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Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.

The first consideration towards constructing a field propulsion system would likely be allowed for it to have a very strong field [1-4]. Now most electromagnetic fields radiate so that a strong field can be achieved, a continuous amount of energy it also must be fed in the form of power from a reliable and autonomous source. Thus it is necessary to realize an appropriate research on superconducting materials that joint with a magnetic field created in the reactor, which produces a permanent diamagnetic effect and whose repulsion force of the magnetic field with the superconductor be expelled and controlled for a rotation ring whose movement must generate and feed the electromagnetic remnants of this same interaction inducing the momentum of impulse through a momentum of torsion produced by the electromagnetic forces [5-8]. This imitating the forces that conform and generate the sidereal objects movements. This type of engendered by magnetic fields and superconductor materials in the universe create all the movements in sidereal objects like stars and galaxies following an intrinsic geometry due to these fields [6,9], for example, the galaxy is moved on a magnetic disk with their spiral arms alignment due to their intersidereal magnetic field, their rotation that is engendered for magnetic field and their interaction with the superconductor materials, creating an electromagnetic rotation as described by the Helmholtz theorem [1,6,10], or their evolution from their formation passing for several forms from the ellipsoid in their early stage until their adult stage with form of spiral disk or plate [9,10], see the

and using the magnetic energy of the superconductor in an external magnetic field perpendicular at a plate (disc):

Then the space engendered by the perpendicular field of the disk results in isomorphic (in the context of electromagnetic actions), to the space of field H_{c}(1 – n), which is an ellipsoid [8,10]. If in ellipsoid a = b = c, then we have a sphere of the electromagnetic nature. Now it is just necessary to consider the electromagnetic performance to navigation and horizontal displacement of ship without effects irradiative due to the strong electromagnetic forces [4-6].

A good intent to build a strong local non-radiating electromagnetic field is to build it as a standing wave in the flight of horizontal displacement with a permanent effect of magnetic levitation and suspension in the space, but outside enclave to part of any field that exists in the media [1,4]. The electromagnetic part standing wave field does not radiate. In this point we’ve got in past researches that the electromagnetic field of impulse and levitation that comes of the interaction superconductormagnetic field must place a shield in the structure of the vehicle that to nano-metric level produces the effects of levitation and suspension required to their flight [8,12], but with the iso-rotations established to the movement like a wave through altering the actions of the fields in their interaction reactor-rotor/ring of the vehicle [

If we consider that the Maxwell equations can also be obtained like solution to a variational problem , then due to the actions of the fields F, that produce the movement of all the particles in the space M, and using the corresponding vector bundle of these electromagnetic field to define it gemetrically, we can define those action as [1, 16]:

with rule of correspondence

and the energy due to L_{MAX}, is

If we consider the global evaluation of the operator that acts on the space of points x(s), this comes like

The integral Equation (6), represents the action Á(g), by the Hamilton principle that establishes that the particle will cover that trajectory that minimizes the action. Likewise, the equation of movement comes pre-determined for the minimum of this action Á(g), and pre-established for the variation condition [

In particular, if we want the evaluation of this action of Maxwell along an elected trajectory into the field of minimal trajectories, by the principle of the minimal action,

(with an electro-gravitational field)

we have the execution of the action of the Maxwell fields [1,18],

where m_{s}_{ }is the corresponding measure of the trajectory g, in M. But the system we want to build must be considered the by action Á, of the electromagnetic field F, to suspend or make levitation and to displace an object Ì M, in the space M.

The laws of conservation of the electromagnetic fields which establish the levitation and movement of translation of the object , (vehicle) establishes that the energy of , under this constant frame comes as

where L_{MAX}_{(SC)}, is the corresponding Lagrangian of Maxwell of the superconductor SC. Likewise, the action given by Á_{M },_{ }is will transmitter to all particle x(s), of , characterises it like a superconductor._{ }

If we consider the global evaluation of the operator that acts on the space of points x(s), this comes given for Equation (6), as (this is magnetic conscience operator! [4,6]):

But in that global action of the magnetic field on the superconductor, the thermodynamically effects mentioned of the field arisen as meaningless part in the process [10,16], is to say

where W, depends on the geometrical form of , in our case the design of the vehicle will be an ellipsoid or a disc, convenient geometries of the form of the vehicle that will be discussed after and that represents intermediate superconductors states in the region of interaction of field [

The term L_{MAX}_{(SC}_{)} explains the thermodynamics effects of the action of the field in the neighborhood of the reactor. If there isn’t these magnetic effects then Wò_{O }H^{2}dV = 0, and = F(V, T)_{0}, is the corresponding thermodynamic action that only depends of the volume (size of the reactor), and not of their form [

In the case of the kinetic energy, this depends of their rotation, which is an effect of the action of their magnetic moment of spin. To our object , in the case of that is an intermediate state of a superconductor, the produced energy to their electromagnetic impulse provided of the twistor surface that is generated under , and whose action is given by the action of the corresponding moment of rotation. This twistor surface is a magnetic field whose action is the synergic impulse of the vehicle using the energy of the same like superconductor. Of this form, the total action of auto-levitation and movement on the vehicle , will come given by the equation

whose energy is given by (9), with execution operator given for

and which is transmitted to whole particle x(s), of the structure of , through the law of conservation of magnetic energy in all moment in the process of the superconductor.

Lemma. 1.1. (Bulnes, F) [8,14]. The energy of action given by Á_{M}, of the vehicle all like a diamagnetic given by Á_{M} satisfies all vector magnetic potential A, (1-form of the corresponding Maxwell equations to the levitation: rot B = 4pj (1/c) and B = 0, [10,13]), the following Hamiltonian

Proof. See [

One can obtain considering the synergic action prosaid in (13), the following synergic principle deduced of our Equations (12), (13) and (14):

Principle: “The force that exercises the imam (it leaves conformed by magnetic rotation ring), and superconductor is the sum of contributions of each element of local surface and each one of them is the double that would correspond to the direct force among the local image (superconductor) and the imam”.

This clearly satisfies the property of our integral synergic operators given in (12):

[14,17](15)

Considering the combined actions, we can give a general scheme to design a possible reactor that, see

Definition. 2.1. A E_{t}ÄH-field, is an element of a bisided ideal of the Maxwell fields [1,6]. Explicitly is the formal space:

E_{t }Ä H = {(F_{1}, F_{2})ÎW^{2}(O)´ W^{2}(O)| F_{1 }Ä F_{2 }

+ F_{2 }Ä F_{1 }- [F_{1}, F_{2}], with Ä = Ä_{R}},(16)

Lemma. 2.1. All electromagnetic actions (microscopic and macroscopic) used to the flight and movement of , comes of the E_{t}ÄH -fields. See

Proof. To demonstrate this result it is necessary prove two aspects that are correlated: The microscopic properties due to the macroscopic effects produced for the reactor to characterize the quantum densities of field to superconductor electrons e, 2e [5,15]), which comes given by the auto-adjunct part:

[8,12,17]and the macroscopic effects due to the Eddy currents which must comply the following equation of electromagnetic field [8,10]:

Consider the bi-sided ideal given by the space (16), whose actions are extended to all space from , until the infinite (ambient of ) [7,10,19]. By the Lemma 1 (F.

Bulnes), page 5, (published in ASME, 2010), the quantum effects underlying in superconducting phenomena satisfies that

where H^{2}/8p, is the free magnetic energy (B = H/4pm_{0}), and the integral of the Lagrangian L_{M}, of the expulsion by the action Á_{M}, and that is useful to establish the macroscopic wave functions that give place to a microscopic quantum current J_{s}. In effect, by mathematical electrodynamics [_{t}ÄH, (that is to say, a module of the exterior algebra (which is deduced by the universal map applied to each term of the element F_{1 }Ä F_{2 }- F_{1 }Ä F_{2 }- [F_{1}, F_{2}]) [1,7]) that:

where J = Ñy, and y* = conj (y), such that |y|^{2 }= < y, y*>. That is what we want, since we search measure energy. A study on isometric and complete Riemannian manifolds [_{s}, is the extend on all surface of vehicle, such and as it is have foreseen to characterize to , like diamagnetic material in the space. The microscopic effects succeed due to the electromagnetic actions and under the conservative laws foreseen by our integral (13), [

In fact, the integral given by (19), can be calculated for the stokes theorem [1,8], where j = rot B, on surface S, of the superconductor, having a total magnetic flux on all surface of .

How to characterize and produce artificial materials that induce the same microscopic and macroscopic effects necessary into the magnetic conscience induced by the deep conscience (programmed by the structure space defined by (16)), to obtain a superconductor state in the reactor to ambient conditions?

An important thermal fact is observed in the study of superconductors. If T_{c}, is the critical temperature of a material to risk transition to their superconductor characterization (foreseen by (11)), then is clear that if T, is a temperature of any material in nature condition to be conductor, and if we want characterize it like superconductor is necessary that T_{c} > T, [

For other side, magnetic effects are intimately related with the microscopic effects that are produced by the quantum macroscopic effects where these last are gene-

rated for the magnetic field at all moment will produce the diamagnetic effect on the ship, such and like is predicted in the (11). But into superconductor theory the element ambient also has inherence into the action Á_{M}, (of fact this also will be relevant in the displacement of the ship like a wave and will produce condensation effects such and like has been signed into the demonstration of the Lemma. 2. 1 see the Figures 6 and 8). Thus the material that we must think must be a material with the sufficient qualities like conductor with propitious properties to diamagnetism (that is to say with components of conductor metals with a magnetic susceptibility adequate to risk the transition state), and qualities of not rapidly decreasing in a short interval to reliever of oxygen atoms in a special alloy thought-out to the construction of the reactor. Precisely the existence of oxygen atoms can give us the condensed matter effects from quantum level, that here in the atmospheric continuum media, will do that the flight be relevant with high qualities like traveler magneto-hydrodynamic wave, including mimetic or camouflage effects. The clouds are condensed water in the sky!

We suggest the following patent of alloys rich in oxygen atoms, with a functional relation to the number of oxygen atoms related with tetragonal configuration with oxygen of the Cu-metal, and proportional parts of metals such how the Ba (Barium), Y (Yttrium), La (Lanthanum), inclusive Yb (Ytterbium). But always Cuprum present [

Proposition. 2.1. The inequality T_{c} > T, risks a larger interval of the molecular bi-atomicity parameter to Oxygen atoms, when the alloy is of the family of the type, YBACUO (z) [12,15] (because it is require maxim T_{c}) that which it is get when in the functional space ~II_{e}(j, r), [_{r}_{ }Å J_{0}, is the total induced current by the magnetic field H, in the ship), comply in their superconducting characteristic (patent of component in process PMx [

~II_{e}(j, r) = {jÎJr_{ }_{ }Å J_{0}| j = (r^{-}m^{-}+r^{+}m^{+}){j_{0 }+ j_{e}}, such that rot B = 4pj(1/c)},(19)

with the Eddy currents [8,10],

Proof. See [

In the disc obtained by the rotation and superconducting transformation [^{+}, and P^{- }[1-3,6], that are consequences of the expulsion of the magnetic field by the superconductor of the reactor. In these orbital spaces generates the currents r^{-}m^{-}{j_{0} + j_{e}}, and r^{+}m^{+}{j_{0} + j_{e}}, where the sign +/-, indicates the direction (oriented orbital spaces) of the current lines of the current density. The magnetic field degenerate in infinite magnetic line with residues to quantum level, such and as comes pre-whose in the (18). The parameter z, must be designed to give a material that under conditions of temperature given by T_{c} > T, realizes the actions established in (9), but this is obtained with the family IBACUO, that which among other things (and using the diamagnetic effect due to the Eddy currents) produces an effect of diamagnetic field, comparable with the Earth magnetic field; (namely, »0.1 gauss [11,12]), producing the suspension and levitation effects necessary to levitation and suspension to ambient conditions of temperature. But this situation is only satisfied into a space with similar conditions like the given in the sidereal space, that is to say, the space ~II_{e}(j, v).

Using all the before study foreseen on Eddy currents and relating the behavior of magnetic flux with skin effect given to the Eddy currents on surface of vehicle O (considering the macroscopic quantum effects), and studied in [10,12], and [

Theorem (F. Bulnes) 3.1. We consider (18), and with the Hamiltonian foreseen in (14), by lemma. 1., and their proof, it is have of inequality on magnetic energy necessary to all magnetic process of reactor

Then a sensor-chip to magnetic flux (pressure on the surface of O) to super-currents is defined by the inequality

where,_{ }is a fluxoid (= hc/e* = 2.07 × 10^{–7 }gauss·cm^{2}), being e* = 2e, where e is the charge of electron.

Proof. See [_{t}ÄH, to quantum level [7,8,12]. Of this manage; we obtain the magnetic energy required for our levitation and suspension of vehicle. ¡

Let the magnetic energy foreseen in the Lemma. 1.1, together with the necessary geometric considerations to engender the twistor surfaces in the area of fluxoids existence (Lemma 2.1), then we can obtain by means of a specialized simulation program in magnetism [

After obtaining a micro-controller of Eddy Currents deduced of the interaction of the superconductor with the magnetic flow already obtained by the rotation ring with certain magnetic moment predicted (Lemma 2), it is also necessary to program the micro-controller so that it stabilizes the object (our vehicle), [

thing so that the object does not oscillate or that, in any event, its movement is minimum. To achieve the objective of manipulating the magnetic fields we have to design our own computation architecture that establishes and optimizes the use of memory and the time of processor to manage in parallel all the variables to process. This prosecution system is designed with FPGA (Field Programmable Gate Array) for implementation of the system prosecution) in such a way that we control the variables [

The rotation of the ring (iso-rotation in a plane), it is managed in the variable of the vector z(k) to feed the mechanical system [15,22,24]. The magnetic field is controlled by means of the acquisition by means of the adjustment of the probes of the sensors that feedback to the system. See

In this moment we are in the preparation of the real prototypes with all the mechanism and devices that will do possible and feasible the flight of our design and development of the vehicle. See _{t}ÄH -field (diamagnetic field that must vender the gravitational forces) for permanent waves with velocities of major phases that the light velocity can create a macro-quantum with the superconducting effects of the fluxoids calculated and foreseen by the Inequality (23), and that will also produce the Eddy currents in the encapsulate of the ship like if it were an enormous particle with the foreseen geometrical form (a plate, a sphere or an ellipsoid), can be associated like

quantum macro-particles using the Bohm re-interpretation [1,2], in an analogous model to quantum scheme to the macroscopic scales mentioned with before (19), that using the equivalences defined by the isomorphism of the cohomological classes H^{1}(P(X), W) @ H^{1}(PT, O(-2-2)), (see the meaning of the notation used to characterize the spaces mentioned in this work), and with images in the cohomological class H^{2}(,), (integrals that are functional), the wave functions can be re-interpreted like vertexes of a graph of displacement trajectories to consider the translation of the vehicle, being able to design a ship control (based in the design of the

The future designs of ships must be in functionality and behavior very seemed to the sidereal and natural objects that exist in the universe, since in these natural objects fulfilled the unlimited energy to use the proper object to displacement and other functions that designed these. In this moment are about to obtain the exact alloy with high qualities to obtain all the effects described in this work. The problem that we have is to obtain the enough financing to do it. We hope to obtain it soon.

w_{H}—Rotational Magnetic Field.

L_{MAX}—Lagrangian Operator of Maxwell.

j_{s}—Superficial currents (are the super-currents of Eddy currents).

L_{M}—Lagrangian Operator of Maxwell it comes of the magnetic action.

Á_{M}—Action of magnetic field.

F—Tensor of Maxwell or electromagnetic tensor (is a fundamental 2-form defined by F = F_{ij}dx_{i}dx_{j}).

J_{0}—Functional space of currents proveniences of magnetic field with the condition rot H = j.

—Vehicle or flight ship under principle of magnetic impulse, levitation and/or suspension.

v—Velocities field.

O—Integration domain of the vehicle .

_{M}—Reactor of magnetic impulse, levitation and/or suspension of the ship or flight vehicle (is composite for the superconductor and magnetic ring).

J_{r}—Functional space of the electrical currents proveniences from electric field.

C(T)—Space of classes that are submanifolds of a maximal complex torus. Such submanifolds are toroids or rings. To our study case, these are of magnetic origin and are produced by rotation and the superconductor action of .

G/C(T)—Homogeneous space of classes that admit Riemannian complex invariants structures, that means, invariants complex surfaces under the action of the compact group K. To our case, the group of the electromagnetic field action operators, which is K = SU(2).

SU(2)—Topological group of the electromagnetic fields action operator SU(2) = {FÎW^{2}(R^{4})½F_{ij }= -F_{ji}}. Their elements have linear representations as well matrices of range 2 ´ 2 on R.

A—Vector Potential.

F—Magnetic flux.

Flux—Flux operator on vector field.

M—Vector of Magnetization.

H—Intensity of magnetic field (In the intermediate state theory, represents their magnetic state).

~II_{e}(j,r)—Domain Space of an electronic fluid continuum media with dynamical characteristics. Also, from a point of mathematical view is the functional space of total currents from the Magnetic field acting. In electrodynamics is the space conformed for movements caused by the magnetic forces where movements will be observed like the topological distortions of the fluid in the space (twistor surfaces).

~II_{H}(E,s)—Domain Space of a magnetic fluid continuum media with dynamical characteristic. Also, from a point of mathematical view is the functional space of the magnetic fields responsible of the transportation of the materials in the ring of the galaxies.

B—Density of magnetic flux. Also, vector of magnetic induction.

M—Magnetic moment turn.

R^{3}—Real space of three dimensions.

W^{2}(R^{4})—Space of real 2-forms on a space of dimension four.

j—Density of electrical current. Also, vector of density of electrical current.

L_{MAX}_{(SC)}—Lagrangian operator of Maxwell of superconductor.

SC—Superconductor.

n_{s}—Normal vector to the surface S.

H_{cr}—Intensity of critical magnetic field (also it is known as critical magnetic state).

Á_{rot}—Rotational action (mechanical rotations on the ring of due at magnetic moment of turn).

C—Space of the complex numbers of one dimension.

P^{+}—Orbit given by a magnetic torus under of (surface of torus or ring).

P^{-}—Orbit given by a magnetic torus over of (surface of torus or ring).

H(Flux, Potential)—Hamiltonian operator.

H^{1}(A, B)—Cohomological Space of dimension one from A to B. This space establishes a duality of objects geometrical and integral precedence (like resulted of the integration process) that has some objects such as forms, functions vector fields, hyper-surfaces, densities, etc. Usually it can be understood like a space of integrals that are functions or other objects as forms or densities.

H^{2}(A, B)—Cohomological Space of dimension two from A to B. This space establishes a duality of objects geometrical and of functional precedence (like resulted of the integration process in the evaluation) that has some objects such as forms, functions, vector fields, hypersurfaces, densities, etc. Usually it can be understood like a space of integrals that are functional.

T —Twistor object. In this work the twistor will surfaces magnetic impulse of ship.

PT—Orbital twistor space. PT = P^{+ }È P^{-}.

P(X)—Space designed by densities like singular states or nodes into transition graph of displacement trajectories of the vehicle. Also P(X), is the set of energy states of the ship like macro-particle.

R—1-dimensional space of real numbers.

F_{0}—Fluxoid (elemental unit of magnetic vortex).

M—Set space of the points x(s), on such act the interactions of superconductor and the magnetic field to produce an autonomous levitation effect in (space in where is immerse).

SO(2)—Topological group of the orthogonal rotations in the space M. Is a space of range two matrices on.

V—Volume of a superconductor element.

T_{c}—Temperature of a superconductor element.

E_{t}ÄH – Super-canonical algebra with structure of Lie algebra to SU(2) gifted with the tensor product Ä, used to explain the quantum effects of macroscopic level and the quantum structure of the densities of field y, in the quantum equation of the super-current in their auto-adjunct part:

of fact E_{t }Ä H = {F_{12 }_{½}_{ } F_{12 }= F_{1 }Ä F_{2}} and J_{s }it inherits the structure of E_{t}ÄH.

y—Function of density or density of field.

PMx—Mexican design patent.

h—Max Planck constant » 6.6256 ´ 10^{–}^{34}Joules ´ seg.

L_{M}—Langragian operator due at total magnetic field H.

L_{rot}—Lagrangian operator due at rotational movement (iso-rotations) that establishes constant rotations in all point of the ring of due to their magnetic movement.