arbitrary volume

USAGE SUMMARY

The phrase "arbitrary volume" is correct and usable in written English.
It can be used in contexts related to science, mathematics, or discussions about measurements where the volume is not fixed or predetermined. Example: "In our experiment, we can select an arbitrary volume of liquid to test the reaction rate."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

12 human-written examples

A general solution of the steady-state heat conduction problem has been suggested for an arbitrary volume power density.

Optics & Laser Technology

One model provides a method to construct candidate ARs using a fully connected network of continuously stirred tank reactors (CSTRs) of arbitrary volume.

Chemical Engineering Science

By using arbitrary volume forms, we establish Laplacian comparison theorems for Finsler manifolds under certain curvature conditions.

Journal of Inequalities and Applications

In the present paper, we will further claim that for an arbitrary volume form Calabi-Yau's result still holds.

Journal of Inequalities and Applications

In what follows, we shall generalize Calabi-Yau's linear volume growth theorem to Finsler manifolds with an arbitrary volume form.

Journal of Inequalities and Applications

The arbitrary volume that consists of ITO NWs and air can be regarded as an effective medium with an effective refractive index (n).

Nanoscale Research Letters

Human-verified similar examples from authoritative sources

Similar Expressions

48 human-written examples

Because fully automatic decomposition methods that can generate high-quality hexahedral meshes for arbitrary volumes have yet to be realized, manual decomposition is still required frequently.

Journal of Computational Design and Engineering

Integration of the equations of change over an arbitrary engineering volume exchanging mass and energy with the surroundings gives the basic concepts at the macroscopic level.

Modeling in Transport Phenomena A Conceptual Approach

The algorithm allows for the generation of arbitrary particle volume fractions and produces periodic geometries based on the erosion procedure suggested by Christoffersen (1983).

International Journal of Solids and Structures

Reversing the argument used to go from (10) to (14), we get (38) for an arbitrary source volume, analogous to (10); the extra factor of occurs because the and have different mean-square values.

Earth, Planets and Space

To calculate the flow field using the dynamic mesh, the integral form of the conservation equation for a general scalar φ on an arbitrary control volume V with moving boundary is employed: (8).

Nanoscale Research Letters

Expert writing Tips

Best practice

When using "arbitrary volume" in technical writing, clearly define the context in which the volume is considered arbitrary. Specify any constraints or limitations, even if they are minimal, to avoid ambiguity.

Common error

Avoid treating an "arbitrary volume" as irrelevant to the results. Even if the specific value is not predetermined, it can still influence outcomes, so ensure its potential effects are considered and, if necessary, controlled.

Linguistic Context

The phrase "arbitrary volume" typically functions as a noun phrase where "arbitrary" modifies the noun "volume". According to Ludwig AI, it is used to denote a volume that is not predetermined or fixed. Examples from Ludwig illustrate its use in scientific and technical contexts.

Expression frequency: Uncommon

Frequent in

Science

90%

Academia

5%

News & Media

3%

Less common in

Formal & Business

1%

Wiki

1%

Social Media

0%

Ludwig's WRAP-UP

In summary, "arbitrary volume" is a phrase used to describe a volume that is not fixed or predetermined, commonly found in scientific and technical contexts. Ludwig AI confirms its grammatical correctness and usability. While not extremely frequent, it serves a crucial function in scenarios where the precise volume is irrelevant, as demonstrated across numerous scientific publications. The phrase's formal register makes it suitable for academic and professional writing, emphasizing the importance of context and clarity when employing it.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

random volume

Emphasizes the lack of a specific pattern or intention in selecting the volume.

unspecified volume

Highlights that the volume hasn't been defined or detailed beforehand.

variable volume

Indicates the volume is subject to change or variation.

undefined volume

Suggests the volume is currently unknown or lacks precise determination.

discretionary volume

Highlights that the volume is determined by someone's choice or judgment.

unrestricted volume

Implies no limitations or constraints on the volume's size.

chosen volume

Emphasizes that a specific volume has been selected, but without inherent constraints.

any volume

Indicates that the volume can be any amount without preference.

flexible volume

Suggests the volume can easily adapt or change to meet different needs.

unfixed volume

Focuses on the fact that the volume is not static or predetermined.

FAQs

How can I use "arbitrary volume" in a sentence?

You can use "arbitrary volume" to describe a quantity that is not fixed or predetermined, for example: "We selected an arbitrary volume of the solution for testing."

What phrases are similar in meaning to "arbitrary volume"?

Alternatives include "random volume", "unspecified volume", or "variable volume", depending on the specific nuance you want to convey.

Is it appropriate to use "arbitrary volume" in formal writing?

Yes, "arbitrary volume" is appropriate for formal and technical writing, especially in scientific and engineering contexts where precise measurements are important but a specific volume is not required.

What is the difference between "arbitrary volume" and "fixed volume"?

"Arbitrary volume" indicates a volume that can be any value within certain constraints or no constraints at all, while "fixed volume" refers to a volume that is precisely defined and unchanging.