The information about breathing science is contained in Swarodhaya Shastra. It is also referred to as Shiva Swarodaya and Phonetical astrology . Though I have never read the scripture myself, I am quoting from my friend's notes on Swarodhaya Shastra. It was incomplete and so I could give only a limited answer.
When the breath flows through the right nostril, it is called Surya Swara (or surya nadi) and when it flows through the left nostril, it is called Chandra Swara (or chandra nadi). The process by which the flow changes from one nostril to the other is called Swara Sankranti. Rarely, the breath may flow through both the nostrils, which is termed as Vishvat Kala.
The Surya Swara represents male energy and the Chandra Swara represents female energy. So, the power of breath for a man is highest in the Surya Swara and for a female, it is highest in the Chandra Swara.