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Purpose In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium. Design/methodology/approach The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis. Findings The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed. Originality/value To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

The duration of lag phase can be used as an organismal fitness marker; however, it is often underreported as its estimation may be challenging and method and parameters dependent. Moreover, there are no publicly available tools to calculate lag duration by different methods. We developed a shiny‐based web application (https://microbialgrowth.shinyapps.io/lag_calulator/) where the lag duration can be calculated based on the user‐specified growth curve data, and for various explicitly specified methods, parameters and data preprocessing techniques. Additionally, we release an R package ‘miLAG’ that can be further customised and developed. We also describe in short the assumptions, advantages and disadvantages of the most popular lag calculation methods and propose a decision tree to choose a method most suited to one's data. Finally, we show some working examples of how to calculate lag duration using our shiny server.

It is possible to eliminate phase-lag and all of its derivatives up to order five by employing a method that takes fading phase-lag into consideration. Improving algebraic order ( AOR ) and decreasing function evaluations ( FEvs ) are the goals of the new method called the cost-efficient approach . The unique method is illustrated by the symbol PF 5 DPHFITN 142 SPS . This approach is P-Stable , which means it is infinitely periodic. A wide variety of periodic and oscillatory issues can be solved using the suggested approach. The challenging problem of Schrödinger-type coupled differential equations in quantum chemistry was tackled using this novel approach. With only 5 F E v s needed to complete each step, the new method could be considered as a cost-effective approach. An AOR of 14 allows us to significantly improve our present condition.

Using a technique that accounts for disappearing phase-lag might lead to the elimination of phase-lag and all of its derivatives up to order four. The new technique known as the cost-efficient approach aims to improve algebraic order ( AOR ) and decrease function evaluations ( FEvs ). The one-of-a-kind approach is shown by Equation PF 4 DPHFITN 142 SPS . This method is endlessly periodic since it is P-Stable . The proposed method may be used to solve many different types of periodic and/or oscillatory problems. This innovative method was used to address the difficult issue of Schrödinger-type coupled differential equations in quantum chemistry. The new technique might be seen as a cost-efficient solution since it only requires 5 FEvs to execute each step. We are able to greatly ameliorate our current situation with an AOR of 14.

Applying a phase-fitting method might potentially vanish the phase-lag and its first derivative. Improving algebraic order ( AOR ) and decreasing function evaluations ( FEvs ) are the goals of the new strategy called the cost-efficient approach . Equation PF 1 DPHFITN 142 SPS demonstrates the unique method. The suggested approach is P-Stable , meaning it is indefinitely periodic. The proposed method is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5 FEvs to run each stage, it may be considered a cost-efficient approach . With an AOR of 14, we can significantly improve our present predicament.

By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The cost-efficient approach is a new strategy whose aims are to boost algebraic order ( AOR ) and reduce function evaluations ( FEVs ). The symbolic representation of the one-of-a-kind approach is PF 6 DPHFITN 142 SPS . This method is infinitely periodic since it is P-Stable . The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires 5 F E V s , the new method could be seen as a cost-effective strategy. With a AOR of 14, we can greatly enhance our current situation.

Applying a phase-fitting method might potentially vanish the phase-lag and its first derivative. Improving algebraic order ( AOR ) and decreasing function evaluations ( FEvs ) are the goals of the new strategy called the cost-efficient approach . Equation PF 2 DPHFITN 142 SPS demonstrates the unique method. The suggested approach is P-Stable , meaning it is indefinitely periodic. The proposed method is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5 FEvs to run each stage, it may be considered a cost-efficient approach . With an AOR of 14, we can significantly improve our present predicament.

The phase lag and its first derivative can all vanish when utilising a phase-fitting strategy. Since the new method employs the highest possible algebraic order ( AOR ) while simultaneously requiring the fewest possible function evaluations ( FEvs ), it has been termed the economical method . A formula of PF 1 DPFN 142 SPS represents this novel approach. The P-Stable method is the one that is being proposed (i.e. infinitely periodic). Numerous issues with periodic and/or oscillating solutions can be addressed with the proposed method. We took this novel strategy to solve the difficult problem of Schrödinger—type coupled differential equations in quantum chemistry. The new tactic is known as a economic algorithm since it requires just 5 FEvs at each stage to reach a 14 AOR .

A phase-fitting approach allows vanishing for not only the phase lag but also its first, second, third, fourth, fifth, and sixth derivatives to be considered. The new technique is dubbed economical method because it uses the maximum possible algebraic order ( AOR ) while simultaneously performing the fewest possible function evaluations ( FEvs ). The formula for this innovative method is PF 6 DPFN 2 SPS . The proposed technique is P-Stable (i.e. infinitely periodic). The proposed approach can be used to solve a variety of problems with periodic and/or oscillating solutions. To address the intractable nature of Schrödinger-type coupled differential equations in quantum chemistry, we adopted this unique approach. The new strategy is classified as a economic algorithm since it uses 5 FEvs at each step to achieve a 12 AOR .

The phase-lag and all of its derivatives (first, second, third, fourth, fifth, and sixth) might be eliminated using a phase-fitting technique. The new approach, which is referred to as the economical method , targets maximizing algebraic order ( AOR ) and reducing function evaluations ( FEvs ). The one-of-a-kind approach is demonstrated by Equation PF 6 DPFN 142 SPS .The proposed method is infinitely periodic i.e. P-Stable . To many periodic and/or oscillatory problems, the suggested strategy can be applied. Using this innovative method, the difficult issue of Schrödinger-type coupled differential equations was tackled in quantum chemistry. Every step of the new approach only requires 5 FEvs to execute, making it a economic algorithm . By accomplishing a AOR of 14, this allows us to greatly enhance our current situation.