Mentioning isolated effect using alone/lone [closed]
You can't use "lone" in this fashion, anyway, the reason being essentially that this is an adjective you use before nouns only; as well, the fact that it is a rather literary term makes its use in a scientific text somewhat bizarre.
(OALD) lone[only before noun] without any other people or things
SYNONYM solitary
♦ a lone sailor crossing the Atlantic
♦ The attack was carried out by a lone gunman in a crowded shopping centre.
- the pressure induced by the sole element …
(OALD) sole [only before noun] only; single
♦ the sole surviving member of the family
♦ My sole reason for coming here was to see you.
I think that you may have misunderstood the gist of Swan's advice in Practical English Usage. Here is what he says about alone and lone in section 42 of the 1995 edition of his book:
42 alone, lonely, lonesome and lone
Alone suggests that a person or thing is separate – there are no others around. Lonely (and informal US lonesome) refers to unhappiness caused by being alone. [Examples omitted.] Alone is not used before a noun (see 15.3 [which says, "Some adjectives beginning with a-, and a few others, are used mainly in predicative position – after a verb. Common examples: afloat, afraid, alight, alike, alive, alone, asleep, awake."]) Lone and solitary can be used instead; lone is rather literary. [Example:] The only green thing was a lone/solitary pine tree.
Swan says flatly that you shouldn't use alone as a modifier in front of a noun or noun phrase such as pine tree. But in the phrase "The element alone induced pressure," alone doesn't appear before the noun (in this case, element); rather, it appears after the noun but before the verb—and in this position, alone has been standard in idiomatic English for several centuries at least. For example, an Ngram search for the phrase "I alone can" for the period 1650–2050 yields the following chart:
If you're interested in seeing specific Google Books examples of that phrase in real-world literary use, click the links beneath the graph version of the chart here.
It would be incorrect to say, "Alone is used only in predicative position"—but in fact what Swan says is that alone is "used mainly in predicative position – after a verb." Obviously mainly is not the same as only. Your wording "The element alone induced pressure" is perfectly good English.
Lone, on the other hand, sounds natural as a modifier preceding a noun or noun phrase (as in the "lone pine tree" example that Swan mentions)—but it doesn't do well as a modifier after a noun (as in your "The element lone induced pressure" example). No native English speaker would use that particular wording.