Symmetric Conditions Research Articles

Predicting spatial curvature ΩK in globally CPT -symmetric universes

Boyle and Turok’s CPT-symmetric universe model posits that the Universe was symmetric at the big bang, addressing numerous problems in both cosmology and the Standard Model of particle physics. We extend this model by incorporating the symmetric conditions at the end of the Universe, which impose constraints on the allowed perturbation modes. These constrained modes conflict with the integer wave vectors required by the global spatial geometry in a closed universe. To resolve this conflict, only specific values of curvature are permissible, and in particular the curvature density is constrained to be ΩK∈{−0.016,−0.011,−0.004,…}, consistent with observations. Published by the American Physical Society 2024

Effect of an Applied Magnetic Field on Joule Heating-Induced Thermal Convection

Thermal convection induced by internal heating appears in different natural situations and technological applications with different internal sources of heat (e.g., radiation, electric or magnetic fields, chemical reactions). Thermal convection due to Joule heating in weak electrical conducting liquids such as molten salts with symmetric thermal boundary conditions is investigated using linear stability analysis. We show that, in the quasi-static approximation where the induced magnetic field is negligible, the effect of the external magnetic field consists of the delay in the threshold of thermal convection and the increase in the size of thermoconvective rolls for an intense magnetic field. Analysis of the budget of the perturbations’ kinetic energy reveals that the Lorentz force contributes to the dissipation of the kinetic energy.

Structural and electronic tuning of single-benzene fluorophores with simple methylations

Recent advancements in the development of low molecular-weight fluorophores have led to the study of a single-benzene fluorophore (SBF) containing both electron-withdrawing and electron-donating groups within an aromatic ring, resulting in unique photophysical properties. In this study, we explored the modulation of emissions by adjusting the electron-donating properties via the simple methylation of the 2,5-diamino or 2,5-dihydroxy terephthalate structure. Introducing additional functional groups under both symmetrical and unsymmetrical conditions demonstrated changes in the photophysical properties, which was not only owing to the structural variations in the location and number of methyl groups but also due to alterations in the electron-donating properties. The observed effects appeared to be owing to the interactions between the amine and ester groups, as confirmed via single-crystal X-ray diffraction. Finally, hydrolysis of the ester to the corresponding carboxylic acid resulted in various emission wavelengths at different pH values via protonation and deprotonation. This study provides valuable insights for predicting the structural and electronic effects of additional functional groups in SBF.

Technologies for Increasing the Control Efficiency of Small Spacecraft with Solar Panels by Taking into Account Temperature Shock

The problem of the effective control of a small spacecraft is very relevant for solving a number of target tasks. Such tasks include, for example, remote sensing of the Earth or the implementation of gravity-sensitive processes. Therefore, it is necessary to develop new technologies for controlling small spacecraft. These technologies must take into account a number of disturbing factors that have not been taken into account previously. Temperature shock is one such factor for small spacecraft with solar panels. Therefore, the goal of the work is to create a new technology for controlling a small spacecraft based on a mathematical model of the stressed/deformed state of a solar panel during a temperature shock. The main methods for solving the problem are mathematical methods for solving initial/boundary value problems, in particular, the initial/boundary value problem of the third kind. As a result, an approximate solution for the deformation of a solar panel during a temperature shock was obtained. This solution is more general than those obtained previously. In particular, it satisfies the symmetrical condition of the solar panel. This could not be achieved by the previous solutions. We also observe an improvement (as compared to the previous solutions) in the fulfillment of the boundary conditions for the whole duration of the temperature shock. Based on this, a new technology for controlling a small spacecraft was created and its effectiveness was demonstrated. Application of the developed technology will improve the performance of the target tasks such as remote sensing of the Earth or the implementation of gravity-sensitive processes.

Optimized hybrid osprey with PSO control for improved VSC-HVDC-wind power integration

Innovative power systems include offshore wind farms (OWFs) to generate electricity from renewable sources. So, reliable control systems are also necessary to make sure these power systems run smoothly. The purpose of this study is to combine the Osprey Optimization with Particle Swarm Optimization (OOPSO) to fine-tune the gains of Proportional-Integral (PI) controllers within the investigated wind energy conversion system (WECS) to enhance its performance. The study confirms the effectiveness of using the Hybrid OOPSO algorithm to optimize PI controllers in a WECS. The WECS includes two voltage source converter (VSC) stations at each end of a high voltage direct current (HVDC) transmission system. The transmission system links OWFs to the grid. The research demonstrates that the Hybrid OOPSO algorithm is superior to the genetic algorithm (GA) and PSO by enhancing setup stability and allowing fast voltage regaining following different fault cases. The introduced method performs more remarkably than traditional methods such as GA and PSO. The results of this study have shown that the proposed OOPSO enhances the overshoot in onshore voltage transient response under a symmetrical fault condition by 26% over PSO, 24% over GA, and 16% over OOA. The study is conducted using MATLAB/Simulink. The study underscores the importance of advanced optimization methods to guarantee offshore wind energy systems' efficient and dependable functioning.

Analysis of bolt load uniformity in raised flange connection

Aiming at the problem of uneven preload of raised flange, a model considering elastic interaction is established to study the uniformity of bolt load under raised flange connection. Firstly, the elastic interaction coefficient method of bolt flange connection structure is extended to multiple times, and the initial preload of all bolts at each tightening step is determined by analytical model; secondly, a three-dimensional finite element model of bolt flange connection structure is established, and the correctness of the finite element model is verified by comparing with the literature test, and the influence of tightening sequence and tightening steps on bolt preload is explored; finally, the results of raised flange under symmetrical tightening conditions with and without considering elastic interaction are compared and analyzed. The results show that when the tightening method is symmetrical tightening and the tightening steps are three steps, the elastic interaction of each bolt is the smallest, and the final preload uniformity is better; on this basis, the results of the model considering elastic interaction further improve the uniformity of the final preload and are closer to the target preload. The problem of bolt preload dispersion caused by elastic interaction is solved, and the research results can provide guidance for the safety and reliability design of bolt flange connection structure.

Flexural Behaviour and Environmental Impact of African Fan Palm Reinforced Concrete Beams under Symmetrical Loading Conditions

The paper presents the results of investigation on reinforced beams adopting eco-friendly materials for sustainable concrete. The use of African fan palm is explored to mitigate the environmental impact aimed at reducing carbon emissions associated with the production and use of steel reinforcement. The beams were tested under a four -point loading system with the ends simply supported. The test comprised twenty-three beams that were reinforced with African fan palm bars whilst two beams were reinforced with mild steel bars to serve as control beams. The study investigated the flexural strength and deformation characteristics of the beams under monotonic loading. Two concrete strengths of 15.34N/mm2 or 22.37N/mm2 were adopted and proposed optimal tensile ratios for an under reinforced fan palm section. The parameters considered included the tension bars ratio (ρ), concrete compressive strength, span-to-effective-depth ratio and loading conditions. A linear elastic behaviour of both fan palm and steel reinforced concrete beams was observed to the point of first crack load beyond which the beam stiffness continued to reduce until failure. A comparison of the experimental results with results of theoretical analysis of the beams revealed that a 1.22% increase in the tensile ratio of steel in the control beams increased the cracking moment (Mcr) to 36%, while the fan palm beam of the same size and same concrete strength with a higher tensile ratio of 9.69% exhibited a lower Mcr of 11.86%. This shows a significant effect of reinforcing steel bars on concrete cracking compared to the fan palm. The averages of experimental to theoretical failure loads of fan palm to steel were compared with failure loads of 36.52kN to 20.19kN and 32kN to 19.78kN respectively. These results of the study based on the failure mode, and failure loads, highlights the suitability of using African fan palm as substitute reinforcing material for low rise buildings. Furthermore, the study also proposed minimum and maximum tensile ratio of 0.76% and 5.60% respectively for fan palm reinforced concrete beams based on the Indian Standard and modulus of elasticity of steel.

Existence of Positive Solutions for Singular Difference Equations with Nonlinear Boundary Conditions

In this paper, we delve into a discrete nonlinear singular semipositone problem, characterized by a nonlinear boundary condition. The nonlinearity, given by f(u)−auα with α>0, exhibits a singularity at u=0 and tends towards −∞ as u approaches 0+. By constructing some suitable auxiliary problems, the difficulty that arises from the singularity and semipositone of nonlinearity and the lack of a maximum principle is overcome. Subsequently, employing the Krasnosel’skii fixed-point theorem, we determine the parameter range that ensures the existence of at least one positive solution and the emergence of at least two positive solutions. Furthermore, based on our existence results, one can obtain the symmetry of the solutions after adding some symmetric conditions on the given functions by using a standard argument.

Spontaneous asymmetry effect induced by uniform magnetic fields in capacitively coupled plasmas under perfectly symmetric conditions

Abstract Introducing asymmetry in capacitively coupled plasmas (CCPs) is a common strategy for achieving independent control of ion mean energy and flux. Our 1d3v particle-in-cell/Monte Carlo collision simulations reveal that a uniform magnetic field within a specific range can induce spatial asymmetry in low-pressure CCPs, even under perfectly symmetric conditions. This asymmetry, characterized by a shift in the plasma density distribution and significant differences in electron kinetics between the two sides of the plasma, leads to strong ionization and most electron losses on the low-density side, while the high-density side experiences weak ionization and minimal electron losses. The underlying mechanism triggering this spontaneous asymmetry is the differential influence of the magnetic field on low-energy (local) and high-energy (relatively nonlocal) electrons. Under conditions of low pressure and an appropriate magnetic field, this disparity in electron kinetic behavior leads to a spontaneous amplification of the asymmetry induced by random fluctuations until a steady state is reached, culminating in a spontaneous asymmetric effect.

Molecular dynamics study of the thermal radiatively pressure-driven flow of two immiscible hybrid nanofluids through a curved pipe with viscous dissipation

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. Therefore, the current article scrutinizes the characteristics of heat transfer on the thermally radiative flow of two immiscible hybrid nanofluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with base fluid kerosene oil containing copper (Cu) and carbon nanotube (CNT) nanoparticles, while (ii) Region 2 (peripheral) is filled with base fluid water containing zinc oxide (ZnO) and aluminum oxide (Al2O3) nanoparticles. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. The fluid in the core region is assumed to be more viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio, and density ratio on the axial velocity and temperature is studied through 2-dimensional graphs, contour plots, and streamlines. The results show that the axial velocity of immiscible fluids flow decreases with an increase in the concentration of nanomaterials. Heat transport characteristics of nanofluid are increased by the addition of nanomaterials.

Rheological impact of viscous fluid in the core region of heated curved pipe surrounded by Casson rheological fluid

The immiscible fluids can help design more efficient systems for drug delivery and understanding the blood flow through diseased arteries. It can also have implications for the design of flow control devices or medical implants that involve curved geometries. Therefore, the current article scrutinizes the characteristics of heat transfer on the flow of two immiscible Casson and Newtonian fluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with Newtonian fluid while (ii) Region 2 (peripheral) is filled with non-Newtonian Casson fluid. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Casson fluid parameter, Reynolds number, viscosity ratio, density ratio, Eckert number, and conductivity ratio on the axial velocity and temperature is studied through 2-dimensional graphs and contour plots. In addition, the volumetric flow rate and shear stress are also presented to evaluate the effects of various key parameters. The results show that the axial velocity of immiscible fluids flow increases with an increase in the values of the viscosity ratio parameter and the fluid temperature is decreased by increasing the conductivity ratio parameter.

An improved analytical solution on viscous dissipation effect in extended Stokes’ second problem in microchannel with isothermal boundaries

In this analytical study, the fluid motion within a microchannel is induced by the oscillation of one surface parallel to the other stationary surface, termed the extended Stokes’ problem. The novelty and research gap are acquiring the thermal effect of such motion due to the viscous dissipation or fluid friction, subject to symmetric isothermal boundary conditions. The study may shed light on the role of viscous dissipation in temperature rise in the synovial fluid of an artificial hip joint, or in the fluid layer of a mechanical bearing. The full exact analytical temperature field, until now, has been unsolved, as it involves unsteady flow with manipulation of a complicated velocity field. The assumptions in the model are one-dimensional, incompressible, laminar, Newtonian flow with constant properties in a microchannel. Through the methodology of partial differential equation analysis, the temperature field is obtained in terms of Brinkman number, Prandtl number and a dimensionless angular frequency, and results are verified with a reported numerical solution, for specified range of the variables. Results complement recent approximate solutions which are valid only for the limited condition of the dimensionless angular frequency being less than or equal to unity, whereby suggesting a new Stokes number.

On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem with Symmetric Boundary Conditions for One Nonlinear Fourth-Order Ordinary Differential Equation

On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem with Symmetric Boundary Conditions for One Nonlinear Fourth-Order Ordinary Differential Equation

Boundary condition and reflection anomaly in $2+1$ dimensions

It is known that the 2+12+1d single Majorana fermion theory has an anomaly of the reflection, which is canceled out when 16 copies of the theory are combined. Therefore, it is expected that the reflection symmetric boundary condition is impossible for one Majorana fermion, but possible for 16 Majorana fermions. In this paper, we consider a reflection symmetric boundary condition that varies at a single point, and find that there is a problem with one Majorana fermion. The problem is the absence of a corresponding outgoing wave to a specific incoming wave into the boundary, which leads to the non-conservation of the energy. For 16 Majorana fermions, it is possible to connect every incoming wave to an outgoing wave without breaking the reflection symmetry. In addition, we discuss the connection with the fermion-monopole scattering in 3+13+1 dimensions.

Perturbation of Dual Group Generalized Inverse and Group Inverse

Symmetry plays a crucial role in the study of dual matrices and dual matrix group inverses. This paper is mainly divided into two parts. We present the definition of the spectral norm of a dual real matrix A^, (which is usually represented in the form A^=A+εA0, A and A0 are, respectively, the standard part and the infinitesimal part of A^) and two matrix decompositions over dual rings. The group inverse has been extensively investigated and widely applied in the solution of singular linear systems and computations of various aspects of Markov chains. The forms of the dual group generalized inverse (DGGI for short) are given by using two matrix decompositions. The relationships among the range, the null space, and the DGGI of dual real matrices are also discussed under symmetric conditions. We use the above-mentioned facts to provide the symmetric expression of the perturbed dual real matrix and apply the dual spectral norm to discuss the perturbation of the DGGI. In the real field, we present the symmetric expression of the group inverse after the matrix perturbation under the rank condition. We also estimate the error between the group inverse and the DGGI with respect to the P-norm. Especially, we find that the error is the infinitesimal quantity of the square of a real number, which is small enough and not equal to 0.

Subconvexity of twisted Shintani zeta functions

Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version. The method demonstrated here has applications to the subconvexity of some of the twisted zeta functions introduced by F. Sato. The argument demonstrates that the symmetric space condition used by Sato is not necessary to estimate the zeta function in the critical strip.

A new approach to instantaneous power based control of DFIG using active disturbance rejection control

This paper presents the design and control of a wind energy converter system that uses a doubly fed induction generator. It introduces a model that incorporates instantaneous active and reactive power as state variables to represent both the stator and rotor sides of the doubly fed induction generator. Subsequently, a linear active disturbance rejection-based control regulator is proposed for the control loops. The parameters of the linear active disturbance rejection controllers (ADRC) are adjusted by two methods: the single parameter tuning approach and the genetic algorithm (GA) method. The performance of the suggested controller is ultimately compared with a tuned proportional-integral (PI) control regulator in the MATLAB environment. In order to examine the performance of the system, various test scenarios are taken into account. These scenarios include different percentages of load change in both sub-synchronous and super-synchronous modes of operation, faults with different fault periods are considered in both modes of operation. The conventional PI controller-based approach requires 35 control cycles to reach steady state under load change conditions and 50 control cycles under symmetrical fault conditions, regardless of whether the system is operating in sub synchronous or super synchronous mode. The single parameter-based tuned ADRC approach only requires 15 control cycles for load change and 20 control cycles for symmetrical fault scenarios. In contrast, for both the load change and symmetrical fault scenarios, the ADRC with GA-based parameter tuning reaches steady state in just 5 control cycles. Furthermore, a case involving wind speed variation is presented to demonstrate the maximum power point tracking capability of the proposed control structure. Similarly, for the robustness test of the control regulator, variations in resistance and inductance are introduced to observe their impact on the response of the control regulators. Finally, a real-time hardware in loop setup is presented to validate the control strategy during the load change in the sub-synchronous mode of operation of the doubly fed induction generator.

Dance of two brains: Interval subdivision in alternated condition enhances resistance to interference by others

The accomplishment of interpersonal sensorimotor synchronization is a challenging endeavor because it requires the achievement of a balance between accurate temporal control within individuals and smooth communication between them. This raises a critical question: How does the brain comprehend and process the perceptual information of others to guarantee accurate temporal control of action goals in a social context? A joint synchronization - continuation tapping task was conducted together with varying relative phases (0°/180°) and intervals of tempos (400 ms/800 ms/1600 ms) while neural data was collected using fNIRS (functional near-infrared spectroscopy). Individuals showed better behavioral performance and greater interpersonal brain synchronization(IBS) in the left dorsolateral prefrontal cortex at alternated condition (180° relative phase) compared to symmetric condition (0° relative phase), suggesting that the individual can better maintain behavioral performance and show improved IBS when the partner taps between the individual's gaps. Meanwhile, in most levels of alternated condition, IBS is inversely proportional to interference from partner, implying the counteraction of IBS against interference from others. In addition, when the interval of tempo was 1600 ms, behavioral performance showed a sharp decline, accompanied by a decrease in IBS, reflecting that IBS in SMS reflects effective information exchange between individuals rather than ineffective interference with each other. This study provides insight into the mechanisms underlying sensorimotor synchronization between individuals.

Theoretical study on sequential splitting of droplets flowing through fractal tree-shaped microchannel networks

A theoretical model for describing the sequential splitting of droplets flowing through the fractal tree-shaped microchannel network with arbitrary branch level is developed to explore the mechanisms underlying the hydraulic imbalance on the high-throughput droplets production. Accordingly, detailed droplet splitting characteristics are presented, including the droplet velocities in branches, droplet distribution coefficient, and monodispersity of droplets production. It is found that the uniformity of droplet mainly depends on two key dimensionless parameters, namely Λ1 and Λ2, where Λ1 is determined by the initial working condition involving the initial lengths and viscosity of the continuous and discrete phases, the width of the 0th level channel, and the initial capillary number, and Λ2 is concerned with the outlet pressure pout, [2n-1] and the pressure drops of the continuous and discrete phases at the 0th level channel. The monodispersity of droplets goes down with the decreasing Λ1 and the increasing Λ2. Based on the Λ1 and Λ2, the optimal design strategies contributing to enhancing the droplet generation uniformity are recommended, including increasing Ca, enlarging the length of continuous phase flow at the main channel, and increasing the lengths of each level channels. Furthermore, the tree-shaped microchannel networks with higher branch level (n) have stronger ability to resist asymmetric disturbances. In particular, in our work, the width fractal dimension Δ = 2 is adopted as a proper key structure parameter, so as to ensure sequential breakup of droplet at each T-junction under symmetric condition.

The swing of synchronization mediated by chimera states in fractional-order coupled Stuart-Landau oscillators

In this letter, we investigate the various dynamical behaviors in fractional-order coupled Stuart-Landau oscillator networks with the nonisochronicity parameter. We find that the nonisochronicity parameter can induce the swing of synchronization mediated by the imperfect synchronized state and the amplitude cluster state, and we verify the accuracy of the emergence of the swing of synchronization by the strength of incoherence and stability theory. Moreover, we discuss the effects of different parameters on the swing of synchronization mediated by the chimera state. First, as the nonisochronicity parameter increases, the range of the swing increases. Second, the decreasing of fractional-order derivative will lead to the reduction in the range of swing intervals. Third, the system exhibits the swing of synchronization mediated by the imperfect synchronized state when different initial conditions are employed. In particular, the system can show the imperfect breathing chimera state under symmetric initial conditions.