How can I search for currently trending, new scientific articles?
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.