at their boundary

USAGE SUMMARY

The phrase "at their boundary" is correct and usable in written English.
It can be used to describe a specific location or limit where two entities meet or interact, often in a physical or metaphorical sense. Example: "The two ecosystems thrive at their boundary, where diverse species coexist."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

7 human-written examples

We first extend existing results on asymptotic stability of linear infinite dimensional systems controlled at their boundary to the case of stable Port Hamiltonian controllers including some physical constraints as clamping.

IFAC Proceedings Volumes

Only valid objects have contours at their boundary.

EURASIP Journal on Advances in Signal Processing

In this scenario, the energy was released in the down-dip portion but not in the up-dip portion, resulting in a large energy accumulation at their boundary prior to the mainshock.

Earth, Planets and Space

If space is continuous such that an atom could straddle two atoms at their boundary and so form something like the aforementioned three-block pyramid, then imagine two such pyramids joined at their bases so that a gap is formed between the two top atoms.

SEP

The pressure difference between two grains at their boundary therefore causes atoms to preferentially migrate from smaller to larger grains.

Geochemistry, Geophysics, Geosystems

Due to the higher resolution of the comparative BAC-map, it is possible to pinpoint potential rearrangements by focussing on inconsistently mapped BACs that connect two BAC-contigs at their boundary regions.

BMC Genomics

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

Such supermassive black holes are so powerful that activity at their boundaries can ripple throughout their host galaxies.

Massachusetts Institute of Technology

I will discuss my research in these areas (and at their boundaries) that aims to resolve the above two questions.

Cornell University

As they grow on the surface of the water, ice floes will meet and raft up onto one another, creating miniature mountain ranges at their boundaries.

The Guardian

The retreat of ice sheets produced basins through mechanical action and through the damming effect of their ice masses at their boundaries.

Encyclopedia Britannica

Two processes are active during this period: a dimensional thinning and a deterioration of the ice crystal grains at their boundaries.

Encyclopedia Britannica

Expert writing Tips

Best practice

When describing spatial relationships or interactions between distinct areas, entities, or concepts, use "at their boundary" to denote the specific location where these elements meet or interact. For example, "Different ecosystems often exhibit unique biodiversity at their boundary".

Common error

Avoid using "at their boundary" when "within their boundaries" is more appropriate. "At their boundary" refers to the specific location where two entities meet, whereas "within their boundaries" refers to something contained or occurring inside the limits of a single entity. For example, instead of "The anomaly was observed at the city's boundary", consider "The anomaly was observed within the city's boundaries" if the anomaly is inside the city.

Linguistic Context

The phrase "at their boundary" primarily functions as a prepositional phrase, modifying a noun or clause to specify a location or point of interaction. As Ludwig AI confirms, this phrase correctly indicates where distinct entities meet. Examples show its use in scientific and general contexts.

Expression frequency: Uncommon

Frequent in

Science

50%

News & Media

25%

Academia

25%

Less common in

Encyclopedias

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "at their boundary" functions as a prepositional phrase used to denote a specific location where two or more entities meet or interact. As Ludwig AI confirms, the phrase is considered correct and is employed across a range of formal and scientific contexts, along with general and news media. While "at their boundary" is useful for describing spatial relationships, it's important not to confuse it with "within their boundaries", which implies something contained inside the limits of an entity. Related phrases, such as ""at their edge"" or ""on their border"", can provide alternative ways to express similar concepts depending on the specific context.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

at their limit

Replaces "boundary" with "limit", suggesting the furthest extent rather than a dividing line.

at their edge

Substitutes "boundary" with "edge", implying a less defined or sharp division.

at their perimeter

Uses "perimeter" to specify the outer boundary, often used in spatial contexts.

on their border

Replaces "boundary" with "border", focusing on a political or geographical division.

along their border

Adds "along" to emphasize the linear aspect of the boundary.

along their edge

Adds "along" to emphasize the linear aspect of the edge.

at their interface

Emphasizes the interaction and contact between two entities at their boundary.

where they meet

Simplifies the phrase to indicate the point of convergence.

where they connect

Focuses on the connection or junction point between entities.

adjoining them

Uses a verb form to describe the relationship, indicating direct adjacency.

FAQs

How can I use "at their boundary" in a sentence?

"At their boundary" indicates a location where two distinct areas or entities meet. For instance, "The species interact "at their boundary", creating a unique ecosystem".

What phrases are similar to "at their boundary"?

Alternatives include "at their edge", "at their limit", or "on their border", depending on the specific context.

Is it correct to say "at it's boundary" instead of "at their boundary"?

No, "at it's boundary" is incorrect. "It's" is a contraction of "it is" or "it has", while "its" is the possessive form. If you're referring to a singular entity's boundary, you should use "at its boundary". If you're referring to the boundary of multiple entities, "at their boundary" is correct.

What is the difference between "at their boundary" and "within their boundaries"?

"At their boundary" indicates the location where different entities meet or interact, while "within their boundaries" refers to something contained or happening inside the limits of a specific entity. For example, the interaction between two species happens "at their boundary", whereas regulations apply "within their boundaries".