Cooroll Mills
Cooroll Mills
The cooroll mills are constructed as running industrial machines for k = 2, 4 or 6 roll mills which are mixing polymer solutions.
The new name added is used for their demonstrations concerning nano technology, often as videos. Some well understood names are informally added for possible applications planed in future. In macroscopic constructions, polymer is replaced by other fluids like water, incredients to be mixed or by gases. The coorolls have different shapes and use for different k.
The projective geometry is added for quantum mechanical subspace geometries and uses 7 dimensional vectors. As points located in a minimal projective Fano model, four points are for the minimal, affine Einstein model of spacetime with the Minkowski metric for Euclidean spin vectors and a linear time vector as a watches second (also for the lights symmetry as a 7th rolled Kaluza-Klein circle). The other dimensions are added for the 6 cooroll mill as kinetic force and mass vectors.
Operation of a 3 cooroll mill
A 3 cooroll mill is experimentally demonstrated as a wheel driven by water. This is not the known three roll mill, a machine that uses three horizontally positioned rolls rotating in opposite directions. The 3 cooroll mill has three pairs of shovels or shoes located at a the ends of a stick Sv with opposite orientations of the shovels. Water sets Sv in motion when send in the two opposite directions to a shovel pair such that it moves like an ordinary wheel driven by water. There are 3 sticks pairwise located orthogonal and alternatively set for this wheel. The 3 cooroll mill generates as axes the local Euclidean v = x,y,z space coordinates for all cooroll mills.
Operation of a 1 cooroll mill
In the center of the generated local coordinates is a 1 cooroll mill as barycenter and origin, carrying mass or a mass carrying potential vector. It is constructed as a solid ball with a Schwarzschild radius. Its symmetry is described by a 2x2-matrix operator of order 6. It refers to Higgs bosons. Beside setting 6 masses of demonstrating fermionic series it also can set for electrical charge replacing mass the 6 electrical charges, measured by drawing on a circle the 6th roots of unity.
Operation of a 2 cooroll mill
In it has two corotating rolls and a quadric potential with a generated flow having as 2-dimensional cross cut two axes x + y 1, x - y 1 and in between the four branches of two hyperbola collections of the flow. This is for the two potentials, belonging to the electrical and mass charges of quarks.
A unified Laplacian for the two potentials can be found in. It is projective 5 dimensional.
Operation of a 6 cooroll mill
The potential of a 6 cooroll mill is described in by the elliptic umbilic catastrophe which has a rich geometry.
The 6 coorolls carry the six color charges of quarks together with appropriate energy vectors added to be integrated as forces. The flat cross cut is replaced by the hedgehog figure with six color charge carrying vectors attached. The force vectors are for electrical charge, heat, kinetic, magnetic rotational energies and mass, The gluon exchange between paired quarks of the strong interaction integrates them to potentials or speed carrying or momentum vectors through suitable energy exchanges.
This cooroll mill is driven by three motors POTm, SIm and WIm. For the potential and strong motors it is assumed that they have the same speed, different than the weak WIm motors speed.
Operation of a 4 cooroll mill
The 3 cooroll mill is for constructing atoms kernels formed by paired protons and neutrons with 6 quarks named in a sequence uuddud and in a 6-cycle shifted to the left. Its use was for setting localized Minkowski coordinates for spacetime to which lights imaginary linear coordinate as time expansion was added. Local and linear rolled coordinates are generated by the 4 cooroll mill without an SIm motor. However, the parity braking of the weak integration is reversing the orientation of one cooroll from the 6 cooroll mill. Spherical coordinates are rolled, often 1 dimensional as circles for periodic functions.
Light has a single period as helix line on its cylindrical expansion in time. Weak interaction and electromagnetic geometries generate by the Hopf geometry of Pauli's spin double periods with toroidal locations U(1)xU(1). Twice applied for electrical and for magnetic energies, a Heegard decomposition shows their Hopf geometry as a the symmetry of a 3 dimensional weak sphere.
Application and rollers
In video or machine demonstrations for the nano technology, which can run macroscopically, 3 cooroll mills are used to generate a local coordinate frame for an energy system P, at present mostly for videos and laboratory work. A 1 cooroll mill sets a barycenter of P and general relativistic scalings of Minkowski metric as well as the generation of fermionic 12 series with addition of the conjugation operator which reverses all quantum numbers. The 2 cooroll mill carries two vectorial poles for the electrical charge and mass potential of quarks and is used in a 5 dimensional Laplacian unification of electromagnetism with gravity. The 6 cooroll mill is a structural description for the strong force with gluon exchanges between quarks. The inner discrete dynamics of (proton or neutron) nucleons and properties can be tested by this macroscopic running machine with 3 motors.
The 4 cooroll mill shows in particular the use of linear coordinates, rolled as fundamental domains for periodic functions to circles with a stereographic point at infinity added. In higher dimensions, this is persented by the 3 dimensional Hopf sphere in a 4 dimensional real space and a 5 dimensional unit sphere in a complex 3 dimensional space as geometrical factor of the strong geometry. The 2 dimensional sphere (hedgehog) is used for an idealized boundary of P as open, not closed physical system which can perform energy exchanges with the environment.
The cooroll mills are constructed as running industrial machines for k = 2, 4 or 6 roll mills which are mixing polymer solutions.
The new name added is used for their demonstrations concerning nano technology, often as videos. Some well understood names are informally added for possible applications planed in future. In macroscopic constructions, polymer is replaced by other fluids like water, incredients to be mixed or by gases. The coorolls have different shapes and use for different k.
The projective geometry is added for quantum mechanical subspace geometries and uses 7 dimensional vectors. As points located in a minimal projective Fano model, four points are for the minimal, affine Einstein model of spacetime with the Minkowski metric for Euclidean spin vectors and a linear time vector as a watches second (also for the lights symmetry as a 7th rolled Kaluza-Klein circle). The other dimensions are added for the 6 cooroll mill as kinetic force and mass vectors.
Operation of a 3 cooroll mill
A 3 cooroll mill is experimentally demonstrated as a wheel driven by water. This is not the known three roll mill, a machine that uses three horizontally positioned rolls rotating in opposite directions. The 3 cooroll mill has three pairs of shovels or shoes located at a the ends of a stick Sv with opposite orientations of the shovels. Water sets Sv in motion when send in the two opposite directions to a shovel pair such that it moves like an ordinary wheel driven by water. There are 3 sticks pairwise located orthogonal and alternatively set for this wheel. The 3 cooroll mill generates as axes the local Euclidean v = x,y,z space coordinates for all cooroll mills.
Operation of a 1 cooroll mill
In the center of the generated local coordinates is a 1 cooroll mill as barycenter and origin, carrying mass or a mass carrying potential vector. It is constructed as a solid ball with a Schwarzschild radius. Its symmetry is described by a 2x2-matrix operator of order 6. It refers to Higgs bosons. Beside setting 6 masses of demonstrating fermionic series it also can set for electrical charge replacing mass the 6 electrical charges, measured by drawing on a circle the 6th roots of unity.
Operation of a 2 cooroll mill
In it has two corotating rolls and a quadric potential with a generated flow having as 2-dimensional cross cut two axes x + y 1, x - y 1 and in between the four branches of two hyperbola collections of the flow. This is for the two potentials, belonging to the electrical and mass charges of quarks.
A unified Laplacian for the two potentials can be found in. It is projective 5 dimensional.
Operation of a 6 cooroll mill
The potential of a 6 cooroll mill is described in by the elliptic umbilic catastrophe which has a rich geometry.
The 6 coorolls carry the six color charges of quarks together with appropriate energy vectors added to be integrated as forces. The flat cross cut is replaced by the hedgehog figure with six color charge carrying vectors attached. The force vectors are for electrical charge, heat, kinetic, magnetic rotational energies and mass, The gluon exchange between paired quarks of the strong interaction integrates them to potentials or speed carrying or momentum vectors through suitable energy exchanges.
This cooroll mill is driven by three motors POTm, SIm and WIm. For the potential and strong motors it is assumed that they have the same speed, different than the weak WIm motors speed.
Operation of a 4 cooroll mill
The 3 cooroll mill is for constructing atoms kernels formed by paired protons and neutrons with 6 quarks named in a sequence uuddud and in a 6-cycle shifted to the left. Its use was for setting localized Minkowski coordinates for spacetime to which lights imaginary linear coordinate as time expansion was added. Local and linear rolled coordinates are generated by the 4 cooroll mill without an SIm motor. However, the parity braking of the weak integration is reversing the orientation of one cooroll from the 6 cooroll mill. Spherical coordinates are rolled, often 1 dimensional as circles for periodic functions.
Light has a single period as helix line on its cylindrical expansion in time. Weak interaction and electromagnetic geometries generate by the Hopf geometry of Pauli's spin double periods with toroidal locations U(1)xU(1). Twice applied for electrical and for magnetic energies, a Heegard decomposition shows their Hopf geometry as a the symmetry of a 3 dimensional weak sphere.
Application and rollers
In video or machine demonstrations for the nano technology, which can run macroscopically, 3 cooroll mills are used to generate a local coordinate frame for an energy system P, at present mostly for videos and laboratory work. A 1 cooroll mill sets a barycenter of P and general relativistic scalings of Minkowski metric as well as the generation of fermionic 12 series with addition of the conjugation operator which reverses all quantum numbers. The 2 cooroll mill carries two vectorial poles for the electrical charge and mass potential of quarks and is used in a 5 dimensional Laplacian unification of electromagnetism with gravity. The 6 cooroll mill is a structural description for the strong force with gluon exchanges between quarks. The inner discrete dynamics of (proton or neutron) nucleons and properties can be tested by this macroscopic running machine with 3 motors.
The 4 cooroll mill shows in particular the use of linear coordinates, rolled as fundamental domains for periodic functions to circles with a stereographic point at infinity added. In higher dimensions, this is persented by the 3 dimensional Hopf sphere in a 4 dimensional real space and a 5 dimensional unit sphere in a complex 3 dimensional space as geometrical factor of the strong geometry. The 2 dimensional sphere (hedgehog) is used for an idealized boundary of P as open, not closed physical system which can perform energy exchanges with the environment.
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