fermi was that, at the starting point for simplicity that electrons do not interact with each other and using classic terms, therefore, one can describe the kinetic energy as a functional of electron density of non-interacting electrons in a homogeneous electron gas. 3 years later, in 1930, Dirac [34] succeeded to include the many-body exchange and correlation terms of the electrons and actually he formulated the local density approximation (LDA), that is still used in our days. However, the Thomas-Fermi and Dirac model that are based on homogeneous electron gas do not cover the accuracy demand in current applications. In same the years as Thomas and Fermi, Hartree [35] also introduce a procedure to calculate approximate wavefunctions and energies for atoms and that was called Hartree function. Some years later, to deal with antisymmetry of the electron system, his students Fock [36] and Slater[37], separately published self-consistent functions taking into account Pauli exclusion principals and they expressed the multi-electron wavefunction in the form of single-particle orbitals namely Slater-determinants. Since the calculations within the Hartree-Fock model are complicated it was not popular until 1950s. The fundamental concepts of density functional theory were proposed by Hohenberg and Kohn in their very well known paper in the year 1964 [38]. The main idea was trying to use the electron density instead of complex and complicated wavefunction. A wavefunction contains 3N variables, where N is the number of electrons and each electron has 3 spatial degrees of freedom. In contrast to that electron density contains only 3 variables. Therefore, the implementation of the electron density with 3 variables will be more easy to handle than 3N wavefunction variables. In their work, Hohenberg and Kohn proved that all ground state properties of a quantum system, in particular the ground state total energy, are unique functionals of the ground state density. However, the Hohenberg-Kohn (HK) formulation is not useful for actual calculations of ground state properties with enough accuracy. A major improvement was achieved one year later, in 1965. Kohn and Sham [39] proposed a formulation by partially going back to a wavefunction description in terms of orbitals of independent quasi particles. The main idea was that the many-body problem can be mapped onto a system of non-interacting quasiparticles. This approach simplified the multi-electron problem into a problem of non-interacting electrons in an effective potential. This potential includes the external potential and the effects of the Coulomb interactions between the electrons, e.g., the exchange and correlation interactions. Since then up to now the Kohn-Sham equations are used in practically all calculations based on DFT. 2.1.2 Schr ¨odinger’s Equation In quantum mechanics, analogue to Newtons equations in classical mechanics, the Schr ¨odinger equation is used. This is a partial differential equation and used to describe the physical quantities at the quantum level. The Schr ¨odinger equation forms the basis of many ab initio approaches and its non-relativistic form is an eigenvalue equation of the form: HˆÎ ¨(ri,Rj)= EÃŽ ¨(ri,Rj) (2.1) where ÃŽ ¨(ri,Rj) is the wavefunction of the system depending on the electron coordinates ri,i =1N and the coordinates of all nuclei in the system Rj,j =1M. Hˆis the Hamiltonian of a system that contains M nuclei and N electrons. Therefore, the Schr ¨odinger equation that involves both nuclei and electrons has to be solved for the many-body eigenfunctions ÃŽ ¨(r1,r2, , rN ; R1,R2, , RM ). The many-body Hamiltonian can be written in the form: Hˆ= Tˆe + Tˆn + Vˆnn + Vˆen + Vˆee (2.2) ˆˆ where all of parts are operators. Te and Tn are the kinetic energies of the ˆˆ electrons and nuclei, respectively. Ven, Vee and Vˆnn represent the attractive electrostatic interaction between the electron and the nuclei and the repulsive potential due to the electron-electron and nucleus-nucleus interactions. One can also write them down explicitly: N f2 ˆ Te = − 2 i (2.3) 2me i=1 M 2Mn n=1 f2 ˆ Tn = − 2 n (2.4) 11 M ZnZme2 = (2.5) 4Ï€ 0 2 |Rn − Rm| =1;n,mn =m ˆ Vnn ˆ Ven = − 11 MN Zne2 (2.6) 4Ï€ 0 2 |ri − Rn| n=1 i=1 j= M e = (2.7) 4Ï€ 0 2 |ri − rj| i,j=1;i 2 11 ˆ Vee where me and Mn are the electron and nuclei masses, Zn is the nuclear number of the n-th atom, e is the electronic charge and f is the Planck constant. For simplicity one can also use atomic units. Then the Hamiltonian takes the form: NMM ZnZm in 22 |Rn − Rm| i=1 n=1 n,m=1;n =m 1 1 ˆ H = − 2 2 − + (2.8) j= MNMZn − + |ri − Rn||ri − rj| n=1 i=1 i,j=1;i 2.1.3 Born-Oppenheimer Approximation It is clear that forces on both electrons or nuclei is in the same order of magnitude because of their electric charge. Therefore, the expected momen 1 tum changes due to that forces must be the same. However electrons are much smaller than nuclei (e.g. even for Hydorgen case nuclei nearly 1500 times larger than an electron) they must have higher velocity than nuclei. One can conclude that electrons will very rapidly adjust themselves to reach the ground state configuration if the nuclei start moving. Born and Oppenheimer [40] published their work in 1927, they simply separated the nuclear motion from electronic motion which is now known as the Born-Oppenheimer approximation. Therefore, while solving the Hamiltonian Equation in (2.8) one can simply assume nuclei as stationary and solve the electronic ground state at first then calculate the energy of the system in that configuration and solve the nuclei motion. Then the separation of electronic and nuclear motion leads to an separation of the wavefunctions ÃŽ ¨ = ψφ of electrons and nuclei, respectively. Via the separation one can treat the nuclear motion externally by not in cluding the Hamiltonian and the â€Å"electronic† Hamiltonian can be written as: Hˆe = Tˆe + Vˆen + Vˆee (2.9) Solving the equation (2.9), one can get the total energy of the ground state of the system, which can be defined as: E0 = ψ0|He|ψ0 + Vnn (2.10) where E0 is the ground state total energy of the system and ψ0 is the eigenfunction of the electronic ground state. 2.1.4 Hohenberg-Kohn Theorem However, the Hamiltonian in Equation (2.9) is quite complicated to solve for realistic systems due to the high number of electrons and especially the term Vee makes it impossible to solve the problem exactly. Therefore, instead of solving the many-body wavefunctions, Hohenberg-Kohn deal with that problem by reducing it to the electron density Ï (r). This approach makes the fundamentals of DFT. According to Hohenberg and Kohn, the total energy of the system can be defined via the electron density as E = E[Ï (r)] and it will be the minimum for the ground state electron distribution, namely Ï 0(r). Therefore, the exact theory of many-body systems reduced to the electron density that can be defined as: Ï (r)= d3 r2d3 rN |ψ(r1, rN )|2 (2.11) and has to obey the relation: Ï (r)d3 r = N (2.12) where N is the total number of electrons in the system. One can also summarize the HK theorem in the form of the two main theorems, Theorem I : The external potential vext(r), which is the potential energy generated by the nuclei, can be determine from the ground state electron density Ï 0(r). Then Hamiltonian will be fully defined, also the wavefunction for the ground state will also be known. Theorem II : E0,the ground state total energy of the system with a particular vext will be the global minimum when Ï  = Ï 0. From the perspective of these two theorems one can write down the total electronic energy as: E[Ï ]= Te[Ï (r)] + Ï (r)vext[Ï (r)] + EH [Ï (r)] + Exc[Ï (r)]d3 r (2.13) One can also add the kinetic energy of the electrons T − e[Ï (r)], the classical Coulomb interaction (or Hartree interaction) between electrons EH [Ï (r)] and the remaining complex non-classical electron exchange correlations Exc[Ï (r)] into an universal functional FHK [Ï (r)]: E[Ï ]= FHK [Ï ]+ Ï (r)vext[Ï (r)]d3 r (2.14) The remaining will be to apply the variational principle to extract the ground state energy ÃŽ ´E[Ï (r)] |Ï =Ï 0 = 0 (2.15) ÃŽ ´Ã (r) 2.2 Kohn-Sham Equations However, the Equation (2.14) does not give an accurate solution. In that point, Kohn and Sham reformulated the current approach and introduced a new scheme by considering the orbitals by mapping the fully interacting electronic system onto a fictitious system of non-interacting quasi particles moving in an effective potential.The Kohn-Sham equations solution can be written as: ˆ HKSψi = iψi (2.16) where the Hamiltonian is HˆKS =[− 1 2 + Veff (r)] (2.17) 2 Therefore, the problem of finding the many-body Schr ¨odinger equation is now replaced by solving single particle equations. Since the KS Hamiltonian is a functional of just one electron at the point r then the electron density can be defined according to HK theorem: occ. Ï (r)= |ψi(r)|2 (2.18) i=1 Besides, kinetic energy term and the classical Coulomb interaction energy of the electrons can be define as: N 1 d3 Te = − r|ψi(r)|2 (2.19) 2 i=1 1 Ï (r)Ï (r ) EH [Ï ]= d3rd3 r(2.20) 2 |r − r | Then the Hohenberg-Kohn ground state energy cn be written according to Kohn-Sham approach: N ÃŽ ´Exc EKS = i − EH [Ï ]+ Exc − (2.21) ÃŽ ´Ã (r) i i are the one electron energies and are coming from the results of KS equations results, however it has low physical meaning. The most significant term in the Equation (2.20) is the last term. which is the exchange correlation term that contains all the many-body interactions of exchange and interactions of the electrons. One can also write down it as in the form of Hohenberg-Kohn universal functional from the equation: Exc[Ï ]= FHK [Ï ] − (Te[Ï ]+ EH [Ï ]) (2.22) The total ground state energy can be obtained from EKS in Equation (2.21). Since it contains only the electronic energy, the total ground state energy of the system is calculated by adding the nuclei-nuclei repulsion term: E0(R1, , RM )= i − EH [Ï 0]+ Exc[Ï 0] − vxcÏ 0dr + Vnn(R1, , RM ) (2.23) where E0 is the total ground state energy for a given atomic configuration (R1, , R2). Therefore, the total energy depend on ionic positions that is actually depends on the volume and cell shape, so one can easily compute the ground state structure by minimizing the total energy. Also one can find the force acting on the particular atom, say atom A, by taking the derivative of the energy with respect to ionic position of A: ÃŽ ´E0(R1, .., RM ) FA(RA) = (2.24) ÃŽ ´RA which also shows the total energy dependence on atomic positions. 2.3 Calculating the Exchange-Correlation Energy The derived and brieà ¯Ã‚ ¬Ã¢â‚¬Å¡y explained KS equations from the fundamentals of all modern DFT calculations today. The most important point in the solution of KS equations are the exchange-correlation functional Exc which also determines the quality of the calculation. There are two well known approximation methods to get the exchange correlations: local density approximation (LDA)[39] and generalized gradient approximation (GGA)[41, 42]. 2.3.1 Local Density Approximation The local density approximation starts with a very simple approximation that, for regions of material where the charge density is slowly varying, the exchange-correlation energy at that point can be considered as the same as for a local uniform electron gas of the same charge density. In that case one can write the Exc as: Exc = Ï (r) xc(r) (2.25) where xc(r) is the exchange correlation energy per electron in an homogenous electron gas of density Ï (r). Even though the approximation is seemingly simple it is suprisingly accurate. However, it also has some drawbacks such as under-predict on of ground state energies and ionisation, while overpredicting binding energies as well as slightly favouring the high spin state structures and does not work fine for some systems where the charge density is rapidly changing. 2.3.2 Generalized Gradient Approximation Knowing the drawbacks of LDA the most logical step to go beyond LDA is not to limit oneself to the information about the charge densitiy Ï (r) at a particular point r, but also adding the information about the gradient of the charge density Ï (r) to be able to take into account the unhomogeneous density in the system. Then one can write the exchange correlation energy as : Exc[Ï ]= f(Ï , Ï )dr (2.26) That way of description leads to an improvement over LDA, nevertheless in some systems LDA still works better. There also several different parameterizations of GGA while in LDA its only one. In GGA some of these parameterizations are semi-emprical, in that experimental data (e.g. atomization energies) is used in their derivation. Others are found entirely from first principles. A commonly used functional is the PW91 functional, due to Perdew and Yang [43, 44] and most commonly used today is PBE [45, 46] by Perdew, Burke and Ernzerhof. 2.4 Ultra-Soft Pseudopotentials and the Projector-Augmented Wave Method In the previous section, the calculation of Exc is described. Nevertheless this is not the single sensitive point of DFT calculations. The other point is the treatment of the electron-nuclei interaction. There are several available methods that describes the electron-nuclei interaction, but the most effective

Ancient Mesopotamia and Greek inventions Essay

Our world today wasn’t entirely created from recent achievements. We have collected knowledge from ancient civilizations such as Mesopotamia and Greece by studying their history and improving their accomplishments. These cultures have had a major impact on the daily lives of the people in the modern world. Although Ancient Mesopotamia and Greece were some of the earliest civilized cultures, they differ greatly in their achievements and innovations that played important roles for future humans. As the world’s earliest civilization, Ancient Mesopotamia’s innovations continue to affect the world. It made vital contributions in fields like science, mathematics and astronomy; they even developed a writing system. The early Mesopotamian civilization was known for inventing the first 30-day lunar calendar. Using the phases of the Moon, they counted 12 lunar months as a year. Moreover, Mesopotamians first observed a seven-day week. The invention of the calendar was a rem arkable contribution that later had a major influence on our modern calendar. The Mesopotamians also developed mathematics to a very advanced level and created the sexagesimal system for the calculation of time and angles. This system is still practical, because of the multiply divisibility of the number 60. For example, in modern times we still use 60-minute hours, 24-hour days and the 360-degree circle. The Mesopotamians developed theories to measure the area of solids and shapes, and the circumference of circles. The Mesopotamian’ s achievements laid many of the foundations for modern mathematics. One of the most remarkable contributions was the development of the first historically significant writing system of the Middle East known as cuneiform. They wrote with a stylus on special tablets of soft, wet clay, because it was the perfect surface on which to leave marks. The fact that people started to use soft clay not only for bricks and jars, but also for the writing, implied their intellect and potential future progress. Cuneiform was not a language ; however, it was the most widespread writing system in the ancient Middle East, which helped us to learn more about the Mesopotamian history and culture. Another civilization that made numerous influential contributions was Ancient Greece. The Greek civilization was famous for many admirable scholars who were recognized for remarkable achievements in the areas of math and science, medicine and architecture, which gave a rise to further discoveries by following generations. The Greeks were engaged in  mathematical study of logic; they provided one of the first proofs in mathematics and discovered irrational numbers. Even today, people still use the Pythagorean theorem, to understand and measure triangles. Greeks achieved such great progress in mathematics by using deductive reasoning, which also helped in every other discipline. Hippocrates made one of the most prominent achievements that expanded humankind’s understanding of medicine. He was the â€Å"father of medicine†, who determined the natural causes of diseases rather than blaming them on the gods punishments, and then established procedures for medical treatment. Hippocrates’ modern concepts like diet, rest, and a clean environment were be lieved to be beneficial for the human body to heal itself. Also, doctors were responsible for the patient’s well being and privacy in ancient Greece, and they strictly followed a number of professional ethical standards, later called, the Hippocratic oath. The modern version of this oath is still used today; it confides the ideas that the doctor is responsible for his/her actions in case problems arise. The ancient Greeks created the most impressive and highly distinctive architectural styles that influenced the architecture of the past two millennia. Greek architecture developed three distinct orders, the Doric, Ionic, and Corinthian; their parts and proportions were ordered and coordinated. The design, arrangement and decoration of the columns were remarkable and unique with a pure aesthetic effect. The style of Greek architecture provided the finest and the most magnificent buildings, with constant symmetry, proportion and harmony. Greek architecture can still be seen today. For example, the United States Capitol building and other federal monuments in Washington DC have notable similarities in the design, decoration of the columns with the classic Greek architecture. The ancient Mesopotamia was the first civilized territory on the globe that â€Å"began the history† by inventing a form of writing. The inventions and innovations of this civilization contributed to the evolution of humankind. The ability to write made a great impact on people’s intellectual capacities and potential future success in exploring and studying major concepts that later became fundamental for the future development of the whole humankind. Even though the Mesopotamians were the first who pioneered in mathematical studies, the Greeks’ logical approach to the mathematical problems helped them to excel in this discipline. Moreover they applied this knowledge into other areas of  science and technology, which shaped the foundation of Western civilization. Ancient Mesopotamia and Greece civilizations played a key role in the development and progress of our modern world. Without their astounding inventions we wouldn’t be able to succeed in many imp ortant spheres of science, mathematics, astronomy and technology. They say there is nothing new under the sun, which means that anything new that we create is merely an improvement on another invention from a previous inventor.