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ISSN : 1598-6721(Print)
ISSN : 2288-0771(Online)
The Korean Society of Manufacturing Process Engineers Vol.19 No.2 pp.9-17
DOI : https://doi.org/10.14775/ksmpe.2020.19.02.009

# Laser-Induced Plasma Spectroscopy Measurement on Surface Roughness in Surface Treatment of Titanium Alloys

Ji-Hun Kim*, Joohan Kim*#
*Department of Mechanical Engineering, Seoul National University of Science and Technology
Corresponding Author : joohankim@seoultech.ac.kr Tel: +82-2-970-6314, Fax: +82-2-949-1458
21/11/2019 16/12/2019 21/12/2019

## Abstract

In this study, the surface changes of titanium alloy using laser surface treatment and the surface analysis using laser-induced plasma spectroscopy were carried out. The laser surface treatment induced changes in surface roughness and the diffusion of atmospheric elements. Excessive melting or less melting caused roughness changes, but when moderate levels of energy were applied, a smoother surface could be obtained than the initial surface. In the process, the diffusion of atmospheric elements took place. To analyze the diffusion of atmospheric elements with respect to surface morphology, the surfaces were re-shaped with grinding. In this experimental conditions, the effect of plasma formation by surface roughness was identified. Compensated plasma signals for the material properties were obtained and analysed by removing the background plasma signal.

# 티타늄 합금의 표면 처리에 있어 표면 거칠기에 대한 레이저 유도 플라즈마 분광분석법 측정 적용 연구

김 지훈*, 김 주한*#
*서울과학기술대학교 기계공학과

## 초록

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1. Introduction

The surface quality of metal products is a critical factor determining the overall quality of the products. For this reason, many studies have been conducted to improve the surface properties by processing the surface of metal materials[1,2]. One of the frequently used surface treatment processes involves forming chemicals on the material surface through heat treatment[3]. The chemicals grow from the material surface to the interface layer by diffusion, and the characteristics of the material surface are changed by a structural change of the surface[4-6]. When this process is performed, the reliability of surface diffusion by heat treatment needs to be verified. The reliability of heat treatment includes changes in the element diffusion characteristics caused by the chemical bonding between elements at the diffusion interface and the surface roughness, which is a physical characteristic of the surface.

Laser-induced breakdown spectroscopy (LIBS) is an element analysis technology based on laser spectroscopy that enables qualitative and quantitative analyses of materials. LIBS analyzes element signals using spectroscopy of plasma generated by a laser irradiated to the material surface[7]. The plasma behavior can be changed by material properties, and the properties of the material surface can be quantitatively evaluated by analyzing the changes in plasma behavior. For example, surface roughness analysis[8], hardness analysis[9,10], corrosion analysis [11], and element analysis[12,13] using LIBS have been researched. In these measurements using a laser, the plasma created by a laser is the final result of complex causes, and its reliability is somewhat low. Therefore, the first task is the quantitative analysis of the effects of various factors on the plasma behavior. Among them, surface roughness is selected first, because the energy absorption characteristics can be changed by the surface roughness and the formation of plasma is the result of the absorbed energy.

According to existing studies that analyzed LIBS plasma signals according to surface roughness, the same material can generate different plasma signals depending on the surface structure. The plasma behavior caused by surface roughness was examined until the initial surface was fully removed by laser ablation, and element analysis assuming surface roughness can be performed by applying this[14]. When this is expanded, the chemical changes of homogeneous materials can be analyzed by applying the surface roughness result. This method can simultaneously evaluate the surface roughness and chemical changes caused by the surface treatment of the material.

The metal analyzed in this study is titanium alloy, which has been researched and applied to industries for a long time owing to its excellent mechanical properties[15,16]. Titanium alloy can also be used by applying local surface heat treatment using a laser. In this laser surface treatment, the surface of the alloy reaches a very high temperature locally due to the laser optical energy. It is then liquefied or vaporized, which causes changes in the surface roughness[17]. It has been reported that the diffusion of atmospheric elements occurs simultaneously at high temperatures[18-20]. In this study, the chemical formation by atmospheric diffusion is evaluated using LIBS, and the changes in surface roughness according to laser surface heat treatment are analyzed.

## 2. Background Theory

### 2.1 Diffusion theory

When homogeneous semi-infinite rods with different components are joined together, diffusion occurs at their interface. In one-dimensional diffusion, as shown in Fig. 1, when the position is x, the time is t, and the position of the junction interface is x=0, the initial composition at x<0 is Co (i.e., C(x, 0) = Co) and the composition at x>0 is 0 (i.e., C(x, 0) = 0). $x ^$ is a variable that represents the initial position in the medium. If the composition of the semi-infinite medium at x<0 is not changed, the composition of x=0 at t>0 remains Co . Since the atmosphere has a huge volume, it can be assumed that the composition does not change, and this is applicable to the surfaces of solids exposed to the atmosphere. Therefore, the atmospheric elements are diffused to solids according to Fick's law, and the concentration by position over time can be expressed as Eq. (1) [21].

$C ( x , t ) = C o e r f c ( x 2 D t )$
(1)

### 2.2 LIBS measurement method

LIBS is an element analysis method that measures the component elements by focusing a laser beam on materials, thus generating plasma, and analyzing its spectrum. The plasma, which has a high excitation temperature, discharges an energy for a certain time and returns to the ground state again. Element analysis is possible because each element discharges its unique wavelength. When a laser beam is focused on a material, the incident beam is reflected, transmitted, or absorbed. If the beam is not transmitted, the transmission energy is zero, and only absorption and reflection occur. In this case, absorption is significantly affected by the surface condition of the material. If the surface is smooth, single absorption and reflection occur. However, if the surface is rough, the reflected beam is re-absorbed and the absorbed energy increases as a result. The absorbed energy can be expressed as Eqs. (2) and (3):

$E I = E A + E R + E T$
(2)

$E A = E I ( 1 − R ) ∑ n R n − 1 = E I A R a$
(3)

where R is the beam reflectance, n is the number of multiple reflections, and $A R a$ is the absorption rate caused by surface morphology. If the surface is rough, the true area that absorbs energy increases, and the absorbed energy per unit area decreases. When this happens, the plasma signals decrease because the critical energy for generating plasma cannot be exceeded[22]. Therefore, to analyze the surface, the plasma behavior caused by surface roughness needs to be analyzed. When the background signals are removed, the reliability of the plasma signals caused by other surface factors can be improved.

## 3. Experimental Method

Titanium alloy (Ti-6Al-4V) was used in the gas/solid diffusion induction experiment involving laser surface treatment. Table 1 shows the composition of the alloy. The surface roughness of the specimen was Ra 0.27 μm, and its thickness was 1.2 mm. The laser used for surface processing was the pulse laser of yttrium garnet (Nd:YAG) doped with neodymium at a wavelength of 1064 nm. The surface treatment process was performed at the machining interval of 50 μm and the confocal size of 1 mm, as shown in Table 2. To ensure the machining reliability of titanium alloy, a short pulse width of 5 ns was set. The process atmosphere was 25℃ and the oxygen concentration was 20%. To verify the change of physicochemical properties by surface treatment, the surface roughness of the machined alloy was measured, and the changes in surface elements were measured using LIBS. Fig. 2 shows the experimental settings of LIBS. An Nd:YAG pulse laser with a wavelength of 266 nm was used with an energy per pulse of 25 mJ and a pulse width of 5 ns. Since the laser beam irradiated for element analysis also raises the surface temperature of the specimen, the atmospheric elements may be diffused depending on the measurement atmosphere. To prevent this, the experiment was conducted in an inert argon gas atmosphere. The pulse was irradiated 30 times per position. The signals of titanium 368 nm and oxygen 777 nm were used at various spectrum peaks of each element. Table 3 shows the measurement variables of each element. The titanium signals were measured in 1 ms of delay time, and the oxygen signals were measured in 0.1 ms of delay time.

To verify the plasma behavior according to surface roughness, titanium alloys of various surface roughness values were prepared, including an alloy with a smooth surface. The LIBS settings were the same as above. The plasma signals for surface roughness were obtained by irradiating the titanium alloy surface with the laser. These signals were compared with the plasma signals from the laser-surface-treated titanium alloy to examine the chemical changes by surface treatment.

## 4. Results and Discussion

### 4.1 Laser surface treatment and diffusion

When a material surface is irradiated with a pulse laser, the surface temperature rises rapidly, causing melting and transformation. When the surface roughness caused by laser surface treatment was measured, the roughness of the initial specimen was Ra 0.27 μm. Fig. 3 outlines the surface roughness according to the laser surface treatment variables. Not only changes in surface roughness caused by surface treatment but also color changes were observed. This is the result of the diffusion of atmospheric elements into the titanium alloy to form oxides and nitrides and the apparent color change due to optical interference. Increasing the amount of energy irradiated to the surface is expected to increase the thermal effect and cause more atmospheric element diffusion.

The oxygen, nitrogen, and aluminum elements on the surface were examined using the energy dispersive X-ray spectroscopy (EDS) method, and the results are summarized in Fig. 4. According to the EDS results, when the laser energy irradiated to titanium alloy increased, the oxygen signals measured on the surface increased, but the titanium signals decreased. This suggests that an oxide film was formed and grown by the laser surface treatment.

As a result of analyzing the laser-surface-treated titanium alloy using LIBS, when the laser fluence increased in surface treatment, the signals of oxygen generated from the initial pulse increased. Furthermore, as the fluence increased, the signals were generated more continuously. Fig. 5 summarizes the behaviors of oxygen plasma signals relative to fluence and pulse order. Although the effect of surface roughness on oxygen signals was small, when diffusion was induced by a local temperature increase, the signals generated from the initial pulse increased approximately 13-fold. This suggests that oxides were formed by the surface diffusion of titanium alloy.

### 4.2 LIBS surface element analysis for roughness

In the case of a smooth surface in LIBS, the initial surface was removed by only one pulse irradiation, but a rough surface required multiple pulse irradiations to remove the initial surface. The titanium plasma signals generated from this process were analyzed for surface roughness. In the present experimental conditions, the titanium plasma signals tended to decrease as the surface roughness increased. Fig. 6 shows the titanium plasma signals according to the pulse order, and Fig. 7 shows the titanium plasma signals according to the surface roughness. Although multiple absorptions occurred by surface morphology, it is presumed that the plasma intensity decreased because the increase in area had a greater effect. The plasma signals for roughness can be calibrated using this data. Furthermore, in the case of oxygen, oxygen plasma signals were generated because an oxidation layer was formed by natural diffusion in atmospheric conditions. In the oxygen signal measuring condition, plasma signals increased with the surface roughness, but their effect was very small. This suggests that the effect of oxygen on the plasma signals to be calibrated is limited.

In the case of titanium signals, because a valid plasma behavior caused by surface roughness was verified, the signals were analyzed after removing the surface roughness background signals. Consequently, the amplitude of signals generated from the initial pulse increased as the laser fluence in the titanium signals increased. Fig. 8 summarizes the calibrated titanium plasma signals relative to fluence. The signals were calibrated using three laser fluences. For each laser fluence, the roughness values in the relationship between surface roughness and laser fluence in Fig. 3 can be inferred by applying the laser spot size and laser scanning speed. The calibration factor was determined by substituting the inferred surface roughness value in the titanium plasma signals relative to roughness. Fig. 8 shows the graph obtained by applying this calibration factor. The maximum signal of the titanium plasma increased 1.45-fold when the laser fluence increased 1.40-fold from 0.91 J/mm2 to 1.28 J/mm2 and 2.18-fold when the fluence increased 2.34-fold to 2.13 J/mm2. This is an interesting result of surface analysis using LIBS. Surface analysis using LIBS has low reliability due to various factors. When the background signals caused by surface roughness are removed, plasma signals calibrated by other factors can be obtained. These experiments using LIBS allowed for more accurate evaluation of the surface roughness of materials and the generation of chemicals by atmospheric diffusion.

## 5. Conclusion

The changes in the titanium alloy surface by laser surface treatment were analyzed using LIBS. The changes in surface roughness and the diffusion of atmospheric elements were induced by laser surface treatment and were measured and analyzed using LIBS. When the surface was treated with the initial surface roughness of Ra 0.27 μm, changes in surface roughness by melting and solidification were observed. Rough surfaces of 0.71 μm at the maximum to smooth surfaces of 0.15 μm at the minimum were obtained. In this process, the atmospheric elements were diffused, and the physicochemical changes of the surface were measured. The diffusion of the atmospheric elements was analyzed to verify the incidental effects of the surface treatment process. To examine the differences in LIBS measurements by roughness, surfaces with different roughness values were formed by artificial polishing, and the plasma signals generated from them were analyzed. In the present experimental conditions, titanium plasma signals tended to decrease with increasing surface roughness, and accurate plasma signals could be obtained by removing the background signals. These signals increased with the surface treatment laser fluence, and this was similar to the result of the surface analysis through EDS. These experimental results demonstrated that the plasma formation was affected by the surface roughness of the specimen. In addition, the plasma behavior resulting from the thermal changes of diffusion or microstructural changes could be clearly identified by removing the background signals related to surface roughness.

## Acknowledgement

This study was supported by the Research Program funded by the SeoulTech(Seoul National University of Science and Technology).

## Figure

Gas/Metal diffusion model
Schematic of LIBS setup for gas/solid interface analysis
Ra surface roughness respect to laser surface treatment parameters
EDS element profiles by laser surface treatments: (a)EDS image, (b) Oxygen, (c) Titanium, (d) Nitrogen, (e)Aluminium
Oxygen 777nm plasma signal for the different laser surface treatment fluence as a function of the number of pulses
Titanium 368nm plasma signal for the different surface roughness as a function of the number of pulses
Titanium 368nm plasma signal relative to surface roughness
Calibrated titanium 368nm plasma signal obtained by removing surface roughness background signal

## Table

Composition of Ti-6Al-4V specimen (wt%)
parameters of laser surface treatment
LIBS analysis setup by target

## Reference

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text:
1. Aug 29, 2010

quanto

... to becoming a professor. I was looking around and saw how difficult many people say it is to become a uni professor so I am going to skip that question "How Hard is it?!!?" but let me just make sure if i have this right
PhD.
Postdoctorate
Assisstant Professor (tenure track)
Full time professor (tenured)...Here is my question how long does one do postdoc for? Because that isn't permanent is it? I think you do research make publications and then in due time they can ask you to make your own way right?

I guess one could just choose to go into R&D right after they finish masters? or do you need phd for that too?

2. Aug 29, 2010

Pengwuino

You can do R&D out of a masters but your skills will limit you in what you can do compared to someone with a PhD. A postdoc is generally 2 years and people tend to do 1 or 2, it's not a permanent job.

3. Aug 29, 2010

twofish-quant

Post-docs are for three years, and most physics Ph.D.'s get two. The problem is that if you don't get something permanent by end of the second, the third is extremely difficult and the fourth is impossible.

There's also the problem that the goal posts are likely to move. We are talking about 15 years from undergraduate to tenured prof, and it's quite possible that in 15 years the academic system may be radically different. It wouldn't surprise me at all if in 2025, there are no new tenured professors anywhere.

The good news is that you will be doing physics research by second year grad school at the latest, and you can do it at the undergraduate level.

4. Aug 29, 2010

phyzguy

It's good to remember that nothing in life is "permanent" - life is a journey, not a destination. If you don't enjoy what you're doing along the way, you're going to be unhappy and should look for something else that you do enjoy.

5. Aug 29, 2010

sEsposito

Why is this?

6. Aug 29, 2010

Choppy

The fate of post-docs I think varies from field to field. I know a few people who seem to have made careers of jumping from post-doc to post-doc. It certainly is not ideal from a financial stability point of view, but in other ways it has some advantages - for one you can spend the majority of your time actually doing research.

Post doctoral fellowships are essentially contract positions. You join a group to work on a specific project. Usually the money comes from a grant.

With regards to the possibility of tenured positions disappearing, I'd have to agree (that it's possible - not that it necessarily will happen in that time frame). From a business point of view, why would a university hire someone into a permanent position when there is a steady supply of fresh PhDs willing to work as sessional lecturers for peanuts? Why pay someone to go on sabatical? Why should they hire full-time, permanent faculty when they can reach out into industry and make adjunct appointments which will connect students to the "real" world? (NOTE: there are good arguments against this, but the trick is to get univeristy administators to pay as much attention to them as they do to the immediate financial bottom line).

7. Aug 29, 2010

chingkui

But that's because everyone think there is a chance of getting a tenure-track position later on in life. If this motivation is taken away, who would do that?

8. Aug 29, 2010

quanto

hmm..very true. I don't suppose that a time will come when unis close down tenure-track positions. After all, research is an integral part of any reputable university. And without full time professors who have been there 10 years or plus that would be very hard to do.

9. Aug 29, 2010

twofish-quant

1) Because 15 years is a relatively long time, and a lot can change.

2) Because of supply and demand. There isn't a lack of people that would work as researchers and teachers without tenure. There is a *LOT* of institutional inertia, but if one university can show that they can run without tenure, then its going to disappear rather quickly.

I'm not saying that it will happen. Institutional inertia may keep things going for a long, long time. I'm just saying that you shouldn't be surprised at all if tenure disappears for new hires.

Something that I'd like to understand better is how tenure became the "holy grail" of academia,

10. Aug 29, 2010

twofish-quant

But then we have a major problem in that there just aren't enough tenured positions to go around.

One of my annoyances is that academia is supposed to be based on "seeking truth" and if you have to have hiring practices that require you convincing people of something that isn't true, then you are going to have a lot of problems with the "seeking truth" bit.

11. Sep 5, 2010

lisab

Staff Emeritus
12. Sep 5, 2010

Staff Emeritus
Changing tenure will make little difference to the university funding situation. Take the University of Michigan (chosen because it's easy to find financial information on the web). They have a budget of $4.7B. Of this,$164M is for tenured faculty salary - 3.4%.

13. Sep 6, 2010

twofish-quant

However, $2.4B of University of Michigan involves the hospital they run. http://www.vpcomm.umich.edu/budget/understanding.html#aa The general fund is$1.5 billion and the state appropriation is \$300 billion.

The problem with removing tenure is that once you no longer have tenure, then administration will have a pretty free hand in closing departments and schools, and doing your standard corporate reorgs that they don't do now.

Not to say that's a good thing....

14. Sep 6, 2010

sEsposito

It seems to me that tenure jobs will never completely disappear. Think of Academia as a funnel; new PhDs looking for work is the load and there's a lot more than can fit through the funnel. But, some still get through, these are the people that are replacing the tenure track Professors as they go out, albeit at a very slow rate. This leaves the rest of the PhDs to just wait for there chance to get through the funnel and in the interim take adjunct jobs.

15. Sep 6, 2010

lisab

Staff Emeritus
True. And not many candidates would get into the funnel if there was no opening at the bottom. Meaning, no one would take adjunct work (which is low-paying and offers no job security), if the hope of getting tenure is zero.

So one argument for tenure: using it as a dangling carrot ensures an endless supply of cheap labor.

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# I Deriving the second Friedman equation from the first.

1. Aug 3, 2015

### thebiggerbang

Hello!

My professors asked me why we don't usually consider the second Friedman equation. He told me that the solutions for the first always give a solution for the second. He told me that the first equation along with it's time derivative can imply the second equation. I have been trying the algebra for a long time now, but I am not being able to get ahead.

I wanted to know if the statement that the professor made is true in the first place.

2. Aug 3, 2015

### Orodruin

Staff Emeritus
You cannot just take the time derivative. You will also need to apply the continuity equation (i.e., the fact that the stress-energy tensor is divergence free).

3. Mar 5, 2016

### thebiggerbang

Thank you, that helped!


text:
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The solution trajectories taken by these algorithms naturally exhibit rotation, sometimes forming cycles, a behavior that is not expected with (full-batch) gradient descent. Many existing machine learning (ML) algorithms cannot be viewed as gradient descent on some single objective. To access these papers, it is required that a PDF viewer is available on your device. We develop a parameter-efficient, deep semi-supervised generative model for the purpose of exploiting this untapped data source. Solving Large Sustainable Supply Chain Networks using Variational Inequalities. Additionally, in order to handle the large size of standard VI game formulations, we further enhance the tool to accommodate more sophisticated numerical algorithms and propose a heuristic for efficient use of generated trajectories. Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the function. USLegal received the following as compared to 9 other form sites. We propose a method, D3C, for online adjustment of agent incentives that reduces the loss incurred at a Nash equilibrium. We call this successful technique Crossing-the-Curl, named for its mathematical derivation as well as its intuition: identify the game's axis of rotation and move "across" space in the direction towards smaller "curling". We draw on interdependence theory from social psychology and imbue reinforcement learning agents with Social Value Orientation (SVO), a flexible formalization of preferences over group outcome distributions. Welcome to Gemp-Swccg! The cycle problem is a canonical equilibrium problem for which naive optimization approaches, e.g., simultaneous SGD, fail. Consequently, you save hours (if not days or weeks) and get rid of unnecessary payments. The Gemp family name was found in the USA, and Canada between 1880 and 1920. However, these algorithms can be viewed more generally as solving for the equilibrium of a game with possibly multiple competing objectives. Several new algorithms and techniques have been proposed to stabilize GAN training, but nearly all employ Adam or RMSProp. In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to design reliable, convergent, and robust reinforcement learning algorithms (ii) how to guarantee that reinforcement learning satisfies pre-specified "safety" guarantees, and remains in a stable region of the parameter space (iii) how to design "off-policy" temporal difference learning algorithms in a reliable and stable manner, and finally (iv) how to integrate the study of reinforcement learning into the rich theory of stochastic optimization. As a graduate, you can study medicine through GEMP at Wits. St. Vincent 2006 – 2011 Mathematics Past Papers. In this paper, we explore the effectiveness of novel Runge-Kutta methods on finding equilibrium solutions to two real-world games defined by oligopolistic economies. GEMP is listed in the World's largest and most authoritative dictionary database of abbreviations and acronyms GEMP is listed in the World's largest and most authoritative dictionary database of abbreviations and acronyms and borrowing tools from dynamical systems theory for analyzing the complex dynamics of GAN training. The simulations also indicate that N-cadherin We then borrow a tool from dynamical systems to cope with our model’s lack of theoretical guarantees. USLegal fulfills industry-leading security and compliance standards. MASTER GEMP: A GENERAL PERSPECTIVE Master in Business Law and Public Manager (Italian acronym: GEMP), organized by the Law Department of University of Pisa since 2003, reached now its twelfth edition. Social Studies Mock Exam August 2016 (Interactive) Read more →... Register Login Contact us . Go to the e-autograph solution to add an electronic signature to the form. #1 Internet-trusted security seal. A high-level overview of Gemphire Therapeutics Inc. (GEMP) stock. Finally, Legendre transforms enable a variety of other benefits, including modeling sparsity and domain geometry. Equally importantly, proximal operator theory enables the systematic development of operator splitting methods that show how to safely and reliably decompose complex products of gradients that occur in recent variants of gradient-based temporal difference learning. Simulations were fit to two measures of release, evoked by flash-photolysis of caged Ca2+: exocytotic capacitance changes from individual rods and postsynaptic currents of second-order neurons. A completed undergraduate university degree at a minimum of Bachelor’s or Bachelor of Technology degree level with an average of at least 60% over the final two completed years of study. Social Diversity and Social Preferences in Mixed-Motive Reinforcement Learning. SM-games codify a common design pattern in machine learning that includes (some) GANs, adversarial training, and other recent algorithms. Cadherin-dependent cell morphology in an epithelium: constructing a quantitative dynamical model. Quantitative analysis of synaptic release at the photoreceptor synapse. It is a clean, ecological, sustainable and renewable alternative. We demonstrate the utility of online monotone game theory on a variety of problem domains including variational inequalities, reinforcement learning, and generative adversarial networks. Inverting Variational Autoencoders for Improved Generative Accuracy. Here, we aim to understand how Adam circumvents some of the difficulties associated with GAN training. Bank-level security and role-based permissions puts you in control of who has access to your content and critical business files. After analyzing the effect of informative priors, we propose a simple modification of the NVDM model using a logit-normal posterior that we show achieves better alignment to user-desired topics versus other NTM models. Journal of Artificial Intelligence Research. The initial phase of one and a half (1½) years of the programme is run on a semester basis and not as course credit system, in an integrated approach. Monotone games are games where agent strategies naturally converge to an equilibrium state. Stay up to date on the latest stock price, chart, news, analysis, fundamentals, trading and investment tools. Our forms are regularly updated in accordance with the latest legislative changes. When the codomain ($\mathbf{y}$) has known structure, a large un\emph{featured} dataset ($\mathbf{y}_u$) is potentially available. Moreover, some recent ML models, specifically generative adversarial net- works (GANs) and its variants, are now explicitly formulated as equilibrium problems. Past papers are available on the GEMP websites. We develop a parameter-efficient, deep semi-supervised generative model for the purpose of exploiting this untapped data source. Generative adversarial networks (GANs) are a framework for producing a generative model by way of a two-player minimax game. We also introduce a family of policy iteration methods that approximate fictitious play. Get your online template and fill it in using progressive features. Our work builds extensively on recent work on the convergence of saddle-point algorithms, and on the theory of monotone operators. Training GANs is difficult, although not nearly as difficult as expected given theoretical results on finding a Nash (PPAD complete) and our understanding of dynamical systems. Understanding how Adam works in this context helps reveal reasons for its unexpected success. Our thesis is that creative activity involves dealing not with a single objective function, which optimization requires, but rather balancing multiple divergent and possibly contradictory goals. In the case where the codomain has known structure, a large unfeatured dataset (y) is potentially available. Given the potentially large size of real-world games, suitable algorithms must be designed that can scale gracefully with the dimension of the problems (e.g., number of players). The very long questions on random things, like Ethics and Family Medicine, are very often repeated and rotated. Finding Equilibria in Large Games using Variational Inequalities. Past papers are available on the GEMP websites. Ensures that a website is free of malware attacks. The purely adversarial nature of such games allows for conceptually simple and principled application of RL methods. designing a no-regret framework for solving monotone equilibrium problems in online or streaming settings (with applications to Reinforcement Learning). We analyze the properties of this PCA game and the behavior of its gradient based updates. To provide a quantitative description of the photoreceptor Ca2+ sensor for exocytosis, we tested a family of conventional and allosteric computational models describing the final Ca2+-binding steps leading to exocytosis. Define GEMP at AcronymFinder.com. This was about 70% of all the recorded Gemp's in the USA. ENTRY REQUIREMENTS. The application process for this programme is available on the WITS website. We use the framework of Variational Inequalities to analyze popular training algorithms for a fundamental GAN variant: the Wasserstein Linear-Quadratic GAN. We provide a brief review of this paradigm for readers unfamiliar with the underlying mathematics, and sketch out how VIs can account for creativity and play in human and animal cognition. What is the maximum number of long tubes? Learning to Play No-Press Diplomacy with Best Response Policy Iteration. We explore a number of design perspectives with the discriminator role ranging from formidable adversary to forgiving teacher. There are a total of 62 tennis balls. This gives these students the opportunity to complete their undergraduate medical studies in a period of only four years after which they enter their internship and government mandated community service period. The GEMP allows entry of suitably qualified candidates who meet certain minimum requirements into the third year of the MBBCh degree. To prepare for these exams obviously you need to study, but it's also very useful to go over the past papers as you do. The Legendre transform elegantly generalizes past algorithms for solving reinforcement learning problems, such as natural gradient methods, which we show relate closely to the previously unconnected framework of mirror descent methods. Given the defining characteristic of mixedmotive games—the imperfect correlation of incentives between group members—we study the effect of population heterogeneity on mixed-motive reinforcement learning. We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. GEMP Stands for Graduate Entry Medical Programme and it is offered by Wits University at the moment. Maybe you’ve religiously watched all of the seasons of Grey’s Anatomy, and you know everything about Dr House and his team of impressive investigative doctors. Image generation tasks comparing the proposed framework to standard GANs demonstrate GMAN produces higher quality samples in a fraction of the iterations when measured by a pairwise GAM-type metric. Proximal Gradient Temporal Difference Learning: Stable Reinforcement Learning with Polynomial Sample Complexity. Global Convergence to the Equilibrium of GANs using Variational Inequalities. Hemp is the plant that has the potential to help us reinvent the future of plastic and other materials. Experimental It sounds like WAPT covers Bsc type content - so the test might be similar to papers your daughter has done in Bsc? In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. The designation of the programme is Graduate Entry Medical Programme (GEMP). We therefore introduce smooth markets (SM-games), a class of n-player games with pairwise zero sum interactions. Fill out the requested fields which are marked in yellow. National Diplomas, Technical Diplomas, Certificates and similar qualifications cannot be considered … What are the minimum requirements for … Recent advances in semi-supervised learning with deep generative models have shown promise in generalizing from small labeled datasets ($\mathbf{x}_l,\mathbf{y}_l$) to large unlabeled ones ($\mathbf{x}_u$). Over the past three decades, researchers from economics, sociology, psychology, and other disciplines have tried to understand why women are under-represented in STEM, even as this under-representation shrank. The proposed framework generalizes the popular online convex optimization framework and extends it to its natural limit allowing it to capture a notion of regret that is intuitive for more general problems such as those encountered in game theory and variational inequalities. Find. It's not the best idea and don't rely on the past papers alone. Follow GEMP. Inspired by Sameer Singh; Powered by Bootstrap. Currently such preprocessing is manual. Kentucky had the highest population of Gemp families in 1880. Press the green arrow with the inscription Next to jump from field to field. Share and collaborate with unlimited storage. Exploring the Dynamics of Variational Inequality Games with Non-Concave Utilities. ICLR Workshop: Learning with Limited Labeled Data. You're studying to eventually save a life. VIs represent a comprehensive framework that provides a way to model and analyze both cooperative and non-cooperative games. The Unreasonable Effectiveness of Adam on Cycles. explained by a simple model incorporating salient features of morphogenesis that include the timing of N-cadherin Empirical results show improved performance in disentangling variable semantics as well as improved discriminative prediction on a new MNIST task. With the success of modern machine learning, it is becoming increasingly importantly to understand and control how learning algorithms interact. Empirical results show improved performance in disentangling latent variable semantics as well as improved discriminative prediction on Martian spectroscopic and handwritten digit domains. Download View … The GEMP system is a system that allows graduate students from other degrees to get into medicine at a third-year level provided you pass an entrance exam. Recent state-of-the-art topic models such as NVDM, referred to herein as Neural Topic Models (NTMs), fall under the variational autoencoder framework. Equilibrium problems present challenges beyond those encountered in optimization such as limit-cycles and chaotic attractors and are able to abstract away some of the difficulties encountered when training models like GANs. Using this framework, we prove that a simple update scheme provides a no-regret algorithm for monotone systems. This key technical innovation makes it possible to finally design "true" stochastic gradient methods for reinforcement learning. We show that the steepest descent direction causes divergence from the equilibrium, and guaranteed convergence to the equilibrium is achieved through following a particular orthogonal direction. We propose a simple yet effective approximate best response operator, designed to handle large combinatorial action spaces and simultaneous moves. The key idea that emerges is the use of primal dual spaces connected through the use of a Legendre transform. Variational inequality (VI) theory has proven useful in modeling and analyzing a variety economic markets. Fill out the requested fields which are marked in yellow. In fact, training a GAN with SGD instead of Adam often fails. We argue in this paper that the current model of optimization that drives much of modern machine learning research is far too restrictive a paradigm to mathematically model the richness of human cognition. In this paper, we explore the effectiveness of novel Runge-Kutta methods on finding equilibrium solutions to two real-world games defined by oligopolistic economies. We show that SM-games are amenable to analysis and optimization using first-order methods. We demonstrate that heterogeneity in SVO generates meaningful and complex behavioral variation among agents similar to that suggested by interdependence theory. improving state-of-the-art image generation with techniques derived from theory. Such modes of cognition are better modeled using the framework of variational inequalities (VIs). In this paper, we provide detailed answers to all these questions using the powerful framework of proximal operators. Instead, we propose a much more flexible and powerful framework of equilibration, which not only generalizes optimization, but also captures a rich variety of other problems, from game theory, complementarity problems, network equilibrium problems in economics, and equation solving. Enjoy smart fillable fields and interactivity. The best simulations supported the occupancy of only two Ca2+ binding sites on the rod Ca2+ sensor rather than the typical four or five. Our challenge is to compute the steady state behaviors of networks of sustainable supply chains with possibly conflicting objectives. The GEMP will be the pilot programme of the UGMS for this transformation which will employ the modern trend of integrated medical programmes. Simple, Secure, Amazingly Fast. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. It's not the best idea and don't rely on the past papers alone. Follow the simple instructions below: Business, tax, legal as well as other e-documents demand an advanced level of protection and compliance with the legislation. In previous work, the successful training of GANs requires modifying the minimax objective to accelerate training early on. Past Deans ; Contact Us ; Statement on COVID-19 ; Academics . NIPS Workshop: Learning, Inference, and Control of Multi-Agent Systems. Highest customer reviews on one of the most highly-trusted product review platforms. Those who are planning to prepare for self-study can follow the 8-week study plan … CBSE Sample Paper for Class 7 Maths. What does GEMP stand for? From now on, complete Wits Gemp Past Papers from home, workplace, or even while on the go. The no.1 Shopify drag & drop landing page builder. New search features Acronym Blog Free tools "AcronymFinder.com. GEMP Master trains business law experts with a solid technique, capable of facing challenges of legal advice for the public and private entities operating in the market. In this paper, we propose the Generative Multi-Adversarial Network (GMAN), a framework that extends GANs to multiple discriminators. Generative model for the purpose of exploiting this untapped data source interest games has emphasized the of... Ca2+ unbinding were unexpectedly slow therefore introduce smooth markets ( SM-games ), a class of n-player games addition partial... Not be viewed more generally as solving for the equilibrium of a system-wide loss function we developed! Register on the us and Canada are challenging for RL algorithms mixed-motive learning! 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# Induced EMF in Non-Uniform Magnetic Field

1. Jul 8, 2011

### arl146

1. The problem statement, all variables and given/known data
A square wire loop of dimensions L X L (L = 15.5 cm) oriented in the xy-plane and centered on the x-axis enters a region where the magnetic field (B = 0.855 T) is first oriented in the +z- and then in the -z-direction as shown in the diagram below. (Note: W = 15.501 cm and the magnetic field is zero outside the shaded area.) The loop moves at speed v = 4.55 ms in the +x-direction. In the questions that follow, when asked for the emf, a positive emf will be defined as an emf induced counterclockwise (if viewed from above the loop); and vice versa.

(i.) What is the induced emf in the loop when the center of the loop is at x = -W?
(ii.) What is the induced emf in the loop when the center of the loop is at the origin?
(iii.) What is the induced emf in the loop when the center of the loop is at x = +W/2?
(iv.) What is the induced emf in the loop when the center of the loop is at x = +W?

2. Relevant equations
See below

3. The attempt at a solution
I think if I get help on one of them, then I should be able to figure out the others.
I'm not too sure how to approach this one, but I was thinking to use E=Blv or the flux=BA equation. But I'm not sure how that works out

2. Jul 11, 2011

### arl146

no one can help me with this ? =/

3. Jul 14, 2011

### arl146

still looking for help ...

4. Jul 14, 2011

### WatermelonPig

In general emf = vBL for these sorts of situations but a drawing would be nice.

5. Jul 14, 2011

### cupid.callin

As WatermelonPig said, EMF=vBl
and its polatiry can be found out by F=q vXB (cross product)

bt we need a diagram to understand the question

6. Jul 15, 2011

### arl146

Oh, sorry, wasnt paying attention that I didn't have one attached!

#### Attached Files:

• ###### prob14a.gif
File size:
6.5 KB
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203
7. Jul 15, 2011

### cupid.callin

(i) when center will be at x=-w ... which part of loop will be inside mag. field area and which part will induce emf (for this, you should have studied motional emf)

8. Jul 15, 2011

### arl146

only half of the loop will be inside the magnetic field that is pointing up. the left side half isn't in a B field. So just the right side that's in the magnetic field induces emf?

9. Jul 15, 2011

### cupid.callin

yes, thats correct :)

10. Jul 15, 2011

### arl146

so, what does that mean haha i still am not sure what to do for it

11. Jul 15, 2011

### cupid.callin

you did first
now for second, you need to find polarity of induced emf in on the 2 wires (left and right) of loop ...

for this use the formula of force on moving charge in mag. field, $\vec{F} \ = \ q \ \vec{v} \times \vec{B}$

As you would know, the wire moving in mag. field will act like a battery with a (+) and a (-) pole.
suppose there is a positive charge in wire moving with wire ... find direction force on it (generally along wire in these kind of questions). the side where + charge moves is (+) and other is (-)

thus find net emf in wire in case (ii)

12. Jul 16, 2011

### arl146

so wait .. i dont get it, how did i do the first one?

and for (ii.) how do you use that without q ?

Last edited: Jul 16, 2011
13. Jul 16, 2011

### vela

Staff Emeritus
Since you're dealing with a loop, it would be more straightforward to calculate the rate of change of the magnetic flux through the loop to find the emf.

14. Jul 17, 2011

### cupid.callin

motional EMF in a wire moving in mag field is vBL , here v is velocity B is mag field and L is the length.

15. Jul 17, 2011

### arl146

i did that already it was wrong

16. Jul 17, 2011

### cupid.callin

is it sign problem or magnitude is wrong?

17. Jul 17, 2011

### arl146

Oh wait, I got it now :)
Okay, for the second: i dont get what youre saying for that ..

18. Jul 25, 2011

### arl146

Can I please have some help on the other one's then?

19. Jul 25, 2011

### cupid.callin

do you know how to find polarity of the charges in a wire?

20. Jul 25, 2011

### arl146

i dont think ... im not too sure what that means


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# Black-Scholes model of option pricing

Consider a public company with stock price $X(t)$ at time $t$. A European style option on the stock of this company is a contract to have the option to buy the stock at a predetermined price on a predetermined future time. The option is described by the strike price $K$, the strike time $t$ and its price $c$. Paying $c$ to buy an option gives us the opportunity to buy the stock for the strike price $K$ at the strike time $t$. At time $t$, the worth of the option depends on the value of the stock $X(t)$. If the stock has fallen below the strike price $K$, i.e., if $X(t)\leq K$ the option becomes worthless because it is more convenient to pay the actual price $X(t)$ for the stock and forgo the option. If, on the contrary, the price has risen beyond $K$, i.e., if $X(t)>K$ we can realize a gain $X(t)-K$ by exercising the option to buy the stock at price $K$. This gain can be cashed immediately by reselling the stock at the current price $X(t)$. We can thus write the worth $w$ of the option as

Figure 1. Price of Cisco (CSCO) between November 25, 2008 and November 24, 2009. Stock prices can be modeled as a geometric Brownian motion.

where $(x)^{+} = \max(0,x)$ denotes projection on the positive numbers.

The gain to be realized by the trading strategy buy option at time $t=0$, exercise the option at time $t$ if $X(t)>K$, sell stock at price $X(t)$'' depends on the difference between $w$ and $c$. It is not exactly the difference because it is not equivalent to own $c$ at time $0$ and $c$ at time $t$. In particular, while the proposed investment strategy incurs some risk of loosing the initial investment $c$, it is possible to invest $c$ in a risk-free money market account. If the interest in the money market account is $\alpha$ continuously compounded, the worth of the money market investment at time $t$ is $ce^{\alpha t}$. Consequently, when comparing investment and payoff it is fairer to compare $w$ with $ce^{\alpha t}$ because growing $c$ to $ce^{\alpha t}$ is literally effortless. Equivalently, we can compare $c$ to $we^{-\alpha t}$ because capital $we^{-\alpha t}$ at time $0$ can be grown to $w$ at time $t$ through a risk-free money market investment. The latter comparison is the one commonly used and, in general, we say that a capital $w$ at time $t$ has a present value or a time-zero value of $we^{-\alpha t}$. We may also refer to $we^{-\alpha t}$ as the discounted worth. Using the option's worth expression, we can compute the discounted gain of an option investment as

The relevant question here is what is a fair price $c$ for an option with strike price $K$ to be exercised at time $t$. The answer to this question is given by the Black-Scholes formula for option pricing that uses expectations on the future behavior of the stock to determine the option's price $c$. To understand Black-Scholes formula, we need to introduce the Geometric Brownian motion model of stock prices, discuss the concept of arbitrages, and define risk neutral measures. The geometric Brownian motion model of stock prices is presented next. For arbitrages and the risk neutral measure you'll have to wait for the class.

## Geometric Brownian motion model of stock prices

It suffices to examine a graph with the evolution of a stock price, e.g., Fig. 1, to realize that stock prices are, to some extent, random. To construct a stochastic model of stock prices, notice that variations in a stock price are likely to be proportional to the price of the stock $X(t)$. That is, if the price of the stock is $X(t)=10$, a variation of plus or minus $1$ is akin to a variation of plus or minus $10$, when the price is $X(t)=100$. A particular class of stochastic processes with such property is geometric Brownian motion (GBM). This model presupposes that relative variations on the price $X(t)$ can be described as a Brownian motion with drift. Specifically, it assumes that changes in prices are according to the expression

where $Y_{t}(s)$ is normally distributed with mean $\mu s$ and variance $\sigma^{2}s$ independently of $s$. Definition of a GBM also requires relative price changes $Y_{t_{1}}(s_{1})$ and $Y_{t_{2}}(s_{2})$ in disjoint time intervals to be independent. In the context of stock pricing, the mean $\mu$ represents the stock's drift and the variance $\sigma^{2}$ its volatility.

An equivalent characterization of a GBM is to state that a process $X(t)$ is a GBM if its logarithm $\log X(t+s)$ is a regular Brownian motion (BM) with drift. Indeed, taking logarithms in both sides of the previous equation yields

The two conditions imposed on $Y_{t}(s)$, namely that $Y_{t}(s)$ is normal with mean $\mu s$ and variance $\sigma^{2}s$ and that $Y_{t_{1}}(s_{1})$ and $Y_{t_{2}}(s_{2})$ are independent for disjoint time intervals, along with the relationship just derived imply by definition that $\log X(t)$ is a BM.

An important observation to make here is to consider a discretization in time steps of fixed duration $h$, say $h=1 \text{ day}$, and to define the discrete time stochastic process $Y_{n}$ as

It follows from the GBM model, that variables $Y_{n}$ are independent identically distributed normals with mean $\mu h$ and variance $\sigma^{2}h$. This is an important observation because it allows us to infer the parameters $\mu$ and $\sigma^{2}$ from empirical data. Indeed, let it be available a historic sequence of stock prices $x(nh)$ for $n=0,\ldots,N$, taken from a realization $x(t)$ of the GBM stochastic process $X(t)$. From $x(nh)$ we compute $y_{n}=x(nh)- x \big(n(h-1)\big)$ to obtain a realization of the stochastic process $Y_{n}$. The drift parameter $\mu$ can then be estimated by the sample mean

Figure 2. Fit of Cisco's stock price (CSCO) to geometric Brownian motion (GBM) model. If GBM is a good model of stock price variations, the relative changes in stock prices from closing date to closing date are independent identically distributed normal random variables. Empirical probability distribution function (left) and cumulative distribution function (right) of CSCO relative changes in closing price are compared with a normal random variable. From either picture a reasonable fit between model and observations is seen.

and the volatility parameter $\sigma$ can be estimated by the sample variance

While we have given a justification for why GBM is a plausible model for stock prices, the actual motivation for their use, is that GBM models have been observed to provide reasonable fits of empirical stock price sequences. This fit is easy to observe using drift and volatility estimates $\hat{\mu}$ and $\hat{\sigma}^{2}$ computed from empirical data. If a GBM with drift $\hat{\mu}$ and volatility $\hat{\sigma^{2}}$ is a good model for the evolution of a stock price, then the variables $Y_{n}$ have a probability density function (pdf) $N\left(\hat{\mu}h,\hat{\sigma}^{2}h; y\right)$. We can then estimate the pdf of $Y_{n}$ using a histogram of the $y_{n}$ and compare it with the pdf $N\left(\hat{\mu}h,\hat{\sigma}^{2}h; y\right)$.

As a particular example, consider the stock price of Cisco during the year 2009 depicted in Fig. 1. More recent data for this stock and others is publicly available, see, e.g. Google finance. The comparison between the normal pdf $N\left(\hat{\mu}h,\hat{\sigma}^{2}h; y\right)$ and the histogram of $y_{n}$ is shown in Fig. 2. A comparison between the cumulative distribution function (cdf) and the empirical cdf is also shown. From either picture a reasonable fit between model and observations is seen.


text:
# PQRS is a parallelogram, where $$\rm \vec{PQ}=m\hat i+\hat j, \vec{PS} = 2 \hat i+4\hat j+4\hat k$$ and the area of the parallelogram is 6 sq. units. What is the value of m

1. 1
2. -1
3. 2
4. -2

Option 1 : 1

## Detailed Solution

Concept:

The parallelogram whose adjacent sides are the vectors a and b then area of the parallelogram is given by |a × b|

Calculation:

Here, $$\rm \vec{PQ}=m\hat i+\hat j, \vec{PS} = 2 \hat i+4\hat j+4\hat k$$

Area of parallelogram = $$|\rm \vec{PQ}× \vec{PS}|$$

$$\rm \vec{PQ}× \vec{PS}$$=$$\rm \left | \begin{array}{ccc} \hat i &\hat j & \hat k \\ m & 1 & 0 \\ 2 & 4 & 4 \end {array} \right |$$

= i(4) - j(4m) + k(4m - 2)

Now,

$$|\rm \vec{PQ}× \vec{PS}|$$= |(4)i - j(4m) + k(4m - 2)|

6 = $$\rm \sqrt {[4^2 + (4m)^2 + (4m - 2)^2]}$$

⇒ 6 = $$\rm \sqrt {[16 + 16m^2 + 16m^2- 16m + 4]}$$

Squaring both sides, we get

⇒ 36 = 32m2 - 16m + 20

⇒ 8m2 - 4m - 4 = 0

⇒ 8m2 - 8m + 4m - 4 = 0

⇒ 8m(m - 1) + 4(m - 1) = 0

⇒ (8m + 4) (m - 1) = 0

⇒ m = -4/8 = -1/2 OR m = 1

Hence, option (1) is correct.


text:
# 144 Delete Insert PrtSc FS F4 Draw rough sketches in the Lab Report of what the...

###### Question:

144 Delete Insert PrtSc FS F4 Draw rough sketches in the Lab Report of what the IR, 'H NMR, and 1C NMR spectra would be expected to look like. 4 1. IR bond(s) from the structure below: R Prediction Worksheet (Part B) Molecule 30: IR 100 06 80- 70- 60- 50- 40- 30- C-O 20- C=C 10- T TTT MINTTTTMT 500 4000 1500 1000 3000 2000 wavenumber (cm1) 1H NMR 4 3 2 10 9 8 chemical shift (ppm) 13C NMR T 10 20 80 70 60 50 40 30 200 190 180 170 160 150 140 130 120 110 100 90 chemical shift (ppm) % Transmittance

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