code: public static function findPublishedByIdOrAlias($varId, array $arrOptions=array())
  	{
  		$t = static::$strTable;
  		$arrColumns = !preg_match('/^[1-9]\d*$/', $varId) ? array("$t.alias=?") : array("$t.id=?");
  
  		if (!static::isPreviewMode($arrOptions))
  		{
  			$time = Date::floorToMinute();
  			$arrColumns[] = "($t.start='' OR $t.start<='$time') AND ($t.stop='' OR $t.stop>'" . ($time + 60) . "') AND $t.published='1'";
  		}
  
  		return static::findBy($arrColumns, $varId, $arrOptions);
  	}
docs: Find published pages by their ID or aliases
  
  @param mixed $varId      The numeric ID or the alias name
  @param array $arrOptions An optional options array
  
  @return Collection|PageModel[]|PageModel|null A collection of models or null if there are no pages