## Archive for the ‘Physics’ Category

Theoretical physicists use mathematics to describe certain aspects of Nature. Sir Isaac Newton was the first theoretical physicist, although in his own time his profession was called “natural philosophy”.

By Newton’s era people had already used **algebra** and **geometry** to build marvelous works of architecture, including the great cathedrals of Europe, but algebra and geometry only describe things that are sitting still. In order to describe things that are moving or changing in some way, Newton invented **calculus**.

The most puzzling and intriguing moving things visible to humans have always been been the sun, the moon, the planets and the stars we can see in the night sky. Newton’s new **calculus**, combined with his “Laws of Motion”, made a mathematical model for the force of gravity that not only described the observed motions of planets and stars in the night sky, but also of swinging weights and flying cannonballs in England.

Today’s theoretical physicists are often working on the boundaries of known mathematics, sometimes inventing new mathematics as they need it, like Newton did with calculus.

Newton was both a theorist and an experimentalist. He spent many many long hours, to the point of neglecting his health, observing the way Nature behaved so that he might describe it better. The so-called “Newton’s Laws of Motion” are not abstract laws that Nature is somehow forced to obey, but the observed behavior of Nature that is described in the language of mathematics. In Newton’s time, theory and experiment went together.

Today the functions of theory and observation are divided into two distinct communities in physics. Both experiments and theories are much more complex than back in Newton’s time. Theorists are exploring areas of Nature in mathematics that technology so far does not allow us to observe in experiments. Many of the theoretical physicists who are alive today may not live to see how the real Nature compares with her mathematical description in their work. Today’s theorists have to learn to live with ambiguity and uncertainty in their mission to describe Nature using math.

source: http://superstringtheory.com/basics/basic1.html

**Davydov soliton** is a quantum quasiparticle representing an excitation propagating along the protein α-helix self-trapped amide I. It is a solution of the Davydov Hamiltonian. It is named for the Soviet and Ukrainian physicist Alexander Davydov. The Davydov model describes the interaction of the amide I vibrations with the hydrogen bonds that stabilize the α-helix of proteins. The elementary excitations within the α-helix are given by the phonons which correspond to the deformational oscillations of the lattice, and the excitons which describe the internal amide I excitations of the peptide groups. Referring to the atomic structure of an α-helix region of protein the mechanism that creates the Davydov soliton (polaron, exciton) can be described as follows: vibrational energy of the C=O stretching (or amide I) oscillators that is localized on the α-helix acts through a phonon coupling effect to distort the structure of the α-helix, while the helical distortion reacts again through phonon coupling to trap the amide I oscillation energy and prevent its dispersion. This effect is called *self-localization* or *self-trapping*.^{[1]}^{[2]}^{[3]} Solitons in which the energy is distributed in a fashion preserving the helical symmetry are dynamically unstable, and such symmetrical solitons once formed decay rapidly when they propagate. On the other hand, an asymmetric soliton which spontaneously breaks the local translational and helical symmetries possesses the lowest energy and is a robust localized entity