Military Aircraft Essays - Stealth Aircraft, Monoplanes,

Military Aircraft Thesis: Military aircraft has become more sophisticated in variety, effectiveness in war situations, and special maneuvering techniques in recent years. Military aircraft has become more sophisticated in variety, effectiveness in war situations, and special maneuvering techniques in recent years. With the advance of stealth technology, many new and very effective aircraft have been developed. The F-117A was used during Operation Dessert Storm and every plane came back without a scratch. The very expensive B-2 stealth bomber has never been used in actual war, but during testing it was a success. The Advanced Tactical Fighter program was started to make an aircraft that could supercruise, the ability to cruise at supersonic speeds, and didn't cost very much. The YF-22 and YF-23 were the first planes to accomplish this. With all the planes we know of, there are also top secret programs probably going on right now. A new fighter that has never been heard of before has been spotted. As John Welch, the assistant secretary of Air Force said, "Stealth gives us back that fundamental element of war called surprise" (Goodall 9). After it was found that aircraft could be very useful in war, it was used for large scale reconnaissance. Then people started to add bombs to aircraft and then airplanes started to become an essence of war. After World War 2, new bombers were developed with fast speed, and could travel far distances. They could also carry nuclear bombs and missiles. The use of the bomber aircraft then led to the fighter, which was equipped with guns and missiles. Helicopters were also found to be good strike aircraft. They were armed with cannons, machine guns, rockets, torpedoes, and a variety of missiles. Vertical takeoff made the helicopter an advantage. The first flight of the F-117A was in June of 1981 in Groom Lake test facility. The total cost for the development of the F-117A was just under two billion dollars, but it only cost $43 million to make each plane. It became operational in October of 1983 and was the first operational stealth aircraft ever built. The F-117A is a night attack plane powered by two, nonafterburning General Electric engines. F-117As were designed for first-strike capabilities and to be able to fly into any countries airspace undetected. The primary task of the F-117A is to break through enemy airspace, destroy high value targets, and return back unharmed. They were considered to first be used in several different tasks, but weren't used until Operation Dessert Storm where they did an excellent job. As Donald Rice, Secretary of the Air Force, said, "Everyone now agrees the F-117 was a real bargain" (9). During Operation Dessert Storm the F-117As were found out to be very successful. The war began on January 16, 1991 when the F-117A fighters entered the Iraqi airspace on their way to downtown Baghdad. There were 43 of them over the skies of Iraq and not one was lost even though they went against one of the most modern air-defense systems in the world. Operation Dessert Storm was the largest aerial bombing attack in war history. It was also the first time a stealth aircraft was used as a main weapon. On the first day of Desert Storm the Lockheed F-117As dropped sixty-two 2,000 pound bombs on Baghdad destroying the most critical targets of the Iraqi military, including the headquarters of the Iraqi air force. "We've seen that not only does stealth work, but that it puts fewer assets at risk and saves lives" (9), as Donald Rice said. The pilots of those F-117As flew through the hardest anti-aircraft missiles any pilot has ever flown through. When you think of stealth, most people probably think of B-2 stealth bomber, but most people don't realize that it hasn't even been used in a real war situation yet. In November of 1987 the Pentagon ordered the first four B-2s to be built for $2 billion. Each B-2 cost $437.4 million to build. After the military liked the bomber, they originally ordered 133 of them, then they cut back to 75 because of the deficit-reduction bill. Then, in 1992, the House of Representatives voted to buy only twenty, and later only 15 saying that 10 would be enough. With four General Electric

Entregar Conjugation in Spanish, Translation, and Examples

Entregar Conjugation in Spanish, Translation, and Examples The Spanish verb entregar means to deliver, to turn in or hand in, or to hand over. Entregar can also be used as a reflexive verb, entregarse, which means to turn yourself in or surrender. Entregarse can also mean to devote yourself or dedicate yourself to something. Entregar Conjugation Entregar is a regular -ar verb and follows the same conjugation pattern as verbs like usar and tratar; however, a spelling change is required in some of the conjugations. In order to maintain the hard g sound, a u should be added when the g is followed by the vowel e. For example, the first person preterite conjugation of entregar should be entreguà ©, with a u to create the hard g sound. (The combination ge by itself produces the soft g sound, like the English h.) This article includes the conjugations of entregar in the most frequently used verb tenses: present, past, conditional, and future indicative, the present and past subjunctive, the imperative mood, and other verb forms. Entregar Present Indicative Yo entrego I deliver Yo entregola tarea a tiempo. Tà º entregas You deliver Tà º entregas la carta personalmente. Usted/à ©l/ella entrega You/he/she delivers Ella entregalos pedidos de los clientes. Nosotros entregamos We deliver Nosotros entregamoslas llaves del apartamento. Vosotros entregis Youdeliver Vosotros entregisel ladrà ³n a la policà ­a. Ustedes/ellos/ellas entregan You/they deliver Ellos entreganel poder despuà ©s de las elecciones. Entregar Preterite Indicative In the preterite tense there is a spelling change only for the first person singular conjugation. Yo entreguà © I delivered Yo entreguà © la tarea a tiempo. Tà º entregaste You delivered Tà º entregaste la carta personalmente. Usted/à ©l/ella entregà ³ You/he/she delivered Ella entregà ³ los pedidos de los clientes. Nosotros entregamos We delivered Nosotros entregamoslas llaves del apartamento. Vosotros entregasteis Youdelivered Vosotros entregasteis el ladrà ³n a la policà ­a. Ustedes/ellos/ellas entregaron You/they delivered Ellos entregaron el poder despuà ©s de las elecciones. Entregar Imperfect Indicative The imperfect tense can be translated to English as was delivering or used to deliver. Yo entregaba I used to deliver Yo entregaba la tarea a tiempo. Tà º entregabas You used to deliver Tà º entregabas la carta personalmente. Usted/à ©l/ella entregaba You/he/she used to deliver Ella entregaba los pedidos de los clientes. Nosotros entregbamos We used to deliver Nosotros entregbamoslas llaves del apartamento. Vosotros entregabais Youused to deliver Vosotros entregabais el ladrà ³n a la policà ­a. Ustedes/ellos/ellas entregaban You/they used to deliver Ellos entregaban el poder despuà ©s de las elecciones. Entregar Future Indicative Yo entregarà © I will deliver Yo entregarà © la tarea a tiempo. Tà º entregars You will deliver Tà º entregars la carta personalmente. Usted/à ©l/ella entregar You/he/she will deliver Ella entregarlos pedidos de los clientes. Nosotros entregaremos We will deliver Nosotros entregaremoslas llaves del apartamento. Vosotros entregarà ©is Youwill deliver Vosotros entregarà ©is el ladrà ³n a la policà ­a. Ustedes/ellos/ellas entregarn You/they will deliver Ellos entregarn el poder despuà ©s de las elecciones. Entregar Periphrastic  Future Indicative   To conjugate the periphrastic future, use the present indicative conjugation of the verb ir (to go), the preposition a, and the infinitive entregar. Yo voy a entregar I am going to deliver Yo voy a entregar la tarea a tiempo. Tà º vasa entregar You aregoing todeliver Tà º vasa entregar la carta personalmente. Usted/à ©l/ella vaa entregar You/he/she isgoing todeliver Ella vaa entregar los pedidos de los clientes. Nosotros vamosa entregar We aregoing todeliver Nosotros vamosa entregar las llaves del apartamento. Vosotros vaisa entregar Youaregoing todeliver Vosotros vaisa entregar el ladrà ³n a la policà ­a. Ustedes/ellos/ellas vana entregar You/they aregoing todeliver Ellos vana entregar el poder despuà ©s de las elecciones. Entregar Present Progressive/Gerund Form The gerund or present participle is a verb form that can be used as an adverb or to create progressive verb forms like the present progressive. Present Progressive ofEntregar est entregando Is delivering Ella est entregando los pedidos de los clientes. Entregar Past Participle The past participle is a verb form that can be used as an adjective or to form perfect tenses like the present perfect. Present Perfect of Entregar ha entregado Has delivered Ella ha entregado los pedidos de los clientes. Entregar Conditional Indicative The conditional tense is used to talk about possibilities. Yo entregarà ­a I would deliver Yo entregarà ­a la tarea a tiempo si la hubiera hecho. Tà º entregarà ­as You would deliver Tà º entregarà ­as la carta personalmente, pero no tienes tiempo. Usted/à ©l/ella entregarà ­a You/he/she would deliver Ella entregarà ­alos pedidos de los clientes, pero no tiene las direcciones. Nosotros entregarà ­amos We would deliver Nosotros entregarà ­amoslas llaves del apartamento si nos mudramos. Vosotros entregarà ­ais Youwould deliver Vosotros entregarà ­ais el ladrà ³n a la policà ­a si supierais dà ³nde se esconde. Ustedes/ellos/ellas entregarà ­an You/they would deliver Ellos entregarà ­an el poder despuà ©s de las elecciones, pero no se conocen los resultados. Entregar Present Subjunctive The spelling change - add a u for the hard g sound- occurs in all of the present subjunctive conjugations. Que yo entregue That I deliver La maestra quiere que yo entregue la tarea a tiempo. Que tà º entregues That you deliver La directora pide que tà º entregues la carta personalmente. Que usted/à ©l/ella entregue That you/he/she deliver El gerente espera que ella entregue los pedidos de los clientes. Que nosotros entreguemos That we deliver El propietario quiere que nosotros entreguemos las llaves del apartamento. Que vosotros entreguà ©is That you deliver La và ­ctima pide que vosotros entreguà ©isel ladrà ³n a la policà ­a. Que ustedes/ellos/ellas entreguen That you/they deliver El gobernador quiere que ellos entreguen el poder despuà ©s de las elecciones. Entregar Imperfect Subjunctive There are two different ways of conjugating the imperfect subjunctive: Option 1 Que yo entregara That I delivered La maestra querà ­a que yo entregara la tarea a tiempo. Que tà º entregaras That you delivered La directora pedà ­a que tà º entregaras la carta personalmente. Que usted/à ©l/ella entregara That you/he/she delivered El gerente esperaba que ella entregara los pedidos de los clientes. Que nosotros entregramos That we delivered El propietario querà ­a que nosotros entregramoslas llaves del apartamento. Que vosotros entregarais That you delivered La và ­ctima pedà ­a que vosotros entregaraisel ladrà ³n a la policà ­a. Que ustedes/ellos/ellas entregaran That you/they delivered El gobernador querà ­a que ellos entregaran el poder despuà ©s de las elecciones. Option 2 Que yo entregase That I delivered La maestra querà ­a que yo entregase la tarea a tiempo. Que tà º entregases That you delivered La directora pedà ­a que tà º entregases la carta personalmente. Que usted/à ©l/ella entregase That you/he/she delivered El gerente esperaba que ella entregase los pedidos de los clientes. Que nosotros entregsemos That we delivered El propietario querà ­a que nosotros entregsemoslas llaves del apartamento. Que vosotros entregarais That you delivered La và ­ctima pedà ­a que vosotros entregaseisel ladrà ³n a la policà ­a. Que ustedes/ellos/ellas entregasen That you/they delivered El gobernador querà ­a que ellos entregasen el poder despuà ©s de las elecciones. Entregar Imperative The imperative mood is used to give commands. Notice that some of the imperative conjugations require a spelling change for the hard g sound. Positive Commands Tà º entrega Deliver!  ¡Entrega la carta personalmente! Usted entregue Deliver!  ¡Entregue los pedidos de los clientes! Nosotros entreguemos Let's deliver!  ¡Entreguemos las llaves del apartamento! Vosotros entregad Deliver!  ¡Entregad el ladrà ³n a la policà ­a! Ustedes entreguen Deliver!  ¡Entreguen el poder despuà ©s de las elecciones! Negative Commands Tà º no entregues Don't deliver!  ¡No entregues la carta personalmente! Usted no entregue Don't deliver!  ¡No entregue los pedidos de los clientes! Nosotros no entreguemos Let's not deliver!  ¡No entreguemos las llaves del apartamento! Vosotros no entreguà ©is Don't deliver!  ¡No entreguà ©is el ladrà ³n a la policà ­a! Ustedes no entreguen Don't deliver!  ¡No entreguen el poder despuà ©s de las elecciones!

The Social Impact of Economic Crises Research Proposal

The Social Impact of Economic Crises - Research Proposal Example Most of the economic problems were attributed to World War I. In the aftermath, economies were trying to recover from the losses while nations in Europe strived to repay the debts acquired in the war. The United States was affected by the depression to a large extent and it ended just before the beginning of Second World War which again led to enormous spending to finance the war. Its impact affected the social lives of people even long after it ended. In a bid to conquer the impact of the great depression, President Roosevelt of the United States established a peace time strategy which had wide transformation within the free trade structure thereby encouraging the formation of the welfare states. The government would intervene in to socio-economic activities with the aim of assisting the citizens at a wider perspective. After the great depression, the government and the citizens learned to appreciate the role of the government in ensuring the welfare of the people as well in economi c development. The programs created by President Roosevelt culminated in political alliances. These alliances were important in the eventual formation of the Democratic Party. The depression played a significant role in shaping the lives of many Americans. None of them would like a repeat of the suffering that they underwent within that period. They could now see the need to save money for future use. This ended up improving their asset ownership in order to secure property that could assist them in such difficult times.

The Human Edge Essay Example | Topics and Well Written Essays - 500 words

The Human Edge - Essay Example This is done by reducing the effects of the bad mutation on human species. For example, there is a treatment of PKU with a diet with low levels of phenylalanine (Palca 1). This means such individuals can reproduce and thus pass the defective genes to the subsequent generation. This makes it difficult to eliminate defective genes in the population. On the other hand, human beings have made advances in science that helps in overcoming disadvantageous mutations. For example, the problem of poor eyesight has been resolved by wearing eyeglasses, and contact lenses (Palca 1). This helps in overcoming problems faced by the ancestors. Consequently, man has managed to defy nature as he can routinely repair, remove or even insert genes on people. The characteristics have given the â€Å"Human Edge† in different ways. First, the ability of the human to modify the conditions provided a favorable way to have the â€Å"Human Edge†. This is because as the environment became unfavorable, human managed to change it to make it favorable for survival. This gave human an advantage as compared to other species and hence managed to survive and reproduce. On the other hand, other species were exterminated due to poor environment. This means they failed to produce and have subsequent generations. Second, the ability to maintain harmful mutations helped in reproducing without elimination of the species. This is because if defective genes are not regulated, they lead to eradication of species. However, human has managed to overcome this through the development of science. He can establish a specific gene that pose a risk to survival and adopts ways of minimizing risks. Therefore, human can survive even in the presence of a def ective gene in the population. The other thing that gives human a competitive advantage is the ability to overcome deleterious mutation. This is because unhealthy mutation makes one not

Introduction to Business Law examples Essay Example | Topics and Well Written Essays - 500 words

Introduction to Business Law examples - Essay Example These included details like the apartment description, payment terms, lease period as well as certain restriction or "house rules" which both parties had to follow. Fourth, both parties have the capacity to enter into a contract given that are both past the age of majority, which in most states in the US is set at 18 years old (Emerson, 2003). Lastly, the said contract was valid because it was in accordance with public policy (Miller & Jentz, 2004), i.e. we ensured that no law was violated in relation with our agreement. 2. Write a short contract to provide service to someone. You may request for monetary reimbursement or something else of equal value from the other party. Make certain that your work satisfies the basic requirements of a legal contract. That Mr / Ms (Your name) binds himself to provide lawn mowing services to Mr / Ms (Your neighbor's name) every Saturday at 8 a.m. at the latter's residence located at (Your neighbor's address) in consideration of the monthly service fee amounting to two hundred dollars ($200.00); 3. You invite a painter over to your home to discuss some painting that needs to be done. You discuss what needs to be painted, the desired color scheme, and the final price. Nothing is written down. You agree on the terms and the painter then performs the work, for which you pay him. Have you entered into a contract If so, what type Given that both parties ha

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

Movie Violence Essay -- essays research papers

Since I am not a fan of viewing blood, and the violent actions that causes it; I decided to watch a movie in which the violence is less grotesque. The movie that I chose to watch was â€Å"Harry Potter and the Chamber of Secrets.† I chose this movie because I have recently read that the children’s book series Harry Potter has been rated amongst the most violent books meant for young readers.  Ã‚  Ã‚  Ã‚  Ã‚   If you look at â€Å"Harry Potter† through a uses and gratifications perspective, children would most likely watch the first â€Å"Harry Potter† for entertainment, but continue to follow the series out of curiosity. Since â€Å"Harry Potter† is an ongoing series that is continually publicized by the media; more children want to know what it is about, so therefore in order to ease their curiosity they watch the movie. The more a child watches of â€Å"Harry Potter† the more of a Harry Potter fan he or she becomes. Since Harry Potter is now becoming a role model for these kids, they will eventually start to play Harry Potter, and most likely mimic what they see in the movies. Most of the scenes in the â€Å"Harry Potter† series contain at least one or more acts of violence. One of the worst scenes in Harry Potter is one that includes two of the professors, and their demonstration on how to battle with their wands. After their demonstration they also c hose two students; Harry and Malfoy, to do a student demonstration. This scene practically tells children that are viewing it that it is oka...