Higher Multipoles of the Cow
Source: Hacker News โ
The spherical cow approximation is widely used in the literature, but is rarely justified. Here, I propose several schemes for extending the spherical cow approximation to a full multipole expansion, in which the spherical cow is simply the first term. This allows for the computation of bovine potentials and interactions beyond spherical symmetry, and also provides a scheme for defining the geometry of the cow itself at higher multipole moments. This is especially important for the treatment of physical processes that are suppressed by spherical symmetry, such as the spindown of a rotating cow due to the emission of gravitational waves.
I demonstrate the computation of multipole coefficients for a benchmark cow, and illustrate the applicability of the multipolar cow to several important problems. ar Xiv Labs is a framework that allows collaborators to develop and share new ar Xiv features directly on our website. Both individuals and organizations that work with ar Xiv Labs have embraced and accepted our values of openness, community, excellence, and user data privacy. ar Xiv is committed to these values and only works with partners that adhere to them.
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๐World Economylow impact
What this means for you
- โถTrading partners on the other side of the world may feel a distant nudge.
- โถA story like this rarely stays local for long in a connected economy.
๐๏ธLocal Economymedium impact
What this means for you
- โถThe high street usually mirrors big-picture shifts, just a touch down the road.
- โถYour local economy has a way of catching these currents eventually.
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- โถAny move in rates would probably come later, not overnight.
- โถInterest rates and mortgage bills are unlikely to jump straight away from this alone.
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- โถTaking a break from the headlines can do more good than scrolling on.
- โถUnsettling news can weigh on sleep and mood, so peace of mind matters.
๐ทWealthmedium impact
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- โถIt's a reasonable moment to check your investments are still on track.
- โถMoney set aside for the future can afford to sit tight through this.
๐ Housinglow impact
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- โถMortgage deals could edge around if lenders read the wider mood.
- โถRenters might see costs drift a bit as landlords weigh their own bills.
๐ Effects for your country
The U.S.'s central bank rate currently stands at 3.75%, so a global rates move like this could feed through to local borrowing costs. The U.S.'s economy is growing at 2.3% with inflation at 3.2%, the backdrop this story's effects play out against locally. Housing-market effects like this are usually felt most where mortgage rates track the U.S.'s own central bank rate closely. With the U.S.'s unemployment at 4.4%, personal-finance effects like this land on a labour market that is currently fairly stable. Health-system effects are harder to localise from economic indicators alone โ the real impact in the U.S. depends more on local healthcare capacity than the figures above.
The UK's central bank rate currently stands at 3.75%, so a global rates move like this could feed through to local borrowing costs. The UK's economy is growing at 0.8% with inflation at 3.2%, the backdrop this story's effects play out against locally. Housing-market effects like this are usually felt most where mortgage rates track the UK's own central bank rate closely. With the UK's unemployment at 5.6%, personal-finance effects like this land on a labour market that is currently fairly stable. Health-system effects are harder to localise from economic indicators alone โ the real impact in the UK depends more on local healthcare capacity than the figures above.
France's central bank rate currently stands at 2%, so a global rates move like this could feed through to local borrowing costs. France's economy is growing at 0.9% with inflation at 1.8%, the backdrop this story's effects play out against locally. Housing-market effects like this are usually felt most where mortgage rates track France's own central bank rate closely. With France's unemployment at 7.9%, personal-finance effects like this land on a labour market that is already under strain. Health-system effects are harder to localise from economic indicators alone โ the real impact in France depends more on local healthcare capacity than the figures above.
Romania's central bank rate currently stands at 6.5%, so a global rates move like this could feed through to local borrowing costs. Romania's economy is growing at 0.7% with inflation at 7.8%, the backdrop this story's effects play out against locally. Housing-market effects like this are usually felt most where mortgage rates track Romania's own central bank rate closely. With Romania's unemployment at 6%, personal-finance effects like this land on a labour market that is currently fairly stable. Health-system effects are harder to localise from economic indicators alone โ the real impact in Romania depends more on local healthcare capacity than the figures above.
The UAE's central bank rate currently stands at 3.65%, so a global rates move like this could feed through to local borrowing costs. The UAE's economy is growing at 3.1% with inflation at 2.5%, the backdrop this story's effects play out against locally. Housing-market effects like this are usually felt most where mortgage rates track the UAE's own central bank rate closely. Health-system effects are harder to localise from economic indicators alone โ the real impact in the UAE depends more on local healthcare capacity than the figures above.