The phrase "a difference arises" is correct and usable in written English.
It can be used to indicate that a distinction or variation comes into existence in a particular context or situation.
Example: "When comparing the two methods, a difference arises in their efficiency and effectiveness."
Alternatives: "a distinction occurs" or "a variation emerges."
In 1894 a difference arose between Eulenburg and Caprivi concerning the bill for an amendment of the criminal code (the Umsturz Vorlage), and in October the emperor dismissed both.
The point decided there was, that, though an agreement to submit a difference arising on a contract to arbitration is not a good plea in bar to an action on such contract, the breach of it may be a good ground of action.
Numerical results of both software systems resulted to be comparable in terms of noise analysis, whereas a difference arose for uniformity.
We therefore suggest that the sex difference in breeding adult birds may be explained by a difference arising during reproductive maturation.
It is also possible that a difference arose from ascertainment of highly polymorphic loci in the genotyping panels used in our study compared to the relatively bias-free approach offered by comparative genomics.
Experimentally, a further difference arises from the fact that electrons can lose varying amounts of energy in the specimen and continue to the detector, whereas x-rays are annihilated when they create a photoelectron (which does not reach the detector).
A larger difference arises when we consider the probability of progressing from latency to active disease in each of the models.
In fact, this difference arises from a mistake made for the computations of the regional model, previously highlighted by D'Ajello Caracciolo et al. (2011).
We observe that similar grain size distributions are indeed obtained within a factor of 3. The difference arises because the scaling of the cratering volume (or Mej) with is not perfect (Subsection 2.2).
