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In this manuscript, we obtain different characterization for hybrid electromagnetic flow $ \mathbf {B}_{2}- $ B 2 − density of $ \mathbf {B}_{2}- $ B 2 − hybrid phase by new frame in ordinary space. Thus, we define new optical conditions of $ \mathbf {B}_{2}- $ B 2 − electromagnetic $ \mathbf {B}_{2}- $ B 2 − phase with optical fields. We obtain electromagnetic Lorentz $ \mathbf {B}_{2}- $ B 2 − flux for optical fields with Landau Lifshitz method. Finally, electromagnetic $ \mathbf {B}_{2}- $ B 2 − phase of $ \mathbf {B}_{2}- $ B 2 − surface are demonstrated in optical magnetic $ \mathbf {B}_{2}- $ B 2 − surfaces by optical geometric results for hybrid Landau Lifshitz method. [ABSTRACT FROM AUTHOR]

In this paper, we extract distinctive determination for quasi magnetic flux of the quasi binormal magnetic flows of magnetic quasi $ \mathbf {b}^{\mathbf {q}} $ b q -particle by considering directional frame in 3D ordinary space. Also, we construct some advanced optical qualifications for magnetic quasi Lorentz flux for magnetic quasi- $ \mathbf {b}^{\mathbf {q}} $ b q particle along with the quasi directional frame fields. Then, we calculate quasi magnetic Lorentz flux with directional-quasi magnetic fields. Besides, we obtain original simulations with regard to directional potentials for directional-quasi magnetic binormal flows with Heisenberg optical ferromagnetic model. Magnetic optical flux surfaces are demonstrated in a homogeneous optical flux surface by fractional numerical and applied developments. By using above models, we get new fractional model with q-homotopy analysis transform method (qHATM) and its illustrative presentation to consider magnetic optical flux surface. [ABSTRACT FROM AUTHOR]

The intent of this article is to study the traversable wormhole (WH) models with shape function and adequate choice of redshift function in the context of Finsler geometry. The solutions obtained for the shape function of the generated wormhole satisfy the requisite metric criteria, as manifested in other investigations in the literature. By taking into account the anisotropic energy–momentum tensor, we investigate the validity of the solution of the Finsler wormhole by considering all energy conditions. We also established a wormhole solution without the need for exotic matter by considering the redshift function. Further, the result can be viewed as a graphical representation and the anisotropic factor to determine the nature of gravity of the wormhole is discussed. [ABSTRACT FROM AUTHOR]

In this article, we illustrate surface flow a l f a - microfluidical mKdV spherical electromotive phase in sphere space. Also, we obtain antiferromagnetic axially electrical a l f a - microfluidical mKdV electric flux path circuit. We have electrical a l f a - microfluidical geometrical mKdV free surface flow density in sphere space. Finally, we design antiferromagnetic wave propagation for a l f a - microfluidical geometric mKdV surface flux density. [ABSTRACT FROM AUTHOR]

This paper aims to study the Finslerian equivalent of Schwarzschild–de Sitter space-time. We propose the gravitational field equation with a non-vanishing cosmological constant in Finslerian geometry. And we have observed that our presented Finslerian gravitational field equation corresponds to the non-zero value of the Ricci scalar. We have obtained the Finslerian-modified expressions of the black hole horizon, cosmological horizon, and static radius. Also, we have found that the Finslerian Schwarzschild–de Sitter space-time does not have constant flag curvature. Further, particle motion is discussed in Finslerian Schwarzschild–de Sitter space-time. [ABSTRACT FROM AUTHOR]

In this paper, we define a new different model for Heisenberg velocity microfluidic mKdV electromotive forces. Also, we construct some relations for ferromagnetic Heisenberg velocity microfluidic mKdV magnetic flux density. We design ferromagnetic Heisenberg velocity microfluidic optical mKdV flux domain representation. Finally, we obtain Heisenberg velocity microfluidic mKdV flux density. [ABSTRACT FROM AUTHOR]

In this note, we formulate and study a Hamilton–Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton–Jacobi theory consistently describes thermodynamic transformations on the space of externally controllable parameters or equivalently the space of equilibrium states. It turns out that in the Hamilton–Jacobi description, the choice of the principal function is not unique but, the resultant dynamical description for a given transformation remains the same irrespective of this choice. Some examples involving thermodynamic transformations of the ideal gas are discussed where the characteristic curves on the space of equilibrium states completely describe the dynamics. The geometric Hamilton–Jacobi formulation which has emerged recently is also discussed in the context of thermodynamics. [ABSTRACT FROM AUTHOR]

In this manuscript, we describe optical hybrid visco ferromagnetic hybrid B M ϕ T visco , hybrid B M ϕ B 1 visco , hybrid B M ϕ B 2 visco microscales with hybrid electrolytic thruster. Also, we obtain new optical electromagnetic hybrid microfluidic electrical visco ferromagnetic hybrid E M ϕ T visco , hybrid E M ϕ B 1 visco , hybrid E M ϕ B 2 visco microscales by using electromagnetic hybrid optimistic density in cold plasma. Finally, we illustrate electromagnetic phase of hybrid surface by using the hybrid electrolytic thruster. [ABSTRACT FROM AUTHOR]

In this article, we construct a new design for optical spherical Heisenberg total recursion flux with a normalized microscale in spherical Heisenberg space. Moreover, we demonstrate spherical Heisenberg normalized microscale by Heisenberg recursion operator for some magnetic fibers. Thus, we obtain optical spherical Heisenberg ferromagnetic recursion flux by using optical spherical Heisenberg ferromagnetic normalized microscale in spherical Heisenberg space. [ABSTRACT FROM AUTHOR]

We review the geometric evolution of a linearly polarized light wave coupling into an optical fiber and the rotation of the polarization plane in a three dimensional ordinary space. We demonstrate that the evolution of a linearly polarized light wave is associated with the Berry phase or the geometric phase. We define other Fermi-Walker parallel transportation laws and connect them with the famous Rytov parallel transportation law for an electric field E , which is considered as the direction of the state of the linearly polarized light wave in the optical fiber in the 3D space. Later, we define a special class of magnetic curves called by quasi electromagnetic curves ( q E M -curves), which are generated by the electric field E along the linearly polarized monochromatic light wave propagating in the optical fiber. In this way, not only we define a special class of linearly polarized point-particles corresponding to q E M -curves of the electromagnetic field along with the optical fiber in the 3D space, but we also calculate, both numerically and analytically, the electromagnetic force, Poynting vector, energy-exchanges rate, optical angular and linear momentum, and optical magnetic-torque experienced by the linearly polarizable point-particles along with the optical fiber in the 3D space. [ABSTRACT FROM AUTHOR]

We study and present the results of curvature for different symmetry classes (BDI, AIII and A) of model Hamiltonians and also present the transformation of model Hamiltonian from one distinct symmetry class to the other based on the curvature property. We observe the mirror symmetric curvature for the Hamiltonian with BDI symmetry class but there is no evidence of such behaviour for Hamiltonians of AIII symmetry class. We show the origin of torsion and its consequences on the parameter space of topological phase of the system. We find the evidence of torsion for the Hamiltonian of A symmetry class. We present Serret–Frenet equations for all model Hamiltonians in R 3 space. To the best of our knowledge, this is the first application of curvature theory to the model Hamiltonian of different symmetry classes which belong to the topological state of matter. [ABSTRACT FROM AUTHOR]

Finding the geodesic path defined as the shortest paths between two points on three-dimensional surface P is a well known problem in differential and computational geometry. Surfaces are not differentiable in a discrete way, hence known geometry algorithms can’t be used directly - they have to be discretized first. Classic algorithms for geodesic distance calculation such as Mitchell-Mount-Papadimitriou method (MMP) are precise but slow. Therefore modern solutions are developed for fast calculations. One of them is Heat Method which approximates such paths with some accuracy. In this paper we propose the extension of Heat Method to reduce the approximation error. A new formula for calculating value of the parameter t (wave propagation time step) which outperforms the original one in terms of mean and median error is presented. Also, correlation between mesh properties and best wave propagation time step as well as influence of variable node spacing on heat map based method were thoroughly analysed.

We review the geometric evolution of a linearly polarized light wave coupling into an optical fiber and the rotation of the polarization plane in De-Sitter 2-space. The optical fiber is assumed to be a one-dimensional object imbedded in the De-Sitter 2-space S 1 2 along with the paper. Mathematically, De-Sitter 2-space S 1 2 is described to be a 2-sphere in a Lorentzian space with positive curvature. Thus, in the De-Sitter 2-space, we have demonstrated that the evolution of a linearly polarized light wave is associated with the Berry phase or more commonly known as the geometric phase. The ordinary condition for parallel transportation is defined by the Fermi–Walker parallelism law. We define other Fermi–Walker parallel transportation laws and connect them with the famous Rytov parallel transportation law for an electric field E , which is considered as the direction of the state of the linearly polarized light wave traveling through the optical fiber in De-Sitter 2-space. Later, we have defined a special class of magnetic curves called by Lorentzian spherical electromagnetic curves (LSEM curves), which are generated by the electric field E along with the linearly polarized monochromatic light wave propagating in the optical fiber. In this way, not only we are able to define a special class of linearly polarized point particles corresponding to LSEM -curves of the electromagnetic field along with the optical fiber in the De-Sitter 2-space, but we can also calculate, both numerically and analytically, the electromagnetic force, Poynting vector, energy-exchanges rate, optical angular and linear momentum, and optical magnetic torque experienced by the linearly polarizable point particles along with the optical fiber in the De-Sitter 2-space. [ABSTRACT FROM AUTHOR]

In this work, we first present the theory of Heisenberg ferromagnetic model of directional velocity magnetic flows of particles with the help of the quasi-frame in ordinary space. Afterward, we give new integrability conditions of directional velocity magnetic flows by using quasi-frame fields. Additionally, we derive the total phase for quasi-vector fields. Finally, we obtain new constructions for quasi-curvatures of directional velocity magnetic flows by Heisenberg ferromagnetic model. [ABSTRACT FROM AUTHOR]

The behavior of solution trajectories usually changes if we replace the classical derivative in a system with a fractional one. In this article, we throw light on the relation between two trajectories X(t) and Y(t) of such a system, where the initial point Y(0) is at some point X (t 1) of the trajectory X(t). In contrast with classical systems, these trajectories X and Y do not follow the same path. Further, we provide a Frenet apparatus for both trajectories in various cases and discuss their effect. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G3. We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces using Frenet frame in Galilean space. Also, for the sake of visualizing of this study, we plot an example for this surfaces family.

We consider a loop of a chain thrown like a lasso on a fixed right circular cone. The system is in the standard homogeneous gravity field. The axis of the cone is vertical. It is shown that under certain vertex angles chain’s loop has an oblique equilibrium.

We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Lie symmetries of the (1 + 1)-dimensional celebrated Toda lattice and the (2 + 1)-dimensional modified semidiscrete Toda lattice by using the extended Harrison and Estabrook's geometric approach. Two closed ideals written in terms of a set of differential forms are constructed for Toda lattices. Moreover, commutation relations of a Kac–Moody–Virasoro type Lie algebra are obtained by direct computation. [ABSTRACT FROM AUTHOR]

We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra . Such a derivation, introduced by Brešar in 1991, is given by a linear mapping such that there exists a usual derivation, d, of satisfying the generalized Leibniz rule u( ab) = u( a) b + ad( b) for all . The generalized geometry 'is tested' in the case of the algebra of smooth functions on a manifold. We then apply this machinery to study generalized general relativity. We define the Einstein-Hilbert action and deduce from it Einstein's field equations. We show that for a special class of metrics containing, besides the usual metric components, only one nonzero term, the action reduces to the O'Hanlon action that is the Brans-Dicke action with potential and with the parameter ω equal to zero. We also show that the generalized Einstein equations (with zero energy-stress tensor) are equivalent to those of the Kaluza-Klein theory satisfying a 'modified cylinder condition' and having a noncompact extra dimension. This opens a possibility to consider Kaluza-Klein models with a noncompact extra dimension that remains invisible for a macroscopic observer. In our approach, this extra dimension is not an additional physical space-time dimension but appears because of the generalization of the derivation concept. [ABSTRACT FROM AUTHOR]

In this paper, we complement the analysis involving the 'fundamental' solutions of the Klein-Gordon equation in de Sitter space-times given by Yagdjian and A. Galstian ( Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Using the symmetry generators, we classify and reduce the underlying equations and show how this process may lead to exact solutions by quadratures. [ABSTRACT FROM AUTHOR]

We review the general theory of the Jacobi last multipliers in geometric terms and then apply the theory to different problems in integrability and the inverse problem for one-dimensional mechanical systems. Within this unified framework, we derive the explicit form of a Lagrangian obtained by several authors for a given dynamical system in terms of known constants of the motion via a Jacobi multiplier for both autonomous and nonautonomous systems, and some examples are used to illustrate the general theory. Finally, some geometric results on Jacobi multipliers and their use in the study of Hojman symmetry are given. [ABSTRACT FROM AUTHOR]

The present work extends the application of a modified Ricci flow equation to an asymptotically nonflat space, namely, Marder's cylindrially symmetric space. It is found that the flow equation has a solution at least in a particular case. [ABSTRACT FROM AUTHOR]