How can I search for currently trending, new scientific articles? I often find myself wanting to find brand-new scientific articles within certain search parameters (e.g., words in the title, journal, etc.) that are currently "trending" in scholarly or public attention. As far as I know, standard academic search engines that allow the use of such search parameters offer only metrics such as citation counts, whereas I am interested in something more immediate like Altmetrics. Searching sites like Twitter or Google News better captures instantaneous public attention, but allows only the most rudimentary of searches.

I found ScienceOpen, but it seems to have an extremely limited set of journal articles. 

What's the closest thing to a Google Scholar-Altmetrics lovechild?
You can see the arxiv repository site that is very interesting. This site Arxiv has an electronic archive and distribution server for research articles in Physics, mathematics, computer science, nonlinear sciences, quantitative biology and statistics. The interesting point is that you can access to the recent papers in these fields as soon as possible even before long story of publication process! 
Also, you can subscribe to automatic email alerts from the subjects you'd like to see recent submitted papers in them.