Energy Density Equation Research Articles

Symmetric teleparallel gravity with variable deceleration parameter

In this paper, our investigation focuses on the cosmic history in modified [Formula: see text] gravity, a different theory that describes the gravitational force using a non-metricity scalar. The equations of the theory are solved by assuming a parametric form for the deceleration parameter. The parameters of the model are estimated by using the Cosmic Chronometer dataset. A number of parameters, like the deceleration parameter, whose signature changes with redshift and shows typical behavior in late-time cosmology, are subject of our analysis. We also show the evolution of other parameters, such as the equation of state parameter and energy density. The parametrization approach used here in [Formula: see text] modified gravity provides a better description of the late-time cosmic evolution without dark energy.

Constraining the parameters of generalized and viscous modified Chaplygin gas and black hole accretion in Einstein-Aether gravity

In this paper, we investigate the phenomenon of the accelerated cosmic expansion in the late universe and the mass accretion process for a four-dimensional Einstein-Aether black hole. Starting with the basics of Einstein-Aether gravity theory, we first consider the field equations and two well-known models of Chaplygin gas, i.e., the generalized cosmic Chaplygin gas model and viscous modified Chaplygin gas model. We then obtain the energy density and Hubble parameter equations for these models in terms of various dimensionless density parameters and some unknown parameters. After finding the required parameters, we proceed with the mass accretion process. For both models, we obtain the equation of mass in terms of the redshift function and graphically represent the change in the mass of the black hole with a redshift. At the same time, we perform a graphical comparison between these models and the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model of the universe. Finally, we conclude that the mass of a four-dimensional black hole will increase along the evolution of the universe within the framework of Einstein-Aether gravity.

Barrow holographic dark energy models in Lyra and general relativity theories

This study investigates the Barrow holographic dark energy (BHDE) matter distribution in the Bianchi I universe model in Lyra and General Relativity Theories. To this end, it obtains exact solutions by Hubble parameter, conservation equation, and BHDE energy density equation and supports them with graphics. The results show that the solutions are in harmony with the functioning of the universe and the nature of dark energy. It finally discusses the need for further research.

Constrained Wave-telescope Technique

Constrained Wave-telescope Technique

Revisiting the dynamics of interacting vector-like dark energy

We revise the dynamics of interacting vector-like dark energy, a theoretical framework proposed to explain the accelerated expansion of the universe. By investigating the interaction between vector-like dark energy and dark matter, we analyze its effects on the cosmic expansion history and the thermodynamics of the accelerating universe. Our results demonstrate that the presence of interaction significantly influences the evolution of vector-like dark energy, leading to distinct features in its equation of state and energy density. We compare our findings with observational data and highlight the importance of considering interactions in future cosmological studies.

New gravastar model in generalised cylindrically symmetric space–time and prediction of mass limit

We present a class of new Gravastar solutions following the works of Mazur and Mottola for a Gravitational Bose–Einstein Condensate (GBEC) star in generalised cylindrically symmetric space–time. A stable gravastar consists of 3 distinct regions, namely: (i) an interior de-Sitter space (p=−ρ), which exerts an outwards repulsive force at all points on the thin shell, (ii) an intermediate thin shell with a slice of finite length separating the interior and exterior regions is supposed to be consisting of an ultra-relativistic stiff fluid, with the equation of state p=ρ and (iii) an exterior vacuum region. This thin shell, which is considered as the critical surface for the quantum phase transition, replaces both the classical de-Sitter space and Schwarzschild event horizon. The new solutions are free from any singularities. The energy density, total energy, proper length, and the entropy of this shell are explored in this model. From the thin shell solution and using Lanczos equations for stress energy density, we have predicted the mass contained into the gravastar shell. The stability of the gravastar model is analysed through the consideration of gravitational surface redshift and entropy calculation. We have also obtained a constraint on the possible mass of the thin shell without violating the condition for stable gravastar configuration. All these features indicate that the present model is physically viable.

Application Design of Newton-Rapshon method in Proving Maximum Wavelength on Wien’s Displacement Law

The Calculation of the maximum wavelength (?m) of radiation emitted by a black body can be determined from the Wien displacement law, which states the ratio between the Wien constant and the absolute temperature (T). Wien's displacement law can be derived analytically from the Energy Density equation (U?) in Plank's law. The solution for U? is obtained by calculating the first derivative of the function with respect to ? or dU?/d?, and then proceeding with finding a solution to the equation for the derivative. The solution of dU?/d? is the value of ? that makes dU?/d? equal to zero. The resulting wavelength is the maximum wavelength ?m, which is the wavelength value that makes the value in the equation U? the maximum value. The final result of this calculation is the Wien’s displacement law, namely the multiplication of ?m with T equals the Wien constant. So basically, the derivation of Wien's displacement law is to find the maximum value of the function f(x). The maximum value of the function f(x) can be done numerically. Solving numerically can be done with the Modified Newton-Rapshon method. The modified Newton-Rapshon method is usually implemented in the form of computer program code. In this research, the results of the calculation of the maximum wavelength ?m analytically are very close to the results of numerical calculations (modified NR). This can be seen from the results of linear regression with gradient values (m), regression constants (c) and coefficient of determination (R2) close to the ideal values of 1, 0 and 1, respectively.

Process window prediction in stainless steel selective laser melting using various energy densities: laser power, scan speed, and defocusing distance

Abstract The process window of selective laser melting (SLM), a set of optimum process parameters, is crucial for producing defect-free components with excellent mechanical properties. This study aims to predict the optimum process window for SLM of stainless steel by varying the defocusing distance (f) which changes the laser beam diameter (d) and using laser power (P) and scan speed (V) as process parameters. The process window was predicted using empirical formulae related to the energy density equations, instead of the conventional approach based on simple experimental results. To predict the process window, we analyzed the melt pool geometry of components with different features, such as depth (D), width (W), layer thickness (t), and hatch distance (h). Using the energy density equation, we correlated the effect of these process variables on the melt pool geometry and derived empirical equations. The upper limit of the process window (D/W) was strongly correlated with local applied energy and expressed as P ≤ 34Vd2. The lower limits, D/t and W/h, showed good correlation with linear energy density and laser energy density, respectively, and expressed as P > 2.16Vd and P < 0.13V. Finally, we used these empirical equations to predict the process window, which was experimentally verified.

Effect of orbital angular momentum on dust-ion-acoustic waves in a superthermal plasma

Laser or electromagnetic radiation, in general, interacts with plasma in very interesting ways. In most cases, they induce orbital angular momentum (OAM) in such plasmas due to their polarization effects. Dust-ion-acoustic waves (DIAWs) with immovable dust particles are studied with the effect of rotation produced due to laser or electromagnetic interaction. The electrons are considered in the non-Maxwellian limit, with inertial ions and static dust grains possessing negative charges. Fluid theory is employed for obtaining the linear paraxial equation with regard to ion density perturbations. The fundamental Gaussian and Laguerre Gaussian (LG) beam solutions are talked over with the later being proved to be the source for OAM. By calculating the electrostatic potential for such linear waves, the components of the electric field with respect to the LG potential are shown. Finally, the energy density equation is used to calculate the OAM associated with DIAWs. The Laguerre Gauss mode is numerically shown to have greatly changed by varying the values of relevant plasma parameters, such as the electron superthermality parameter, radial and angular mode numbers, beam waist, and azimuthal angle. The present results may be useful in apprehending dust-ion-acoustic wave excitation due to Brillouin backscattering phenomenon of laser light interacting with plasma.

Energy Flow Analysis Model of High-Frequency Vibration Response for Plates with Free Layer Damping Treatment

The energy flow analysis (EFA) model is developed for predicting the vibrational response of plates with free layer damping (FLD) treatment under high-frequency excitation. For the plate with fully free layer damping (FFLD) treatment, the energy density equation of the laminated plate with high damping is deduced by combining the equivalent complex stiffness method with the EFA theory. For the plate with partially free layer damping (PFLD) treatment, the relationship between energy density and energy intensity is obtained based on the wave theory of coupled plate by analyzing the energy transfer relationship at the damping boundary. The high-frequency energy density response of the structure with FLD treatment is solved through the energy finite element analysis (EFEA) method. To verify the developed EFEA model, several numerical analyses are performed for the plate with FFLD and PFLD treatments. The numerical results demonstrate that the obtained EFEA solutions consistently converge to the time-averaged modal analytical solutions at various analysis frequencies. Finally, the influences of the loss factor and the thickness of the damping layer on the resulting energy density are investigated in detail.

Noether symmetries of tachyonic teleparallel cosmology with boundary term

The nature of dark energy is an important issue studied in the field of cosmology. Currently, several models have been presented to describe the acceleration dynamics of the world. One of the models that adequately explains the acceleration of the universe is the tachyonic scalar model, which has been considered for the first time in string theories and retains appealing cosmological aspects. We are interested to examine tachyonic fields in the teleparallel gravity with a boundary term. We initially consider the background equations of the proposed model and conclude that the accelerated expansion can be adequately explained, so the tachyonic field remains a suitable candidate for dark energy. We applied the Noether symmetry approach to select unknown functions such as potential [Formula: see text] and coupling coefficients [Formula: see text] and [Formula: see text], and in addition to accurately determining these functions, we were capable to obtain the conserved quantity is called the Noether charge. Next, according to these possible solutions, we solved the background equations numerically and typically obtained the parameters of Hubble, equation of state, energy density and deceleration parameter. We compared the model parameters with the observational data and concluded that our model could be well consistent with the observations in the coupling coefficient range of [Formula: see text].

Vibration analysis of wedge beam with variable thickness based on energy finite element method

The variable thickness beam structure is widely used in various engineering structures due to its superior mechanical properties. However, the problem of high-frequency vibration is also quite obvious. Energy Finite Element Analysis (EFEA) is very effective for high frequency vibration response analysis. In order to apply the energy finite element analysis to accurately predict the high-frequency vibration response of a wedge beam structure with variable thickness, in this paper, the energy flow model of wedge beam with variable thickness is established. Firstly, the governing equation of energy density of wedge beam with variable thickness is derived by geometric acoustic approximation method, and the energy finite element matrix equation of the obtained governing equation of energy density is obtained by Galerkin variational method. The energy transfer characteristics of the structure coupled with the uniform beam at the coupling boundary are studied. Based on the energy transfer coefficient, the energy transfer relationship at the coupling boundary is established, and the overall finite element equation of the coupled beam structure is further obtained. The established analysis model can be used to analyze and predict the energy density of the wedge beam structure and the structure coupled with uniform beam.

Interaction of divergence-free deceleration parameter in Weyl-type f(Q,T) gravity

We study an extension of symmetric teleparallel gravity i.e. Weyl-type f(Q,T) gravity and the divergence-free parametrization of the deceleration parameter q(z)=q0+q1z(1+z)1+z2 (q0 and q1 are free constants) to explore the evolution of the universe. By considering the above parametric form of q, we derive the Hubble solution and further impose it in the Friedmann equations of Weyl-type f(Q,T) gravity. To see whether this model can challenge the ΛCDM limits, we computed the constraints on the model parameters using the Bayesian analysis for the Observational Hubble data (OHD) and the Pantheon sample (SNeIa). Furthermore, the deceleration parameter depicts the accelerating behavior of the universe with the present value q0 and the transition redshift zt (at which the expansion transits from deceleration to acceleration) with 1−σ and 2−σ confidence level. We also examine the evolution of the energy density, pressure, and effective equation of state parameters. Finally, we demonstrate that the divergence-free parametric form of the deceleration parameter is consistent with the Weyl-type f(Q,T) gravity.

Anisotropic expansion, dissipative hydrodynamics from kinetic theory

In this paper, we consider Kasner space-time describing anisotropic three-dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative solution of relativistic Boltzmann equation with relaxation time approximation. We show that our results for second- and third-order evolution equations reduce to those of one-dimensional expansion case under suitable conditions for the anisotropic parameters in Kasner space-time.

Frequency dependencies of the characteristics of an inductively coupled radiofrequency discharge at reduced pressure

The dependence of parameters of an inductively coupled radiofrequency plasma on the electromagnetic field frequency in range 0.25–40 MHz at reduced pressure (113 Pa) was studied. The study was carried out in a 2D axisymmetric time-dependent setting, implemented in the Comsol multiphysics software package using the Navier–Stokes equations, continuity equation for electron density, electron energy density equation, ion density equation, metastable atom density equation, heat transfer equation, Maxwell and Poisson equations for electromagnetic fields. The distributions of the plasma parameters at the output of the discharge tube in dependence on electromagnetic field frequency were obtained. It was found that the dependences of the electron density, electron temperature, and gas temperature on the field frequency are non-linear. The maximum value of these quantities were achieved at different frequencies depending on the discharge power. A mechanism relating the frequency and power to the shift in the positions of the maxima of these plasma parameters is proposed.

Physics and Modeling of Multidomain FeFET With Domain Wall-Induced Negative Capacitance

In this article, we present the dynamics and modeling of multidomains in the ferroelectric FET (FeFET). Due to the periodic texture of domains, the electrostatics of the FeFET exhibit an oscillatory conduction band profile. To capture such oscillations, we solve coupled 2-D Poisson’s equation with the net ferroelectric energy density (gradient energy + free energy + depolarization energy) equation. Multidomain dynamics are captured by minimizing the net ferroelectric energy, leading to a thermodynamically stable state. Furthermore, we show that the motion of domain walls originates from local bound charge density in the ferroelectric region, which induces the negative capacitance (NC) effect. The strength of domain wall-induced NC is determined by the gradient energy of the ferroelectric material. FeFET exhibits variability in the drain current with domain period due to the inherent NC effect. Additionally, the impact of domain wall transition (soft <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightleftharpoons $ </tex-math></inline-formula> hard) on the device’s electrostatic/transport is also analyzed. The model also accurately captures both nucleations of a new domain and the motion of the domain wall. Furthermore, the model is thoroughly validated against experimental results and phase-field simulations.

Experimental and simulated investigation of microdischarge characteristics in a pin-to-pin dielectric barrier discharge (DBD) reactor

Both experimental and simulated studies of microdischarge (MD) are carried out in a dielectric barrier discharge with a pin-to-pin gap of 3.5 mm, ignited by a sinusoidal voltage with a peak voltage of 10 kV and a driving frequency of 5 kHz. Statistical results have shown that the probability of the single current pulse in the positive half-period (HP) reaches 73.6% under these conditions. Experimental results show that great luminous intensity is concentrated on the dielectric surface and the tip of the metal electrode. A 1D plasma fluid model is implemented by coupling the species continuity equations, electron energy density equations, Poisson equation, and Helmholtz equations to analyze the MD dynamics on the microscale. The simulated results are in good qualitative agreement with the experimental results. The simulated results show that the MD dynamics can be divided into three phases: the Townsend phase, the streamer propagation phase, and the discharge decay phase. During the streamer propagation phase, the electric field and electron density increase with the streamer propagation from the anode to the cathode, and their maximal values reach 625.48 Td and 2.31 × 1019 m−3, as well as 790.13 Td and 3.58 × 1019 m−3 in the positive and negative HP, respectively. Furthermore, a transient glow-like discharge is detected around the anode during the same period of streamer propagation. The formation of transient glow-like discharge is attributed to electrons drifting back to the anode, which is driven by the residual voltage in the air gap.

Evolution equations dynamical system of the Lemaître–Tolman–Bondi metric containing coupled dark energy

In this paper, we consider inhomogeneous spherically symmetric models based on the Lemaître–Tolman–Bondi (LTB) metric, assuming as its source an interactive mixture of ordinary baryonic matter, cold dark matter and dark energy with a coupling term proportional to the addition of energy densities of both dark fluids. We reduce Einstein’s field equations to a first-order seven-dimensional autonomous dynamical system of evolution equations and algebraic constraints. We study in detail the evolution of the energy density and spatial curvature profiles along the phase–space by means of two subspace projections: a three-dimensional projection associated with the solutions of the Friedman–Lemaître–Robertson–Walker metric (invariant subspace) and a four-dimensional projection describing the evolution of the inhomogeneous fluctuations. We also classify and study the critical points of the system in comparison with previous work on similar sources, as well as solving numerically the equations for initial energy density and curvature profiles that lead to a spherical bounce whose collapsing time we estimate appropriately.

Effect of a modified energy density equation to achieve a more uniform energy input during LPBF for improved repeatability

The main priority for additive manufacturing research must be an improvement in process repeatability and reproducibility. This paper proposes a modified energy density equation as a basis for location dependent control of process parameters. This equation was used to adapt the process parameters in laser powder bed fusion of cobalt chrome alloy to achieve a more uniform energy density input across the build. Using this modified equation, the standard deviation of the mechanical properties was reduced by 40%. This improvement in consistency was verified using additional testing using 316L. The reduction in the variation in local mechanical property values was verified to be statistically significant.

Agegraphic dark energy cosmology and Quantum loop-correction

In this paper, we extend the agegraphic dark energy model through quantum loop-correction on Einstein–Hilbert action. We investigate the evolution of the equation of state and energy density of proposed agegraphic dark energy for non-interaction and interaction scenarios. Also, the deceleration parameter and square of sound speed of both scenarios are studied and we have shown model is stable classically only for the interaction case. Moreover, considering the interaction scenario shows for the very early universe, this new agegraphic dark energy may treat such as inflation field.