Media playback is unsupported on your device Media caption China has launched its first domestically built aircraft carrier

US pre-eminence in the Pacific is no more.

For a long time experts have been speaking about China's rapid military modernisation referring to it as "a rising power".

But this analysis may be out of date. China is not so much a rising power; it has risen; and in many ways it now challenges the US across a number of military domains.

This is the conclusion of a new report from the US Studies Centre at the University of Sydney in Australia.

It warns that US defence strategy in the Indo-Pacific region "is in the throes of an unprecedented crisis" and that Washington might struggle to defend its allies against China.

"America no longer enjoys military primacy in the Indo-Pacific", it notes, "and its capacity to uphold a favourable balance of power is increasingly uncertain."

The report points to Beijing's extraordinary arsenal of missiles that threaten the key bases of the US and its allies. These installations, it asserts, "could be rendered useless by precision strikes in the opening hours of a conflict".

China is not a global superpower like the United States. Indeed it is doubtful if its military ambitions extend that far (though this too may be changing as it slowly develops a network of ports and bases abroad).

For now its global reach depends much more on the power of its economy. China lacks the "proselytising zeal" - the sense of over-seas mission, that over the twentieth century saw the US strive for global dominance.

It also has nothing like the soft-power pull of the United States - no equivalent to blue jeans, Hollywood or burgers - to encourage people to share its values.

Indeed according to many indices Washington's raw military punch still greatly out-weighs that of Beijing. Washington's nuclear arsenal (and indeed Moscow's) is significantly larger than that available to Beijing.

The US still retains a technological edge in key areas like intelligence collection; ballistic missile defence; and the latest generation warplanes. The US can also rely upon a deeply entrenched network of alliances both in Asia and through Nato in Europe.

China has nothing like this kind of alliance system. But it is fast eroding Washington's technical edge. And in any case what matters to China is Asia and what it sees in expansive terms as its own back-yard. Two key factors - focus and proximity - mean that in Asia, China is already a superpower to rival the US.

Media playback is unsupported on your device Media caption A BBC team flew over the disputed South China Sea islands in a US military plane

China has studied US capabilities and warfighting and has come up with an effective strategy to mitigate the traditional sources of US military power, not least the US Navy's powerful carrier battle groups, the central element of Washington's ability to project military force.

Dubbed in military-speak, an "anti-access and area denial" approach, China has single-mindedly focused on a range of sensors and weapons systems that it hopes will compel US forces to operate as far away from its own shores as possible.

At the outset this was inherently a defensive posture. But increasingly analysts see China's capabilities as enabling it to seize the initiative, confident that it can deter and cope with any likely US response.

"Chinese counter-intervention systems," the Australian study notes, "have undermined America's ability to project power into the Indo-pacific, raising the risk that China could use limited force to achieve a fait accompli victory before America can respond, challenging US security guarantees in the process."

China's goal is in a time of crisis is to deny the US access to the area within the "first island chain" (the South China Sea bounded by a line running from the bottom of Japan, encompassing Taiwan, and passing to the west of the Philippines).

But it also seeks to restrict access to the outer "second island chain" with weapons that can reach as far as the US bases on Guam. This overall strategy can be bolstered by Chinese land-based aircraft and missiles.

Of course, it is not as if the Pentagon is unaware of the China challenge. After decades of counter-insurgency warfare the US military is being re-structured and re-equipped for renewed big-power competition. In the Cold War the focus was the Soviet Union. Today it is largely China.

However the Sydney University report questions whether Washington is sufficiently focused on the task in hand. It says that "an outdated superpower mindset in the (US) foreign policy establishment is likely to limit Washington's ability to scale back other global commitments or to make the strategic trade-offs required to succeed in the Indo-Pacific."

Money is going into new weaponry and research. But the task is huge.

"America has an atrophying force that is not sufficiently ready, equipped or postured for great power competition" and the report warns that a back-log of simultaneous modernisation priorities "will likely outstrip its budget capacity."

It is a sobering document written by a prestigious institution from one of Washington's closest allies in the region.

China clearly feels empowered - you can see this from the tone of its recently published defence white paper.

President Xi Jinping has decided not just to stand up to President Trump in the ongoing trade war but to take a much more assertive position, whether it be towards the pro-democracy demonstrations in Hong Kong or to China's long-standing claims over Taiwan.

China's military rise to match its growing economic muscle was inevitable. But some analysts fear that President Trump has made a difficult situation worse.

Many in the US feel it was time to stand-up to China on trade - but the way the US is going about it leads several experts to fear that Washington may simply lose the trade war.

Overall the Trump Administration's foreign policy often lacks a clear strategic aspect and is prone to the whims of the Presidential twitter feed and bizarre distractions like his apparent desire to purchase Greenland.

In contrast China knows exactly where it wants to go and it has the strategy and the means to get there. Indeed, for all intents and purposes, it may have already arrived.