Fundamentally why the Dollars is strengthen when the DOW is down

With reference from http://www.fxcm.com/analyze-currencies.jsp

Stock and the country currencies
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There is a high correlation between the performance of the US stock market and the USD (against the Euro). A rallying stock market in any part of the world provides an ideal investment opportunity for individuals regardless of geographic location and as a result there is a strong correlation between a country’s equity market and its currency. If the equity market is rising, investment dollars will flow in to seize the opportunity. Alternatively, falling equity makes will have domestic investors selling their shares to seize investment opportunities abroad.

Stock up -> Currency strengthen
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Interest Rates
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If the market has uncertainty regarding interest rates, then any bit of news regarding interest rates can directly affect the currency markets. Traditionally, if a country raises its interest rates, the currency of that country will strengthen in relation to other countries, as investors shift assets to that country to gain a higher return. Hikes in interest rates, however, are generally bad news for stock markets. Some investors will transfer money out of a country's stock market when interest rates are hiked, believing that higher borrowing costs will affect ballance sheet negatively and result in devalued stock, causing the country's currency to weaken. Which effect dominates can be tricky, but generally there is a consensus beforehand as to what the interest rate move will do.

Interest Rate up -> Currency strengthen
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Unemployment Rate
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The unemployment rate is a strong indicator of a country’s economic strength. When unemployment is high, the economy may be weak – and hence its currency may fall in value.

Unemplyment Rate up -> Currency weaken
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