independent of scale

USAGE SUMMARY

The phrase "independent of scale" is correct and usable in written English.
It can be used in contexts where you want to express that something remains constant or unaffected regardless of the size or magnitude involved. Example: "The results of the experiment were independent of scale, demonstrating that the same principles apply whether the sample size is large or small."

✓ Grammatically correct

Science

Industrial Engineering

Engineering

Human-verified examples from authoritative sources

Exact Expressions

18 human-written examples

The spatial distribution of turbulent kinetic energy within the vessels was determined to be independent of scale.

Chemical Engineering Science

The factory coordinate system merges the digital image of the factory (digital shadow) with the real production process practically in realtime and independent of scale.

Procedia Manufacturing

The paper closes with a discussion of leads in the Arctic sea ice cover and with evidence that failure mechanisms may be independent of scale.

Engineering Fracture Mechanics

To successfully describe product cooling, cooling rate should be quantified in a specific and relevant manner that is independent of scale and freezer model, and enables measurement of multiple unit containers across a freezer load of interest.

Cryobiology

Further comparisons with large-scale and small-scale foundation models available in the literature suggest that, similar to Meyerhod's equivalent width concept, the proposed formulation is relatively independent of scale effects.

Engineering Structures

This correlation criterion is independent of scale and offset in lighting (Sutton et al.

International Journal of Concrete Structures and Materials

Human-verified similar examples from authoritative sources

Similar Expressions

42 human-written examples

Compared with AIC, MSC includes normalization and is therefore independent of scaling of the data points.

EJNMMI Physics

Because individual colonies may be impacted by idiosyncratic factors operating on fine-scales, independent of large-scale climatic influences, patterns of occupancy and trend at regional and continental-scales are required to understand the role of changing climate on habitat suitability.

Nature

The constant returns to scale model assumes a production process in which the optimal mix of inputs and outputs is independent of the scale of operation.

BMC International Health and Human Rights

The amplitudes of these small (adiabatic) fluctuations remained independent of comoving scale during the period of inflation.

Encyclopedia Britannica

The method is efficient, robust to tracking errors and independent of the scale of the face being tracked.

Robotics and Autonomous Systems

Expert writing Tips

Best practice

When describing experimental results or models, use "independent of scale" to emphasize that the findings apply across different sizes or magnitudes, enhancing the generalizability of your work.

Common error

Avoid assuming that "independent of scale" means the same as being unaffected by the choice of measurement units. Scale independence refers to consistent behavior across different sizes, while unit independence means results don't change when using meters versus feet, for example.

Linguistic Context

The phrase "independent of scale" functions as an adjective phrase, modifying a noun to indicate that a particular property, result, or phenomenon is not affected by changes in size or magnitude. As Ludwig AI indicates, it signifies that something remains constant regardless of scale.

Expression frequency: Uncommon

Frequent in

Science

80%

Engineering

10%

Academia

5%

Less common in

News & Media

2%

Formal & Business

1%

Encyclopedias

2%

Ludwig's WRAP-UP

The phrase "independent of scale" is an adjective phrase used to describe something that remains consistent regardless of size or magnitude. Ludwig AI validates the phrase as grammatically correct. Its usage is classified as uncommon, predominantly appearing in formal and scientific contexts. The analysis reveals that it's used to emphasize the robustness and generalizability of findings across different dimensions. Alternatives include "scale-independent" and "invariant to scale". When employing the phrase, it's important to distinguish it from unit independence. Ultimately, understanding the nuances of "independent of scale" enhances clarity and precision in technical and scientific writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

scale-independent

Hyphenated form emphasizing the lack of dependence on scale.

invariant to scale

Focuses on the property of remaining unchanged despite scale variations.

not scale-dependent

Directly states the absence of dependence on scale.

scale-free

Implies that the phenomenon is not characterized by any specific scale.

unaffected by scale

Highlights that scale has no impact.

scale-insensitive

Suggests a reduced sensitivity to changes in scale.

size-independent

Similar to scale-independent but uses "size" instead of "scale".

constant across scales

Emphasizes the consistency of a property or relationship regardless of scale.

not influenced by scale

Highlights the lack of influence from scale variations.

dimensionless

More technical term meaning without physical dimensions and thus scale-free.

FAQs

How can I use "independent of scale" in a sentence?

You can use "independent of scale" to describe a phenomenon, result, or property that remains consistent regardless of the size or magnitude being considered. For example, "The spatial distribution of turbulent kinetic energy within the vessels was determined to be "independent of scale"."

What are some alternatives to "independent of scale"?

Alternatives include "scale-independent", "invariant to scale", or "not scale-dependent". The best choice depends on the specific nuance you wish to convey.

Is it correct to say "scale-independent" instead of "independent of scale"?

Yes, "scale-independent" is a valid and often more concise way to express the same concept as "independent of scale". Both terms indicate that something is not affected by changes in size or magnitude.

In what contexts is "independent of scale" commonly used?

"Independent of scale" is frequently used in scientific and engineering contexts, particularly when discussing models, experiments, or systems where the results or behavior are consistent across different sizes or magnitudes. Ludwig's examples include chemical engineering, manufacturing, and fracture mechanics.