In the spirit of Which journals publish expository work? please advise:
What consistently high quality journals (1) today publish results that would otherwise go to a pure mathematics journal were it not for (2) the included applied content, the motivation, and/or the examples?
PNAS (if the paper is not long), Lecture Notes in Mathematics (if it is long), Journal of Interdisciplinary Mathematics, SIAM subject journals, *Journal of Modern Dynamics, Journal of Mathematical Biology, Bulletin of Mathematical Biology, and International Journal of General Systems go without saying.
(But are the last three read by working mathematicians these days?)
What about others?
To make the question answerable:
Ideally suggest a journal per answer with comments. So that others can vote on it, and an answer can be accepted eventually.
1 - Many applied journals are neither read nor refereed by mathematicians, primarily working in mathematics.
That makes it difficult to get appropriate referees to give advise on submitted papers, either at all or else in a timely manner. If only because of, for example, notation or terminology lag (APS journals for example).
Please only suggest journals that are not too obscure or seem like they going to be obscure in the future. Journals that, due to the founders or team are likely "up and comers" are OK. (Nothing wrong with obscurity, but as you probably know . . . arXiv by itself is often more widely read in comparison . . . )
2 - Content that is inappropriate in a pure mathematics journal, for it contains sufficiently detailed applications. Yet the applications by themselves cannot be coherently published separately from the majority of the paper, which begins with and discusses a problem of primarily mathematical interest and with conventional mathematical rigour.
Updated. After a couple years maybe some new journals were founded that are not well known yet but may be good quality, especially with application to computer science. If so, those would be good answers.