Conformally symmetric wormhole solutions supported by non-commutative geometry in f(Q,T)gravity

This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.

Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part II. A New Geometric Theory of Phyllotaxis (Bodnar’s Geometry)

This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.

The He–McKellar–Wilkens effect for spin-1 particles on non-commutative space

By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.

An Effective Non-Commutative Encryption Approach with Optimized Genetic Algorithm for Ensuring Data Protection in Cloud Computing

Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storage and access,our proposed work designs a Novel Quantum Key Distribution(QKD)relying upon a non-commutative encryption framework.It makes use of a Novel Quantum Key Distribution approach,which guarantees high level secured data transmission.Along with this,a shared secret is generated using Diffie Hellman(DH)to certify secured key generation at reduced time complexity.Moreover,a non-commutative approach is used,which effectively allows the users to store and access the encrypted data into the cloud server.Also,to prevent data loss or corruption caused by the insiders in the cloud,Optimized Genetic Algorithm(OGA)is utilized,which effectively recovers the data and retrieve it if the missed data without loss.It is then followed with the decryption process as if requested by the user.Thus our proposed framework ensures authentication and paves way for secure data access,with enhanced performance and reduced complexities experienced with the prior works.

Non-commutative Chiral QCD2 Model

The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains aterm corresponding to a Wess-Zumino-Witten-like term.

Fractal Geometry:Axioms,Fractal Derivative and Its Geometrical Meaning

Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.

Non-Commutative Fock-Darwin System and Magnetic Field Limits

A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of ω/ωe and certain algebra realization （SU（2）and SU（1,1））, and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.

Non-commutative Fock-Darwin system and its magnetism properties

The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further, we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures, the occurrence of the magnetization in a zero magnetic field and zero temperature limit, and so on.

Ideal-based Zero-divisor Graphs of Non-commutative Rings

This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings,denoted ΓI（R）.ΓI（R） is a directed graph.The properties and possible structures of the graph is studied.

Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space

For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.

Investigation of pore geometry influence on fluid flow in heterogeneous porous media:A pore-scale study

Brazilian pre-salt reservoirs are renowned for their intricate pore networks and vuggy nature,posing significant challenges in modeling and simulating fluid flow within these carbonate reservoirs.Despite possessing excellent petrophysical properties,such as high porosity and permeability,these reservoirs typically exhibit a notably low recovery factor,sometimes falling below 10%.Previous research has indicated that various enhanced oil recovery(EOR)methods,such as water alternating gas(WAG),can substantially augment the recovery factor in pre-salt reservoirs,resulting in improvements of up to 20%.Nevertheless,the fluid flow mechanism within Brazilian carbonate reservoirs,characterized by complex pore geometry,remains unclear.Our study examines the behavior of fluid flow in a similar heterogeneous porous material,utilizing a plug sample obtained from a vugular segment of a Brazilian stromatolite outcrop,known to share analogies with certain pre-salt reservoirs.We conducted single-phase and multi-phase core flooding experiments,complemented by medical-CT scanning,to generate flow streamlines and evaluate the efficiency of water flooding.Subsequently,micro-CT scanning of the core sample was performed,and two cross-sections from horizontal and vertical plates were constructed.These cross-sections were then employed as geometries in a numerical simulator,enabling us to investigate the impact of pore geometry on fluid flow.Analysis of the pore-scale modeling and experimental data unveiled that the presence of dead-end pores and vugs results in a significant portion of the fluid remaining stagnant within these regions.Consequently,the injected fluid exhibits channeling-like behavior,leading to rapid breakthrough and low areal swept efficiency.Additionally,the numerical simulation results demonstrated that,irrespective of the size of the dead-end regions,the pressure variation within the dead-end vugs and pores is negligible.Despite the stromatolite's favorable petrophysical properties,including relatively high porosity and permeability,as well as the presence of interconnected large vugs,the recovery factor during water flooding remained low due to early breakthrough.These findings align with field data obtained from pre-salt reservoirs,providing an explanation for the observed low recovery factor during water flooding in such reservoirs.

Geometrical Modeling of Crystal Structures with Use of Space of Elliptic Riemannian Geometry

The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.

Motion of a Nonrelativistic Quantum Particle in Non-commutative Phase Space

The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.

Continuity Equation in Presence of a Non-Local Potential in Non-Commutative Phase-Space

We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.

Solution of Dirac Equation with the Time-Dependent Linear Potential in Non-Commutative Phase Space

In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.

Theoretical model of current propagation in a helical coil with varying geometry and screen tube

An analytical model of current propagation in a helical coil with varying geometry is developed.It can be used for post-acceleration and post-focusing of ions produced via laser-driven target normal sheath acceleration and generation of electromagnetic pulses.We calculate the current that propagates in a helical coil and suggest a method for improving its dispersion properties using a screening tube and with pitch and radius variation.The electromagnetic fields calculated with the analytical model are in agreement with particle-in-cell simulations.The model provides insights into the physics of current propagation in helical coils with varying geometries and enables a numerical implementation for rapid proton spectrum computations,which facilitate the design of such coils for future experiments.

A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry With Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters,which lowers the cost of the array feeding network due to the utilization of radio frequency(RF)switches.The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems.This work proposes the generalized array factor(AF)for the hexagonal antenna array geometry based on time modulation.The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation,giving more flexibility over time.Furthermore,a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level(SLL).The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array(TMHA),time-modulated concentric hexagonal array(TMCHA),time-modulated hexagonal cylindrical array(TMHCA),and time-modulated hexagonal concentric cylindrical array(TMHCCA).The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization(CSO)approach.

A photogrammetric approach for quantifying the evolution of rock joint void geometry under varying contact states

Accurate measurement of the evolution of rock joint void geometry is essential for comprehending the distribution characteristics of asperities responsible for shear and seepage behaviors.However,existing techniques often require specialized equipment and skilled operators,posing practical challenges.In this study,a cost-effective photogrammetric approach is proposed.Particularly,local coordinate systems are established to facilitate the alignment and precise quantification of the relative position between two halves of a rock joint.Push/pull tests are conducted on rock joints with varying roughness levels to induce different contact states.A high-precision laser scanner serves as a benchmark for evaluating the photogrammetry method.Despite certain deviations exist,the measured evolution of void geometry is generally consistent with the qualitative findings of previous studies.The photogrammetric measurements yield comparable accuracy to laser scanning,with maximum errors of 13.2%for aperture and 14.4%for void volume.Most joint matching coefficient(JMC)measurement errors are below 20%.Larger measurement errors occur primarily in highly mismatched rock joints with JMC values below 0.2,but even in cases where measurement errors exceed 80%,the maximum JMC error is only 0.0434.Thus,the proposed photogrammetric approach holds promise for widespread application in void geometry measurements in rock joints.

CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY

This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

Optimal AP Deployment in Cell-Free Massive MIMO Systems with LoS/NLoS Transmissions:A Stochastic Geometry Approach

Cell-free massive multiple-input multipleoutput(MIMO)is a promising technology for future wireless communications,where a large number of distributed access points(APs)simultaneously serve all users over the same time-frequency resources.Since users and APs may locate close to each other,the line-of-sight(Lo S)transmission occurs more frequently in cell-free massive MIMO systems.Hence,in this paper,we investigate the cell-free massive MIMO system with Lo S and non-line-of-sight(NLo S)transmissions,where APs and users are both distributed according to Poisson point process.Using tools from stochastic geometry,we derive a tight lower bound for the user downlink achievable rate and we further obtain the energy efficiency(EE)by considering the power consumption on downlink payload transmissions and circuitry dissipation.Based on the analysis,the optimal AP density and AP antenna number that maximize the EE are obtained.It is found that compared with the previous work that only considers NLo S transmissions,the actual optimal AP density should be much smaller,and the maximized EE is actually much higher.