That's definitely possible. You'll just need to define a new server block in your Nginx configuration, pointing to the directory holding the static files. You also need to set server_name for each block so Nginx knows how to direct the requests.

Here's an example:

upstream app_server { server 127.0.0.1:8080 fail_timeout=0; }

server {
    listen   80;
    root /home/rails/public;
    server_name app.mydomain.com;
    index index.htm index.html;

    location / {
        try_files $uri/index.html $uri.html $uri @app;
    }

    location ~* ^.+\.(jpg|jpeg|gif|png|ico|zip|tgz|gz|rar|bz2|doc|xls|exe|pdf|ppt|txt|tar|mid|midi|wav|bmp|rtf|mp3|flv|mpeg|avi)$ {
                    try_files $uri @app;
    }

    location @app {
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header Host $http_host;
        proxy_redirect off;
        proxy_pass http://app_server;
    }
}

server {
    listen   80;
    root /var/www/html;
    server_name mydomain.com;
    index index.htm index.html;

    location / {
        try_files $uri $uri/ =404;
    }

    error_page 404 /404.html;
    error_page 500 502 503 504 /50x.html;
    location = /50x.html {
        root /usr/share/nginx/html;
    }
}

For more information, check out these tutorials:

• How To Set Up Nginx Server Blocks (Virtual Hosts) on Ubuntu 14.04 LTS
• Understanding Nginx Server and Location Block Selection Algorithms