Values Of Free Parameters Research Articles

Traversable wormhole solutions utilizing the Karmarkar condition in f(R,G) gravity

The main objective of this paper is to reveal the evolving traversable wormhole solutions in the context of modified f(R,G) gravity, which affects the gravitational interaction. These results are derived by applying the Karmarkar condition, which creates wormhole geometry that meets the necessary conditions and connects two asymptotically flat areas of spacetime. The proposed study’s main goal is to construct the wormhole structures by splitting the f(R,G) gravity model into two forms Firstly, we split the model into an exponential-like f(R) gravity model and a power law f(G) gravity model, and secondly, we consider the Starobinsky f(R) gravity model along with a power law f(G) gravity model. Besides, we address the feasibility of shape functions and the structural analysis of wormhole structures for specific models. These models are then confined to be compatible with current experimental evidence. Further, the energy conditions of the wormhole are geometrically probed, and it is proven that they adhere to the null energy conditions in areas close to the throat. Moreover, the fascinating aspect of this study involves conducting an examination and comparison of evolving wormhole geometries in the vicinity of the throat in our chosen models, utilizing two- and three-dimensional graphical representations. We observe that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter, correlating to the proper choice of f(R,G) gravity models and acceptable free parameter values. In summary, we conclude that our findings meet all the criteria for the existence of wormholes, affirming the viability and consistency of our study.

Semi-analytic modelling of Pop. III star formation and metallicity evolution - I. Impact on the UV luminosity functions at z = 9 − 16

Abstract We implemented Population III (Pop. III) star formation in mini-halos within the meraxes semi-analytic galaxy formation and reionisation model, run on top of a N-body simulation with L = 10h−1 cMpc with 20483 particles resolving all dark matter halos down to the mini-halos (∼105M⊙). Our modelling includes the chemical evolution of the IGM, with metals released through supernova-driven bubbles that expand according to the Sedov-Taylor model. We found that SN-driven metal bubbles are generally small, with radii typically of 150 ckpc at z = 6. Hence, the majority of the first galaxies are likely enriched by their own star formation. However, as reionization progresses, the feedback effects from the UV background become more pronounced, leading to a halt in star formation in low-mass galaxies, after which external chemical enrichment becomes more relevant. We explore the sensitivity of the star formation rate density and stellar mass functions on the unknown values of free parameters. We also discuss the observability of Pop. III dominated systems with JWST, finding that the inclusion of Pop. III galaxies can have a significant effect on the total UV luminosity function at z = 12 − 16. Our results support the idea that the excess of bright galaxies detected with JWST might be explained by the presence of bright top-heavy Pop. III dominated galaxies without requiring an increased star formation efficiency.

New solutions to a generalized fifth-order KdV like equation with prime number [formula omitted] via a generalized bilinear differential operator

In this research, the generalized Hirota bilinear strategy (GHBS) by the number prime p=3 is applied. This strategy is advertised to explore for a kind of knot arrangement and three classes of interaction arrangements according to a unused combination of positive quadratic capacities, trigonometric capacities and hyperbolic capacities to the (2+1)-dimensional generalized fifth-order KdV (GFOKdV) like equation with applications within the quantum field hypothesis, feebly nonlinear dispersive water waves and nonlinear optics. By choosing arbitrarily the extraordinary values of free parameters, the lump arrangement, interaction wonders and single occasional wave arrangements are appeared distinctive designs. The detailed comes about might play an vital part within the quantum field hypothesis and nonlinear optics for clarifying the physical meaning of the examined demonstrate. he gotten comes about too illustrate that the GHBS is more competent than the other connected strategy connected by creators within the writing. Hence, it is appeared that the connected strategy gives a more capable scientific instrument for developing correct traveling wave arrangements for numerous other nonlinear advancement conditions emerges in scientific material science and nonlinear optics. All arrangements have been confirmed back into its comparing condition with the help of maple bundle program. We delineated the physical clarification of the extricated arrangements with the free choice of the diverse parameters by plotting a few 2D and 3D outlines.

Utilizing the extended tanh-function technique to scrutinize fractional order nonlinear partial differential equations

In a range of nonlinear fields, for example molecular biology, physics in plasma, quantum mechanics, elastic media, nonlinear optics, the surface of water waves, and others, many complicated nonlinear behaviors can be pronounced using nonlinear fractional partial differential equations. The nonlinear traveling waves, including nonlinear space-time fractional order differential equations such as the time fractional Sharma-Tasso-Olver (STO) and the space-time fractional Kowerteg-de Vries-Burgers (KdV-Burgers) equations, are analysis through a resourceful approach, namely the extended tanh-function by the definition of the conformable derivative. The stated equations are prevalently used in marine and coastal infrastructure, such as fluid flow, plasma engineering, fiber optics, fusion and fission phenomena, and so on. By renovating fractional order differential equations to ordinary differential equations, fractional order differential transformation simplifies the solution process. Several types of solutions, such as soliton types, bell types, kink types, and some other kinds of results, are developed and portrayed for definite values of free parameters that are plotted in terms of 3D, contour, and spherical shapes. The method is an algebraic approach that is both direct and efficient for dealing with nonlinear equations and yield a distinct category of solutions known as solitons. The suggested method is being used in this study to generate attractive, and effective results that are flexible, easy, and quicker to simulate using general mathematical techniques, namely Maple. It is worth declaring that all resultant solutions are verified for accuracy by exchanging them directly within the original equation through the software package and originating them accurately.MSC: 35C25, 35C07, 35C08, 35Q20, 76B25

Effect of massive graviton on dark energy star structure

The presence of massive gravitons in the field of massive gravity is considered an important factor in investigating the structure of compact objects. Hence, we are encouraged to study the dark energy star structure in the Vegh’s massive gravity. We consider that the equation of state governing the inner spacetime of the star is the extended Chaplygin gas, and then using this equation of state, we numerically solve the Tolman–Oppenheimer–Volkoff (TOV) equation in massive gravity. In the following, assuming different values of free parameters defined in massive gravity, we calculate the properties of dark energy stars such as radial pressure, transverse pressure, anisotropy parameter, and other characteristics. Then, after obtaining the maximum mass and its corresponding radius, we compute redshift and compactness. The obtained results show that for this model of dark energy star, the maximum mass and its corresponding radius depend on the massive gravity’s free parameters and anisotropy parameter. These results are consistent with the observational data and cover the lower mass gap. We also demonstrate that all energy conditions are satisfied for this model, and in the presence of anisotropy, the dark energy star is potentially unstable.

Новый подход к настройке гауссовой суррогатной модели целевой функции в задаче параметрической оптимизации проектных решений

The paper considers methods for solving the problem of design solution parametric optimization based on constructing the Gaussian surrogate model of this problem objective function. The problem is set of finding optimal values of the surrogate model free parameters (hyper-parameters), it is called the problem of its adjustment. The adjustment problem is built over the top of the surrogate model synthesis problem and has a higher computational complexity. The approach to adjusting a surrogate model is proposed, which is able to make the adjustment procedure acceptable in terms of the computational costs. This approach includes the setup and operation stages. The adjustment stage contains the following main steps: formation of a set of test objective functions; generation of a set of learning samples for each of them; determination of their characteristic features values for the generated samples; determination of the hyper-parameters optimal values for all considered test functions and learning samples; formation of a set of pairs, characteristic features of the sample--hyper-parameters optimal values; building on this basis a predictive model forecasting the hyper-parameters optimal values according to the learning sample characteristic features. For the initial problem at the operation stage, a learning sample was generated, its characteristic features were determined, and the hyper-parameters optimal values of the surrogate model were predicted. Based on the specified learning sample, the objective function surrogate model was synthesized. Using the surrogate model, the original optimization problem was solved, where the hyper-parameters predictive values were applied as the optimal values. The approach is able to provide an increase of up to 30 % in efficiency of the basic optimization algorithm

Toward machine-assisted tuning avoiding the underestimation of uncertainty in climate change projections.

Documenting the uncertainty of climate change projections is a fundamental objective of the inter-comparison exercises organized to feed into the Intergovernmental Panel on Climate Change (IPCC) reports. Usually, each modeling center contributes to these exercises with one or two configurations of its climate model, corresponding to a particular choice of "free parameter" values, resulting from a long and often tedious "model tuning" phase. How much uncertainty is omitted by this selection and how might readers of IPCC reports and users of climate projections be misled by its omission? We show here how recent machine learning approaches can transform the way climate model tuning is approached, opening the way to a simultaneous acceleration of model improvement and parametric uncertainty quantification. We show how an automatic selection of model configurations defined by different values of free parameters can produce different "warming worlds," all consistent with present-day observations of the climate system.

Investigation of traversable wormhole solutions in modified f(R) gravity with scalar potential

The objective of this manuscript is to investigate the traversable wormhole solutions in the background of the f(R, phi ) theory of gravity, where R is the Ricci scalar and phi is the scalar potential respectively. For this reason, we use the Karmarkar criterion for traversable static wormhole geometry to create a wormhole shape function. The suggested shape function creates wormhole geometry that links two asymptotically flat spacetime regions and meets the necessary requirements. The embedding diagram in three-dimensional Euclidean space is also discussed in order to demonstrate the wormhole configurations. For our current analysis, we choose the suitable values of free parameters for f(R, phi ) gravity models to discuss the wormhole geometry. It can be observed that our proposed shape function provides the wormhole solutions with less amount of exotic matter. It can be noticed that energy conditions especially null energy conditions are violated for all considered models. The violation of energy conditions indicates the existence of exotic matter and wormhole geometry. It is concluded that the shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter correlating to the chosen f(R, phi ) gravity models.

The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional

It is renowned that Hirota–Satsuma–Ito (HSI) equation is widely used to study wave dynamics of shallow water. In this work, two new HSI-like equations are investigated which could be extended to diversify problems in natural phenomena and give admirable contributions by applying the generalized exponential rational function method (GERFM). With the aid of symbolic calculations, various constraints on the free parameters are given, while classes of wave solutions are explicitly constructed from the coefficients of the combined non-linear and dissipative terms. After specifying values for free parameters, singular, periodic singular and anti-kink waves are demonstrated in 3D figures to exhibit different kinds of wave propagations. The fact that parameters directly influence the wave amplitude and speed of traveling waves is illustrated. The derived results are innovative and have important applications in the current field of mathematical physics research. Eventually, we show that generalized exponential rational function method is effective and straightforward to solve higher-order and high-dimensional non-linear evolution equations.

NOVEL TRAVELING-WAVE SOLUTIONS OF SPATIAL-TEMPORAL FRACTIONAL MODEL OF DYNAMICAL BENJAMIN–BONA–MAHONY SYSTEM

This paper investigates the dynamics of exact traveling-wave solutions for nonlinear spatial and temporal fractional partial differential equations with conformable order derivatives arising in nonlinear propagation waves of small amplitude including nonlinear fractional modified Benjamin–Bona–Mahony equation, fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation and fractional (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation as well. By utilizing the Sine-Gordon expansion method (SGEM), new real- and complex-valued exact traveling-wave solutions are reported by preferring suitable values of physical free parameters. The nonlinear governing equations are reduced into auxiliary nonlinear ordinary differential equations with aid of fractional traveling-wave transformation, in which the fractional derivative is evaluated in a conformable sense. The productivity process of the proposed method for predicting the desirable solutions is also provided. Some of the obtained solutions are simulated graphically in 3D and contour plots. Meanwhile, the effects of the fractional parameter [Formula: see text] in the space and the time direction are illustrated in 2D plots to ensure the novelty, applicability and credibility of the SGEM. These results reveal that the suggested method is general and adequate for dealing with nonlinear models featuring fractional derivatives and can be employed to analyze wide classes of complex phenomena of partial differential equations occurring in engineering and nonlinear dynamics.

Cubic first integrals of autonomous dynamical systems in E2 by an algorithmic approach

In a recent paper of Mitsopoulos and Tsamparlis [J. Geom. Phys. 170, 104383 (2021)], a general theorem is given, which provides an algorithmic method for the computation of first integrals (FIs) of autonomous dynamical systems in terms of the symmetries of the kinetic metric defined by the dynamical equations of the system. In the present work, we apply this theorem to compute the cubic FIs of autonomous conservative Newtonian dynamical systems with two degrees of freedom. We show that the known results on this topic, which have been obtained by means of various divertive methods, and the additional ones derived in this work can be obtained by the single algorithmic method provided by this theorem. The results are collected in Tables I–IV, which can be used as an updated reference for these types of integrable and superintegrable potentials. The results we find are for special values of free parameters; therefore, using the methods developed here, other researchers by a different suitable choice of the parameters will be able to find new integrable and superintegrable potentials.

Diverse solitary wave solutions of fractional order Hirota-Satsuma coupled KdV system using two expansion methods

The generalized Hirota-Satsuma coupled KdV system with fractional-order derivative plays a significant role to simulate the interaction of nearby identical-weight particles in a crystal lattice structure, two long waves interaction with different dispersion relationships, the description of shallow-water wave propagation, ion-acoustic waves, plasma physics and some other fields. In this study, diverse analytical wave solutions in general and standard structures are established of the stated equation by introducing two viable techniques, namely, the generalized Kudryashov scheme and the two variables G'/G,1/G-expansion approach. The solutions are established in terms of elementary functions, specifically trigonometric functions, rational functions, exponential functions, and hyperbolic functions. For definite values of free parameters, the obtained analytical wave solutions transform into solitary wave solutions. The graphical patterns of the wave solutions with there-, two-, and contour plots are depicted magnificently to elucidate the internal structure of the phenomenon. The methods contribute as powerful mathematical tools and appear to be further effective, computerized, and user-friendly to investigate nonlinear fractional equations as well as comprehensive analytical solutions of nonlinear evolution equations in engineering, technology, and mathematical physics.

Method for Calculating the Scanning Unit of a Laser Scanner and Optimizing Its Overall Dimensions

A prism deflector, which is a multifaceted prism with reflective edges, is the most common scanning element that allows fast filling of a wide scanning area with laser radiation pulses along one coordinate. To carry out the movement of laser radiation along the second coordinate of the region under study a second scanning element, for example, a flat oscillating mirror, should be used. The overall dimensions of the scanning elements and the scanning unit as a whole depend on the free parameters that are set at the system development stage. The paper proposes a mathematical model designed for automated calculation of a scanning unit consisting of a prism deflector, a fixed flat mirror, an oscillating flat mirror, and a laser exit window. The described model makes it possible to calculate the overall parameters of system optical elements and the layout of the block based on the required characteristics of the scanned area and free parameters, which include the angle of radiation supply to the face of the prism deflector, the tilt angle of the fixed mirror, and one of the coordinates of the laser output window position relatively to the center of the prism deflector. In this case, the first two mentioned parameters are of the greatest interest from the point of view of minimizing and optimizing the overall dimensions of the scanning elements and the scanning unit as a whole. Based on the above model, an analysis of the dependence of the overall dimensions of the scanning elements and the scanning unit as a whole was carried out. The paper describes the layout features of the scanning unit. Recommendations for choosing the value of such free parameters as the angle of radiation supply to the face of the prism deflector and the angle of inclination of a flat fixed mirror are given. The obtained results can be used in the development of automated systems for the design of laser scanning devices.

Overtaking collisions of m shock waves and interactions of n(n→∞)-lump, m(m→∞)-solitons, τ(τ→∞)-periodic waves solutions to a generalized (2+1)-dimensional new KdV model

We consider a new generalized (2+1)-dimensional KdV model to investigate m ( m → ∞ ) shock and n ( n → ∞ ) breather wave solutions via two integral schemes. For the treatment of the model in an auxiliary equation approach, we first convert a nonlinear Burger equation to an ordinary differential equation (ODE) through a certain transformation. This ODE is used as an auxiliary equation of the method to obtain m ( m → ∞ ) shock wave solutions of the model. For different values of the parameters, we present head on and overtaking collisions with scattering ways of particle of the m ( m → ∞ ) shock wave solutions. We construct n soliton solutions of the model by using Hirota-bilinear approach. We obtain one lump type breather waves, interactions of one breather wave with a kink wave, interactions of two lump type breather waves by choosing complex conjugate values of free parameters in the n -soliton solutions of the model. Finally, we introduce two lemmas, a theorem and few corollaries on the hybrid interaction ( n → ∞ lumps, m → ∞ solitons and τ → ∞ periodic waves) solutions of the model. The theories and results are illustrated with adequate examples and suitable graphs. • We propose a generalized (2+1)- dimensional new KdV model for investigation waves solutions. • Derive m (m → ∞ ) shock wave solutions of the model. • Present head on and overtaking collisions with scattering ways of particle of the m (m → ∞ ) shock wave solutions. • We introduce two lemmas, a theorem and few corollaries on the hybrid interaction (n → ∞ lumps, m → ∞ solitons and τ → ∞ periodic waves) solutions of the model. • The theories and results are illustrated with adequate examples and suitable graphs.

Dynamical systems of cosmological models for different possibilities of G and rho _{Lambda }

The present paper deals with the dynamics of spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model with a time varying cosmological constant Lambda where Lambda evolves with the cosmic time t through the Hubble parameter H, that is, Lambda (H). We use the expression of Lambda (H) in the form of Taylor series with respect to H keeping only the even powers of H because of the general covariance of the effective action of quantum field theory in a curved background. Dynamical systems for three different cases based on the possibilities of gravitational constant G and the vacuum energy density rho _{Lambda } have been analysed. In Case I, both G and rho _{Lambda } are taken to be constant. We analyse stability of the system by using the notion of spectral radius, behavior of perturbation along each of the axes with respect to cosmic time and Poincaré sphere. In Case II, we have dynamical system analysis for G=hbox {constant} and rho _{Lambda } ne constant where we study stability by using the concept of spectral radius and perturbation function. In Case III, we take G ne constant and rho _{Lambda } ne constant where we introduce a new set of variables to set up the corresponding dynamical system. We find out the fixed points of the system and analyse the stability from different directions: by analysing behaviour of the perturbation along each of the axes, Center Manifold Theory and stability at infinity using Poincaré sphere respectively. Phase plots and perturbation plots have been presented. We deeply study the cosmological scenario with respect to the fixed points obtained and analyse the late time behavior of the Universe. The effective equation of state parameter omega _{eff}, total energy density Omega _{tt} are also evaluated at the fixed points for each of the three cases and these values are in agreement with the observational values in Aghanim et al. (Astron Astrophys 641(A6): 2020, 2018). We have also presented the EoS parameter for dark energy sector omega _{de}(z_{r}), the Hubble parameter H(z_{r}) and the deceleration parameter q(z_{r}) as functions of redshift z_{r} for all the three cases and their plots over redshift are also provided. We analyse the quintessence-like, phantom-like or the purely cosmological-constant type dark energy, etc behavior when the EoS approaches the fixed point value near -1. The present values of omega _{de}(z_{r}), H(z_{r}), q(z_{r}) and z_{rt} have been tabulated in Table 4 and they fall within the range of cosmological observations. The transition redshift value (z_{rt}) for each of the three cases have also been evaluated. In each of the cases the developed model agrees with the fact that the Universe is in the epoch of accelerated expansion for suitable values of free parameters chosen. The developed cosmological models associated with each of the three cases have a deep connection with the accelerated expansion phenomena of the evolving Universe.

Data-driven predictive modeling of Hubble parameter

We redesign the generalized pressure dark energy (GPDE) model, which is covering three common types of pressure parameterizations, with the help of a caloric framework to construct a theoretical ground for the machine learning (ML) analysis of cosmic Hubble parameter. The theoretical setup was optimized to find out appropriate values of its arbitrary parameters with the help of genetic neural network (GNN) algorithm and the most recent observational measurements of Hubble parameter. Since there is a shortcoming that the GNN process does not provide a direct method to calculate errors on the optimized values of free model parameters, we therefore take the Fisher Information Matrix (FIM) algorithm into account to deal with this issue. We see that the best-fitting value of Hubble constant and dimensionless dark energy density are in very good agreement with the most recent observations. Also, we discussed the optimized model from a cosmological perspective by making use of the evolutionary behavior of some cosmological parameters to present additional cosmological aspects of our theoretical proposal. It is concluded that our model implies physically meaningful results. In summary, the constructed model can explain the current accelerated expansion phase of the cosmos via Hubble parameter successfully.

On inflationary parameters in scalar–tensor theories

The equivalence between [Formula: see text] and scalar–tensor theories is revisited, we consequently explored different [Formula: see text] models. After consideration of specific definition of the scalar field, we derived the potentials [Formula: see text] for each [Formula: see text] model focusing on the early Universe, mostly the inflation epoch. For a given potential, we applied the slow-roll approximation approach to each [Formula: see text] model and obtained the expressions for the spectral index [Formula: see text] and tensor-to-scalar ratio [Formula: see text]. We determined the corresponding numerical values associated with each of the [Formula: see text] models. Our results showed that for certain choice of parameter space, the values of [Formula: see text] and [Formula: see text] are consistent with the Planck survey results and others produce numerical values that are in the same range as suggested by Planck data. We further constructed the Klein–Gordon equations (KGEs) of each [Formula: see text] model. We found numerical solutions to each KGE considering different values of free parameters and initial conditions of each [Formula: see text] model. All models showed that the scalar field decreases as time increases, an indication that there is less content of the scalar field in the late Universe.

Quantum gravity effects in the infrared: a theoretical derivation of the low-energy fine structure constant and mass ratios of elementary particles

We have recently proposed a pre-quantum, pre-spacetime theory as a matrix-valued Lagrangian dynamics on an octonionic spacetime. This theory offers the prospect of unifying internal symmetries of the standard model with pre-gravitation. We explain why such a quantum gravitational dynamics is in principle essential even at energies much smaller than Planck scale. The dynamics can also predict the values of free parameters of the low-energy standard model: these parameters arising in the Lagrangian are related to the algebra of the octonions, which define the underlying non-commutative spacetime on which the dynamical degrees of freedom evolve. These free parameters are related to the exceptional Jordan algebra \(J_3(8)\), which describes the three fermion generations. We use the octonionic representation of fermions to compute the eigenvalues of the characteristic equation of this algebra and compare the resulting eigenvalues with known mass ratios for quarks and leptons. We show that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios. In conjunction with the trace dynamics Lagrangian, these eigenvalues also yield a theoretical derivation of the low-energy fine structure constant.

Entropy generation and mixed convection of CuO–water near an oblique stagnation point: modified Chebyshev wavelets approach

In this article, an analysis of CuO–water nanofluid over a moving wall with oblique stagnation point has been studied under the influence of a heat source. CuO nanoparticles having shapes of platelet, brick and spheres were used in this study. The aim of this study is to explore the impact of the shapes of nanoparticles on the flow properties near an oblique stagnation point flow. The flow system was governed by a set of nonlinear partial differential equations (PDEs). These PDEs were converted to nonlinear ordinary differential equations, which were further solved numerically using a modified Chebyshev wavelet method. The effects of parameters appeared in analysis on skin friction, local Nusselt number, velocity, temperature and entropy are plotted graphically. Streamlines are also plotted to analyze patterns of flow for different levels of stretching and different angles of strike. Tabular results are generated to specify numerical values of free parameter A, components of skin friction, local Nusselt number and stagnation point. It is found that platelets shaped nanoparticles show more efficient results for inertial and thermal boundary layer. Entropy of system is influenced by stretching, angle of intact and mixed convection parameter.

Deep learning of CMB radiation temperature

Focusing on an astrophysical scenario based on the variable polytropic gas (VPG) model, we mainly discuss evolution of the cosmic microwave background (CMB) radiation temperature from deep learning (DL) perspective. To reach this aim, we start with reconstructing a new formulation for the temperature-red shift relation of the CMB photons. Subsequently, with help of some astrophysical measurements given in literature for galaxy cluster and quasar samples, we obtain the best-fitting values of free model parameters via the genetic neural network (GNN) mechanism. Since, there is an important shortcoming for the GNN algorithm (it does not directly calculate the corresponding error on the derived best-fit value of a free parameter), we use the Fisher information matrix (FIM) approach to handle this issue. Finally, with the help of a DL algorithm including not only the long short-term memory (LSTM) cell approach but also the Dropout tool, which can remove the over-fitting problem raised in a DL study, we investigate an other numerical feature of our theoretical formulation from the machine learning perspective.