Presentation outline: Consequences of the creation of IBM Watson

Presentation outline: Consequences of the creation of IBM Watson

May 18, 2017   Communicative presentations, IBM, In English, Outline, Presentation, Watson,

Presentation preparation outline for Consequences of the creation of IBM Watson.

• Specific Purpose: To inform the audience about the new supercomputer, its abilities, and possible consequences of its creation in the future.
• Central Idea: IBM Watson is a first successfully working developed artificial intelligence, which can cause a lot of changes in the future, due to the fact that some jobs can become obsolete.

I. INTRODUCTION

1. (Attention getter) Computers have been around us for more than 60 years, but only now we begin to understand the actual abilities that they have. Science fiction ideas and dreams that were expressed in numerous movies and books about an almighty artificial intelligence which controls the world can soon become partly true.
2. (Establish Credibility)  I have been studying computer science for over 5 years, mainly concentrating on the supercomputer computations and artificial intelligence.
3. (Relevancy Statement) Our generation will face with a lot of changes due to massive computerization. Therefore, you must know what to expect and to react appropriately.
4. (Preview of main points) Today I am going to tell you all about the IBM Watson and two of its implications in real life.

(Transition) Let’s start with what IBM Watson is and why it is such a big deal.

II. MAIN POINT 1 IBM Watson is a new type of a computer program which uses a radically new type of computing, different from the programmable systems that preceded it.

(Internal preview of SPs) - I’ll begin by explaining the focus of conventional programs, differences between the IBM Watson and conventional programs, and give a few examples of tasks and programs which Watson will solve faster and easier.

1. Conventional programs
1. IBM Watson
2. Text analysis (able to read, but not able to understand)
2. IBM Watson
1. Cognitive computing
2. Jeopardy!
3. Goal (structure information, finds hidden patterns)
3. Examples of programs
1. Diagnosing tool
2. Retirement portfolio advisor
3. Cooking chef

(Internal summary of SPs) Well, I’ve told you the very basics of IBM Watson and how it differ from conventional style systems,  and what type of tasks it can accomplish.

(Transition) Once you got an idea of what IBM Watson is, you can think about how it will affect our daily lives in the future.

IIll. MAIN POINT 2 Main effects of IBM Watson will be in the sphere of healthcare, the area, that IBM is particularly interested in.

(Internal Preview of SPs) Let me turn now to describing the capabilities of Watson and implications of its creation in healthcare.

1. Applications of Watson
1. Clinical Decision Support Systems
2. Lung cancer specialist
1. Studied medicine
2. A change in the size -> larger affordability
2. Results
1. 90% correct
2. Doesn’t take over yet
3. 3 years in Anderson Cancer Center
1. Problem with published articles
3. Future of healthcare
1. Shattering of the economics
2. Future ways of development

(Internal Summary of SPs) - Well, I have told you about some applications, results, and the effects that IBM Watson can cause in healthcare in the near future.

 

(Transition) Next, I will take a look at applications and plans of Watson in business. Nowadays, business is the topic that people are the most interested in. As a consequence of that and the fact that there are so many businessmen and businesses, effects of Watson in this area will be of the most importance for you to survive in this highly competitive world.

IV. MAIN POINT 3 - One of main areas of concentration for IBM company is the business sector, in which Watson already strongly holds a position with a lot of customers.

(Internal preview of SPs) I’d like now to discuss the goals of IBM in business and types of projects that Watson will solve with a great ease.

1. The goal of IBM
1. Create working environment
2. Embedded helping system
3. The main purpose of the system
2. Ability to create private projects with the use of Watson
1. Chef Watson
2. Shop helper

                                                 

(Internal summary of SPs)  That’s all I have to say about the goals, effects, and abilities of Watson in business. Now you can see that IBM is really concerned about commercial usage of their project.

(Transition) Now you have heard what I think about the effects of Watson on healthcare and business, and understand that it’s very important to analyze current researches and trends in order to predict the direction of the world economics in future.

V. CONCLUSION

1. (Summary statement). Finally, let me remind you of some of the issues I have covered. First, IBM Watson is a new type of computer system that can actually think and understand. Second, it has a lot of applications and implications, but two of the main areas that will be affected are healthcare and business. Maybe not in the nearest future, but there will be a time when Watson-like systems will cause regular doctors’ jobs to become obsolete. Moreover, a lot of other jobs will be obsolete as well due to the automatization. Therefore, it is very important to keep track of current researches and learn new technologies, which sometimes can be very challenging…
2. (Memorable Closing Statement)  ...but “Success is the sum of small efforts, repeated day in and day out.”
   
   
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Article: Universities shouldn’t force students to attend classes

Article: Universities shouldn’t force students to attend classes

April 05, 2017   Academic writing, In English, students, university,

The quality of education and, as a consequence, students’ knowledge and understanding of university level subjects dramatically diminish throughout the time. This causes educational institutions as well as federal departments of education to think about how they can improve the quality of students’ knowledge. One of the first questions which comes to everybody’s mind is whether students should be forced to attend lectures or not. Japan and USA are the examples of those countries where attending classes is mandatory for all students. In my opinion, this requirement is very straightforward and should be seriously reconsidered. 

First of all, every person ought to know that university is not a school or a kindergarten and that it takes a lot of time and effort to successfully receive a degree. Students choose to attend university themselves, so they must know how to manage enough time for studying as well as understand what type of studying is appropriate for them. Otherwise, if students aren’t able to do it, they are not yet ready for the university education or they probably don’t need it. These people must be expelled from a university so they will not distract other students. This behavior doesn’t differ from the one that is necessary at most of the jobs: most of the time, the employee has a task to fulfill and the employer doesn’t give him the list of instructions of how to manage this problem, but expect his employee to solve the problem no matter what. If the person doesn’t fulfill his duties, he will be dismissed. Students are considered to be adults, so they have to follow the same rules. It relates not only to the education in general but also to exams, finals, and projects in particular. If the person has not shown up, then the only solution is either to rate his work as F or, if the education system allows, to mark him as absent.

Second, even if the mentioned requirement works fine for lazy students, it may demotivate those students who are very productive and goal oriented, but who have their own pace. Moreover, the fact that a university lets students decide whether they want to visit classes or not shows that administration trusts its students, treat them as adults and expect them to behave appropriately.

Finally, so much attention to the student’s attendance may seem like a university is concentrated on the vision of hard work more than on actual education. This fact can make good students think about other universities.

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Presentation: Capitalism

Presentation: Capitalism

April 05, 2017   Capitalism, Global Business, In English, Presentation,

This article and the presentation, which you can find at the end of the article, are the results of the home assignment of three students for the Global Business class at EF New York 2016-2017.

Merchant Capitalism

The underlying theme of capitalism is the use of wealth to create more wealth. Capitalistic ideas appeared in the Middle Ages as a merchant capitalism (16th to 18th centuries). The simplest form of this is lending money at interest. At a more sophisticated level capitalism involves investing money in a project in return for a share of the profit. It began to develop into its modern form during the Early Modern period in the Protestant countries of North-Western Europe. Traders in Amsterdam and London created the first chartered joint-stock companies driving up commerce and trade, and the first stock exchanges and banking and insurance institutions were established.

Industrial Capitalism

In the mid-18th century, a new group of economic theorists, led by David Hume and Adam Smith, challenged fundamental mercantilist doctrines such as the belief that the world's wealth remained constant and that a state could only increase its wealth at the expense of another state. During the Industrial Revolution, industrialists replaced merchants as a dominant factor in the capitalist system. Also during this period, the surplus generated by the rise of commercial agriculture encouraged increased mechanization of agriculture. Industrial capitalism marked the development of the factory system of manufacturing, characterized by a complex division of labor between and within work process and the routine of work tasks; and finally established the global domination of the capitalist mode of production. In the 19th century, Richard Cobden and John Bright, who based their beliefs on the Manchester School, initiated a movement to lower tariffs. In the 1840s, Britain adopted a less protectionist policy, with the repeal of the Corn Laws and the Navigation Acts. Britain reduced tariffs and quotas, in line with David Ricardo's advocacy for free trade.

(In economics, protectionism is the economic policy of restraining trade between states (countries) through methods such as tariffs on imported goods, restrictive quotas, and a variety of other government regulations.)

Modern Capitalism

In the 20th century, capitalism overcame a challenge by centrally-planned economies and is now the encompassing system worldwide, with the mixed economy being its dominant form in the industrialized Western world. In this period, the global financial system was mainly tied to the gold standard. The United Kingdom first formally adopted this standard in 1821. Soon to follow were Canada in 1853, Newfoundland in 1865, the United States and Germany (de jure) in 1873. New technologies, such as the telegraph, the transatlantic cable, the radiotelephone, the steamship, and railway allowed goods and information to move around the world to an unprecedented degree. In the period following the global depression of the 1930s, the state played an increasingly prominent role in the capitalistic system throughout much of the world. The postwar boom ended in the late 1960s and early 1970s, and the situation was worsened by the rise of stagflation. Monetarism, a modification of Keynesianism that is more compatible with laissez-faire, gained increasing prominence in the capitalist world, especially under the leadership of Ronald Reagan in the US and Margaret Thatcher in the UK in the 1980s. Public and political interest began shifting away from the so-called collectivist concerns of Keynes's managed capitalism to a focus on individual choice, called "re-marketized capitalism".

Presentation link: google slides

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Policy Memo: Swiss-Russian import of medical products policy

Policy Memo: Swiss-Russian import of medical products policy

March 27, 2017   In English, Policy, Russia, Switzerland,

The Russian-Swiss Joint Intergovernmental Commission on Trade and Economic Cooperation was established in January 1994. In July 2009, with the support of the Russian Chamber of Commerce and Industry, a business council on cooperation with Switzerland was established.[3]

Nowadays, the state of Russian-Swiss relations is characterized by positive dynamics, having continuous support from political dialogue at the highest levels.[3] 

Russia is a priority country of Swiss foreign policy. The two countries share many interests. As a member of the UN Security Council and the G-20, Russia is a major international player. Since the signing of a memorandum of understanding (MoU) in 2007, bilateral relations have developed significantly. The MoU defines the framework for systematic and closer cooperation in the areas of:

• Foreign policy and security;

• Justice, police and migration;

• Economics and science;

• Education and cultural affairs.

Representatives of both foreign ministries meet regularly for consultations. There are close contacts at the parliamentary level too, with active parliamentary friendships groups in both countries. Since 2009, Switzerland has represented Russia's interests in Georgia and Georgia's interests in Russia, after the two countries broke off diplomatic relations.[2] 

At the same time, the ties linking the business communities of both states are expanding and strengthening. It is quite evident from a large number of bilateral events such as meetings, forums, and conferences held at the trade mission level. Such events have already become traditional and are usually held in an atmosphere of mutual respect and desire to expand the frontiers of bilateral partnership.[3]

Russia's exports to Switzerland primarily consist of minerals (50.5 percent), gem stones and precious metals (38.7 percent), chemical products (6.3 percent) and metals and metal products (2.5 percent). Imports from Switzerland include cars, equipment and vehicles (42.1 percent), chemicals (33.0 percent), food and agricultural raw materials (9.6 percent) and other products, mainly watches (9.0 percent), metals and metal goods (3.7 percent).[1]

Major Swiss investors in Russia include Nestlé (food industry), Asea Brown Boveri (high-voltage and low-voltage equipment for industrial production, construction, housing, and utilities) and Schindler (elevators and escalators). Over 600 companies with Swiss capital are registered in Russia. Some major Russian investors in Switzerland include the Renova Group, Rusal, and the SUAL Group.[1]

Currently, more than 600 companies with Swiss capital are operating in Russia, on the other hand, many Russian companies are working on the Swiss market. However, the volume of bilateral trade has been constantly growing, and this suggests that the potential for bilateral cooperation is far from exhausted. Russia and Switzerland are also brought together by a number of major investment projects, designed to be implemented in the years to come.[3]

First of all, we are talking about projects in such important spheres as science-intensive high-tech industries including energy, space, medicine, nuclear and IT-technology. In particular, the most well-known and highly advocated bilateral projects deal with innovation and nanotechnology issues.[3]

In the last several years experts observe increased imports to Russia of Swiss machinery and equipment, electronic goods, which is encouraged by the economic growth and stable demand on the Russian market.[3]

In 2014, relations between Russia and the West deteriorated due to the crisis in Ukraine. In late July, the EU and the US moved from targeted sanctions against specific individuals and companies toward measures against whole sectors of the Russian economy. Switzerland did not join the EU sanctions.[1]

Russian's Ban on Medical Imports

Medvedev told Russian journalists a suggested bill to restrict imported medical devices and supplies would not be supported by his government unless treatment quality for patients could be maintained.[4]

The list of items suggested for the ban included everything from X-ray machines, defibrillators, incubators for newborns and prosthetic devices to crutches, bandages, and condoms.[4]

Russia's medical community criticized the proposal for failing to first consult doctors and medical experts as Russian producers can not make the same quality of products or do not make them at all.[4]

Russia's "import substitution" policy aims to encourage Russia's domestic producers to develop supplies for markets now dependent on foreign imports. It was accelerated after western sanctions were put in place following Russia's annexation of Crimea in neighboring Ukraine in 2014.[4] 

Although the Ban on Medical Imports is not accepted yet, there is a positive dynamics in this direction, which indicates that it can happen in the nearest future. Before it happens, Russia has to be prepared for such a drastic change.

Proposal

Russia is a large market with great potential for Swiss companies. Switzerland is committed to creating optimal conditions for Swiss businesses and has an action plan on developing economic relations to achieve this. A bilateral mixed economic commission meets on an annual basis. The Swiss Business Hub, which is integrated within the Swiss embassy, advises Swiss companies intending to enter the Russian market and promotes Switzerland as a business location.[2]

According to Russian laws "Goods are considered to be of Russian origin, if they are made or have been sufficiently processed in the country according to customs regulations that are applicable in Russia. A supplier is considered Russian if it is a legal entity registered in Russia (which can be fully foreign-owned, except in cases of specifically regulated sectors, such as media) or a Russian citizen."[5]

Taking into consideration these two facts and the necessity of developing the Russian sector of medicine, I propose such Swiss companies like Novartis (Sandoz), Hoffmann-La Roche, Basilea Pharmaceutica, Actelion and Straumann to create assembly factories on the territory of Russia and, therefore, to gain a foothold in the Russian market. 

Both Switzerland and Russia will benefit from it, which means that it is a win-win proposal:

• Switzerland: Swiss pharmaceutical industry will be expanded to Russian territory and, therefore, bring more profit and improve international relations between countries;

• Russia: not mentioning the increase in the number of workplaces, Russia will improve the quality of the medical product which will allow Russia to finally accept the Ban on Medical Imports and not to depend on other countries in the field of medicine. Moreover, the Russian government will increase its budget with the taxes from new pharmaceutical companies.

REFERENCES 

[1]  Sputnik, “Russian-Swiss Relations: Facts and Details”, 8 Dec 2014, 

http://sptnkne.ws/dVkD.

[2] FDFA,“BilateralrelationsSwitzerland–Russia”, 8 Apr 2016,

https://www.eda.admin.ch/eda/en/home/representations-and-travel-advice/russia/ switzerland-russia.html.

[3]  MiroshnichenkoV., “Russian-Swisstraderelations”, Business Mir #22, Aug 2012,

http://www.businessmir.ch/?p=159596&language=en.

[4]  VoaNews, “Russia’s PM Halts Ban on Medical Imports”, 3 Sep 2015,

 http://www.voanews.com/a/ russia-pm-halts-ban-on-medical-imports/2944103.html.

[5]  GoncharoffP., “AsTrumpPushes’MadeinUSA’, PutinPromotes Products ’Made 

in Russia’”, 16 Jan 2017, http://russia-insider.com/en/business/ri18556. 

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A Case Study of using MATLAB, Simulink and Stateflow for Model-Based Design of a Fuel Management System for the Airbus A380

A Case Study of using MATLAB, Simulink and Stateflow for Model-Based Design of a Fuel Management System for the Airbus A380

March 13, 2017   Airbus, Case study, Global Business, In English, MathWorks, Matlab,

The Airbus A380 is one of the largest commercial aircraft these days. Its flight range is more than 12,000 kilometers. Such long distances are enabled because A380 has 11 fuel tanks which all together contain 320, 000 liters of fuel.

The problem which engineers from Airbus had to solve was to create a sophisticated fuel management system which manages fuel flows to engines and between tanks during the flight. The system was required to be able to move fuel between tanks to optimize the aircraft’s center of gravity, reduce wing bending, and keep fuel within the acceptable temperature range.

Challenge

Two main problems that engineers of Airbus had to overcome are:

• the A380’s fuel management system must be able to safely handle any failure in the system, but because of the complexity of the system: 21 pumps, 43 valves, and other mechanical components, it’s challenging for engineers at the requirements stage to predict problems that can result from combinations of relatively minor failures;
• the complexity of the system resulted in ambiguous and difficult to understand specification document which even had a few conflicts in its requirement list.

Background

Engineering problems that engineers must solve nowadays are very challenging and time-consuming, they require a lot of man-hours. Computer programming became an essential part of today’s engineering process: cars use computers to measure and manage fuel supply, airplanes use computers for proper navigation, spacecraft use computers for trajectory computation, houses use computer-controlled video cameras for security purposes, etc. Moreover, scientists use computer simulations in order to analyze physical phenomena which is very expensive or impossible to analyze by performing experiments, aerodynamics, for instance, is one of these phenomena. A sequence of actions that usually was performed for solving such problems can be seen in (Figure 1).

Unfortunately, it is very unlikely to create a software using a low-level programming language (like C/C++/Java) from scratch to research a particular engineering problem and expect good results from the very beginning. In order for the software to give valuable information, it will take researchers a lot of time to debug it and create necessary algorithms for

Figure 1: Old Sequence of Actions

a particular problem, which is not trivial and extremely time-consuming.
The new way of attacking such problems can be seen in (Figure 2). Using a high-level programming language for

Figure 2: New Sequence of Actions

the research phase drastically reduces the time consumption. Moreover, because high-level languages are much easier, scientists can use them without the help of professional programmers and, therefore, the use of high-level languages reduces the number of people that have to be hired to solve the problem.

Alternatives

There are not that many software packages for Model-Based Design, and MathWorks package which consists of Matlab, Simulink and Stateflow is the most developed one in the world. So the main question, in this case, is either to create a private closed software or to use a 3rd party applications (Matlab, Simulink, Stateflow) which will reduce the time of the development, but the presence of 3rd party applications eliminates the ability to make the software closed.

The decision-making must be based on how much profit each decision would possibly make. Hence, in order to understand which solution is more preferable, we need to evaluate all pros and cons of each solution.

The process of “creating software” which can be seen in (Figure 1), (Figure 2). Because of the complexity of low-level programming languages, the “old” process of creating software, which is illustrated in (Figure 1), takes usually from 2 to 4 times more man-hours to complete comparing to the “new” one in (Figure 2).

The main criteria that we take into consideration are salaries for programmers and researchers, and the price for the MathWorks package which was used. According to the “glassdoor.com”, the average salary of programmers who use low-level languages is lower than the salary of those who use high-level languages:

• Python, Matlab: about $90,000-$110,000;
• Java, C++, C#: about $80,000-$90,000.

The full cost of MathWorks tools for the fuel management system for the Airbus A380 starts from $12,700:

• Matlab: $2,150;
• Simulink: $3,250;
• Simscape: $2,150;
• Additional tools: $2,150 each; 
• Stateflow: $3,000.

In the following section you can see a very rough estimation of how much money is needed to complete the project.

• “Old scheme”: 9 months of using low-level languages to perform a research and create the final program (a group of 20 people: $1,275,000). The overall cost is about $1,275,000;
• “New scheme”: 4 months of working with high-level languages and 3rd parties programming tools (a group of 10 people: $333,333), 2 months of using low-level languages to create the final program if necessary (a group of 10 people: $141,666) and the cost of MathWorks tools ($12,700). The overall cost is about $488,000.

The rough estimation shows the $787,000 profit and the reduction of time for the development which actually means that the overall profit is much bigger than the one which is listed above. If it happens that the overall cost is equal in both cases or even the “New scheme” is more expensive than the “Old scheme” (which is highly unlikely), then the difference in the time which is needed for the completion of the project will still make the “New scheme” more preferable, because the company will make much more money in this period of time than the difference of costs between the “New scheme” and the “Old scheme”.
Solution
Airbus used Model-Based Design to model the A380’s fuel management system, validate requirements through simulation, and clearly communicate the functional specification.

Airbus engineers used Simulink and Stateflow to model the system’s control logic, which comprises 45 top-level charts, almost 6000 states, and more than 8700 transitions.

This model defines modes of operation on the ground (including refuel, defuel, and ground transfer) and in flight (including normal engine feed, center of gravity control, load alleviation, and fuel jettison).

Using Parallel Computing ToolboxTM and MATLAB Distributed Computing ServerTM, the team performed Monte Carlo simulations on a 50-worker computing cluster. Over a weekend, they could run 100,000 simulated flights under varied environmental conditions and aircraft operational scenarios.

The team created a desktop simulator by generating code from the plant and control logic models with Simulink CoderTM. A MATLAB® based user interface enables suppliers, airline customers, maintenance engineers, and other Airbus teams to visualize how the fuel management system works and interacts with other aircraft systems.

After successful flight tests of the A380, the team used System Identification ToolboxTM to tune their plant model using measured flight test data. They used Signal Processing ToolboxTM to remove noise from the test data, and Curve Fitting ToolboxTM to evaluate differences between the measured data and predicted results and to predict system performance beyond the usual flight envelopes. While refining the plant model, they used Simscape Power SystemsTM to incorporate relays and other elements of the electrical power system.

Results

• Months of development time eliminated. “On earlier projects, it took up to nine months to integrate our fuel system design with the simulated cockpit, or iron bird. Using Model-Based Design on the A380, it took less than a month,” says Slack, computational analysis expert in fuel systems at Airbus. “Similarly, by reusing the model to commission the HIL rig, we saved three months of development and shortened the time from initial concept to first flight.” “With Model-Based Design, the model we used to represent the functional specification enabled us to validate requirements months earlier than was previously possible,” says Christopher Slack.
• Models reused throughout development. “The Simulink and Stateflow models enabled us to validate requirements early and communicate the functional specification to our suppliers, complementing the written requirements in conformance with ARP 4754,” says Slack. “These models were reused to create desktop simulators, commission our HIL test rig, run on our virtual integration bench, and demonstrate system functionality to customers.”
• Additional complexity handled without staff increases. “The fuel system of the A380 is three to four times more complex than that of the A340,” notes Slack. “Model-Based Design enabled us to handle a substantially more complex project with the same size engineering team.” 

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Article: Computational Plasma Physics

Article: Computational Plasma Physics

March 09, 2017   In English, numerical methods, Physics, plasma,

Nowadays engineers put increasingly complex goals in front of them: to perform a thermonuclear synthesis, to land a man on Mars, to explore the solar system, to create an even faster airplane, to explore the dynamics of volcanos, etc. All of these tasks require to explore and understand a new field of physics, which is called “Plasma physics”. Due to the complexity of phenomena, in order to fulfill this goal, computational methods for computer simulations should be developed.

First, this review article gives an insight into the history of the development of plasma physics and what subfields arose during the development of the field, because it is of the most importance to understand what problems can be solved using such complicated object as plasma. Next, four main mathematical models of plasma are introduced in the article. They play the key role in the plasma physics, because they set differential equations, which specify scales on which model is correct and the mathematical complexity of the object. Computational methods are discussed later on in the article in order to give the reader all necessary information about algorithms which can be used to simulate a chosen mathematical model. At the end, one of the most commonly used computational methods, the Particle-in-Cell method, is described a little more in detail. Not only does this method plays an important role in today’s explorations, it also has implications for future prospects due to improvements in computing power and architecture.

History of plasma physics

Plasma is a dynamically complicated collection of negatively charged electrons and positively charged ions which interact with each other. It appears after an atomic decomposition when an environment’s temperature exceeds energies of an atomic ionization. One may think that plasma is a substance which rarely can be found in nature whereas it is the most common aggregation state in the universe: some scientists state that 90% of the whole Universe consists of plasma (Fitzpatrick, 2014). Moreover, it’s necessary to mention that 100% of the newborn Universe consisted of plasma. In addition, recent researches showed that Earth moves inside of the solar wind plasma. Such a close interaction with this aggregation state makes it of the greatest importance to understand its effects on our planet. Not only can plasma be found in outer space, but it also can easily be found on Earth (Fitzpatrick, 2014). Professor Fitzpatrick outlines a few phenomena which happen on Earth: “lightning, fluorescent lamps, a variety of laboratory experiments, and a growing array of industrial processes” (Fitzpatrick, 2014).

Originally, the term plasma meant “cleared blood” (oxforddictionaries.com, 2017). Irving Langmuir, the Nobel prize-winning chemist and physicist, was the first person who used this term to describe an ionized gas. He provided an analogy between physical and biological plasmas, saying that “the way blood plasma carries red and white corpuscles by the way an electrified fluid carries electrons and ions” (Fitzpatrick, 2014). The theory of plasma was developed when Langmuir tried to extend the lifetime of the filament of a tungsten-filament light-bulb. After Langmuir’s experiments, the theory of plasma spread in five other directions: electromagnetic wave propagation through nonuniform magnetized plasmas, magnetohydrodynamics, thermonuclear fusion, space plasma physics and laser plasma physics (Fitzpatrick, 2014).

Mathematical models of plasma

In order to be able to analyze physical phenomena, it’s necessary to create a mathematical model — to write mathematical equations which will accurately enough approximate the particular physical phenomenon. Mathematical models of plasma are equations of motions combined with Maxwell's Equations for electromagnetic fields. There are four main types of plasma models: N-body model, kinetic model, fluid model and hybrid kinetic/fluid model.

Fundamentally, a plasma is an N-body system of electromagnetic fields and charged particles, the dynamics of which can be described in some cases, “where transport due to short-range interactions (“collisions”) is weak, it is possible to work” (Escande, Doveil, Elskens, 2012), using just a Newton’s law of motion. For big amounts of plasma, it is impractical to solve these set of equations due to its computational complexity and the abundance of information that will be acquired after the direct integration, there will be much more information than anyone can possibly require. For these reasons different statistical models were developed: kinetic models, fluid models, and hybrid kinetic/fluid models are examples of statistical models of plasma dynamics.

Kinetic models are the most fundamental way to describe plasmas. It uses Vlasov equation, or more precisely Vlasov-Maxwell system of equations:

which is an improvement of Boltzmann’s ideas for plasma. It describes the evolution of the distribution function in 6N-dimensional phase space (Kalitkin, Kostomarov, 2009). Vlasov equation is a very accurate and complete approximation of the phenomenon but it is still most of the time unsolvable which led people to the creation of fluid models of plasma.

   
There are a lot of different fluid models of plasma, but one particular set of models are of the utmost interest to researchers, because they are “simple” relative to other models: they consider only one fluid, and at the same time they contain a lot of important macroscopic properties of a plasma: the plasma velocity field, current density, mass density, and the plasma pressure (Callen, 2003). Magnetohydrodynamics (MHD) is the simplest model of such kind, which contains equations of one-fluid model dynamics coupled with the Maxwell equations for the electromagnetic fields (Callen, 2003).

Kinetic models describe physical phenomena accurately, though it is more complex as well as computationally more intensive. On the other hand, fluid models are less computationally complex, but they can provide reasonably accurate solutions only on macroscopic scales. Nowadays, the most popular approach is to combine kinetic and fluid models into one kinetic/fluid model which treats some components of the system as a fluid, and others kinetically. It is also the most difficult approach because it requires not only a full understanding of equations of both kinetic and fluid models but also when each model can be used in every particular problem in order to get an accurate result.

Computational methods of plasma physics

After describing the most popular plasma models, it’s important to understand what types of numerical algorithms can be used to simulate the dynamics of plasma on a computer. The numerical methods in computational plasma physics closely related to computational fluid dynamics and mechanical N-body problem: fluid models of plasma are highly used for research due to good results and relative simplicity, therefore numerical plasma algorithms are mostly just an improvements of numerical fluid dynamics algorithms. 

The first and the easiest to understand approach to simulate plasma on a computer is to use N-body model. This technique allows computing full trajectories of each plasma particle -- “the first-principle dynamics” (Miloch, 2014). Such a detailed description of plasma particles movement affects exterior electric and magnetic fields and, as a consequence, these fields must be updated on every step of a simulation. Because each particle in the system interacts with every other particle in the system, the computational complexity of solving the N-body model is, which is practically unsolvable if a number of particles are too big (Miloch, 2014).

Another type of computational methods is based on solving the Vlasov-Maxwell equation, which is a nonlinear hyperbolic partial differential equation. The solution of this equation is a “Hamiltonian flow in a phase-space” (Miloch, 2014). There are different algorithms which allow solving numerically the kinetic plasma model: “e.g., semi-Lagrangian method, finite volume methods” (Miloch, 2014), though all of them are very computationally complex.

Fluid models approximate plasma dynamics on large scales and describe the evolution of macroscopic properties: density and pressure. Unlike the difficult Vlasov-Maxwell equation which can be solved only using complicated numerical algorithms and linearisation, MHD equations, which can be rewritten in the form of a first order hyperbolic partial differential equation, can be integrated using well-known Finite Difference methods like “Lax, Lax-Wendroff, leap-frog” (Miloch, 2014) as well as different Finite Volume algorithms. Finite Difference methods are divided into two categories: explicit and implicit algorithms. Explicit schemes are less computationally complicated, but they require a very strict Courant condition for a stable solution. On the other hand, implicit schemes are computationally stable, but they are more difficult in terms of programming and require more computational power. Therefore, researchers usually use hybrid explicit-implicit schemes as a “compromise between accuracy and numerical efficiency” (Miloch, 2014).

The Particle-In-Cell method

The systems that are of the interest to researchers are mostly very large in terms of the number of electrons and ions. To be able to simulate the dynamics of such systems, “super-particles” or “computer particles” are used instead of real particles. A super-particle is a computational particle which contains many real particles; it may be millions of electrons or ions in the case of a plasma simulation, therefore unlike real particles which are represented as mathematical points, super-particles should have a physical radius, because they contain a lot of real particles. Because the Lorentz force depends only on the charge to mass ratio, it is allowed to replace a number of particles with one super-particle with the same charge to mass ratio, and it will follow the same trajectory as the system of real particles (Filipič, 2008).

It’s technically impossible to solve the equations of motion and the system of Maxwell equations in the continuum space. In order to solve this problem the physical volume is divided into cells, creating a mesh, and the electromagnetic fields are getting computed only in the intersection points of this mesh (Filipič, 2008). Each cell has a local charge density which is the “number of particles in the cell divided by the volume of the same cell” (Filipič, 2008). Close interactions between particles have a low importance for a macroscopic problem, so electromagnetic fields are computed using local charge densities to compute potential and then the fields itself rather than “summing contribution of each particle” (Filipič, 2008). It’s also important to keep cell’s length in a very concrete range: it should be small enough, so the charge density separation effect can be noticed in computed fields, and at the same time large enough, so spatial cells will be bigger than the size of super-particles (Filipič, 2008).

The actual algorithm for performing a simulation consists of several steps. After reading the initial conditions, charge densities should be obtained in order to proceed with the integration of field equations. Next, the interpolation of electromagnetic fields from the mesh to the particles’ locations is performed in order to calculate to what extent “each individual grid point affects each particle” (Filipič, 2008). The last step is the integration of the equations of motion and changing the positions and velocities of each particle. After that the procedure repeats (Filipič, 2008).

Conclusion

Although plasma is an aggregate state of matter which appears very often in nature and surrounds us everywhere, it is an extremely complicated object and it requires quite an effort to simulate the dynamics of it. The four main models which approximate the dynamics of plasma are n-body, kinetic, fluid and hybrid kinetic/fluid models. All of them have their advantages and disadvantages, but fluid models of plasma, which underlie the theory of magnetohydrodynamics, are the models used the most, due to their relative simplicity and macroscopic nature. N-body models are usually very simple in terms of mathematics but very computationally complicated. The Particle-in-Cell method is an example of an algorithm which simulates the dynamics of an N-body plasma model using special methods to reduce the computational complexity. As a result, the technique allows to simulate plasma with a good accuracy, requiring an acceptable amount of time. Recent advancements in computer hardware as well as the creation of advanced parallel algorithms like Particle-in-Cell method allow to think that it will be possible to simulate large enough plasma systems which will explain real world phenomena.

Bibliography

Callen, J. (2003) “Plasma Descriptions II: MHD” in Fundamentals Of Plasma Physics, College of Engineering University of Wisconsin-Madison Press, Madison. p. 1.

Escande, D., Elskens, Y., Doveil, F. (2012) Basic microscopic plasma physics unified and simplified by N-body classical mechanics, eprint arXiv:1210.1546.

Filipič, G. (2008) "Computer simulations" in Principles of ”Particle in cell” simulations, University of Ljubljana, Faculty of mathematics and physics, p. 4-5.

Fitzpatrick, R. (2014) “Introduction” in Plasma Physics, CRC Press, Boca Raton, FL, p. 5-8.

Kalitkin, N., Kostomarov, D. (2006) Mathematical models of plasma physics (review), Matem. Mod. (vol. 18) Number 11, p. 67–94

Miloch, W. (2014) “Numerical Methods for Plasma” in Plasma Physics and Numerical Simulations, University of Oslo, p. 7-9.

Plasma, https://en.oxforddictionaries.com/definition/plasma, 2017.

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