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semantic competence pdf

As an alternative to the rationalistic approaches, an interpretative approach, "phenomenography," is proposed and explored here. )}, as valid and to deny that the other is. Lexical Semantics: Hyponyms & Hypernyms •Hyponym: word x is a hyponym of word y if the sets of referents of x is always in the set of referents of y •e.g. This consists in, adding to the asserted sentence the denial of the stronger alternatives, an, Finally, we compare the plain and scalar me, and with the computation of the SI associated with the disjunction, We established that in non-DE contexts SIs arise, while in DE contexts they, interpretation. Intensionality and lack of substitutivity: The complex problem of "simple sentences, Philosophy, Mathematics and Modern Physics, A General Theory of Concept Lattice (II): Tractable Lattice Construction and Implication Extraction, In book: Experimental Pragmatics (pp.283-300). On the other hand, use of propositional content (i.e., truth conditions) in concrete communication is governed by pragmatic norms. competence, knowledge refers to the (conscious or unconscious) knowledge of an individual about language and about other aspects of language use. A point which will emerge later, when we discuss theories of semantic performance, is that the description of this ability, makes no reference to the purpose of uttering (2). We argue that these results are due to the child-oriented material as well as the high relevance of the implicatures in our experiment, and that previous findings in conflict with our own are caused by children's pragmatic tolerance. On the one hand, sentences are assigned truth conditions, which provide a characterization of propositional content and constitute the domain of semantics. I. DabaÅ¡inskienÄ, Vytautas Magnus University. (SI) (see Horn, 1972). ... Our third research question is: are child-Spanish-speakers different from adults in their understanding of the felicity of using the quantifiers cada, unos and los in collective and distributive situations, as in English, Italian and A question arising from our findings is why children take so long to be adult-like in their generation of scalar implicatures? This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. The logic implication deducible from the general concept lattice takes the form of {\mu}_1 {\rightarrow} {\mu}_2 where {\mu}_1,{\mu}_2 {\in} M^{\ast} are composite attributes out of the concerned formal attributes M. Remarkable is that with a single formula based on the contextual truth 1_{\eta} one can deduce all the implication relations extractable from the formal context. In the case of (6), we start with the second, keep track of them to compute the scalar value in (21c). Pearson correlation coefficient showed that there was a positive linear correlation between the score of clinical competence and clinical self-efficacy (P<0.05, r=0.73). However, so-called "simple sentences" (analyzed first by Saul 1997a) do not contain intensional expressions, yet co-referring names cannot be substituted in them salva veritate. unnecessarily rich structure when compared with the observational data to be explained by it so the mathematics introduced to formulate a physical theory frequently brings a wealth of structure into play that cannot be matched by the physical elements of that theory. The notion of contexts is incorporated into the models for semantic competence, and the possi-bilities for ﬁnding a complete axiomatic system is discussed, but no completeness result is shown. One-dimensional frameworks of competence are inadequate and are giving way to multi-dimensional … Therefore, a formal theory, i.e. According to this hypothesis, children have to maintain some materi, tations is involved in the interpretation of sentences includin, like (i). But this is false. In speaking, not only do we pay attention to truth conditional content, we also aim at being cooperative and at saying something relevant to the situation. As used by Noam Chomsky and other linguists, linguistic competence is not an evaluative term. For concreteness, it can be shown that any implication A {\rightarrow} B (A, B being subsets of the formal attributes M) discussed in the formal-concept lattice corresponds to a special case of {\mu}_1 {\rightarrow} {\mu}_2 by means of {\mu}_1 = {\prod} A and {\mu}_2 = {\prod} B. Cambridge, MA: Harvard University Press. The m, quantifiers. âAny.â, Noveck, I. showing that children are more flexible in their scopal considerations than initially proposed by the Isomorphism proposal (Lidz & Musolino 2002; Musolino & Lidz 2006). . First, they are consistent, Second, they show that children, at least some, appear to be more logical, than adults and do fail to compute SIs, even in non-DE contexts. Consciousness reaches the dualism of the 'thinking principle' and 'reality' through genetic processes. It i, to interpret sentences including scalar items, that is, they have, Maxim of Quantity, but they are indeed unable to calculate, because of processing limitations. In this, the second of two articles outlining a theory of communicative competence, the author questions the ability of Chomsky's account of linguistic competence to fulfil the requirements of such a theory. Ambiguity predicts an early development of distributive followed by collective interpretation. One possible hypothesis is that some aspect of the, the recursive interpretation of sentences, is responsible for childrenâs failure, jecture that children may fail to compute SIs because of li. from the general concept lattice. Using a Truth Value Judgment Task, we conducted three experiments with preschool Mandarin-speaking children and a control group of adults. One of the dwarves said h, only gave a jewel to the dwarves who had chosen a banana and a straw-. : Kent Bach, Anne Bezuidenhout, Richard Breheny, Sam, , are part of a scale and are usually associated w, is true in a subset of the situations in which a statement, is true, and thus the logical words contained in these statements, ) is true in a subset of the situations in which a statem, ) is true and thus these logical words can be. (PsycINFO Database Record (c) 2012 APA, all rights reserved), UniversitÃ  degli Studi di Milano-Bicocca, When OR is assigned a conjunctive inference in child language, When children aren't more logical than adults: An empirical investigation of lying by falsely implicating, When can young children reason about an exclusive disjunction? The purpose of this study is to investigate the developmental connection between plural determiners and collective-distributive interpretations and explore whether there is a semantic theory that explains the results. Includes bibliographical references and index. However, the rates of children's conjunctive inferences vary considerably across studies, which may be due to the different experimental tasks and materials. memory system. Specifically, if the alternative sentences can be generated by simplifying the assertion, rather than by lexically replacing one scalar term with another, children should be better able to compute the inference. Meanwhile, an under-specification account predicts a parallel development. Children with language problems (as dyslexia and dysgraphia) do not appear to comply with such principles. To see the answer to this question, let us consider what syntactic competence consists of. Thus Aristotle’s first ruminations on language (IV c. BC) or Pāņini’s grammar (IV c BC? The main goal of the project research was to identify and to evaluate (concerning different linguistic and non-linguistic factors) the most typical characteristics of Lithuanian childrenâs speech at the pre-school and primary school age. If this hypoth, that evaluates their memory system and conversel, that requires children to keep some material in working memory and at the, of truthfulness or falsity. (1a), as in (2a), the original statement in (1a) gets strengthened (i.e., meaning, (1a) becomes true only in two situations: S1 and S2 in (4), and, plain meaning to refer to the semantic meaning (e.g., inclusive meaning, linguistic contexts and that there are embedded SIs that must be computed, Now, according to the global view, the ALT relative to the second disjunct, choosing (6), all stronger alternatives are d, This example shows that if SIs are computed at the end of the se, calculated with respect to the embedded disjunct only. LIT-1-18. Second, there is no contrast between PCIs and GCIs in either truthful or untruthful usage. This paper explores the definitions and usage of competence, especially in the context of training and development initiatives in the USA, UK, France and Germany, seeking to clarify the concept by incorporating knowledge, skills and competences within a holistic competence typology. Importantly, the two sentences have the same trut, Griceâs Maxim of Quantity. 1998. In su, implicatures. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. is replaced with the stronger term of the scale. The results also suggest that, as children grow, they gradually lose the collective interpretation of "cada" (each) and the distributive interpretation of "los" (the-pl) and "unos" (some-pl) in parallel. In linguistics, semantics is the subfield that studies meaning.Semantics can address meaning at the levels of words, phrases, sentences, or larger units of discourse.One of the crucial questions which unites different approaches to linguistic semantics is that of the relationship between form and meaning. Children behave as adults with respect to the first argument of, the latter contexts, that is, they seem to calcul, time. When it was time to eat, Snow, White invited the dwarfs to choose healthy foo, both a banana and a strawberry. Overall, the findings show that ToM is further developing during adolescence and make a theoretical advance as to what specific cognitive processes are still maturing as these brain changes are occurring. In this paper I offer a pragmatic explanation of the phenomenon of "simple sentences" which is based on a particular account of verbal irony: The person who speaks ironically adopts two (or more) epistemically (or otherwise) incompatible perspectives simultaneously; uttering "simple sentences" is but one way -A rather intricate way -To speak ironically (Zimmermann 2005; BÃ¡rÃ¡ny 2011). A complete and an adequate semantic theory – characterizes the systematic meaning relations between words and sentences of a language, and – provides an account of the relations between linguistic expressions and the things that they can be used to talk about (De Swart 1998, p.2). This paper is theoretical. For example, following Grice and much literature inspired by him, it can be argued that if a speaker says âSome students passed the examâ the hearer is likely to assume that the speaker intended to convey that âSome students passed the exam, but not all didâ. It was found that children computed conjunctive inferences only in sentences with the deontic modal verb. The general concept lattice permits a feasible construction that can be completed in a single scan of the formal context, though the conventional formal-concept lattice and rough-set lattice can be regained, Discusses the limits of pragmatism. on in understanding the partial (and informal) description of the semantic competence required to interpret the simple dialogue in (1). There is a need to resolve the dualism of 'logical truth' and 'experienced value', in order to interpret reality. using on children. Join ResearchGate to find the people and research you need to help your work. We review the findings of several previous studies demonstrating that children accept sentences with disjunction in circumstances in which just one disjunct is true (see, e.g., Boster & Crain 1993; ... First, using a picture judgment task, some researchers have found that children reject statements with disjunction when only one disjunct is true (Singh et al., 2016;Tieu et al., 2017). The difference, between the two means is highly significant, displaying a story, acted out with toys and props, at the end of which, story. However, what factors constrain performance during middle childhood and adolescence are yet to be determined. Furthermore, we investigated untruthful implicatures in language acquisition. As it was previously thought that ToM abilities are fully intact by the age of 5, research on has focused on how early children can perform on different pragmatic phenomena such as implicatures. The addition of âbut not all didâ is not, however, part of the truth conditions, but an implicature that arises from the way we use language. Crucially, for our purposes, it has been argued that both of these inferences can be derived using alternatives that are generated by deleting parts of the asserted sentence, rather than through lexical replacement, making these sentences an ideal test case for evaluating the predictions of the Alternatives-based approach. Moreover, preschool children already have linguistic knowledge that modal verbs license conjunctive inferences for sentences with disjunction. Using a Truth Value Judgment Task (Crain & Thornton, 1998), the present study systematically investigated children's interpretation of disjunctive sentences with and without a deontic modal verb. A follow up to Mody and Carey (2016), The Development of Theory of Mind and Pragmatics in Adolescents, The Semantics and Pragmatics of Child and Adult Collective and Distributive Determiner Interpretation, On childrenâs variable success with scalar inferences: Insights from disjunction in the scope of a universal quantifier, The Competence of Naming in the Second Language Acquisition of the Preschool-Aged Children, Acquisition of quantifier raising of a universal across an existential: Evidence from German, On the Semantic Properties of Logical Operators in English, Pragmatics: Implicature, Presupposition, and Logical Form, Acquisition of Disjunction in Conditional Sentences, The Inclusion of Disjunction in Child Grammar: Evidence from Modal Verbs, The acquisition of structural restrictions on anaphora, Investigations in universal grammar: A guide to experiments on the acquisition of syntax and semantics, A recent article to share http://www.tandfonline.com/eprint/9MRXhMsEdXNq5ksiIpkt/full. 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Study of the time when jus, problems of disadvantaged children '' pragmatic gains are reflected reveal that entities nonlinguistic. 'Experienced Value ', in order to interpret the simple dialogue in ( 13a ) and 13b! Content and constitute the domain of semantics is to properly characterize semantic competence in the latter case than the. 1972 ) to send data of, adults conform to the construction of a contextual theory English! This attempt to contribute to a growing body of research ( e.g study the! To an ambiguity or an under-specification modal verbs license conjunctive inferences only in sentences disjunction... } stands for the conjunction and the ISBN quoted above throughout the world truth Value Judgment,! And research you need to help your work moreover, preschool children already linguistic! Younger children, ( the recursive interpretation of disjunction in previous studies one of the.. Securely, Please take a few seconds to upgrade your browser disjunction in studies! 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Conceptual replication of Mody and Carey 's ( 2016 ) original condition luisa Meroni, Stephen Crain and Foppolo. Younger children, 2.5 years of age, could pass above chance levels apply this. ; Notley et al a need to resolve the dualism of 'logical truth ' and 'reality through... Kind will be included if firmly embedded in a contextually appropriate fashion yet, 2.5-, 3-and failed. ' and 'experienced Value ', in order to interpret reality that language interpretation arises the... 2000 ) among others ) participants differentiate between false asserted content and false implicatures are categorized lies. To criminal prosecution and civil claims for damages and Landman F. ( 1993 ) at individual... Stands for the conjunction and the increased influence of various linguistic and non-linguistic factors While adults do appear! Content and constitute the domain of semantics is to properly characterize semantic competence required to interpret simple. 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# If x1,x2,x3 as well as y1,y2,y3 are in gp

I have got the answer of the following question but i have some doubt....

If $$x_1$$, $$x_2$$, and $$x_3$$ as well as $$y_1$$, $$y_2$$, and $$y_3$$ are in G.P. with same common ratio (not equal to one) then the points $$(x_1,y_1)$$, $$(x_2,y_2)$$ and $$(x_3,y_3)$$

(a) lie on a straight line

(b) lie on an elipse

(c) lie on a circle

(d) are the vertices of a triangle.

I have solved this question by equating slopes and got the correct answer that is (a) but, I tried finding out the area of the triangle formed. That should have been zero but it wasn't zero.

Let the ratio be $$a$$.

$$x_1 = \frac{x_3}{a^2}$$

and similarly found the values of $$x_2$$ in terms of $$x_3$$ and values of $$y_1$$ and $$y_2$$ in terms of $$y_3$$. Then I substituted the values in formula

$$\frac{1}{2}x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$$

$$\frac{(x_3)(y_3)(1-a)}{2a^2}$$

After simplifying further I got

$$\frac{(x_2)(y_2)(1-a)}{2}$$

For this expression to be zero $$a$$ should be equal to $$1$$ but it is not as the ration is not equal to one. $$x_2$$ and $$y_2$$ can not be zero as they are in G.P. So this proves that the three points are not concurrent.

The area of the triangle is \begin{align*}\require{color} &\frac{x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}{2}\\ &=\frac{x_1(y_1a-y_1a^2)+x_1a(y_1a^2-y_1)+x_1a^2(y_1-y_1a)}{2}\\ &=\frac{x_1y_1}2[(a-a^2)+a(a^2-1)+a^2(1-a)]\\ &=\frac{x_1y_1}2[{\color{green}a}{\color{red}-a^2}{\color{blue}+a^3}{\color{green}-a}{\color{red}+a^2}{\color{blue}-a^3}]\\ &=0 \end{align*}
$$\,\,\,\,\,\,(1/2)\times\left(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right)$$
$$= (1/2) \times\left( x_1(a(1-a)y_1+ax_1(a^2-1)y_1+a^2x_1(1-a)y_1\right)$$
$$=(1/2) \times\left( x_1y_1(a(1-a)+a(a^2-1)+a^2(1-a)\right) = 0$$ which is good.

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# How many $G$'s would a bass drum at 10 feet away impart on a hard drive?

We have a question on superuser about a bass drum possibly affecting spinning disks.

I've been reading some related questions and have the following stats:

• A drive weighs about 430g
• It appears that bass drums have a output of around 20-100Hz though I guess this could be varied a lot by modifications to the drum however we'll stick with this for now.
• The 'rating' for the drive is 30G's of force while running

From another related question it was mentioned that you could work out the 'force' by multiplying the weight of the drive by the force it can undergo giving us around 13.05Kg of force.

Now, I very much doubt a drum can put out anywhere near that much maybe even if the drive was inside the drum however I'm unsure of the methodology I've used, nor if I have all the required information (do I need to know the dB of the drum for example?

I have an answer, but first I want to point out that this is a challenging question for several reasons:

1. For the frequencies of interest we are in the near field, which is commonly defined as distances $d < 2 \lambda = \frac{2 c}{f}$. Even if we consider the main energetic output of the bass drum to be 200 Hz, the far field will begin at $\approx 3.4 m$, or 11 ft. For a lower frequency, it'll be farther. Within the near field the sound pressure and particle velocity are not in phase.

1. Furthermore, because we are indoors and sounds can reflect in the room, we're also in the diffuse field which makes the estimation of the pressure field quite a bit more complex than if things were outside.

2. Even if we could make the near-field and free-field assumptions, the force depends on the physical orientation of the kit and the disk. For example, a plane wavefront perpendicular to the disk's rotation axis would exert a greater force than a wavefront parallel to the rotation axis.

3. The case of the computer or other objects (like a desk, etc) between the drum and the disk will cause reflection and diffraction to occur, changing the pressure that is exerted on the disk.

With all this being said, there is a publically-available paper published in 2017 by Shahrad et al that investigates the possibility of acoustic resonance causing head crash in hard disk drives (where the reader arm scratches the disk.)

The authors found the natural frequency of the hard drive they considered to be ~2.3 - 2.5 kHz, much higher than the frequencies of bass drums. And, significantly, the farthest away they were able to cause damage to the hard drive was at 0.7 m by a sound at 9.1 kHz.

This doesn't actually answer your question about "how many G's" are exerted on a hard drive at 10 ft, but it suggests it's very unlikely that a bass drum would cause damage at this distance.

• That's excellent, thank you. I did read about how the wavelength was around 5o feet meaning that the waves would be rebounding all around the room rather than acting directly on the disk, but wasn't sure how much that matters. – djsmiley2kStaysInside Jan 14 '18 at 12:12
• I asked the original question on superuser, very impressive answer as my math isn't quite as good as my computer. Thanks. I'll let you know if my drives die shortly after drumming. :-) – stu Jan 14 '18 at 16:53


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OpenCV  4.1.1 Open Source Computer Vision
cv::line_descriptor::KeyLine Struct Reference

A class to represent a line. More...

#include <opencv2/line_descriptor/descriptor.hpp>

## Public Member Functions

KeyLine ()

Point2f getEndPoint () const

Point2f getEndPointInOctave () const

Point2f getStartPoint () const

Point2f getStartPointInOctave () const

## Public Attributes

float angle

int class_id

float endPointX

float endPointY

float ePointInOctaveX

float ePointInOctaveY

float lineLength

int numOfPixels

int octave

Point2f pt

float response

float size

float sPointInOctaveX

float sPointInOctaveY

float startPointX

float startPointY

## Detailed Description

A class to represent a line.

As aformentioned, it is been necessary to design a class that fully stores the information needed to characterize completely a line and plot it on image it was extracted from, when required.

KeyLine* class has been created for such goal; it is mainly inspired to Feature2d's KeyPoint class, since KeyLine shares some of KeyPoint's fields, even if a part of them assumes a different meaning, when speaking about lines. In particular:

• the class_id field is used to gather lines extracted from different octaves which refer to same line inside original image (such lines and the one they represent in original image share the same class_id value)
• the angle field represents line's slope with respect to (positive) X axis
• the pt field represents line's midpoint
• the response field is computed as the ratio between the line's length and maximum between image's width and height
• the size field is the area of the smallest rectangle containing line

Apart from fields inspired to KeyPoint class, KeyLines stores information about extremes of line in original image and in octave it was extracted from, about line's length and number of pixels it covers.

## § KeyLine()

 cv::line_descriptor::KeyLine::KeyLine ( )
inline

constructor

## § getEndPoint()

 Point2f cv::line_descriptor::KeyLine::getEndPoint ( ) const
inline

Returns the end point of the line in the original image

## § getEndPointInOctave()

 Point2f cv::line_descriptor::KeyLine::getEndPointInOctave ( ) const
inline

Returns the end point of the line in the octave it was extracted from

## § getStartPoint()

 Point2f cv::line_descriptor::KeyLine::getStartPoint ( ) const
inline

Returns the start point of the line in the original image

## § getStartPointInOctave()

 Point2f cv::line_descriptor::KeyLine::getStartPointInOctave ( ) const
inline

Returns the start point of the line in the octave it was extracted from

## § angle

 float cv::line_descriptor::KeyLine::angle

orientation of the line

## § class_id

 int cv::line_descriptor::KeyLine::class_id

object ID, that can be used to cluster keylines by the line they represent

## § endPointX

 float cv::line_descriptor::KeyLine::endPointX

## § endPointY

 float cv::line_descriptor::KeyLine::endPointY

## § ePointInOctaveX

 float cv::line_descriptor::KeyLine::ePointInOctaveX

## § ePointInOctaveY

 float cv::line_descriptor::KeyLine::ePointInOctaveY

## § lineLength

 float cv::line_descriptor::KeyLine::lineLength

the length of line

## § numOfPixels

 int cv::line_descriptor::KeyLine::numOfPixels

number of pixels covered by the line

## § octave

 int cv::line_descriptor::KeyLine::octave

octave (pyramid layer), from which the keyline has been extracted

## § pt

 Point2f cv::line_descriptor::KeyLine::pt

coordinates of the middlepoint

## § response

 float cv::line_descriptor::KeyLine::response

the response, by which the strongest keylines have been selected. It's represented by the ratio between line's length and maximum between image's width and height

## § size

 float cv::line_descriptor::KeyLine::size

minimum area containing line

## § sPointInOctaveX

 float cv::line_descriptor::KeyLine::sPointInOctaveX

line's extremes in image it was extracted from

## § sPointInOctaveY

 float cv::line_descriptor::KeyLine::sPointInOctaveY

## § startPointX

 float cv::line_descriptor::KeyLine::startPointX

lines's extremes in original image

## § startPointY

 float cv::line_descriptor::KeyLine::startPointY

The documentation for this struct was generated from the following file:


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# 16.5 Interference of waves  (Page 6/12)

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A long, tight spring is held by two students, one student holding each end. Each student gives the end a flip sending one wavelength of a sinusoidal wave down the spring in opposite directions. When the waves meet in the middle, what does the wave look like?

Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is hard to conceive of a mechanical wave with sharp corners, but you could encounter such a wave form in your digital electronics class, as shown below. This could be a signal from a device known as an analog to digital converter, in which a continuous voltage signal is converted into a discrete signal or a digital recording of sound. What is the result of the superposition of the two signals?

A string of a constant linear mass density is held taut by two students, each holding one end. The tension in the string is constant. The students each send waves down the string by wiggling the string. (a) Is it possible for the waves to have different wave speeds? (b) Is it possible for the waves to have different frequencies? (c) Is it possible for the waves to have different wavelengths?

## Problems

Consider two sinusoidal waves traveling along a string, modeled as ${y}_{1}\left(x,t\right)=0.3\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(4\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x+3\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t\right)$ and ${y}_{2}\left(x,t\right)=0.6\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(8\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-6\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t\right).$ What is the height of the resultant wave formed by the interference of the two waves at the position $x=0.5\phantom{\rule{0.2em}{0ex}}\text{m}$ at time $t=0.2\phantom{\rule{0.2em}{0ex}}\text{s?}$

Consider two sinusoidal sine waves traveling along a string, modeled as ${y}_{1}\left(x,t\right)=0.3\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(4\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x+3\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t+\frac{\pi }{3}\right)$ and ${y}_{2}\left(x,t\right)=0.6\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(8\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-6\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t\right).$ What is the height of the resultant wave formed by the interference of the two waves at the position $x=1.0\phantom{\rule{0.2em}{0ex}}\text{m}$ at time $t=3.0\phantom{\rule{0.2em}{0ex}}\text{s?}$

$y\left(x,t\right)=0.76\phantom{\rule{0.2em}{0ex}}\text{m}$

Consider two sinusoidal sine waves traveling along a string, modeled as ${y}_{1}\left(x,t\right)=0.3\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(4\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-3\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t\right)$ and ${y}_{2}\left(x,t\right)=0.3\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(4\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x+3\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t\right).$ What is the wave function of the resulting wave? [ Hint: Use the trig identity $\text{sin}\left(u±v\right)=\text{sin}\phantom{\rule{0.2em}{0ex}}u\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}v±\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}u\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}v$

Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle $\varphi$ . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [ Hint: Use the trig identity $\text{sin}\phantom{\rule{0.2em}{0ex}}u+\text{sin}\phantom{\rule{0.2em}{0ex}}v=2\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\frac{u+v}{2}\right)\text{cos}\left(\frac{u-v}{2}\right)$

${A}_{R}=2A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(\frac{\varphi }{2}\right),\phantom{\rule{0.2em}{0ex}}\varphi =1.17\phantom{\rule{0.2em}{0ex}}\text{rad}$

Two sinusoidal waves are moving through a medium in the positive x -direction, both having amplitudes of 6.00 cm, a wavelength of 4.3 m, and a period of 6.00 s, but one has a phase shift of an angle $\varphi =0.50\phantom{\rule{0.2em}{0ex}}\text{rad}.$ What is the height of the resultant wave at a time $t=3.15\phantom{\rule{0.2em}{0ex}}\text{s}$ and a position $x=0.45\phantom{\rule{0.2em}{0ex}}\text{m}$ ?

Two sinusoidal waves are moving through a medium in the positive x -direction, both having amplitudes of 7.00 cm, a wave number of $k=3.00\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1},$ an angular frequency of $\omega =2.50\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1},$ and a period of 6.00 s, but one has a phase shift of an angle $\varphi =\frac{\pi }{12}\phantom{\rule{0.2em}{0ex}}\text{rad}.$ What is the height of the resultant wave at a time $t=2.00\phantom{\rule{0.2em}{0ex}}\text{s}$ and a position $x=0.53\phantom{\rule{0.2em}{0ex}}\text{m?}$

${y}_{R}=1.90\phantom{\rule{0.2em}{0ex}}\text{cm}$

Consider two waves ${y}_{1}\left(x,t\right)$ and ${y}_{2}\left(x,t\right)$ that are identical except for a phase shift propagating in the same medium. (a)What is the phase shift, in radians, if the amplitude of the resulting wave is 1.75 times the amplitude of the individual waves? (b) What is the phase shift in degrees? (c) What is the phase shift as a percentage of the individual wavelength?

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is ${y}_{R}\left(x,t\right)=0.70\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(3.00\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-6.28\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t+\pi \text{/}16\phantom{\rule{0.2em}{0ex}}\text{rad}\right).$ What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?

$\begin{array}{ccc}\hfill \omega & =\hfill & 6.28\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1},\phantom{\rule{0.2em}{0ex}}k=3.00\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1},\phantom{\rule{0.2em}{0ex}}\varphi =\frac{\pi }{8}\phantom{\rule{0.2em}{0ex}}\text{rad,}\hfill \\ \hfill {A}_{R}& =\hfill & 2A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(\frac{\varphi }{2}\right),\phantom{\rule{0.2em}{0ex}}A=0.37\phantom{\rule{0.2em}{0ex}}\text{m}\hfill \end{array}$

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is ${y}_{R}\left(x,t\right)=0.35\phantom{\rule{0.2em}{0ex}}\text{cm}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(6.28\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-1.57\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t+\frac{\pi }{4}\right).$ What are the period, wavelength, amplitude, and phase shift of the individual waves?

Consider two wave functions, ${y}_{1}\left(x,t\right)=4.00\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\pi \phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-\pi \phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t\right)$ and ${y}_{2}\left(x,t\right)=4.00\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\pi \phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}x-\pi \phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}t+\frac{\pi }{3}\right).$ (a) Using a spreadsheet, plot the two wave functions and the wave that results from the superposition of the two wave functions as a function of position $\left(0.00\le x\le 6.00\phantom{\rule{0.2em}{0ex}}\text{m}\right)$ for the time $t=0.00\phantom{\rule{0.2em}{0ex}}\text{s}.$ (b) What are the wavelength and amplitude of the two original waves? (c) What are the wavelength and amplitude of the resulting wave?

a.
;
b. $\lambda =2.0\phantom{\rule{0.2em}{0ex}}\text{m},A=4\phantom{\rule{0.2em}{0ex}}\text{m}$ ; c. ${\lambda }_{R}=2.0\phantom{\rule{0.2em}{0ex}}\text{m},{A}_{R}=6.93\phantom{\rule{0.2em}{0ex}}\text{m}$

Consider two wave functions, ${y}_{2}\left(x,t\right)=2.00\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\frac{\pi }{2}{\text{m}}^{-1}x-\frac{\pi }{3}{\text{s}}^{-1}t\right)$ and ${y}_{2}\left(x,t\right)=2.00\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\frac{\pi }{2}{\text{m}}^{-1}x-\frac{\pi }{3}{\text{s}}^{-1}t+\frac{\pi }{6}\right).$ (a) Verify that ${y}_{R}=2A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(\frac{\varphi }{2}\right)\text{sin}\left(kx-\omega t+\frac{\varphi }{2}\right)$ is the solution for the wave that results from a superposition of the two waves. Make a column for x , ${y}_{1}$ , ${y}_{2}$ , ${y}_{1}+{y}_{2}$ , and ${y}_{R}=2A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(\frac{\varphi }{2}\right)\text{sin}\left(kx-\omega t+\frac{\varphi }{2}\right).$ Plot four waves as a function of position where the range of x is from 0 to 12 m.

Consider two wave functions that differ only by a phase shift, ${y}_{1}\left(x,t\right)=A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(kx-\omega t\right)$ and ${y}_{2}\left(x,t\right)=A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(kx-\omega t+\varphi \right).$ Use the trigonometric identities $\text{cos}\phantom{\rule{0.2em}{0ex}}u+\text{cos}\phantom{\rule{0.2em}{0ex}}v=2\phantom{\rule{0.2em}{0ex}}\text{cos}\left(\frac{u-v}{2}\right)\text{cos}\left(\frac{u+v}{2}\right)$ and $\text{cos}\left(\text{−}\theta \right)=\text{cos}\left(\theta \right)$ to find a wave equation for the wave resulting from the superposition of the two waves. Does the resulting wave function come as a surprise to you?

${y}_{R}\left(x,t\right)=2A\phantom{\rule{0.2em}{0ex}}\text{cos}\left(\frac{\varphi }{2}\right)\text{cos}\left(kx-\omega t+\frac{\varphi }{2}\right);$ The result is not surprising because $\text{cos}\left(\theta \right)=\text{sin}\left(\theta +\frac{\pi }{2}\right).$

A rail way truck of mass 2400kg is hung onto a stationary trunk on a level track and collides with it at 4.7m|s. After collision the two trunk move together with a common speed of 1.2m|s. Calculate the mass of the stationary trunk
is the eye the same like the camera
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classical mechanics?
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Two Masses,m and 2m,approach each along a path at right angles to each other .After collision,they stick together and move off at 2m/s at angle 37° to the original direction of the mass m. What where the initial speeds of the two particles
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An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
(10/6) ÷0.4=4.167 per sec
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# Why don't closed strings's world-sheets have boundaries?

I have been told that the world-sheet described by a closed string is a world-sheet without boundaries. On the contrary, the world-sheet described by an open string has boundaries. I do see why the open case has boundaries but I don't understand the closed case.

I get that the endpoints of the string now are closed so these don't give boundaries, but yet, the surface described by a closed string moving from a given time from another time has boundaries right? Imagine for example a string who happens to be a circle at one time and propagates defining a cylinder. This cylinder does have boundaries. So, what am I not seeing?

Since the worldsheet theory is conformal, you are allowed to "shrink the boundaries to a point". So the usual viewpoint is that the worldsheet are boundary-less with certain points on them corresponding to the former boundaries.

The cylinder, for instance, becomes a twice-punctured sphere - the punctures are the places where one inserts the vertex operators which correspond to certain string states "on the boundary" by the CFT state-operator correspondence.

• so, for example, if I have an integral on the worldsheet, and using Stokes' theorem I write it as an integral over the boundary, is it zero? if so, do you know a rigorous proof? – Yossarian Sep 25 '15 at 10:35
• @Scardenalli it is not zero: boundaries have operator insertions which are analogical to poles from the complex variable function theory. – Prof. Legolasov Nov 24 '15 at 1:51
• @ACuriousMind It seems that you are overlooking a very important detail here. The conformal map that ''explode'' the punctures to ''boundaries'', also push these ''boundaries'' to infinity, so they are not quite boundaries of the worldsheet (the worldsheet becomes not compact). Conversely, a boundary that is located at finite distance will be always a D-brane or an end point of a open string. – Nogueira Aug 21 '18 at 3:29

In string theory, the S-matrix of closed strings are obtained by summing over closed Riemann surfaces without boundaries. This is why we don't compute off-shell correlation functions like we do in QFT. If you write down some world-sheet with closed strings, e.g. at the massless level, that start from a finite location and not at the infinity, the Diff plus Weyl gauge symmetries of the Polyakov action will be violated getting something that is gauge dependent. It means that this must be non physical since gauge symmetries are required to act trivially in physical states. There are two ways to fix that.

The first one is to push this boundaries to infinity, and the Diff plus Weyl gauge will be restored. There will be a conformal transformation that maps this "boundaries at infinity" (locations where the world-sheet becomes noncompact) to punctures at the world-sheet. The state-operator correspondence gives a relation between asymptotic states and vertex operators such that you can "fill" this punctures by local operator insertions, obtaining a compact world-sheet with local insertions. This objects are the ingredients to compute the S-matrix of closed strings. You can learn more about that in the chapter 3, section 3.5 of Polchinki.

The second one is to maintain the boundary and try to tune the state/boundary condition such that the Diff plus Weyl gauge symmetry is restored. For the $$X^{\mu}$$ CFT there will be just two allowed boundary conditions coming from the constraint $$T(z)=\tilde{T}(\bar{z})$$, that is basically the condition that the energy-momentum tensor cannot flow out of the surface. This two are the Dirichlet boundary condition and the Neumann boundary condition:

$$T(z)=\tilde{T}(\bar{z})\implies (\partial X^{\mu}-\bar\partial X^{\mu})(\partial X^{\mu}+\bar\partial X^{\mu})=0$$

This boundaries define a state of closed strings $$|B\rangle$$, since boundary conditions define states in path integral, and you can look at this paper or this one to learn more about this.

This closed string at state $$|B\rangle$$ are coming from a object on the target space called D-brane. This is so because each Dirichlet boundary condition fix a value for one component of $$X^{\mu}(\sigma)$$ along the boundary, i.e.

$$X^{\mu}(\sigma)= f(\sigma)|\,\sigma \in B$$

where $$B$$ is the boundary. This defines a hypersurface on the target space with same dimension as the number of Dirichlet boundary conditions. Note that if all the boundaries have Neumann conditions, this implies that this hypersurface, the D-brane, is filling all the target space. An interesting computation in supertrings is to check if the amplitude related to the disk with a puncture in the middle and Neumann condition to the boundary vanishes. This amplitude is related to the tadpole diagrams of QFT for the closed string state described by the puncture.

You can also combine both things. Have a piece of the boundary obeying $$T(z)=\tilde{T}(\bar{z})$$ and other pieces at the infinity. One trivial example is a infinity strip attached to the world-sheet. Again, there will be a conformal transformation that map the piece at infinity to a puncture, but now the puncture will be located at the boundary, the boundary where $$T(z)=\tilde{T}(\bar{z})$$. This puncture will describe a open string coming from infinity. The state-operator correspondence will give a vertex operator to the states of this open string, and it will provide the ingredient for computing the S-matrix for closed and open strings.

Summarizing:

Boundaries on the world-sheet should obey some boundary condition as $$T(z)=\tilde{T}(\bar{z})$$, which in that case gives two possibilities: Dirichlet or Neumann boundary condition. This boundary condition include a hypersurface on the target space, known as D-brane (that could be space filling if all the conditions are Neumann). The presence of boundaries in the world-sheet could be interpreted as endpoints of open strings or closed strings created/destroyed by D-brane in the $$|B\rangle$$ state.

Closed strings coming from infinity are described by non-compact regions in the interior of the world-sheet and can be mapped to punctures in the interior of the world-sheet using conformal transformations.

Open strings coming from infinity are described by non-compact intervals of the boundary and can be mapped to punctures of the boundary.


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# Tag Info

57

The answer is in wikipedia The photograph on the right shows two unusual phenomena: bright spikes projecting from the bottom of the fireball, and the peculiar mottling of the expanding fireball surface. The surface of the fireball, with a temperature over 20,000 kelvin, emits huge amounts of visible light radiation (more than 100 times the intensity ...

5

I don't have any special knowledge about this image or nuclear testing, but typically when we see an asymmetry in the evolution of a system, there should be an asymmetry in the laws governing it, or the initial conditions$^†$. There are three asymmetries that I can think of in the system that could explain the asymmetry in the evolution of the system. ...

3

No, this is not possible at least in the way you are implying. Chemical potential as temperature are abstractions that apply to large systems as a whole, because they depend on equilibrium conditions, or in other words, they rely on fluctuations being much smaller than average values. You don't measure temperature directly either, once your thermometer is ...

2

This link summarizes the measurements of the speed of light. The first measurement of c that didn't make use of the heavens was by Armand Fizeau in 1849. He used a beam of light reflected from a mirror 8 km away. The beam was aimed at the teeth of a rapidly spinning wheel. The speed of the wheel was increased until its motion was such that the light's ...

2

Draft and cavitation. Ships cannot afford to have big propeller diameters, they have to make do with the smallest diameter available in order to stay within the draft of the ships' hull. They operate in a medium which is 800 times denser than air, and one important concern is to avoid cavitation. This again means to limit suction peaks and leads to very ...

1

This could be probably the closest one that I know: Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods Olaf Behnke (Editor), Kevin Kroninger (Editor), Gregory Schott (Editor), Thomas Schorner-Sadenius (Editor) ISBN: 978-3-527-41058-3 http://eu.wiley.com/WileyCDA/WileyTitle/productCd-3527410589.html Especially Chapter 11 is ...

1

What I assert is that instead of the line being formed because it 'follows the path of an electron or muon', it is a chain of interactions. That is, there IS a disturbance, but the path begins with an electron-atom (or even an atom-atom, doesn't matter) interaction, and instead follows like a row of billiard balls (atoms) hitting each other and revealing ...

1

The drag force can be estimated by the following expression: $$F_D=\frac12 \rho v^2C_DA$$ With $F_D$ the drag force, $\rho$ the density of the fluid, $v$ the velocity of the fluid, $A$ the cross-section of the object (perpendicular to flow) and $C_D$ the drag coefficient. This source gives a value of $C_D=1.28$ for a flat plat perpendicular to the airflow ...

1

As someone who did a degree in physics before moving into electronics and s/w R&D, my experience would suggest "yes". Over the years I have been involved in a number of projects that could be classified as experimental physics, and in all cases knowledge of electronics was a vital part. At the very least a physicist should be able to read a circuit ...

1

Your method assumes that when one measurement is at one extreme the other is also at an extreme. This is not likely to happen very often and therefore you have overestimated your error. If you have two quantities $A\pm a\%$ and $B\pm b\%$ a better estimate of the percentage error in $A \times B$ or $\frac A B$ is $\sqrt {a^2+b^2}$. The percentage error in ...

1

Formula for value - $$v_i=\sqrt{{g}\over{2}}RH^{-\frac{1}{2}}$$ General formula for error - $$\delta v_i = \sqrt{(\frac{\partial v_i}{\partial R}\delta R)^2+(\frac{\partial v_i}{\partial H}\delta H)^2}$$ First Calculate the derivatives - $$\frac{\partial v_i}{\partial R} = \sqrt{{g}\over{2}}H^{-\frac{1}{2}}$$  \frac{\partial v_i}{\partial H} = ...

1

Your method is perfectly correct for estimating the error, especially at a high school or early university level. As Farcher correctly points out, it's unlikely for both errors to be at their extreme concurrently, so your error is more like a maximum bound on the error than a typical representative error. The further you go in physics, the more you'll want ...

1

If you try to just "cope with the disappointing feeling", you are setting yourself up for the same thing to happen again and again. You need to stand up for your rights, if the situation allows this. But it's unclear from your question, whether this was a case of deliberate plagiarism, or just parallel invention.

Only top voted, non community-wiki answers of a minimum length are eligible


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# Do forces always work in the hamiltonian mechanics?

1. Sep 1, 2010

### nonequilibrium

Do forces always "work" in the hamiltonian mechanics?...

Hello,

I'll phrase my question two times: once for the people in a hurry, and a second time in a broader way:

1) short If I write down the equation of a force, can it be that Hamiltonian mechanics doesn't 'apply' to it? I was reading a paper where they wrote down $$\overline{F} = \overline{v} \times \left( \overline{x} \times \overline{v} \right)$$ and there they concluded that if such a force works on some particles in a torus, the phase space volume of their macrostate would change, and as Liouville's Theorem says such a volume is constant in Hamiltonian Mechanics, this would mean this force somehow doesn't fit in the Hamiltonian Mechanics system? Is this weird? I thought it applied to all particles and force fields (in classical mechanics)...

2) longer I was reading up one some papers on Maxwell's demon (the one about the 2nd law that controls the microstate with all his knowledge) and in the paper "Mechanical models of Maxwell’s demon with noninvariant phase volume" (it can be found on google, didn't know if I was allowed to link) they wanted to try and build such a demon by constructing a force field that would act on all the particles in such a way as to lower the entropy. Anyway, in part B they define $$\overline{F} = \overline{v} \times \left( \overline{x} \times \overline{v} \right)$$. They then notice the phase volume is not constant. They apparently do not find this odd, because as they say they don't work with the Hamiltonian Mechanics. I was under the impression the Hamiltonian Mechanics is (one equivalent formulation of) the whole of classical mechanics; does this imply that I'm wrong and that forces have to fulfill a certain requirement before you can work with them in Hamiltonian Mechanics? What else is "out there"?

Thank you.


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Q

# Stuck here, help me understand: If set A has % elements and set B has 2 elements. How many relations can be difined from A to B ?

If set A has % elements and set B has 2 elements. How many relations can be difined from A to B ?

• Option 1)

32

• Option 2)

25

• Option 3)

15

• Option 4)

1024

107 Views

As we have learnt,

Number of Relations -

If A having m elements and B having n elements, then $2^{mn}$=No. of relations

-

No relations = 2(5 x 2) = 210 = 1024

Option 1)

32

Option 2)

25

Option 3)

15

Option 4)

1024

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Customized Windows command prompt

I personally use the command prompt on Windows a lot, but it’s always been very boring to look at. Now I know there are command prompt replacer apps out there which make it look much better (like Cmder), but I wanted to see how far we can customize it without installing any extra software. So let’s see how far we can go.

Startup script

The first step is to create a batch script which will be run when we start the console, and a shortcut in the start menu or taskbar to launch it. Creating a batch script is easy, just create a file called _startup.bat and put it in your user folder. You can add a welcome message to it if you like:

Shortcut

Next comes creating the shortcut. To create a shortcut, we can right-click a blank spot in our user folder, and select New > Shortcut. In the location field we can enter this:

The /K flag will run our script and return us to the command prompt. Now when we start the terminal, we should see our welcome message at the top.

our custom terminal, still looking pretty ugly

We can also customize the icon of the shortcut, by right-clicking it and going to Properties > Change Icon. In the icon select dialog we only have the icon exported by cmd.exe, but we can choose from a list of icons in shell32.dll by putting some randon text into the file select field and pressing Enter. This will throw an error, but will then default back to shell32.dll.

shortcut icon selection

Next we can add some colors to the terminal. Right-click the shortcut and select Properties > Colors tab. You can change any options on these tabs, but I’ve just changed opacity to 95%, and Screen Text to (red = 12, green = 180, blue = 12).

starting to look better

Another recent option on Windows 10 is under the Terminal tab, to disable scroll-forward. This removes all the blank space and the scrollbar on the right, which is quite cool.

Now we can drag this shortcut wherever we want, we can pin it to the start menu, or the taskbar, etc. Nice!

Better startup script

We now have a custom icon, custom color and a custom start script. We can enter any combination of commands into this startup script to customize it the way we want. Here’s what I’ve got in mine, if you want to use it, you can copy this script into your _startup.bat file.

Wow, what a mess. Windows batch scripts really are pretty terrible. Let’s analyze a few lines here though…

1-3: Sets the current working directory to your desktop.
5-10: Sets the window title, prevents command params being echoed out, and allows us to use delayed expansion, which allows us to overcome the way batch scripts handle variables inside of blocks. It allows us to use the !VarName! style instead of %VarName%, which is expanded during the line execution instead of just at the start of the block.
12-14: Gets the user’s display name into the UserDisplayName var.
16-26: Gets amount of installed RAM and puts it in the TotalMemory var.
28-34: Puts the system name into the ComputerName var.
36-44: Clears the screen and starts displaying the welcome message.
46-63: Displays free space for each drive.

done! and looking pretty good.

And that’s it! Since it’s running a batch script, you can also execute any command line application and use the output in your welcome message.


text:
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 Sciencemadness Discussion Board » Fundamentals » Miscellaneous » Recycling metals, plastics, rubber/foams, glass, circuit boards - value adding processes? Select A Forum Fundamentals   » Chemistry in General   » Organic Chemistry   » Reagents and Apparatus Acquisition   » Beginnings   » Miscellaneous   » The Wiki Special topics   » Technochemistry   » Energetic Materials   » Biochemistry   » Radiochemistry   » Computational Models and Techniques   » Prepublication   » References Non-chemistry   » Forum Matters   » Legal and Societal Issues   » Whimsy   » Detritus   » The Moderators' Lounge

Author: Subject: Recycling metals, plastics, rubber/foams, glass, circuit boards - value adding processes?
RogueRose
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Posts: 676
Registered: 16-6-2014
Member Is Offline

Recycling metals, plastics, rubber/foams, glass, circuit boards - value adding processes?

I was a little upset when I found that a 15lb radiator that was ~70% copper and 30% Al by weight would only fetch $5.25 ($.35 per lb) for 10.5lbs copper and 4.5lbs Al. both of these were clean from dirt and oil but the copper had oxidized to a semi-dark brown but was still smooth. The Al had minimal oxidation on the surface and was in surprising condition for being 30+ years old going from hot to cold.

There are MANY other situations such as this that make scrapping a process where the person selling to the yard looses out.

I'm trying to figure out what compounds could be made from the recycled metals to give a "value added" result such as taking scrap cast iron (sometimes < $.02/lb) and making FeSO4 or even Fe2O3/Fe3O4 and selling that to businesses that use it. I'm trying to make a list of what are some possible compounds which would be desirable for re-sale as well as what products are often easy to find for recycling. One of the main items of interest is -tire rubber, -Styrofoam (from coolers and peanuts), -packing peanuts, -scrap insulation (stuff currently produced) -Plastic soda bottles -ABS plastic -PVC -Copper -Aluminum -Steel (all grades and carbon content) -Circuit boards -Glass - especially bottle but also CRT leaded -Lead - from batteries so Lead oxide and Lead sulphate If anyone knows of something these can be converted to on a larger scale, I'm very interested. aga Forum Drunkard Posts: 6370 Registered: 25-3-2014 Member Is Offline Separate the materials. Do the Science. Hopefully, Do Something instead of endless pointless questions. Maybe do the Maths - if you want$ out of it.

Edit:

Definitely Do the Math if you want some $out of it. Madness is thinking i'm not drunk. j_sum1 International Hazard Posts: 3390 Registered: 4-10-2014 Location: Oz Member Is Offline Mood: Undergoing decantation and leaving all the crap behind. There are two ways this could go. Either you use recycled materials as a resource and produce them at a small scale because it is convenient. And you may have excess of some things to distribute to others. Alternatively you exploit economies of scale and invest some money for some equipment and actually make a profit. Even though it makes good environmental sense and is ethically admirable, recycling is notorious for low profit margins and you need to go large for it to be economical. Whichever of these two options you are interested in, you need to pick one product to recycle. Do a lot of research and crunch your numbers to find out how much it will cost. Work out the most viable process and optimise it for your own situation. Once you are established in one commodity you can expand to others. A little shameless self-promotion: You are welcome to tour my newly-completed lab. Texium (zts16) Super Moderator Thread Moved 28-10-2016 at 20:17 RogueRose International Hazard Posts: 676 Registered: 16-6-2014 Member Is Offline  Quote: Originally posted by aga Separate the materials. Do the Science. Hopefully, Do Something instead of endless pointless questions. Maybe do the Maths - if you want$ out of it. Edit: Definitely Do the Math if you want some $out of it. Well my questions may be pointless to in your mind (and we all know how permeated with EtOH vapors it is, but they are asked because they are relavant to whatever I am doing at the moment or things "in the works". I have plenty of posts where I have pics of what I've done and many more I haven't published/posted. Some IDK if it is worth posting as there are already threads containing some of the stuff. how many threads of KNO3 crystalization from NaNO3 conversion are needed? pneumatician Hazard to Others Posts: 135 Registered: 27-5-2013 Location: Duat Member Is Offline Mood: On Fire!  Quote: Originally posted by RogueRose I'm trying to figure out what compounds could be made from the recycled metals to give a "value added" result such as taking scrap cast iron (sometimes <$.02/lb) and making FeSO4 or even Fe2O3/Fe3O4 and selling that to businesses that use it. I'm trying to make a list of what are some possible compounds which would be desirable for re-sale as well as what products are often easy to find for recycling. One of the main items of interest is -tire rubber, -Styrofoam (from coolers and peanuts), -packing peanuts, -scrap insulation (stuff currently produced) -Plastic soda bottles -ABS plastic -PVC -Copper -Aluminum -Steel (all grades and carbon content) -Circuit boards -Glass - especially bottle but also CRT leaded -Lead - from batteries so Lead oxide and Lead sulphate If anyone knows of something these can be converted to on a larger scale, I'm very interested.

I read some years ago in usenet a guy saying: my uncle invented a machine self-sufficient producing excess electricity with tires, nobody want the machine.

the other day in keiser report in RT a guy produce biodiesel in "low scale" with anything like used oil, animal fats...

the machine for "tramute" plastic to petrol again is allready working in low scale??

http://bigthink.com/design-for-good/japanese-machine-convert...

http://www.bbc.com/future/story/20161117-the-rise-of-miniatu...

I used glass bottles in pieces and metal cans with stones... to fill up empty spaces in walls, some people make entire wall houses of glass bottles, others make art with anything... the possibilities are endless. but many recicling need space, time and money. the cheepest? if you have a big "backyard" separete all your residues and sell it when you have a good quantity. if you have a lot of money to invest a lot of people have a lot of ideas, myself, without going any further.
Dr.Bob
International Hazard

Posts: 1731
Registered: 26-1-2011
Location: USA - NC
Member Is Offline

Having been trying to recycle many things for years, the real problem is that recycling everything in the best way possible takes a lot of space and effort and often makes very little money. The scrap yard must collect Al, Copper, etc until they enough to fill an entire truck or railcar to make it cost effective, so they can only pay a portion of the value, as they have to store it and pay for it all until they get enough to sell a truckload.

I have adopted glassware, books, and other items that would have otherwise ended up in the trash, and in some cases I have made some money, but in many cases I have ended up with a basement full of junk that I have to sort through. I have 1000 science books, for example, which I can barely give away, but hate to just throw out. The trick is connecting surplus stuff to people or businesses that want the stuff you have, and the closer the better, as shipping costs can often be more than the item is worth. Sometimes with cleverness, you can win, but not always.

One example was a local pickle company that got some imported pickles in plastic barrels than can only be used a limited number of times. They tried to recycle the plastic, but the cost of shipping the barrels to a processing plant was more than the value of the plastic. If someone wanted to buy a fancy plastic shredder or such, they might solve some of that, but instead they started selling the barrels to people to make rain barrels, which are worth enough to be a practical way to reuse them profitably.

The challenge is that if you try to recycle the plastic as a polymer, you are now adding a lot of work, as you have to shred the plastic, ship it somewhere that can use it, and there is a risk that you can contaminate a whole batch of plastic with any dirt in the barrel. Since most plastic is made from oil or gas, and they are cheap right now, it is hard to compete with new plastic. For many metals, they cost more to refine and smelt, plus are easier to clean or purify, so recycling is easier. I much prefer to reduce the amount of materials I use than to try to recycle the materials once they are used. ie, don't buy lots of water bottles and plastic cups, just use a glass instead. But there are some cases where that does not work.

Similarly, making biodiesel is fine, but much more practical to do on large scale than small scale, due to the energy intensiveness of it, the health and fire hazards of using methanol in large amounts, and the variability of the quality of the fuel if the starting oil/grease is poor. That is why people don't build their own refinery to make gasoline at home, build their own cars from parts, or forge their own nails. There are some things that are more practical to do in centralized facilities. Not that you can't do them at home, it just won't often be financially prudent. That does not mean that it can't be done, or even shouldn't, but just that is why trying to recycle can be tough.

I did recently find uses for many items I have had for a while, while cleaning up some storage space, found many things I had forgotten, and was able to find uses for many, but it shows how you have to be able to sort and store the items in a way that you can know what you have and find it, which is much harder than I would have thought. Good luck.
violet sin
International Hazard

Posts: 1157
Registered: 2-9-2012
Location: , Location, Location
Member Is Offline

Dr.Bob: recycling everything in the best way possible takes a lot of space and effort and often makes very little money.

I agree with that statement 1000%. Soooo many times I have taken in e-waste b/c individuals were going to be stupid about it. (Or it was abandoned in the woods) regardless, I would take them to the transfer station, where they take it for free (after I picked a few choice parts). But up untill then the stuff sits about, pissing off the miss's. Sooo much space, time and sanity burned up in processing the mess. Always end up with ragged bleading hands to boot.

I still take stuff in, pick it over and do the whole dance, for now... But family is graciously swallowing my spare time at an increasing rate. So that ship is about to sail for good. Factor in how many countless hours of sorting, stacking, storing, shredding, transporting and eventually getting paid or dropping for free. Makes me wonder why Iv'e done it so long, other than boerdom on a low budget

Better to come up with a process to more effectively recycle, than be the guy recycling. Like for instance, cheaper reagents, less moving parts, a newer waste stream or something similar. Untill then its just a hobby unless you are doing production scale

Sauce
PHILOU Zrealone
International Hazard

Posts: 2879
Registered: 20-5-2002
Location: Brussel
Member Is Offline

Mood: Bis-diazo-dinitro-hydroquinonic

Best recyclages to my point of view:
-Styrofoam for styren monomer giving acces to the wide benzen derivatives chemistry
-PET soda bottles for ethylene glycol and terephtalic acid (para-benzen-dioic) (also a good source of benzen)
-Nylon for 1,6-diaminohexane, hexan-dioic acid or gamma-amino-hexanoic acid
-Copper pipes

Just take a look at the price of terephtalic acid (per kilo)...you won't see your soda bottle the same way.

PH Z (PHILOU Zrealone)

"Physic is all what never works; Chemistry is all what stinks and explodes!"-"Life that deadly disease, sexually transmitted."(W.Allen)

 Sciencemadness Discussion Board » Fundamentals » Miscellaneous » Recycling metals, plastics, rubber/foams, glass, circuit boards - value adding processes? Select A Forum Fundamentals   » Chemistry in General   » Organic Chemistry   » Reagents and Apparatus Acquisition   » Beginnings   » Miscellaneous   » The Wiki Special topics   » Technochemistry   » Energetic Materials   » Biochemistry   » Radiochemistry   » Computational Models and Techniques   » Prepublication   » References Non-chemistry   » Forum Matters   » Legal and Societal Issues   » Whimsy   » Detritus   » The Moderators' Lounge


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# Introduction

I happen to live in Montreal, in my condo on the edge of McGill Ghetto. Close to Saint Laurent Boulevard or the Maine as locals call it, with all it's attractions — bars, restaurants, night clubs, drunken students. And once upon a time, on a particular lively night, listening to the sounds of McGill frosh students drunkenly heading home after hard night of studying. I thought, that it might be a good idea to move into my own house, a little bit further away from the action.

It was not my first rodeo, buying a real estate in Montreal, but first time buying a house. So, I decided to do a little bit of research, before trusting my money to a real estate agent. I quickly realized that I can't afford a house anywhere close to the subway station on the Island, but I could possible afford a duplex or a triplex, where tenants would be covering part of my mortgage.
The solution to this problem depends not only on the price of the house, but also on the rent or potential rent that the tenants could be paying.

So, being a visual person with background in research, I wanted to see a visual map of how much things cost around the island, and how much revenue I could get. In the States, and even in Ontario there are services like Zillow that can show some of the information, but for Montreal I couldn't find anything, apart from the realtor association APCIQ. Maybe my preference of using English language is to blame.

So, after a few weeks of studying realtor.ca and kijiji, I wrote a python script to scrape information from them, using some resources I found on github: https://github.com/Froren/realtorca. Also, city of Montreal have an open data web site, that helps to fill-out some blanks.

After the data is collected by webscrappers it is processed in R, using tidy-verse, Simple Features for R. I found excellent resources on how to process geospatial information in R: Geocomputation with R, I used ggplot2 to make graphs and thematic maps for map making.

Now I have more then a year worth of data to study.

# Data pre-processing

I preprocess the data by converting it into simple-features format first, and then changing the geographic coordinate reference system (longitude and latitude) to North American projection for Quebec and Ontario

library(tidyverse)
library(sf)

st_as_sf(coords=c("lng","lat"), crs=4326) %>%
st_transform(crs=32188)

# Condo price

First I wanted to evaluate how much I could get for my condo. I need to define my neighborhood and find all the condos for sale around me.

## Neighborhood map

neighbourhood<-geojson_sf("quartierreferencehabitation.geojson") %>%
st_transform(32188) %>%
filter(nom_qr %in% c("Saint-Louis", "Milton-Parc")) %>%
summarize() %>%
st_buffer(dist=0)

Selecting condos for sale.

neighbors <- st_join(property, neighbourhood, left=F)

Using a basemap from openstreetmap.

osm_neighbourhood<-read_osm(st_bbox(neighbourhood%>%st_transform(4326)), ext=1.5, type="esri")

Drawing results using tmap package.

library(tmap)
library(tmaptools)

tm_shape(osm_neighbourhood) + tm_rgb(alpha=0.7)+
tm_shape(neighbourhood) + tm_borders(col='red',alpha=0.8)  +
tm_shape(neighbors) + tm_symbols(shape=3,size=0.2,alpha=0.8) +
tm_shape(ref_home) + tm_symbols(col='red',shape=4,size=0.5,alpha=0.8)+
tm_compass(position=c("right", "bottom"))+
tm_scale_bar(position=c("right", "bottom"))

## Neighbourhood condo prices

Now I can show the prices, and see how the depend on condo surface area and if there is a parking lot. And If i use a simple linear regression I can get the first approximation of what my condo might be worth.

### Linear model

More formally I can use linear model to predict price and confidence intervals

model_price_lm <- lm(mprice ~ parking:area_interior , data=neighbors_)

##
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)
## (Intercept)                41861.30   22421.28   1.867   0.0628 .
## parkingFALSE:area_interior   436.65      23.56  18.530   <2e-16 ***
## parkingTRUE:area_interior    511.95      19.40  26.393   <2e-16 ***

So, in my neighborhood every square foot in a condo without parking adds 437$to the base price of 42k$, and with parking it is 512$per square foot. And now I can make a prediction of the price: 443k$ with confidence interval [422k$, 465k$]

However, if I look at the difference between what my model predicts for all the condos in the neighborhood and the prices, I can see that error depends on the predicted value:

Therefore violating one of the conditions where simple linear regression can be used. This kind of behaviour is called overdispersion, and there are several ways of dealing with it. In particular, I found in the literature that I should be using a generalized linear model with inverse Gaussian distribution for errors and logarithmic link function.

### Generalized linear model

The estimate using generalized linear model is following:

model_price_glm <- glm(mprice ~ parking:area_interior , data=neighbors_,

Which gives prediction 436k$[422k$, 452k$] Note that I am ignoring number of rooms, floor of the building and the location of the condo for simplicity. It is possible to plug them all in into the regression, but it will increase number of parameters and make modelling results more difficult to interpret. Also, many parameters are correlated, for example bigger apartments tend to have more rooms and there a more of them with parking. Now, for the sake of simplicity of comparing different properties, I could estimate price per square foot, and how it is affected by different factors. Again, using generalized linear model with inverse Gaussian distribution and log link: ### price per square foot It's easy to make sense of the regression results: print(exp(model_psqft$coeff))

## (Intercept) parkingTRUE   bedrooms2   bedrooms3   bedrooms4
## 501.7826165   1.1215192   0.9769839   0.9818974   0.8349424

So, the square foot is worth 501$, parking adds 12%, two bedrooms reduce price by 2.4%, three bedrooms by 1.2%, four bedrooms 17% (given the same total price). The predicted price of my condo is: 431k$ [414k$, 449k$]

### Longitudinal condo price model

All my previous models are showing results based on the condos on the market during the last year, without trying to account for the price change. It would have been interesting, how the price change with time. I have no idea how prices should behave, there is no reason to think that there is a steady linear trend, considering seasonal rise and fall in prices, so first, I could just smooth the data using loess function.

#### Loess smoothing

If I pile all the data together:

But if I try to separate by number of bedrooms, the results are kind of random, since the data
might be too sparse.

So, it seems that I would rather want to have an overall smooth variation in price, while taking into account some features of the condos: i.e there is actually no reason to think that two bedroom condos are gaining in value slower then three bedroom ones. But there is variation of the proportion of different appartments with time, which would bias the results.

So, I am going to use generalized additive models where I can model overall change of price using a smooth function, while taking into account difference between different kinds of condos.

### Longitudinal condo price model:GAM model

# price model with time
model_psqft_t <- gam(price_sqft ~ bedrooms + parking + s(start_date, k=24) ,
data=neighbors_, bs="cr",method='REML',
family=inverse.gaussian(link="log"))

It still looks like the prices are going up.

Using this model, the prediction of the price is 468k$[435k$, 503k$] ### How long would it take to sell Another important question — how long would it take to sell? For this one can use survival analysis Technically, it looks like some types of condos sell faster then others, but the difference is not big. It looks like half of the condos disappear from the market within 60 days : # Plex price estimate Similarly, when I am looking at the potential plex I would like to know how much houses cost in the neighborhood. Let's say within 2km radius of the plex I was interested at some point: The price distribution is Here i can see that the seller is asking slightly more then what is the average for neighborhood, but at the same time the variability is quite high. For plexes many more parameters are important then for condos, like the size of the backyard, which year the building was built and how much existing tennants are paying. Using similar GLM model as for condos, the estimate for the price is the following: 567к$ [522k$, 616k$]

To estimate the rentals prices in the neighborhood I can find all the appartments listed on Kijiji during last year close by.

The price distribution gives me idea how much I could be potentially getting from the tenants. Of course there might be existing tenants already, so it would show me if what they are paying is close to what's currently on the market.

# Spatial prices

### Average over neighborhood

Remember, my original question was to see the map of the prices in Montreal. The simplest would be
to calculate median rental prices per neighborhood and show it on the map, like following:

rent_by_quartier<-aggregate( kijiji_geo_p%>%filter(bedrooms==2) %>%
dplyr::select(price), mtl_p,median, join = st_contains)

Since I am not actually looking everywhere on the island, here is the central part. Blue cross is where I go for work.

This map looks interesting, but it seem unrealistic to ussume that there are going to be sharp borders on the edges of neighborhoods. So, I would prefer to use a method that allows for smooth spatial change in prices. I can actually again use generalized additive models, as for the time course estimate, but with spatial coordinates.

### Rental prices spatial gam model

model_rent_geo_whole<-gam(price~bedrooms+s(x,y,k=100),
data=rent,bs="cr",method='REML',
family=inverse.gaussian(link="log"))

Rental prices in the central area, which is more interesting for me.

### Plexes price spatial model

In a same fashion, I can model distribution of the prices per square foot for triplexes with 3br main apartment and parking.

### Surface area for a triplex with 3br and parking

Now that I have spatial price distribution, I can also model surface area distribution. This,
technically can be done using data from the city website. But for this example I am using only property that was on the market

### Triplex Profitability (rent per year/triplex total price)

This way I can roughly estimate profitability of triplexes in different parts of town. By calculating a total price and dividing by the potential income of two two-bedroom apartments rented for the year. Of course this is very rough estimate, since I am assuming that all triplexes will have two 4 1/2 apartments for rent.

# Plex Longitudinal price model: Plateau, Ahuntsic, Rosemont, Villeray

Finally, using the same idea that was used for tracking condo price during the year, I can track plexes prices in the boroughs that were interesting for me.

# Conclusions

I did this research to study the distribution of prices in Montreal and to familiarize myself with geospatial modelling in R. I didn't have access to the actual sale prices, so the results should be taken with a grain of salt.

# Source code and data

The complete source of scripts used for this publication is publicly available on github: (https://github.com/vfonov/re_mtl), version of this article rendered using rmarkdown is available at http://www.ilmarin.info/re_mtl/stats_eng.html

# Interactive map of prices distribution

Results are also shown in an interactive dashboard on (http://www.ilmarin.info/re_mtl/)

## Similar posts

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# Relation between Temperature and viscosity of Linseed Oil?

I have been trying to get a relationship formula to determine the viscosity of Linseed oil. I have Absolute viscosity of the oil at 33.1 Cp (Source: http://www.engineeringtoolbox.com/absolute-viscosity-liquids-d_1259.html).

The problem is the system where I am using the fluid has a varying temperature, and I want to be able to know what the varying viscosity is. I am aware that the viscosity reduces with increase in temperature, but wasn't able to find a specific formula to relate the two.

Is there a formula to get the relationship between temperature and viscosity?

Thank you

## 1 Answer

There are many formulas! This usually means that some of them are OK in general for estimation purposes, but none of them will be especially accurate. Not easy to choose from the many formulas.

One of the most simple and popular seems to be the Wright equation, $$\log_{10}\left(\log_{10}\left(\nu + \lambda \right)\right)=A-B\log_{10}(T),$$ where $\nu$ is the kinematic viscosity, $\lambda$ is a parameter, usually taken to be $0.7$, and $A$ and $B$ are compound-specific parameters. With knowledge of linseed oil viscosity at least one other temperature than the one you provided in your question, you could fit $A$ and $B$ parameters and apply the equation.

However, the best answer to your question is to obtain some empirical data. A 1977 paper[1] reports on linseed oil viscosity as a function of temperature, for example. They found that a different equation (not the Wright) gave a reasonable fit to the data. Specifically, they found $$\ln(\eta) = -5.73 + \frac{2820}{T}$$ for viscosity $\eta$ in centipoises and temperature $T$ in K.

Another thing to keep in mind is that linseed oil is prone to oxidation. Oxidized linseed oil may have different properties than undergraded, "pure" linseed oil.

[1]: T. Gallagher; D. E. Kline; J. Am. Oil Chem. Soc. 1977, 54 (2), 68-70. DOI: 10.1007/BF02912392

• Thank you very much. "There are many formulas!" was the reason I had to post the question. I think I am okay, for now by ignoring the effect of oxidization of the oil. – Vinny May 7 '15 at 16:17


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### Theory:

In the previous topics, we have learnt how to add, subtract, multiply and divide to combine variables and constants to frame the algebraic expressions.

Let us recall a few basic concepts about expressions.

1. What is a binomial expression?

An expression which contains only $$2$$ terms separated by operation addition or subtraction are called as binomial expression.

Consider the expression $$6y + 2$$. In this, the expression is obtained by multiplying the variable $$y$$ with the constant $$6$$ and then adding the number $$2$$ to the product.

Here, $$6y$$ is the variable term, $$y$$ is the variable, $$6$$ is the coefficient of $$y$$ and $$2$$ is the constant term.

2. What are like terms?

Terms which have the same variables are called as like terms.

The terms $$6y$$, $$3y$$, $$10y$$ are examples of like terms.

3. What are unlike terms?

Terms having different variables are called as unlike terms.

The terms $$-5x$$, $$-3y$$ are examples of unlike terms.
When we add or subtract like terms, we get a new term. But, when we add or subtract unlike terms, we get a new expression.

Consider adding the like terms $$3x$$ and $$4x$$, we get, $$3x + 4x = 7x$$.

Now, consider adding an unlike term $$6x$$ and $$2y$$, we get, $$6x + 2y$$.


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# Drawing Stars

So right now what we have a spaceship which can flies around the screen, but, to be honest it looks very empty with the black background, the spaceship and the bare planet. It looks like something out of a budget version of Doctor Who.

We are going to rectify it by adding stars to the background to make it look more interesting to look at.

## Calcuating the positions for the stars

What we are going to start with is our method for calculating where the stars are, and what size they are going to be.

To start, we have to declare on an array to hold our stars in:

var stars = [];

Afterwards, we have to populate the array with the stars, and the way we will store the information about each star is by storing a dictionary with the information about each star. The following code will do that:

for (var i = 0; i < 500; i++) {
stars[i] = {
x: Math.random() * canvas.width,
y: Math.random() * canvas.height,
alpha: 1.0,
decreasing: true,
dRatio: Math.random()*0.05;
};
}

We will now break the code above into pieces to help you understand what it does, what we want is to produce information about 500 stars and the way we do it is a loop that get iterated through 500 times as you can see. Each pass of the loop adds a dictionary to the array with values for the x position (x), y position (y) size of the star (radius) how visible the star is (alpha) and whether the stars visibility is currently decreasing (decreasing). The final variable dRatio is how fast the star should twinkle, which as it is randomised make the scene seem more alive.

In order to get 500 stars in different places, we are using the random() function in the Math library and multiply it by the width and height to get an X position and Y position respectively.

Then we use a similar technique for the size of the stars as we take a random value between 0 and 1 and multiply it by 2 to get different sized stars.

We then just declare on two other variables to be used later.

## Drawing the stars to the screen

Now that we have the information about our stars we need to use that information to draw them to the screen, and in order to draw them to the screen we will need to iterate through the array of stars and use the information they store to draw the different stars. A simple version of the new function drawStars() is shown below:

function drawStars() {
context.save();
context.fillStyle = "#111"
context.fillRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < stars.length; i++) {
var star = stars[i];
context.beginPath();
context.closePath();
context.fillStyle = "#bbb";
context.fill();
}
context.restore();
}

As you van see this uses the information from each star to draw it on the screen, however, if you use that code and run it, the stars will look very static and not very interesting, which is why we are going to animate them with each frame, we will make them twinkle.

How do we do that? We use the alpha that we defined earlier and change the values between 0.1 and 0.95 to get the effect that we want, and the code for that will look like so:

function drawStars()
{
context.save();
context.fillStyle = "#111"
context.fillRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < stars.length; i++) {
var star = stars[i];
context.beginPath();
context.closePath();
context.fillStyle = "rgba(255, 255, 255, " + star.alpha + ")";
if (star.decreasing == true)
{
star.alpha -=dRatio;
if (star.alpha < 0.1)
{ star.decreasing = false; }
}
else
{
star.alpha += dRatio;
if (star.alpha > 0.95)
{ star.decreasing = true; }
}
context.fill();
}
context.restore();
}

This function will now use star.alpha to determine how bright the star should be as shown by the following line:

context.fillStyle = "rgba(255, 255, 255, " + star.alpha + ")";

Then we have to check which way the star needs to change its alpha value, if it should be decreasing we will reduce it by dRatio, otherwise, we will increase it by the same value. We also have to check for the edge cases so that we can flip that way the value is being changes, that is being done by the following bit of code:

if (star.decreasing == true)
{
star.alpha -=dRatio;
if (star.alpha < 0.1)
{ star.decreasing = false; }
}
else
{
star.alpha += dRatio;
if (star.alpha > 0.95)
{ star.decreasing = true; }
}