Explanation of the Density Anomalies of Water (D1-D22) The density of ice increases on heating (up to 70 K) Water shrinks on melting Pressure reduces ice's melting point Liquid water has a high density that increases on heating (up to 3.984 °C) The surface of water is denser than the bulk Pressure reduces the temperature of maximum density There is a minimum in the density of supercooled water Water has a low coefficient of expansion (thermal expansivity) Water's thermal expansivity reduces increasingly (becoming negative) at low temperatures Water's thermal expansivity increases with increased pressure The number of nearest neighbors increases on melting The number of nearest neighbors increases with temperature Water has unusually low compressibility The compressibility drops as temperature increases up to 46.5 °C There is a maximum in the compressibility-temperature relationship The speed of sound increases with temperature up to 74 °C The speed of sound may show a minimum NMR spin-lattice relaxation time is very small at low temperatures.
Gravity. A mathematical formalisation of dimensional analysis. Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers or the real numbers .
Indeed, the use of number systems is so closely identified with the practice of mathematics that one sometimes forgets that it is possible to do mathematics without explicit reference to any concept of number. For instance, the ancient Greeks were able to prove many theorems in Euclidean geometry, well before the development of Cartesian coordinates and analytic geometry in the seventeenth century, or the formal constructions or axiomatisations of the real number system that emerged in the nineteenth century (not to mention precursor concepts such as zero or negative numbers, whose very existence was highly controversial, if entertained at all, to the ancient Greeks). A similar situation exists in modern physics. (or related systems, such as yards”, combining both a number and is. Physics. Saturday Morning Breakfast Cereal.
Physics. HyperPhysics Concepts. About HyperPhysics Rationale for Development HyperPhysics is an exploration environment for concepts in physics which employs concept maps and other linking strategies to facilitate smooth navigation. For the most part, it is laid out in small segments or "cards", true to its original development in HyperCard. The entire environment is interconnected with thousands of links, reminiscent of a neural network.
The bottom bar of each card contains links to major concept maps for divisions of physics, plus a "go back" feature to allow you to retrace the path of an exploration. Part of the intent for this exploration environment is to provide many opportunities for numerical exploration in the form of active formuli and standard problems implemented in Javascript. New content for HyperPhysics will be posted as it is developed. A resource that was initiated as a resource for local high school physics teachers whom I had taught has expanded into an intensively used website worldwide.
HyperPhysics. Empirical Zeal. Episode Extra: Behemoths of Biomass (This post. Crystal Bliss. Math. Project Tuva: Enhanced Video Player Home. The World of Everyday Experience, In One Equation. Longtime readers know I feel strongly that it should be more widely appreciated that the laws underlying the physics of everyday life are completely understood.
(If you need more convincing: here, here, here.) For purposes of one of my talks next week in Oxford, I thought it would be useful to actually summarize those laws on a slide. Here’s the most compact way I could think to do it, while retaining some useful information. (As Feynman has pointed out, every equation in the world can be written U=0, for some definition of U — but it might not be useful.) Click to embiggen. This is the amplitude to undergo a transition from one configuration to another in the path-integral formalism of quantum mechanics, within the framework of quantum field theory, with field content and dynamics described by general relativity (for gravity) and the Standard Model of particle physics (for everything else).
As physics advances forward, we will add to our understanding. Astronomy Picture of the Day.