Integration Constants Research Articles

Two-dimensional P1 approximation (P1-2D) for the evaluation of the radiant field in annular and tubular photocatalytic reactors

The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in two dimensions using the P1 approximation approach (P1-2D) to describe the radiant field in annular and tubular photocatalytic reactors. The radiant sources employed were assumed to be periodic when applying the boundary conditions to facilitate the determination of the integration constants in the RTE solution. Three different systems were considered: S1 and S2 consisted of annular reactors, while S3 consisted of a tubular reactor. Simulations were conducted using commercial TiO2 P25 and anatase TiO2 as photocatalyst models, with their optical properties sourced from the literature. The linear source spherical emission (LSSE), Gaussian emission (GE), and uniform emission (UE) models were used as radiant sources. The LVRPA was found to decrease from the inner to the outer wall of the reactor for S1 and S2, and from the wall to the center of the reactor for S3; it was close to the values obtained using the Monte Carlo (MC) procedure in S2. The overall volumetric rate of photon absorption (OVRPA) increased exponentially with catalyst loading until a point where no significant increase was observed for each reactor. The apparent optical thickness τ App 1 ​formulated was a more reliable optimization parameter than the optical thickness.

THE EFFECT OF PARTIAL SLIP ON THE SURFACE PRESSURE DISTRIBUTION IN A SLIGHTLY COMPRESIBLE FLOW DEVELOPMENT REGION IN THE BOUNDARY LAYER

The study of laminar incompressible fluid flow in the boundary layer revealed, even earlier, that the condition of complete adhesion of fluid particles to the surface (non-slip condition) of the moving body (half-plane) is not met in the flow development (formation) region. The assumption of constancy of the fluid velocity on the surface of a moving body, hence non-slip, leads, in the flow development region, to the complete absence of the normal component of the velocity field. And this contradicts the very concept of the flow development region, where there should be two velocity components - longitudinal (primary) and normal (secondary) ones. In the previous works of the authors, analytical solutions were obtained for the velocity field in the region of development of incompressible fluid flow in the boundary layer. Since the use of the incompressible fluid flow model is restricted by the Mach number, to further expand the speed range, the problem of the of slightly compressible fluid flow development region in the boundary layer was considered. It is analytically proven that all considerations regarding the impossibility of complete non-slip in the flow development region can be applied to a slightly compressible flow. Slight compressibility at the same time means the subsonic nature of the flow and the neglect of temperature effects due to friction. On the basis of a critical analysis of the existing approaches, which consider the flow of a fluid around a immobile plate in the framework of non-gradient flow (which is just impossible due to the lack of a mechanism for creating the motion of the fluid), it is shown that the system of equations is actually non-closed. For the region of flow development, where the longitudinal pressure gradient is not a constant value, one equation is missing. This equation, as in previous works, is obtained from the necessary condition for the extreme of the fluid rate functional. And although the complete solution for the longitudinal component of the velocity contains four constants of integration, to obtain the asymptotics near the solid surface it is sufficient to know only two quantities - the velocity and its first derivative (gradient). These values, as it turns out from the asymptotic solution, coincide with the case of incompressible flow, which allows us to expand the scope of the previously obtained results for a wider domain of Mach numbers, for example . And such values already correspond to the speeds of modern civil aircraft. The dimensionless distribution of pressure in the slightly compressible flow development region is presented and its significant heterogeneity is shown, which, in turn, indicates the importance of the obtained results.

ANALYTICAL CALCULATION OF A BEAM BASED ON AN ELASTIC WINKLER FOUNDATION WITH RANGE INHOMOGENITY

The aim of the study is the further development of analytical methods for calculating the bending of beams resting on a non-homogeneous continuous Winkler elastic foundation. This paper considers the case when the beam is under the influence of a uniformly distributed constant transverse load, and the inhomogeneity of the elastic foundation is given by a power function with an arbitrary non-negative power exponent . Fundamental functions and a partial solution of the corresponding differential equation of beam bending are found in an explicit closed form. These functions are dimensionless and are represented by absolutely and uniformly convergent power series. In turn, the formulas for the parameters of the stress-strain state of the beam – deflection, angle of rotation, bending moment and transverse force – are expressed through the indicated functions. The unknown constants of integration in these formulas are expressed in terms of the initial parameters, which are after the implementation of the specified boundary conditions. Thus, the calculation of the beam for bending is reduced to the procedure of numerical implementation of explicit analytical formulas for the parameters of the stress-strain state. An example demonstrates the practical application of the obtained solutions. A prismatic concrete beam based on a cubic variable elastic foundation is considered. This case corresponds to the power value . The results of the calculation by the author's method are presented in numerical and graphical formats for the case when the left end of the beam is hinged and the right end is clamped. The numerical values obtained by the author's method are accurate, since the applied calculation method is based on the exact solution of the corresponding differential equation. The availability of such solutions makes it possible to evaluate the accuracy of solutions obtained using various approximate methods by comparison. For the purpose of such a comparison, the paper presents the calculation results obtained by the finite element method (FEM). The absolute error of the FEM method when calculating this design was determined.

Mach's principle and dark matter

In this paper we entertain a Machian setting where local physics is non-locally affected by the whole Universe, taking the liberty to identify the local (“Newton's bucket”) with our visible Universe, and the whole Universe (Mach's “fixed stars”) with the global Universe beyond our horizon. Crucially, we allow for the two to have different properties, so that we are beyond the traditional FRW setting. For definiteness we focus on theories where non-locality arises from evolution in the laws of physics in terms of spatially global time variables dual to the constants of Nature. Since non-local theories are foliation-dependent, the local (but not the global) Hamiltonian constraint is lost. This is true not only while non-locality is taking place, but also after it ceases: the local Hamiltonian constraint is only recovered up to a constant in time, keeping a memory of the integrated past non-locality. We show that this integration constant is equivalent to preserving the local Hamiltonian constraint and adding an extra fluid with the same cosmological properties as conventional pressureless dark matter. The equivalence breaks down in terms of clustering properties, with the new component attracting other matter, but not budging from its location. This is the ultimate “painted-on” dark matter, attracting but not being attracted, and nailing down a preferred frame.

Galerkin Kantorovich Method for Solving the Terzaghi’s One-Dimensional Soil Consolidation Equation

This paper presents the Galerkin-Kantorovich variational method for solving the Terzaghi’s one-dimensional consolidation equation for two-way drainage conditions. The solution was considered as an infinite series of known coordinate (shape) functions and unknown function of time which we sought such that the resulting functional is minimized. The shape functions satisfied the hydraulic boundary conditions at the boundary of the consolidating soil. Galerkin-Kantorovich variational integral equation was thus formulated for the initial boundary value problem using residual minimization principles. The solution resulted in a system of first order ordinary differential equations in which was solved for Orthogonalization principles were used to obtain the integration constants in terms of initial pore water pressure, thus yielding the general solution. Solutions for constant initial excess pore water pressure were obtained and found to be the closed-form solution. The solutions were presented in terms of global (average) degrees of consolidation and tabulated. The results obtained were exact and identical with results previously found using separation of variables techniques.

Bending-based solution methodology using eigenvalue-eigenvector approach for analysis of foldable reinforced Golf Clubs cylindrical shell

This paper is organized to present eigenvalue-eigenvector based solution method for elastic bending analysis of foldable Golf Clubs cylindrical shell reinforced with graphene origami. The axisymmetric kinematic and constitutive relations are extended using the models with shear deformability and three-dimensional relations. The effective material properties are inserted into integration constants and constitutive relations in terms of angle and content of folded structure as well as thermal load. The virtual work principle is extended in order to derive governing equations and the eigenvalue-eigenvector method is applied for analytical solution. The results are presented along the longitudinal and radial coordinates with changes of angle and content of folded structure as well as thermal load. The results of this analysis may be used for optimized design and manufacturing of the golf clubs and other sport equipment.

Growth and dry matter intake curve analysis of crossbred male calves in Ethiopia

ABSTRACT The study was carried out at Holetta agricultural Research center dairy farm to estimate the growth and dry matter intake curves parameters of different genetic groups of crossbred male calves. A total of 48 weaned Friesian Boran (FB) crossbred calves consisting of 24 male calves having 50% Friesian blood level and another 24 growing calves having 75% Friesian blood level were used for this study. The calves were managed under individual feeding management for a fattening period of 626 days. Body weight and dry matter intake data were fitted into Gompertz nonlinear growth model. Mean values for growth parameters in 50% FB and 75% FB crosses were 727.0 and 730.2 kg; 2.85 and 2.78; 0.0019 and 0.0017 kg/day; 547.95 and 595.68 days; 257.46 and 268.63 kg; for mature weight, integration constant, maturity rate, age at inflection point and body weight at inflection point, respectively. This study revealed that 50% FB crossbred bull calves are fast maturing genotype and had significantly lower DMI at mature age than 75% FB crosses. Generally, 50% FB crossbred bull calves can be used for fattening purpose to meet increasing lean meat demand of consumers in Ethiopia with decreased feed cost under improved feeding system.

Non-local effects on displacement in cylindrical structures

This study investigates the influence of non-local effects on displacement variations in polar coordinates for clamped-clamped cylinders, assuming material properties vary as a power function of the thickness coordinate. The displacement expression is derived from a solved differential equation, with particular attention given to the impact of fixation mode on displacement. The findings underscore the importance of non-local factors in determining structural behavior and stress the necessity of considering fixation mode when computing integration constants. Nonlocal effects denote interactions and influences that extend beyond locally observed conditions or alterations within a specific system. Examining clamped-clamped cylinders, this research delves into displacement variations in polar coordinates while considering the influence of non-local effects, assuming material properties change according to a power function of the thickness coordinate. The derivation of the displacement expression from a solved differential equation forms a key aspect, with a specific focus on how fixation mode affects displacement. The study's outcomes highlight the crucial role of non-local factors in shaping structural behavior and underscore the imperative of accounting for fixation mode when calculating integration constants. Focused on clamped-clamped cylinders, this study explores displacement variations in polar coordinates under the influence of non-local effects, presuming material properties to follow a power function of the thickness coordinate. Utilizing a solved differential equation, the investigation derives the displacement expression and scrutinizes how fixation mode impacts displacement. The results elucidate the pivotal significance of non-local factors in delineating structural behavior and stress the requisite consideration of fixation mode in integration constant calculations.

On the direct quantization of Maxwell field

In this paper, we apply the generalized integration constants (GCI) method (Belhadi 2023 https://arxiv.org/abs/2303.08236), in field theory to quantize Maxwell and the Klein–Gordon free fields. The study is performed in both position and momentum spaces, to obtain the equal-time Dirac brackets among the fields and their conjugate momenta. The idea is to compute the brackets near the initial instant using the Taylor polynomial expansion, and then deduce directly their expressions at any later time. In the case of the Maxwell field, the interdependence of the field components (constraints) requires the use of the Helmholtz theorem to separate the transversal and longitudinal parts. Our work finishes with the study of the O(3) nonlinear sigma model using the GCI approach.

Black bounces in conformal Killing gravity

In this work, we analyse black bounce solutions in the recently proposed “Conformal Killing gravity” (CKG), by coupling the theory to nonlinear electrodynamics (NLED) and scalar fields. The original motivation of the theory was essentially to fulfill specific criteria that are absent in existing gravitational theories, namely, to obtain the cosmological constant as an integration constant, derive the energy–momentum conservation law as a consequence of the gravitational field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. In this work, we extend the static and spherically symmetric solutions obtained in the literature, and explore the possibility of black bounces in CKG, coupled to NLED and scalar fields. We find novel NLED Lagrangian densities and scalar potentials, and extend the class of black bounce solutions found in the literature. Furthermore, within black bounce geometries, we find generalizations of the Bardeen-type and Simpson–Visser geometries and explore the regularity conditions of the solutions.

Analytical solution for the interfacial stress and energy release rate at failure initiation of the three-point bending test (ISO 14679:1997)

Determining adhesive failure in adhesively bonded joints is still challenging in the field. While the three-point bending test (3PBT) (ISO 14679:1997) has been helpful in identifying critical forces and displacements related to bond strength, it only allows for a qualitative assessment of the bond line. Recently, a new quantitative methodology has been developed to determine critical stress and fracture toughness using the coupled stress–energy criterion and the 3PBT. However, these assessments require a significant effort using semi-analytical or finite element (FE) analysis. Therefore, the present study proposes a reliable set of analytical equations to determine peel and shear stress distributions using a weak interface formulation and 1D Euler–Bernoulli approach. More precisely, a particular numerical method computes the integration constants from these equations. A new method has been proposed for calculating the interfacial stiffness in peel and shear mode, based on the material and geometrical parameters of the geometry. This method differs from the previous approach, where the interfacial stiffness was calibrated from the experimental behavior of the test. The whole approach has been validated through experimental and numerical analysis, including the costly 3D FE analysis. An analytical expression for interfacial energy release is suggested, developed following the works of Fraisse and Schmit on J-integral assessment of sandwich-type overlaps and depending on the applied force and a rotation, which could be experimentally measured. Therefore, this work is significant progress in determining bond strength using a simple mechanical test and equations applicable to various industries.

Insights on Granda–Oliveros holographic dark energy: possibility of negative dark energy at z≳2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\gtrsim 2$$\\end{document}

In holographic dark energy (HDE) models, infrared cut-offs with derivatives of the Hubble parameter, such as the Granda–Oliveros cut-off, offer a coherent explanation for late-time acceleration while ensuring causal consistency. We show that such HDE will inevitably mimic the dominant energy forms unless we forcefully calibrate the free parameters. This feature reveals the dependency between the model’s ability to explain the late-time acceleration and the integration constant, highlighting that one cannot arbitrarily set this constant to zero. We see that the origins of HDE and the Friedmann equations from the first law of horizon thermodynamics offer a natural explanation for this behaviour. Thus, the holographic principle naturally extends to all energy components, diverging from the prevalent notion in HDE models. The model also allows dark energy to transit from an early negative energy to a present positive value, with a singular dark energy equation of state parameter, which can relax the tension in the BAO Lyman-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} observations. Furthermore, we present observational constraints utilizing Pantheon+,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+,$$\\end{document} OHD, CMB Shift parameter, QSO and BAO data, indicating the presence of early negative energy as an unavoidable consequence. Upon using the SH0ES prior, we see that the model accounts for the Hubble parameter at the cost of affecting the matter density while simultaneously relaxing the tensions in BAO Lyman-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} observations and the age estimations. This study also underscores notable features stemming from the comprehensive utilization of the covariance matrix within cosmic chronometers, BAO and CMB distance prior and clarifies the implications of negative dark energy density derived from the high redshift Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document} sample. Additionally, we provide a brief overview of the theoretical framework surrounding linear perturbation within the wGOHDE model.

New Potential Energy Surface for the H + Cl2 Reaction and Quantum Dynamics Studies.

The reaction of H + Cl2 → HCl + Cl plays a crucial role in various fields. However, no previous study has investigated this reaction using accurate quantum mechanical methods. In this paper, we construct a global potential energy surface (PES) using the neural network method with more than 20,000 ab initio energies obtained by the MRCI-F12+Q method with the aug-cc-pV5Z basis and extrapolated to the complete basis set limit. The spin-orbit coupling of the Cl atom has been considered in the PES. With this new PES, product state-resolved quantum dynamics calculations for the H + Cl2 (v0 = 0, j0 = 0-2) → HCl + Cl reaction was carried out. Numerical results show that the initial rotational excitation of the Cl2 has negligible effects on the reactivity. Product state-resolved integral cross sections (ICS) and rate constants reveal that the HCl is most favorably produced in its v' = 2 vibrational state. The calculated product vibrational state-resolved and total reaction rate constants suggest that the new global PES is accurate enough, as compared with the available experimental measurements.

Analysis of Disc Motor with Asymmetrical Conducting Rotor

The homogenous disc rotor construction allows higher rotational speeds and relatively higher power densities. This paper deals with a two-phase induction motor with homogenous disc rotor construction. The field analysis of an axial flux disk motor with a conducting disc rotor is carried out, using a new application of the Maxwell's field equations. A Suggested model is introduced to establish the geometry of motor construction and to enable the derivation of the field system differential equations. A new strategy is applied for the boundary conditions to complete the field solution. This is carried out by determining the complex integration constants. The current density is completely derived with it is components (the radial, the tangential current density and the axial air gap flux density). The performance of the flux density, rotor current components and the torque-slip characteristics are determined with and without disk rotor ends. The effects of the disk rotor design data and the rotor asymmetry on the motor performance are investigated.

Quantum dynamics of the P(2D) + H2 (X1[formula omitted]) → PH (X3Σ-) + H(2S) reaction

The title reaction is thought to be important for the astronomical PO formation, which may contribute to the generation of bioavailable H3PO3. Using quasi-classical trajectory (QCT) method, the state-specified (v = 0, j = 0) rate constant of this reaction was calculated. The comparison with previous temperature-averaged QCT rate constant shows that the effect of ro-vibrational excitation is relatively small below 2000 K. Then, the time-dependent wave packet (TDWP) method was applied to investigate the quantum reaction mechanisms, obtaining the state-specified (v = 0, j = 0) reaction probability, integral cross sections and rate constants. The number of partial waves and the integral interval of collision energy considered were rigorously tested to ensure the convergence of the TDWP rate constant below 2000 K. The TDWP rate constant agrees better to the latest experimental results at 291 to 685 K than those from the two QCT calculations. Also, the TDWP calculations can produce relatively reliable rate constants at 700 to 2000 K, where the Arrhenius formula fitted by experimental results ignores the temperature dependence of the activation energy. The calculated rate constants are helpful for modelling the phosphorus chemistry and determining the abundances of the P-bearing species in interstellar media (ISM).

Quantum Dynamics of O(3P)+HBr→OH+Br Reaction: Integral Cross Sections and Rate Constants and their Initial State Dependence.

The integral cross sections (ICSs) and rate constants (RCs) for the title reaction are calculated by means of accurate quantum wave packet method employing the recent ab initio potential energy surface developed by Peterson and co-workers. Hundreds of partial wave contributions (up to J=150) are calculated explicitly taking Coriolis coupling into account. The ICSs are found to increase monotonically with energy and their energy dependences are smooth except in the energy range below the potential energy barrier, where several resonance peaks are observed. The temperature dependences of the RCs obey in general the Arrhenius law. These behaviors manifest the dominance of abstract mechanism. Initial rotational state (ji) excitations are found to greatly enhance the reactivity starting from ji=4, while exhibiting a complicated dependence for ji<4. From Boltzmann average of the initial state specified RCs (for ji=0-15) we obtained thermal RCs which are in reasonable agreement with available experimental results.

Product State-Resolved Reactive Scattering Studies of the H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl Reaction by the Time-Dependent Wave Packet Method.

The typical hydrogen atom plus halogen molecule reaction H + Cl2 → HCl + Cl has implications across many fields. In this paper, product state-resolved quantum dynamics calculations for the vibrationally excited reaction H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl were conducted using the time-dependent wave packet method on a newly developed accurate potential energy surface. Numerical results indicate that the initial vibrational excitation of Cl2 does enhance the reactivity for this early barrier reaction, although less than the enhancement of the translational energy. The calculated product vibrational state-resolved integral cross sections and rate constants reveal that the product vibrational state distribution and the initial vibrational state of Cl2 are highly correlated. The thermal rate constant in the temperature range from 100 to 1000 K was given and is found to be in reasonable agreement with the experimental measurements.

4D spherically symmetric time-dependent quantum gravity amplitudes

In these short notes, we compute non-perturbatively the time-dependent quantum gravity amplitudes for a four-dimensional spherically symmetric space-time with space-like and time-like boundaries. We solve the 4D classical and quantum constraints in a novel way. We identify the classical solution of the constraints as a canonical transformation, where the integration constants are the new variables. We apply this canonical transformation to the path integral representation of the amplitudes we are interested in. We use both, the canonical and the path integral formalism. This procedure allows us to reduce the action to the actual degree of freedom of the theory. In the end, we get the time-dependent amplitudes from the path integral without performing an actual path integration. From these amplitudes, we show that for most of the boundary conditions time evolution in quantum gravity is non-unitary. There is however a special case where unitary evolution could be achieved.

An efficient Bayesian observer model of attractive and repulsive temporal context effects when perceiving multistable dot lattices.

In multistable dot lattices, the orientation we perceive is attracted toward the orientation we perceived in the immediately preceding stimulus and repelled from the orientation for which most evidence was present previously (Van Geert, Moors, Haaf, & Wagemans, 2022). Theoretically-inspired models have been proposed to explain the co-occurrence of attractive and repulsive context effects in multistable dot lattice tasks, but these models artificially induced an influence of the previous trial on the current one without detailing the process underlying such an influence (Gepshtein & Kubovy, 2005; Schwiedrzik etal., 2014). We conducted a simulation study to test whether the observed attractive and repulsive context effects could be explained with an efficient Bayesian observer model (Wei & Stocker, 2015). This model assumes variable encoding precision of orientations in line with their frequency of occurrence (i.e., efficient encoding) and takes the dissimilarity between stimulus space and sensory space into account. An efficient Bayesian observer model including both a stimulus and a perceptual level was needed to explain the co-occurrence of both attractive and repulsive temporal context effects. Furthermore, this model could reproduce the empirically observed strong positive correlation between individuals' attractive and repulsive effects (Van Geert etal., 2022), by assuming a positive correlation between temporal integration constants at the stimulus and the perceptual level. To conclude, the study brings evidence that efficient encoding and likelihood repulsion on the stimulus level can explain the repulsive context effect, whereas perceptual prior attraction can explain the attractive temporal context effect when perceiving multistable dot lattices.

On redshift evolution and negative dark energy density in Pantheon + Supernovae

Within the Friedmann–Lemaître–Robertson–Walker (FLRW) framework, the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} is an integration constant. Thus, consistency of the model demands observational constancy of H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}. We demonstrate redshift evolution of best fit 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 parameters (H0,Ωm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H_0, \\Omega _{m})$$\\end{document} in Pantheon+ supernove (SNe). Redshift evolution of best fit cosmological parameters is a prerequisite to finding a statistically significant evolution as well as identifying alternative models that are competitive with 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 in a Bayesian model comparison. To assess statistical significance, we employ three different methods: (i) Bayesian model comparison, (ii) mock simulations and (iii) profile distributions. The first shows a marginal preference for the vanilla 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 over an ad hoc model with 3 additional parameters and an unphysical jump in cosmological parameters at z=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=1$$\\end{document}. From mock simulations, we estimate the statistical significance of redshift evolution of best fit parameters and negative dark energy density (Ωm>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _m > 1$$\\end{document}) to be in the 1-2σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1-2 \\sigma $$\\end{document} range, depending on the criteria employed. Importantly, in direct comparison to the same analysis with the earlier Pantheon sample we find that statistical significance of redshift evolution of best fit parameters has increased, as expected for a physical effect. Our profile distribution analysis demonstrates a shift in (H0,Ωm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H_0, \\Omega _m)$$\\end{document} in excess of 95%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$95\\%$$\\end{document} confidence level for SNe with redshifts z>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z > 1$$\\end{document} and also shows that a degeneracy in MCMC posteriors is not equivalent to a curve of constant χ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^2$$\\end{document}. Our findings can be interpreted as a statistical fluctuation or unexplored systematics in Pantheon+ or 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 breakdown. The first two possibilities are disfavoured by similar trends in independent probes.