Gilberto Silva-Ortigoza's research while affiliated with Benemérita Universidad Autónoma de Puebla and other places
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Publications (104)
In the first part of this work, we introduce a monochromatic solution to the scalar wave equation in free space, defined by a superposition of monochromatic nondiffracting half Bessel-lattice optical fields, which is determined by two scalar functions; one is defined on frequency space, and the other is a complete integral to the eikonal equation i...
In the first part of this work, using the quantum potential approach, we show that a solution to the time-independent Schr"odinger equation determines a subset of classical solutions, only if \textit{the region corresponding to the zeroes of the quantum potential is tangent to the caustic region determined by the classical trajectories}. Thus, the...
This paper presents the design of a smooth starter for a DC motor that employs a full-bridge Buck inverter powered by renewable energy. In order to achieve this, a power supply from renewable energy is considered in the mathematical model associated with the “full-bridge Buck inverter–DC motor” system. Whereas, for the design of the smooth starter,...
In this work we compute, via the quantum potential approach, the Hamiltonian system determined by Hermite–Gaussian beams. Then we show that the integral curves of the Poynting vector, exact optics energy trajectories, conform to a subset of solutions to the corresponding Hamilton equations lying on hyperboloidal surfaces. The geometrical light rays...
The aim of the present work is to introduce two monochromatic solutions
to the scalar wave equation in free space, characterized by a caustic with a singularity
of the hyperbolic umbilical type. The first solution, is a superposition of half-
Mathieu beams, and the second one, is a superposition of parabolic beams. Since
these solutions are determi...
By using the quantum potential approach, we show that: the Airy beam determines a Hamiltonian system with one degree of freedom for a particle of mass $m=1$ evolving under the influence of a quantum potential, such that its associated quantum force is constant, the integral curves of the Poynting vector are parabolic ones and turn out to be a subse...
This paper presents a sliding mode control (SMC) for the “full-bridge Buck inverter–DC motor” system when a photovoltaic (PV) panel is considered as the power supply. The control executes the trajectory tracking task related to the angular velocity of the DC motor shaft without the need for electromechanical sensors. The proposed control is validat...
The aim of the present work is to show that any monochromatic solution to the scalar wave equation in free space defines a conservative Hamiltonian system, describing a particle of mass $m = 1/2$ m = 1 / 2 and energy $E = 1$ E = 1 , under the influence of the so-called quantum potential. We remark that the integral curves of its Poynting vector, ex...
In this investigation, a tracking control is designed for the angular velocity of the DC/DC Boost converter–DC motor system. To this end, the dynamics of the power supply, generated through a renewable energy power source, is considered in both the mathematical model and the designed control. This latter is proposed by using a two-level hierarchica...
The aim of the present work is to show that the Laguerre–Gauss beams determine a Hamiltonian system with two degrees of freedom for a particle of mass $m = 1$ m = 1 under the action of the quantum potential determined by these beams. We show that the integral curves of the Poynting vector constitute a particular subset of solutions to the correspon...
By developing a robust control strategy based on the differential flatness concept, this paper presents a solution for the bidirectional trajectory tracking task in the “full-bridge Buck inverter–DC motor” system. The robustness of the proposed control is achieved by taking advantage of the differential flatness property related to the mathematical...
In this work, we assume that in free space we have an observer, a smooth mirror, and an object placed at arbitrary positions. The aim is to obtain, within the geometrical optics approximation, an exact set of equations that gives the image position of the object registered by the observer. The general results are applied to plane and spherical mirr...
We calculate equations to obtain the exact and third-order design of thick lenses free from spherical and coma aberrations at two points, at the edge and center of the lens, considering the shape factor and the conic constants. We obtained analytical expressions based on the equality of the optical path and the Abbe sine condition calculated for an...
The aim of the present work is to introduce a lens whose faces are a conical surface and a spherical surface. We illuminate this lens by a plane wavefront and its associated refracted wavefronts, light rays and caustic are computed. We find that the caustic region has two branches and can be virtual, real or one part virtual and the other real, dep...
The aim of this work is threefold. First, following Luneburg and using our own notation, we review the Cartesian ovals. Second, we obtain analytical expressions for the reflecting and refracting surfaces that transform a prescribed smooth two-dimensional wavefront into a spherical one. These results are applied to show that the reflecting surface t...
The design of a robust flatness-based tracking control for the DC/DC Buck converter-DC motor system is developed in this paper. The design of the control considers the dynamics of a renewable energy power source that plays the role of the primary power supply associated with the system. The performance and robustness of the control is verified thro...
A sensorless control based on the exact tracking error dynamics passive output feedback (ETEDPOF) methodology is proposed for executing the angular velocity trajectory tracking task on the “full-bridge Buck inverter–DC motor” system. When such a methodology is applied to the system, the tracking task is achieved by considering only the current sens...
The aim of the present work is to introduce a lens whose faces are a conical surface and a spherical surface. We illuminate this lens by a plane wavefront and its associated refracted wavefronts, light rays and caustic are computed. We find that the caustic has two branches. The first is constituted by two segments of a line, one part of this caust...
From a geometric perspective, the caustic is the most classical description of a wave function since its evolution is governed by the Hamilton–Jacobi equation. On the other hand, according to the Madelung–de Broglie–Bohm equations, the most classical description of a solution to the Schrödinger equation is given by the zeros of the Madelung–Bohm po...
The aim of the present work is to determine the reflected light rays, wavefronts, caustic and the ronchigram associated with the reflection phenomenon of a plane wave on a parabolic mirror, in particular on the parabolic antenna of the Large Millimeter Telescope (LMT/GTM). The results presented here are general in the sense that the incident plane...
From a geometric perspective, the caustic is the most classical description of a wavefunction since its evolution is governed by the Hamilton-Jacobi equation. On the other hand, according to the Madelung-de Broglie-Bohm equations, the most classical description of a solution to the Schr\"odinger equation is given by the zeros of the Madelung-Bohm p...
In this paper we compare the intensity distributions in the paraxial and tightly focused regimes corresponding to a double ring perfect optical vortex (DR-POV). Using the scalar diffraction theory and the Richards-Wolf formalism, the fields in the back focal plane of a low and high (tight focusing) NA lens are calculated. In the paraxial case we ex...
We show that $(\textbf{E},\textbf{H})=({\textbf{E}_0},{\textbf{H}_0}){e^{i[{k_0}S(\textbf{r})-\omega t]}}$ ( E , H ) = ( E 0 , H 0 ) e i [ k 0 S ( r ) − ω t ] is an exact solution to the Maxwell equations in free space if and only if $\{{\textbf{E}_0},{\textbf{H}_0},\nabla S\}$ { E 0 , H 0 , ∇ S } form a mutually perpendicular, right-handed set and...
In this paper, the generation of a partially coherent optical vortex composed of the incoherent superposition of N coaxial Bessel vortex beams with linearly increasing topological charges and aligned intensity maxima is proposed. To generate this beam, concentric ring slits with increasing topological charges and random phase shifts are optically F...
We construct exact solutions to the paraxial wave equation in free space characterized by stable caustics. First, we show that any solution of the paraxial wave equation can be written as the superposition of plane waves determined by both the Hamilton–Jacobi and Laplace equations in free space. Then using the five elementary stable catastrophes, w...
The aim of the present work is threefold, first we show that the intensity pattern of a nondiffracting beam determines an arbitrary positive real function and a complete integral of both the eikonal and Laplace equations on the plane; second, by using this result we associate to the intensity pattern a two-parameter family of curves and a one-param...
A frequency response-based linear controller is implemented to regulate the inverted pendulum on a cart at the inverted position. The objective is to improve the performance of the control system by eliminating the limit cycle generated by the dead-zone, induced by static friction, at the actuator of the mechanism. This control strategy has been re...
Nondiffracting beams have the particular property that their time averaged intensity profile does not change when it is measured in every plane normal to the direction of evolution of the beam. Starting from Durnin's solution for the scalar wave equation, we study and characterize nondiffracting beams geometrically. We find that optical scalars des...
This paper has two aims. The first is to develop a robust hierarchical tracking controller for the DC/DC Buck-Boost–inverter–DC motor system. This controller considers a high level control for the inverter–DC motor subsystems and a low level control for the DC/DC Buck-Boost converter subsystem. Such controls solve the tracking task associated with...
Recently, it has been shown that if S(r, θ, φ) is a two-parameter solution of the eikonal and Laplace equations, then is an exact solution of the scalar wave equation in an isotropic optical medium. In particular, if we take , the resulting solution is a superposition of non-diffracting beams in free space with different cone angle θ for the k vect...
The aim of this work is twofold: first we present a general method to design a Ronchi grating, and second we compute its associated analytical ronchigram for a general plano-convex lens illuminated with a plane wave, for any configuration of the Ronchi grating and the detection planes. We remark that the analytical pattern depends directly on the c...
The main contribution of the present work is to use the probability density of an Airy beam to identify its maxima with the family of caustics associated with the wavefronts determined by the level curves of a one-parameter family of solutions to the Hamilton-Jacobi equation with a given potential. To this end, we give a classical mechanics charact...
In this work we compute the wavefronts and the caustics associated with the solutions to the scalar wave equation introduced by Durnin in elliptical cylindrical coordinates generated by the function A ( ϕ ) = c e ν ( ϕ , q ) + i s e ν ( ϕ , q ) , with ν being an integral or nonintegral number. We show that the wavefronts and the caustic are invaria...
Among the best known non-interferometric optical tests are the wire test, the Foucault test and Ronchi test with a low frequency grating. Since the wire test is the seed to understand the other ones, the aim of the present work is to do a thorough study of this test for a lens with symmetry of revolution and to do this study for any configuration o...
The trajectory tracking task in a wheeled mobile robot (WMR) is solved by proposing a three-level hierarchical controller that considers the mathematical model of the mechanical structure (differential drive WMR), actuators (DC motors), and power stage (DC/DC Buck power converters). The highest hierarchical level is a kinematic control for the mech...
The aim of the present work is to obtain an integral representation of the field associated with the refraction of a plane wave by an arbitrary surface. To this end, in the first part we consider two optical media with refraction indexes n 1 and n 2 separated by an arbitrary interface, and we show that the optical path length, ϕ , associated with t...
Optical scalars are functions designed to analyze the behavior of geodesic congruences in general relativity. Refracted rays are three-dimensional congruences of light rays and they can be studied with this formalism. In this work we obtain the optical scalars for such congruences: the expansion Θ, the twist ω, and the shear κ. Furthermore, we appl...
The aim of this work is to present a Ronchi test for a gravitational lens. To this end, we use the geometrical optics point of view of the Ronchi test and the definition of the exact lens equation without reference to a background space-time to introduce the analog of the ideal ronchigram, which we named the gravitoronchigram. We first present the...
The aim of this work is to present a geometrical characterization of parabolic non-diffracting beams. To this end, we compute the corresponding angular spectrum of the separable non-diffracting parabolic beams in order to determine the one-parameter family of solutions of the eikonal equation associated with this type of beam. Using this informatio...
The aim of the present work is to define a DurninWhitney beam as a nondiffracting beam such that its associated caustic locally only has singularities of the fold and cusp types. Since the caustic is structurally stable then the intensity pattern of this beam is also stable and this property is what makes its definition and its theoretical and expe...
The aim of the present work is to give a geometrical characterization of Durnin's beams. That is, we compute the wavefronts and caustic associated with the nondiffracting solutions to the scalar wave equation introduced by Durnin. To this end, first we show that in an isotropic optical medium is an exact solution of the wave equation, if and only i...
In this work we obtain the equations for curvatures of refracted wavefronts for a plano arbitrary lens. The functions H 0 , H 1 , and H 2 that determine the caustic also determine the curvature of these wavefronts. The analysis performed in these calculations allows us to study the behavior of the Ronchigrams for the case of plane incident wavefron...
In this work we use geometrical optics and the caustic touching theorem, introduced by Berry, to describe the internal structure of the null Ronchi grating for a plano–parabolic lens illuminated by a point light source placed on the optical axis. The aim of this work is to explain the role of the caustic region in the process of morphology change b...
In this work we assume that we have three optical media with constant refraction indexes n 0, n 1 and n 2 separated by arbitrary refracting surfaces. In the optical medium with refraction index n 0 we place a point light source at an arbitrary position. The aim of the present work is to obtain exact expressions for the wavefront train and the caust...
In this paper, we propose a method to detect the valid phase pixels of fringe patterns obtained with phase shifting interferometry. From a set of simulated interferogram images, we obtain a set of equations to discriminate between valid and invalid wavefront phase pixels, which allow us to compute the wavefront aberration. This method is useful for...
In this work we assume that we have two given optical media with constant refraction indexes, which are separated by an arbitrary refracting surface. In one of the optical media we place a point light source at an arbitrary position. The aim of this work is to use a particular complete integral of the eikonal equation and Huygens’ principle to obta...
In this work we use geometrical optics to study the global behavior of the morphology of the wave fronts and their respective caustic associated with the refraction of a circular wave propagating between two given optical media with constant refraction indexes, which are separated by an arbitrary curve. For this purpose, we construct an expression...
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transform...
The aim of this work is threefold: first we obtain analytical expressions for the wavefront train and the caustic associated with the refraction of a plane wavefront by an axicon lens, second we describe the structure of the ronchigram when the ronchiruling is placed at the flat surface of the axicon and the screen is placed at different relative p...
In the literature it is possible to find the implementation of interferometric lateral shear tests with a liquid crystal display (LCD). We collected them and implemented others not previously reported. We show the versatility that the LCD offers to test of optical surfaces, so that graduate students can experience the following tests: the Foucault...
Supplementary Video 1 and Supplementary Video 2: Materials used for the prototype construction. These videos show how some parts of the WMR prototype were built. Different machine tools were employed for the construction.
Supplementary Video 3: This video shows different real views of the complete WMR prototype. These included the mechanical and el...
The aim of the present work is twofold: first we obtain analytical expressions for both the wavefronts and the caustic associated with the light rays reflected by a spherical mirror after being emitted by a point light source located at an arbitrary position in free space, and second, we describe, in detail, the structure of the ronchigrams when th...
This paper reports a solution for trajectory tracking control of a differential drive wheeled mobile robot (WMR) based on a hierarchical approach. The general design and construction of the WMR are described. The hierarchical controller proposed has two components: a high-level control and a low-level control. The high-level control law is based on...
The aim of this paper is to obtain expressions for the k -function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a paraboli...
We introduce a dc/dc boost power converter as a didactic prototype intended to support courses on electric circuit analysis experimentally. The corresponding mathematical model is obtained, the converter is designed and an experimental setup is described, constructed and tested. Simplicity of construction as well as low cost of components renders t...
The aim of the present work is to obtain expressions for both the wavefront train and the caustic associated with the light rays reflected by an arbitrary smooth curve after being emitted by a point light source located at an arbitrary position in the two-dimensional free space. To this end, we obtain an expression for the k-function associated wit...
In this work we use the geometrical point of view of the Ronchi test and the caustic-touching theorem to describe the structure of the ronchigrams for a parabolical mirror when the point light source is on and off the optical axis and the grating is placed at the caustic associated with the reflected light rays. We find that for a given position of...
The aim of the present work is to obtain expressions for both the wavefront train and the caustic associated with the light rays reflected by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in free space. To this end, we obtain an expression for the k-function associated with the general inte...
In this paper we present a solution for the trajectory tracking problem in a newt mobile robot. We exploit the differential flatness property of the robot kinematic model to propose an input-output linearization controller which allows both the position and the orientation to track a desired trajectory. An important assumption is that robot has to...
We use geometrical optics and the caustic-touching theorem to study, in an exact way, the change in the topology of the image of an object obtained by reflections on an arbitrary smooth surface. Since the procedure that we use to compute the image is exactly the same as that used to simulate the ideal patterns, referred to as Ronchigrams, in the Ro...
A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often
information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern
is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces th...
A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or imp...
We argue that the well-known problem of the instabilities associated with the self-forces (radiation reaction forces) in classical electrodynamics are possibly stabilized by the introduction of gravitational forces via general relativity.
From the study of the asymptotic behavior of the Einstein or Einstein– Maxwell fields, a rather unusual new structure was found. This structure which is associated with asymptotically shearfree null congruences, appears to have significant physical interest or consequences. More specifically it allows us to define, at future null infinity, the cent...
We describe here what appears to be a new structure that is hidden in all asymptotically vanishing Maxwell fields possessing a non-vanishing total charge. Though we are dealing with real Maxwell fields on real Minkowski space nevertheless, directly from the asymptotic field one can extract a complex analytic world-line defined in complex Minkowski...
In the present work we integrate the null geodesic equations of the light cone of an arbitrary point in the Janis, Newman and Winicour space-time and we construct, in an exact way, the equations that describe the gravitational lensing phenomenon. We show that under certain conditions our exact results reduce to the thin lens equation. Furthermore,...
In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years—from the work of Hermann Bondi—that the energy and momentum of gravitational sources could be determin...
We discuss the existence, arising by analogy to that in algebraically special space-times, of a unique asymptotically shear-free
congruence in any asymptotically flat space-time. Associated with it is a unique complex analytic curve in H-space. The surprising
potential physical significance of this curve is discussed.
We study the Robinson-Trautman-Maxwell Fields in two closely related coordinate systems, the original Robinson-Trautman (RT) coordinates (in a more general context, often referred to as NU coordinates) and Bondi coordinates. In particular, we identify one of the RT variables as a velocity and then from the Bondi energy-momentum 4-vector, we find ki...
In this work we show that on the space of solutions of a certain class of fourth-order ODEs, u'''' = Λ(s, u, u', u'', u'''), a four-dimensional conformal metric, gab, can be constructed such that the four-dimensional eikonal equation, gabu,au,b = 0, holds. Furthermore, we remark that this structure is invariant under contact transformations. Our ge...
The purpose of the present work is to extend the earlier results for
asymptotically flat vacuum space-times to asymptotically flat solutions of the
Einstein-Maxwell equations. Once again, in this case, we get a class of
asymptotically shear-free null geodesic congruences depending on a complex
world-line in the same four-dimensional complex space....
We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many calculations in General Relativity. In the calculations, products of these functions, with their needed decompositions wh...
The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat space-time with a given Bondi shear, one can find (by integrating a partial differential equation) a class of a...
The aim of the present work is twofold: first, we show how all the $n$-dimensional Riemannian and Lorentzian metrics can be constructed from a certain class of systems of second-order PDE's which are in duality to the Hamilton-Jacobi equation and second we impose the Einstein equations to these PDE's.
The aim of this work is to present a formulation to general relativity, which is analogous to the null surface formulation, but now instead of starting with a complete integral of the eikonal equation we start with a complete integral of the Hamilton–Jacobi equation. In the first part of this work we show that on the space of solutions of a certain...
We use geometrical optics to compute, in an exact way and by using the third-order approximation, the disk of least confusion (DLC) or the best image produced by a conic reflector when the point source is located at any position on the optical axis. In the approximate case we obtain analytical formulas to compute the DLC. Furthermore, we apply our...
In the first part of this work we show that on the space of solutions of a certain class of systems of three second-order PDE’s, uαα = Υ(α,β,u,uα,uβ), uββ = Ψ(α,β,u,uα,uβ) and uαβ = Ω(α,β,u,uα,uβ), a three-dimensional definite or indefinite metric, gab, can be constructed such that the three-dimensional Hamilton–Jacobi equation, gabu,au,b = 1 holds...
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three demensional Minkowski metric.
By using two different procedures we show that on the space of solutions of a certain class of second-order ordinary differential equations, u″ = Λ(s,u,u′), a two-dimensional definite or indefinite metric, gab, can be constructed such that the two-dimensional Hamilton–Jacobi equation, gabu,au,b = 1 holds. Furthermore, we show that this structure is...
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three demensional Minkowski metric.
In this work we use geometrical optics to obtain an exact analytical expression for the caustic surface associated with the evolution of an aberrated wavefront in three-dimensional free space. Furthermore, we show that, under a certain condition, the envelope associated with the evolution of the aberrated wavefront is composed of points of the marg...
We compute the radius and the position of the center of the circle of least confusion, in an exact way and by using the third-order approximation, of a rotationally symmetric mirror when the point source is located at any position on the optical axis. For the spherical case we find that for some positions of the point source there is a considerable...
The purpose of this work is to study the structure and nature of the singularities of wavefronts in flat space-time. We computed the behavior at the singularities of important objects that take place in the null surface formulation of general relativity. As a secondary result we show that the Minkowski space-time with non-trivial null surfaces is a...
It is shown that each component of the Dirac field satisfies a decoupled equation, which admits separable solutions, when the background spacetime is the Bertotti–Robinson metric, which is a solution of the Einstein vacuum field equations with a cosmological constant. Furthermore, the seperated functions appearing in the solutions are shown to obey...
Since in all the type-D solutions of the Einstein vacuum field equations with a cosmological term each maximal spin-weighted component of the electromagnetic spinor field satisfies a decoupled equation and there exists a two-index Killing spinor field; we show, via the adjoint operators method, that a symmetry operator for the Maxwell equations can...
In this work we integrate the null geodesic equations in three-dimensional Minkowski space-time in order to obtain the light-cone cut function; that is, the function that describes the intersection, Cx
a, of the light cone from each space-time point, x
a, with future null infinity I
+. Furthermore, using this result, we locate the singularities of...
Since the expressions of the components of the aberration represent a map from ℝ 3 to ℝ 3 , in this work we apply the theory of singularities of differentiable maps to obtain an analytical expression for the caustic of the propagation of an aberrated wavefront.
In an arbitrary Lorentzian manifold we provide a description for the construction of null surfaces and their associated singularities, via solutions of the Eikonal equation. In particular, we study the singularities of the past light-cones from points on null infinity, the future light-cones from arbitrary interior points and the intersection of th...
It is shown that the separation constant not related to isometries that appears in the solution of the spin- perturbations of the Carter A solution, can be defined in an invariant way as the eigenvalue of a certain differential operator made out of a two-index Killing spinor. Furthermore, when the electromagnetic field of the background spacetime i...
It is shown that if the background spacetime is a type-D solution of the Einstein vacuum-field equations with cosmological constant or of the Einstein - Maxwell field equations without cosmological constant, an operator can be constructed that maps a solution of the Rarita - Schwinger equation into another solution. In the case of the spin- fields...
We locate pairs of conjugate points on null geodesics along which there is a `barrier' of Weyl curvature. The existence of conjugate points in this case is predicted by general theorems. We also find that the same conjugate points can be obtained perturbatively off flat space, assuming the barrier to be weak. The conjugate points appear at second o...
The level surfaces of solutions to the eikonal equation define null or characteristic surfaces. In this note we study, in Minkowski space, properties of these surfaces. In particular we are interested both in the singularities of these ``surfaces'' (which can in general self-intersect and be only piece-wise smooth) and in the decomposition of the n...
Assuming that the background spacetime is a solution of the Einstein vacuum equations without cosmological constant, we analyze how the Rarita-Schwinger equations can be obtained via a particular generalization of the usual spin-3/2 massless free field equations. On the basis of this analysis we speculate on the possibility of finding other general...
It is shown that in a type-D vacuum space-time with cosmological constant, the components of the Weyl spinor perturbations along the principal spinors of the background conformal curvature satisfy differential identities, which are valid in all the normalized spin frames {o
A
, ιA
} such that o
A
and ιA
are double principal spinors of the backgroun...
Using the fact that in any type-{2 2} (i.e. type D) vacuum spacetime each component of the Maxwell spinor field satisfies a decoupled equation and there exists a two-index Killing spinor, it is shown, by a simple argument, that one can construct a symmetry operator for the Maxwell equations. An analogous result is also obtained for the Weyl neutrin...
It is shown that the separation constant not related to isometries, which appears in the solution of the Klein-Gordon equation in the Carter A background, can be defined in an invariant way as the eigenvalue of a second-order differential operator made out of a two-index Killing spinor, with the eigenfunctions being the separable solutions.
Citations
... It is important to mention that the present work is a natural extension to that reported in [16]. That is, here we introduce another new solution to the scalar wave equation as a superposition of plane waves, which locally is characterized by a caustic of the hyperbolic umbilical type. ...
... It is important to remark that the results presented here for the time-independent Schrödinger equation and in particular to the 2D isotropic harmonic oscillator can be extended to the time-dependent Schrödinger equation, the scalar wave equation, and the paraxial wave equation for an arbitrary potential and optical medium, respectively. The present work is a natural extension of our results obtained for the Airy, Bessel and Laguerre-Gauss beams in free space [4,[13][14][15][16]. That is, in our previous woks we have considered examples in free space only. ...
... The Simscape solar cell block has predefined parameters for three different parameterizations, and these parameters should be confirmed by measured data to ensure the model's accuracy. Due to the popularity and widespread use of MATLAB/Simulink in the scientific community, many different topics have been studied using simulations that are based on the Simscape solar cell block [16][17][18][19][20]. It is especially suitable for simulating circuits where photovoltaic modules are connected to other circuit elements, such as DC/DC converters, batteries, etc. ...
... In this sense, the system formed by a Buck power converter connected in series to a DC motor has been mostly exploited by the expert community in automatic control [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. However, there have also been a significant number of contributions that take advantage of the Boost topology [24], [25], [26], [27], [28], [29], [30]. Likewise, systems that consider the use of the Buck-Boost [31], [32] Cuk [33] and Luo [28], [34] converters as drivers for the DC motors have been designed. ...
... It is important to remark that the results presented here for the time-independent Schrödinger equation and in particular to the 2D isotropic harmonic oscillator can be extended to the time-dependent Schrödinger equation, the scalar wave equation, and the paraxial wave equation for an arbitrary potential and optical medium, respectively. The present work is a natural extension of our results obtained for the Airy, Bessel and Laguerre-Gauss beams in free space [4,[13][14][15][16]. That is, in our previous woks we have considered examples in free space only. ...
... It is important to remark that the results presented here for the time-independent Schrödinger equation and in particular to the 2D isotropic harmonic oscillator can be extended to the time-dependent Schrödinger equation, the scalar wave equation, and the paraxial wave equation for an arbitrary potential and optical medium, respectively. The present work is a natural extension of our results obtained for the Airy, Bessel and Laguerre-Gauss beams in free space [4,[13][14][15][16]. That is, in our previous woks we have considered examples in free space only. ...
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... Works of this nature have taken advantage of the Buck converters [35], [36], [37], [38], [39], Boost [40], [41], [42], Buck-Boost [43], [44], [45], [46], and Sepic [47]. Another alternative to achieve the bidirectional rotation of the DC motor is by means of the full-bridge Buck inverter [48], [49], [50], [51]. This topology has been used for the handling of AC motors [52], [53] and in the actuators of a wheeled mobile robot [54]. ...
... Next, for each pair of values (d ob , y ob ), we have numerically found the pairs of values (x i , y i ) that satisfy the equations set. The results obtained match those obtained by means of Eq. (15). ...
... However, the conic constant and shape factor are two ways of describing the shape of a surface, and they are related mathematically (Jiménez et al 2022). The conic constant is a dimensionless quantity that describes the deviation of a surface from a perfect sphere, while the shape factor is a more general parameter that describes the shape of any conic section. ...
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... Therefore, a caustic surface analysis has been applied to calculate the corresponding irradiances for rays of different optical elements [11,12]. Furthermore, this is used to analyze geometrical image structures [13], different types of lenses and mirrors [14][15][16][17][18][19], axicons [20], different types of beams [21][22][23], the astroid caustic (in bubble optics) [24][25][26], and the reflection of a plane wave by an arbitrary surface [27]. ...
