Particle behavior in aesthetic field theory

We discuss the structure of a particle system obtained in “aesthetic” field theory and study the evolution of this system in time. We find the particle system to have more structure than particles found by other authors investigating particlelike behavior in nonlinear field theories. Our particle system has a maximum center in proximity to a minimum center. Thus, we can interpret our system as being constructed of two bodies. We find that the maximum center and the minimum center move in straight lines, to computer accuracy. Thus, we have not found any nontrivial force laws. This suggests that the situation with respect to basic principles be kept fluid. So far as we know, we are the first investigators to study the trajectories of a two-body system which arises as a consequence of nonlinear field equations.     

A study of solutions to the aesthetic field equations

We have found hundreds of solutions to the integrability equations in aesthetic field theory. The behavior of the solutions to the aesthetic field equations depends on which solution to the integrability equations we take. From computer runs down a coordinate axis we have found a type of solution where we have a maximum and a minimum, as well as the field going to zero at large distances along both directions. This kind of solution is quite prevalent. We call this type of solution a pulse solution. We have found the pulse solution in two and three dimensions as well as four dimensions. It appears regardless of whether certain symmetries are present or absent. We have taken a two- or three-dimensional and made a four-dimensional theory from it with the use of a four-dimensionale i. This process we call imbedding. We have found imbedding has not affected the overall characteristics of the solution in the cases we considered. We were able to change the character of the solutions to some degree by altering the magnitude of some of the gammas—but this did not lead to solutions with significantly more wiggles. We also found an example of an oscillatory solution. The oscillations occurred in too regular a pattern to give a realistic model for basic behavior. However, this solution indicates that aesthetic field theory has more structure then we have ever seen before. We also obtained a solution in which errors took over so fast that the computer was literally helpless in telling us what is going on. In other solutions the field appears to increase without bounds. Whether this is due to singularities or to the presence of large numbers is not clear.     

Further studies in aesthetic field theory; existence of a bounded particle

We have locked Into various possibilities within aesthetic field theory, particular attention to the case ofg=0. Theg=0 situation can be associated with the introduction of Newtonian absolute time into aesthetic field theory. If can be argued that Lorentz invariant boundary conditions for the universe are unlikely, giving impetus to the study ofg=0. We find that the field equations had to be modified from the form that they take wheng=0. Also, an infinite number of integrability equations have to be satisfied. We have required that our data have an underlying structure that Is invariant under O(3)×T. This set of date appeared satisfactory with respect to integrability and gave rise to a minimum ing _oo at the origin. After a long Computer run along the coordinate axes, we also found a bound on our particle-like object. This is the first time we have been able to obtain such a result.     

A new particle solution in aesthetic field theory

In present theories a particle is commonly associated with a singularity of the field. A more realistic picture would describe the particle by an intense but singularity-free field. We have found a new solution to the aesthetic field equations for which the field associated with the particle has a very large magnitude. The particle appears to be bounded despite the large numbers appearing in the solution. We prove that this present solution is not equivalent to theO(3)-invariant solution discussed in Muraskin (1973b). Since our present solution appears well-behaved, the suggestion is that we do not confine ourselves toO(3)-invariant data in future work. Owing to the large magnitude fields, we were unable to study trajectories of the particle in any detail. There is nothing wrong, in itself, with large numbers. The present solution, which we have now studied, is the first instance in our work on aesthetic field theory in which large numbers appear without the suggestion of unboundedness.     

New solutions in aesthetic field theory

We have obtained a large number of solutions to the aesthetic field equations. We discuss 19 solutions which appear to lead to bounded particle systems. One of the solutions is more complex (although only slightly) than the solution discussed in detail in Muraskin and Ring (1975). The solutions we have found have varied mathematical properties.     

Exact solution of the classical mechanical quadratic Zeeman effect

We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space-time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand’s theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space-time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.      

Exchange of helicity in a knotted electromagnetic field

There are solutions of Maxwell equations in vacuum in which the magnetic and the electric lines have a nontrivial topology. This behaviour has physical consequences since it is related to classical expressions indicating aspects of the photon content of the electromagnetic field. In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the temporal evolution of the magnetic and electric helicities, and explain the exchange of helicity making use of the Chern‐Simon form. We also have found and explained that, as time goes to infinity, both helicities reach the same value and the exchange between the magnetic and electric part of the field stops.     

Sinusoidal solutions to the aesthetic field equations

The aesthetic field equations do not resemble the wave equation, nor was the motivation behind them the wave equation. Nevertheless, we show that there exists a solution to the field equations that satisfies the wave equation. Integrability is also satisfied by this solution. Previously we showed that the Aesthetic Field Equations have particle solutions. Now we see that the equations also have sinusoidal solutions.     

On the global geometry of the stephani universe

A preliminary investigation of global properties of the Stephani solution of the Einstein field equations is presented. This solution generalizes those of Friedman-Robertson-Walker (FRW) in such a way that the spatial curvature indexk (a constant in the FRW models) is a function of the time coordinate. The de Sitter solution, which is also a special case of the Stephani solution, is analyzed in the Stephani coordinates to gain insight into the global structure of the manifold and its foliation. The general metric is found to have several properties in common with this example. It has singularities which can be avoided either by matching the solution to an (as yet unknown) empty-space solution or confining the curvature index to be positive at all times.     

Dynamics of a Néel domain wall with a fine structure in rare-earth orthoferrites

The dynamics of an isolated domain wall (DW) with a fine structure moving at a supersonic velocity in a rare-earth orthoferrite is studied. A set of nonlinear equations of motion of the center of a DW structure line is derived. A steady-state solution to these equations adequately describes the experimental data for yttrium orthoferrite. The effect of an external magnetic field on the steady-state velocity of a DW with structural lines is investigated.     

The spacetime of a Dirac fermion

We present an approximate solution to the minimally coupled Einstein-Dirac equations. We interpret the solution as describing a massive fermion coexisting with its own gravitational field. The solution is axisymmetric but is time dependent. The metric approaches that of a flat spacetime at the spatial infinity. We have calculated a variety of conserved quantities in the system.     

Aesthetic fields—Null theory II

We have again studied a null theory within the complex aesthetic field theory. This time we required that the spatially inverted origin point data represent the imaginary part of the complex origin point data. This was not the case in our previous studies of the null aesthetic field theory. However, this procedure did not lead to effects not previously observed as far as we could tell. Adding an additional term to the origin point data that presented the null character of the theory also did not lead to new effects. We also investigated a real null theory that led to constant fields. This theory was then made complex by a procedure discussed in the early part of the paper. We found that the resulting complex theory remained trivial nevertheless. Again, we found that it was not necessary for the theory to be null to find confluence type solutions.     

Forecast of the trajectory of the center of typhoons and the Maslov decomposition

We predict the trajectory of the center of a typhoon by using the coordinates of the first three positions of the center. From this information, we obtain the initial distribution of the wind velocity using a neural network trained for solving this inverse problem. We take the wind field at the initial time as the sum of a smooth part and a singular part, according to the Maslov theory. This form of the field ensures the stability and self-similarity of the flow. The trajectory is found by solving the shallow water equations numerically. In some cases, the resulting trajectory approximates the actual trajectory fairly well. This work has been supported by the project DSTN 521241 (Dep. Physics, Univ. La Sapienza, Italy, DSTN)     

Phase-controlled absorption-gain properties and optical switching in nanodiamond nitrogen-vacancy center

We study phase-controlled absorption-gain and dynamic switching behaviors in a nanodiamond nitrogen-vacancy (NV) center. The NV center is driven coherently by a weak probe laser field, a control laser field and a microwave field. To describe the transient behavior of the system, we go beyond the steady-state approximation and simultaneously solve the coupled Bloch–Maxwell equations for the NV center and the probe field on numerical grids as functions of space and time. The results show that the continuous-wave input weak probe field can be switched on and off when the relative phase of the applied field is externally varied periodically in time. The proposed scheme may have applications in the design of optical switching and optical gain devices.     

Cosmology with a Shock-Wave

We construct the simplest solution of the Einstein equations that incorporates a shock-wave into a standard Friedmann-Robertson-Walker metric whose equation of state accounts for the Hubble constant and the microwave background radiation temperature. This produces a new solution of the Einstein equations from which we are able to show that the distance from the shock-wave to the center of the explosion at present time is comparable to the Hubble distance. We are motivated by the idea that the expansion of the universe as measured by the Hubble constant might be accounted for by an event more similar to a classical explosion than by the well-accepted scenario of the Big Bang.     

Nonlinear equations of the gravitational field in the special theory of relativity

It is proposed that the nonlinearity of the field be taken into account with the help of a method which essentially consists of the fact that the structure of the Lagrangian, expressed in terms of the potential of the field and its derivatives, is not known a priori, but is obtained from a solution of the self-action equation in phase space in which the Lagrangian is the unknown. This equation has a solution and the Lagrangian turns out to be a nonpolynomial function with respect to the field potential. The gravitational field equations following from the variational principle have a similar structure to the equations of general relativity and coincide with them in the linear approximation. The equations of other fields taking into account gravitation, as well as the equation of motion of a test particle in a gravitational field, are constructed.     

Kaluza-Klein theory and Machian cosmology

We interpret the 15 equations of Kaluza-Klein gravity as 10 Einstein equations, 1 wave equation and 4 equations of motion. An exact cosmological solution of the apparently empty 5D field equations describes a 4D fluid with an effective density and pressure induced by the curvature associated with the fifth dimension. The rest mass of a particle in the fluid depends on the global solution and changes slowly with time. This approach to Kaluza-Klein theory in general results in Machian cosmologies.     

Near field of a loaded circular toroidal antenna

In this paper a special toroidal coordinate system is introduced in order to derive general solutions for the electric and magnetic fields from a toroidal antenna. These solutions depend on the current distribution on the toroid and are in integral forms. Some Fourier expansion techniques have been used in order to simplify these integral equations. The surface current is found under the assumption that the thickness of the toroid is thin compared to the wavelength, which leads to an analytic solution for the fields at the center. Many uniform loading impedances are used with the purpose of producing a plane-wave-like field at the center of the toroid.     

Ionization formation of plasma inhomogeneity by the near-zone field of a magnetic-type source in a magnetized plasma

An investigations is made of the steady-state structure of a plasma inhomogeneity arising as a result of high-frequency heating and additional ionization of a background magnetized plasma by the near-zone field of a magnetic-type source (ring electric current). It is assumed that the source axis is parallel to an external magnetic field; the source frequency belongs in the low hybrid band. The main attention is focused on the particular case (important for possible applications) when the characteristic longitudinal and transverse scales of density distribution considerably exceed the corresponding scales of distribution of the electron temperature and of the source field. Simplified equations for the near-zone field of the source, the electron temperature, and the plasma density are written for this particular case. Based on the numerical solution of these equations, steady-state distributions of plasma parameters in the formed plasma inhomogeneity are found. It is demonstrated that a plasma inhomogeneity proves to be markedly extended along the external magnetic field. It is found that, for the values of the source current that are attainable under the conditions of active ionospheric and model laboratory experiments, the maximum plasma density in a nonuniform plasma may appreciably exceed the background value.     

A Class of Quasi-linear Equations in Coframe Gravity

We have shown recently that the gravity fieldphenomena can be described by a traceless part of thewave-type field equation. This is an essentiallynon-Einsteinian gravity model. It has an exactsphericallysymmetric static solution, that yields to theYilmaz-Rosen metric. This metric is very close to theSchwarzchild metric. The wave-type field equation cannotbe derived from a suitable variational principle by free variations, as was shown by Hehl and hiscollaborators. In the present work we are looking foranother field equation having the same exactspherically-symmetric static solution. Thedifferential-geometric structure on the manifold endowed with a smoothorthonormal coframe field is described by the scalarobjects of anholonomity and its exterior derivative. Weconstruct a list of the first and second order SO(1,3)-covariants (one- and two-indexedquantities) and a quasi-linear field equation with freeparameters. We fix a part of the parameters by acondition that the field equation is satisfied by aquasi-conformal coframe with a harmonic conformal function .Thus we obtain a wide class of field equations with asolution that yields the Majumdar-P apapetrou metricand, in particular, the Yilmaz-Rosen metric, that is viable in the framework of three classicaltests.