Search results
Results from the WOW.Com Content Network
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
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.
In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice that produces a third function, also of n-dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space.
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 ...
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 ).
Complex exponential function: The exponential function exactly maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic spirals in the complex plane with centre at : () = (+) + ⏟ = + = ( + ) ⏟ The pitch angle of the logarithmic spiral is the angle between the line and the imaginary axis.
A suitable bounded function is the arctan function: Example 1 Setting r = a arctan ( k φ ) {\displaystyle \;r=a\arctan(k\varphi )\;} and the choice k = 0.1 , a = 4 , φ ≥ 0 {\displaystyle \;k=0.1,a=4,\;\varphi \geq 0\;} gives a spiral, that starts at the origin (like an Archimedean spiral) and approaches the circle with radius r = a π ...