I have being studying Compressible Fluid Dynamics and 1D Euler equations. I learnt that information propagate in three waves speeds: u-c, u, u+c. So the domain of dependence and range of influence must be bounded by them. I did not understand this?

So we have a linear hyperbolic homogeneous PDE,

del U / del t + A * del U / del x = 0

Assuming A is a 3x3 matrix, we can diagonalise it as A = Q^-1 D Q and let dV = Q^-1 dU. Now, we get three ODE,

• dv_1 = 0 for dx/dt = lambda_1
• dv_2 = 0 for dx/dt = lambda_2
• dv_3 = 0 for dx/dt = lambda_3

Here, lambda_1, lambda_2, lambda_3 are eigenvalues of matrix A. So far so good.

Now, how did we come to the conclusion that the domain of dependence and range of influence must be bounded by the smallest and largest wave speed (eigenvalue)?

How will mesh metrics of FDM differ from FVM for a structured mesh?

For example, non orthogonality should no more be an issue given that in FDM, data is stored at vertices rather than in cell centers like in FVM. Aspect ratio and inflation rate effects will have almost similar effects in both cases. Not sure how skewness will affect a FDM solver.

The rate at which the grid transforms may be a metric? Are there any study done on what rate should grid transform?

Did I get anything wrong or are there other mesh metrics to be taken into account in a FDM mesh?

Say if I somehow figure out to create a cartesian structured mesh around the geometry. Would there be any benefits going with FDM over FVM? Is there any study on this?

Like in case of shockwaves or transonic buffet, which one of these would result a better result?

There are some words which are almost same in Tamil and Telugu so I wonder if the pronunciation of one may have affected the other.

For example, a lot of words in Tamil underwent c > s like cey becoming sey 'to do'. So, what about words starting with c- in your Telugu dialect?

Nasalisation of final -m in Tamil like say kālam 'time' is actually pronounced like kālau. So, how is it in like verbs or nouns in your Telugu dialect ending with -m say the hortative case pōddām 'lets go'?

Words ending with -ai (which is pronounced like 'a' in cat represented as æ) have the Telugu equivalents end with -a. Take Tamil bommæ and Telugu bomma for 'toy' or Tamil korikæ and Telugu korika for 'request, plead'. So, does your dialect use distinct pronunciations when speaking different languages or uses the Tamil one when speaking Telugu?

Sometimes the Tamil word has a geminated cluster while Telugu does not. For example, Tamil pōṭṭi and Telugu pōṭi for 'competition' or Tamil pāṭṭu and Telugu pạ̄ta for 'song'. So, did this affect your dialect?

Sometimes the equivalents have voiced variations. For example, Tamil kanji : Telugu ganji, Tamil palli : Telugu balli, etc. Or v-b variations like Tamil vayalu : Telugu bayalu, Tamil vaṇḍi : Telugu baṇḍi, Tamil vellam : Telugu bellam, etc. How are these handled in your dialects?

Border area Bilingualism

The border area bilingualism is different from bilingualism due to migration. The Tamil-Telugu border area bilinguals are in frequent contact with people of their home state as they are very nearer to the majority. They have marriage relations and other social relations with the majority unlike the bilinguals who migrated to interior part of a State. For example, the Telugus living in middle and southern part of Tamil Nadu do not have this kind of situations.

A bilingual speaker in this border area is to use the other’s language in order to meet the demands of his circumstances and cultural pressure. One of the verbal strategy, bilinguals adopt in their language use, is code-switching i.e., switching Tamil to Telugu or Telugu to Tamil.

As part of an UGC funded Major Research Project, the fieldwork was carried out in 2016-2017 in the following villages in both states near the border:

• Tamil Nadu: Thimmampet, Dhigguvapalayam, Varattanapalli, Megalachinna Palli
• Andhra Pradesh: Palaru, Nayanoor, Birudhaanur, Noormanapalli, Poojarappakotta

Sociology of Bilinguals

• Educated Tamil Speakers in the villages [Palaru, Nayanur, Poojarappakotta] claim that their mother tongue is Telugu, though it was observed that they maintain Tamil in many domains. Similarly, the Telugu speakers of Thimmampet claim that their mother tongue is Tamil though it was observed that they maintain Telugu in many domains. They generally prefer their local language as the medium of instruction.
• In most of the cases they identify with State where the live. It is observed that in villages where the so-called high caste groups live more in number, the mother tongue identity seems to be intact and the language mixing is also to the minimum. 
• There is a confusion regarding the concept of "Mother Tongue". The bilinguals consciously identify with the State linguistic group even though they originally belong to the other linguistic region. This may be interpreted as the people in the border area of TN and AP experience some kind of identity crisis for getting socio–politico–economic benefits.
• The Tamil speakers in the border area felt that their Tamil is "colloquial" and is not Standard Tamil which is contrary to the general attitude of other regional dialect speakers of Tamil. For example, a speaker of Madurai or Thanjavur regional dialect usually identify their dialect with Standard Tamil.
• It is observed that during a discourse, one speaker used to speak in Tamil and the other speaker would response in Telugu and the vice versa. This can be explained by the fact that a person has passive listening skill in second language and active speaking skill in mother tongue. This may be due to lake of confidence or exhibition of power with the use mother tongue in which the speaker is more confident. This is one of the peculiar types of language use in the border area of AP and TN.
• Presence of aged monolinguals indicates that the language policy of the States and the awareness of individuals about the requirement of knowledge in the local language increased the bilingualism in border area.
• The Telugu and Tamil linguistic minorities who are living in the border have marriage relations in their community across the border. However, due to language shift, the newly married women expressed that they have communication problems when they are married to their home State. This indicates that there is a language shift taking place among the younger generation due to increased bilingualism.

Linguistic Features of Telugu among Bilinguals

Some of the lexical borrowing terms from Tamil into Telugu spoken by the bilinguals:

Monolingual Telugu	Bilingual Telugu	Meaning
panasa paṇḍu	palā paṇḍu	jackfruit
ciluka	kiḷi	parrot
allam	inji	ginger
meṭlu	paṭikaṭlu	steps
praśnalu	kēlvilu	questions
mārpu	māṟṟamu	change
guḍla gūba	ānda	owl

It is to be observed that while borrowing the lexical items, the Telugu phonology is retained. For example, take the following sentence spoken by Telugus in the TN,

annā irupadu rūpāyaki rīcārju cēyannā
Please make a recharge of Rs.20

The phonology features as well as syntactic features are retained in Telugu like the dative suffix -ki with a lexical borrowing of irupadu 'twenty' from Tamil. By this statement, I believe the author is referring to the fact there is no c > s change like in Telugu. These dialects also preserve the old masculine suffix -ṇḍu.

One more thing to note that author did not mention is that there is no pluralisation in rūpāya-ki 'for rupee' in contrast to Standard Telugu rūpāya-la-ku where there is the oblique plural suffix -la which I believe is influence of Tamil where there is no pluralisation. Compare Tamil rūpāy-kku.

Note: Due to poor transliteration from the paper used as source, I am not sure if retroflex /ḷ/ is indeed pronounced in these dialects and how is /ṟṟ/ pronounced in the Bilingual Telugu dialect.

Linguistic Features of Tamils among Bilinguals

Some of the lexical borrowing terms from Telugu into Tamil spoken by the bilinguals:

Monolingual Tamil	Bilingual Tamil	Meaning
cemmari āḍu	gorre	sheep
paḍi	meṭṭu	step
paḍikala	cadavala	did not study
paḍikardukku	cadavadarkku	to read
ceppukkuḍam	biṇḍiga	pot

Some phonological features observed in Bilingual Tamil in the surveyed villages by the author of the paper which he suspects could be due to influence of Telugu:

• Voicing of initial consonants are observed which the author thinks is a result of hypercorrection. Eg: tāmara > dāmara 'lotus', koḍe > goḍe 'umbrella', pamparam > bambaram 'top'.
• Deletion of initial /v/. Eg: vengāyam > engāyam 'onion'
• Back vowel after an alveolar stop becomes front vowel. Eg: tamil > temil

The Bilingual Tamil also borrowed some lexical items with semantic shifts from Monolingual Telugu. Eg: Te. gammunu 'quickly' to Ta. gammunu 'silently'. Besides these, the author suggests the addition of interrogative suffix -ā to āmā 'yes' to form āmāvā 'is it?'. I am not very sure of the last two.

Similarities in Bilingual Tamil and Bilingual Telugu

Both Tamil and Telugu bilinguals in AP and TN respectively in the villages surveyed don't refer their languages as Tamil and Telugu. Instead, Tamils in AP refer to their language as enga bāśa 'our language' while Telugus in TN refer to their language as mana bāśa 'our language'. This is only the case with the regions around the surveyed villages.

It is observed that both the bilinguals prefer to borrow a single word expression instead of using a native descriptive expression. For example, Bilingual Tamils use the single word Telugu gorre instead of the long descriptive cemmari āḍu to refer 'sheep'. Similarly, Bilingual Telugus use the single word Tamil ānda instead of the descriptive guḍla gūba.

Source: Notes on Border Area Bilingualism of Tamil Nadu and Andhra Pradesh

For statements like "very happy", a lot of TN dialects and some south KA dialects use "niṇḍa santōsham" while mainstream Telugu uses "cāla" mostly.

Do your dialects still use cāla? If yes, are there any difference between cāla and niṇḍa?

What word is used to say 'enough'? In mainstream Telugu, it would be cālu.

In my dialect,

• White: tella / telupu
• Black: nalla / nalupu
• Red: erra / errupu
• Green: pacca
• Yellow: pasupu
• Blue: nīla

Most of us just say 'blū kalar' (blue colour) for blue. The word nīla is almost obsolete.

The word 'pasupu' for yellow is almost synonymous to turmeric powder that the turmeric powder is also called as 'pasupu' or sometimes being more specific 'pasup(u) poḍi'

There is no word for 'colour' itself to my knowledge. People just say 'pacca colour' (green colour).

What are the words used in your dialect?

I have noticed a good amount of dialects using purinjitandi 'understood' while the standard is arthamaindi so I wanted to know how widespread this is.

Much about it is known to me only by DEDR and Krishnamurti's book which is based on Thomasiah’s unpublished thesis. Are there any resources besides these two for Naikṛi?