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In statistical mechanics, the Zimm–Bragg model is a helix-coil transition model that describes helix-coil transitions of macromolecules, usually polymer chains. Most models provide a reasonable approximation of the fractional helicity of a given polypeptide; the Zimm–Bragg model differs by incorporating the ease of propagation (self-replication) with respect to nucleation.
Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors
The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. [3] A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion. The slope of ...
Helix–coil transition models are formalized techniques in statistical mechanics developed to describe conformations of linear polymers in solution. The models are usually but not exclusively applied to polypeptides as a measure of the relative fraction of the molecule in an alpha helix conformation versus turn or random coil .
Euler's spiral is a type of superspiral that has the property of a monotonic curvature function. [4] The Euler spiral has applications to diffraction computations. They are also widely used in railway and highway engineering to design transition curves between straight and curved sections of railways or roads.
Arc length s of a logarithmic spiral as a function of its parameter θ. Arc length is the distance between two points along a section of a curve . Development of a formulation of arc length suitable for applications to mathematics and the sciences is a focus of calculus .
The efficiency can be plotted versus the helix angle for a constant friction, as shown in the adjacent diagram. The maximum efficiency is a helix angle between 40 and 45 degrees, however a reasonable efficiency is achieved above 15°. Due to difficulties in forming the thread, helix angle greater than 30° are rarely used.
In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral. If the floor projection is a logarithmic spiral , it is called conchospiral (from conch ).