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The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

This study aims to examine the plane wave reflection problem in micropolar orthotropic magneto-thermoelastic half space, considering the influence of impedance as a boundary in a nonlocal elasticity.

This study presents the novel formulation of governing partial differential equations for micropolar orthotropic medium with impact of nonlocal thermo-elasticity under magnetic field.

This study provides the numerical results validation for a particular numerical data and expression for the amplitude ratios of reflected waves and identifies the existence of four different waves, namely, quasi longitudinal displacement qCLD-wave, quasi thermal wave qCT-wave, quasi transverse displacement qCTD-wave and quasi-transverse micro-rotational qCTM-wave. The study derives the velocity equation giving the speed and phase velocity of these waves. The study also shows that the small-scale size effect gives significant impact on phase velocity.

The graphical analysis examines the variation of speeds and coefficients of attenuation of these waves due to frequency, magnetic field and nonlocal parameters. Also, significant conclusions on the variation of reflection coefficient against nonlocal parameter, frequency, impedance parameter and angle of incidence are provided graphically.

The creation of more effective micropolar orthotropic anisotropic materials which are very useful in the daily life and their applications in earth science are greatly impacted by the findings of this study.

The authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

Attenuation characteristics of microstrip transmission lines on alumina substrates up to 50GHz are discussed. The lines under test came from three different manufacturers, each of whom used different processes to realise the transmission lines. Two of the manufacturers used silver (Ag) paste, whereas the process of one of the manufacturers was copper (Cu) based. Each manufacturer used identical alumina substrates and identical test pattern files so that the measured attenuation properties reflected manufacturer’s capability to fabricate microstrips and the quality of the metal system used. Measurements showed that the attenuation of copper microstrips was slightly lower than that of the silver microstrips, but the difference was small. Measured attenuation (S21) of about 50Ω microstrips was approximately 0.5db/cm at 30GHz and 0.8dB/cm at 50GHz, respectively. The loss coefficient, α_t, of about 0.035dB/mm at 40GHz was obtained for the Cu microstrips. Such an attenuation is reasonable for many practical applications in the microwave and millimetre wave regions.

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation.

The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves.

The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also the use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

Introduction of a new model of DPLD in the equation of mass diffusion.

The purpose of this paper is to deal with the study of plane waves and fundamental solution in a modified couple stress generalized thermoelastic solid with three-phase-lag (TPL) model of thermoelasticity.

It is found that for two-dimensional model, there exists two longitudinal waves, namely, longitudinal wave (P-wave), thermal wave (T-wave), and a set of coupled transverse waves (SV1 and SV2 waves). In addition, the fundamental solution for the system of differential equations for steady oscillations in terms of elementary functions has been constructed. Some properties of fundamental solution are also established. Various particular cases of interest are also deduced from the present investigations and compared with the known results.

The phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically to see the effect of TPL model, dual-phase-lag (DPL) model and GN-III model in the presence of couple stress parameter.

The results are compared with couple stress TPL model, couple stress DPL model and GN-III model.

The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions.

Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem.

Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived.

Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

This study highlights the impact of mental accounts on a user's decision-making regarding payment schemes and aims to determine the pricing strategy for the first-enjoy-after-pay service offered by the two-sided media platforms.

This study establishes a game-theoretic model and utilizes backward induction to derive the equilibrium price by maximizing the monopolist's profit.

The findings indicate that the conditions for a two-sided media platform to offer the first-enjoy-after-pay service depend on the trade-off between pleasure attenuation and pain buffering and the effect of time discounts. Moreover, the authors found that the time discount is a critical factor in determining pricing strategies under various payment schemes offered by the platform.

This work adopts a uniform pricing strategy for users who opt for either immediate or post-payment schemes. Nevertheless, it is important to note that this approach has limitations in terms of offering discriminatory pricing for those who choose both payment schemes.

This analytical work provides valuable insights for two-sided media platforms to optimize their payment scheme strategies and pricing considering the influence of a user's mental account.

In a two-sided media platform, the authors provide applicable conditions for the platform to offer first-enjoy-after-pay service considering the effect of mental accounts. Further, the authors show the optimal pricing strategy under different payment schemes provided by the platform.

Presents validation of the Eulerian approach for unsteady two‐phase flows, whose behaviour depends on the coupling between the two phases, on the basis of the study of attentuation and dispersion of an acoustic wave propagating into a one dimensional two‐phase flow. This approach and the corresponding numerical aspects are accurate enough for later applications in more complex geometries, where “vortex shedding” phenomena take place. Attenuation and dispersion of a pressure wave in a two‐phase medium of rest was previously studied by Temkin and Dobbins. Present work is an extension of this theory to the case of a two‐phase flow. This theoretical approach leads to a numerical solution of the problem. Compares the derived results with those obtained from a direct numerical simulation based on MacCormack scheme in a finite volume formulation. Verifies that analytical and numerical approaches are in good agreement.

High‐frequency performance of printed boards (PBs) — a term which encompasses printed wiring boards (PWBs) and printed circuit boards (PCBs) — is becoming increasingly important in digital circuits and knowledge of the electrical characteristics associated with conductors acting as transmission lines is essential. This paper is an introduction to the electrical theory associated with transmission lines and develops the fundamental principles into formulae of use to PB users, designers and manufacturers. Established equations for calculating propagation delay and characteristic impedance based on physical parameters of conductor configurations are then summarised. The concept of ‘critical conductor length’ is proposed as a method of ascertaining whether control of characteristic impedance is required for a particular transmission line. The paper uses the surface microstrip configuration as a vehicle for mathematical analysis but the analysis is equally applicable to other transmission line configurations such as embedded microstrip, symmetrical stripline and dual stripline for which the associated physical parameter equations are included.

Ultrasound is a well-established technology in medical science, though many of the conventional measurement systems (hydrophones and radiation force balances [RFBs]) often lack accuracy and tend to be expensive. This is a significant problem where sensors must be considered to be “disposable” because they inevitably come into contact with biological fluids and expense increases dramatically in cases where a large number of sensors in array form are required. This is inevitably the case where ultrasound is to be used for the in vitro growth stimulation of a large plurality of biological samples in tissue engineering. Traditionally only a single excitation frequency is used (typically 1.5 MHz), but future research demands a larger choice of wavelengths for which a single broadband measurement transducer is desirable. Furthermore, because of implementation conditions there can also be large discrepancies between measurements. The purpose of this paper deals with a very cost-effective alternative to expensive RFBs and hydrophones.

Utilization of cost-effective piezoelectric elements as broadband sensors.

Very effective results with equivalent (if not better) accuracy than expensive alternatives.

This paper concentrates on how very cost-effective piezoelectric ultrasound transducers can be implemented as sensors for ultrasound power measurements with accuracy as good, if not better than those achievable using radiation force balances or hydrophones.