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This study illustrates the successful achievement of tunable defect bands in one-dimensional defective phononic crystals (PnCs) through the incorporation of piezoelectric defects with synthetic negative capacitances (SNCs) for the first time. The efficacy of SNCs in creating tunable bandpass filters across a broad frequency range is thoroughly examined using the proposed analytical and numerical models. A newly developed electroelastically coupled transfer matrix that incorporates SNCs is presented, considering either series or parallel connection between bimorph piezoelectric elements. Defect band and transmittance analyses are conducted using the transfer matrix and S-parameter methods. Two key findings emerge from this investigation. First, when the total equivalent capacitance of the bimorph piezoelectric elements and SNC becomes zero, the defect band representing the point-symmetric defect-mode shape can be customized throughout the entire phononic bandgap. Second, the constant transmittance value, resembling short-circuit conditions, highlights the remarkable ability of SNCs to tune defect bands without energy dissipation, paving the way for fully tunable bandpass filters. To propel this research forward, future investigations could explore expanding the design space with double defects, adopting enhanced modeling techniques to account for lateral and shear effects, developing a control algorithm for the automatic optimization of SNC values in actively tunable bandpass filters, and incorporating artificial intelligence into design methods for piezoelectric defects with electrical connections. [ABSTRACT FROM AUTHOR]

Layered franckeite is a natural superlattice composed of two alternating layers of different compositions, SnS 2 - and PbS-like. This creates incommensurability between the two species along the planes of the layers, resulting in spontaneous symmetry-break periodic ripples in the a-axis orientation. Nevertheless, natural franckeite heterostructure has shown potential for optoelectronic applications mostly because it is a semiconductor with 0.7 eV bandgap, air-stable, and can be easily exfoliated down to ultrathin thicknesses. Here, we demonstrate that few-layer franckeite shows a highly anisotropic nonlinear optical response due to its lattice structure, which allows for the identification of the ripple axis. Moreover, we find that the highly anisotropic third-harmonic emission strongly varies with material thickness. These features are further corroborated by a theoretical nonlinear susceptibility model and the nonlinear transfer matrix method. Overall, our findings help to understand this material and propose a characterization method that could be used in other layered materials and heterostructures to assign their characteristic axes. [ABSTRACT FROM AUTHOR]

Strong coupling of a confined optical field to the excitonic or vibronic transitions of a molecular material results in the formation of new hybrid states called polaritons. Such effects have been extensively studied in Fabry–Pèrot microcavity structures where an organic material is placed between two highly reflective mirrors. Recently, theoretical and experimental evidence has suggested that strong coupling can be used to modify chemical reactivity as well as molecular photophysical functionalities. However, the geometry of conventional microcavity structures limits the ability of molecules "encapsulated" in a cavity to interact with their local environment. Here, we fabricate mirrorless organic membranes that utilize the refractive index contrast between the organic active material and its surrounding medium to confine an optical field with Q-factor values up to 33. Using angle-resolved white light reflectivity measurements, we confirm that our structures operate in the strong coupling regime, with Rabi-splitting energies between 60 and 80 meV in the different structures studied. The experimental results are matched by transfer matrix and coupled oscillator models that simulate the various polariton states of the free standing membranes. Our work demonstrates that mechanically flexible and easy-to-fabricate free standing membranes can support strong light–matter coupling, making such simple and versatile structures highly promising for a range of polariton applications. [ABSTRACT FROM AUTHOR]

In the present study, we have explored the absorption properties of a monolayer graphene-based photonic heterostructure, which consists of topological photonic configurations, graphene, and a Bragg mirror. The optical attributes were computed by using the 4 × 4 transfer matrix method. The results indicate that the creation of topological interface states and strong coupling between these resonant modes result in mode splitting, leading to the formation of hybrid modes known as coupled topological interface states with unity transmittance. The number of absorption modes can be modulated with an appropriate selection of cascaded photonic structures. Our proposed design with 1, 3, 5, and 7 cascaded topological photonic structures provides 1, 5, 9, and 13 absorption modes with greater than 90 % absorption. The findings also reveal that absorption peak strength is greatly influenced by Fermi-level and magnetic fields; switching of the modes from absorption to reflection and vice versa is achieved by suitable electrical and magnetic biasing. Our proposed design offers various applications, such as switchable filters, absorbers, and modulators. [ABSTRACT FROM AUTHOR]

Oxygen vacancies in indium tin oxide (ITO) thin films provide a direct route to effectively tune the free electron density and thereby, controlling the epsilon-near-zero (ENZ) cut-off wavelength, the wavelength at which the real part of permittivity crosses zero of the permittivity axis. In this report, oxygen vacancies in pulsed laser deposited ITO thin films are systematically tuned using different background gases (O 2 , N 2 , Ar, and He). ENZ cut-offs are observed for the films deposited under He and Ar gases. In contrast, no such cut-offs are observed in the case of other two gases. An ITO thin film deposited under He gas exhibits deeper resonance signal than the one deposited under Ar gas. As expected, no such dip in the resonance spectra is observed for the films deposited under O 2 and N 2 gases. This observation is directly correlated to the change in the number of oxygen vacancies under different ambient gases. A modified transfer matrix method which incorporates surface roughness as an effective medium layer is developed to describe the experimentally observed resonance spectra numerically. Angular invariancy of ENZ plasmon resonance and the difference in absorption values for ITO films deposited under different gases is understood in terms of local field intensity enhancement factor. The study presented here will certainly be very useful in understanding the ENZ plasmon resonance phenomena as a whole. Additionally, ITO films deposited under an inert gas environment could be excellent material platforms for realizing several exotic ENZ applications. [ABSTRACT FROM AUTHOR]

Hyperbolic metamaterials (HMMs) are artificial subwavelength-structured media that exhibit excellent hyperbolic properties. The Casimir force for HMMs can be predicted by effective medium theory (EMT), which simplifies the calculations considerably. However, the conditions of EMT in the Casimir force between HMMs have not been investigated. In this work, we compare the exact results of the Casimir force calculated by the transfer matrix method (TMM) with those from EMT. The numerical results suggest that EMT can accurately calculate the Casimir force only when the gap distance is 100 times larger than the period of a unit cell. When the gap distance and period of unit cell values are comparable, EMT is not suitable for TMM, and the main error occurs in the hyperbolic band. Furthermore, the effect of the filling ratio on the applicable conditions of EMT is also studied. This work demonstrates the conditions of EMT in calculating the Casimir force between HMMs and provides help for the development of micro- and nanoelectromechanical systems. [ABSTRACT FROM AUTHOR]

Aperiodic order is ubiquitous in nature and quite relevant in science and technology. There are extensive works in aperiodic structures studying fundamental characteristics in physical properties, such as fractality, self-similarity, and fragmentation. However, there are fewer reports in which aperiodicity signifies an improvement in physical quantities with practical applications. Here, we show that the aperiodicity of fractal or self-similar type optimizes the tunneling magnetoresistance and spin-valley polarization of magnetic silicene structures, raising the prospects of spin-valleytronics. We reach this conclusion by studying the spin-valley-dependent transport properties of complex (Cantor-like) magnetic silicene structures within the lines of the transfer matrix method and the Landauer–Büttiker formalism. We find that the self-similar arrangement of magnetic barriers in conjunction with structural asymmetry reduces the conductance oscillations typical of periodic magnetic silicene superlattices and more importantly makes the K ′ -spin-down conductance component dominant, resulting in nearly perfect positive and negative spin-valley polarization states accessible by simply reversing the magnetization direction. The tunneling magnetoresistance is not as prominent as in periodic magnetic silicene superlattices; however, it is better than in single magnetic junctions. Furthermore, the optimization of the spin-valley-dependent transport properties caused by the complex structure is superior than the corresponding one reported in typical aperiodic structures, such as Fibonacci and Thue–Morse magnetic silicene superlattices. [ABSTRACT FROM AUTHOR]

The well-known formalism for Sum-Frequency Generation (SFG) reflected or transmitted by a three-layer system involves three equations defining the emitted SFG intensity, the effective nonlinear susceptibility, and a set of Fresnel factors specific to the three-layer system. We generalize the equations to an N-layer system, where all media have non-vanishing thicknesses, by leaving the first two equations unchanged and modifying only the Fresnel factors. These universal Fresnel factors bear all the complexity of light propagation and interference in the system, in amplitude and phase. They are analytically known anywhere in the N-layer system, either at any interface or in any of the bulks, and share common expressions for the three beams, incoming or emitted, of the SFG process in reflection. Enclosing an ultrathin layer (e.g., a molecular monolayer) in the system does not modify the Fresnel factors except for boundary conditions at this layer, as in the three-layer case. Specific rules are elaborated to simplify systems containing macroscopic layers. Equations for the four- and five-layer systems are explicitly provided. Simulations in the four-layer system allow for the recovery of the results of the transfer matrix formalism at a lower complexity cost for SFG users. Finally, when several interfaces in the system produce SFG signals, we show that it is possible to probe only the most buried one by canceling all the SFG responses except at this last interface, generalizing the results of the three-layer system. [ABSTRACT FROM AUTHOR]

We assess the cavity molecular dynamics method for the calculation of vibrational polariton spectra using liquid water as a specific example. We begin by disputing a recent suggestion that nuclear quantum effects may lead to a broadening of polariton bands, finding instead that they merely result in anharmonic red shifts in the polariton frequencies. We go on to show that our simulated cavity spectra can be reproduced to graphical accuracy with a harmonic model that uses just the cavity-free spectrum and the geometry of the cavity as input. We end by showing that this harmonic model can be combined with the experimental cavity-free spectrum to give results in good agreement with optical cavity measurements. Since the input to our harmonic model is equivalent to the input to the transfer matrix method of applied optics, we conclude that cavity molecular dynamics cannot provide any more insight into the effect of vibrational strong coupling on the absorption spectrum than this transfer matrix method, which is already widely used by experimentalists to corroborate their cavity results. [ABSTRACT FROM AUTHOR]

A semiclassical method is presented for the calculation of Feshbach resonance positions and widths. This approach, based on semiclassical transfer matrices, relies only on relatively short trajectory fragments, thus avoiding problems associated with the long trajectories needed in more straightforward semiclassical techniques. Complex resonance energies are obtained from an implicit equation that is developed to compensate for the inaccuracy of the stationary phase approximation underlying the semiclassical transfer matrix applications. Although this treatment requires calculation of transfer matrices for complex energies, an initial value representation method makes it possible to extract such quantities from ordinary real-valued classical trajectories. This treatment is applied to obtain positions and widths for resonances in a model two-dimensional system, and the results are compared to those obtained from accurate quantum mechanical calculations. The semiclassical method successfully captures the irregular energy dependence of resonance widths that vary over a range of more than two orders of magnitude. An explicit semiclassical expression for the width of narrow resonances is also presented and serves as a simpler, useful approximation for many cases. [ABSTRACT FROM AUTHOR]

The applicability of the frequency bands-gaps to reduce the vibrations in the pipes conveying fluid is investigated by employing periodic inertial amplification mechanisms. Using the transfer matrix method, the band structures for flexural waves are calculated to study the frequency band-gap ranges and the vibration reduction. Band-gaps can exist in a piping system with fluid loading by means of the periodic inertial amplification mechanisms. Numerical results of the band-gaps of the pipe conveying fluid with periodic inertial amplification mechanisms are validated with the vibration experiments. The effects of the flow velocity, the amplification masses and the amplification angles on the band-gap properties are analyzed. It is found that the periodic inertial amplification mechanisms can enhance the vibration reduction capacity of the fluid conveying pipes. [ABSTRACT FROM AUTHOR]

Dispersion analysis of acoustic guided waves, propagating in a stratified medium, containing an internal sandy layer in contact with the isotropic elastic substrate and the upper elastic isotropic layer, is developed by applying the modified Cauchy formalism coupled with the exponential fundamental matrices and the Thomson–Haskell transfer matrix method. The developed approach is suitable for analyzing dispersion properties of guided waves at the broad variation of the sandy parameter. Several phenomena, concerning anomalous dispersion of guided waves at varying sandy parameter, are observed, revealing the possibility of nondestructive evaluation of sandy layers within the upper crust. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of Lamb waves in an orthotropic elastic sandwich plate is investigated. The surface layers and the core layer may be compressible or incompressible. The main aim of the paper is to derive explicit dispersion equations. First, the dispersion equations of symmetric modes and asymmetric modes are derived for compressible sandwich plates by using the effective boundary condition method along with the transfer matrices for orthotropic elastic layers. These dispersion equations recover the dispersion equations of Lamb waves propagating in compressible isotropic sandwich plates. The dispersion equations for incompressible sandwich plates are obtained by using the incompressible limit method. It is shown numerically that the thickness ratio and the stiff contrast affect strongly higher modes and the incompressibility has strong influence on symmetric modes. Remarkably, the obtained dispersion equations can be used to analyze the dispersion characteristic of Lamb waves propagating in sandwich plates with honeycomb core layers because the honeycomb core layers can be replaced effectively by transversely isotropic elastic layers by mean of homogenization. [ABSTRACT FROM AUTHOR]

The proposed work exhibits the novel Kretschmann (K)-surface plasmon resonance (SPR) sensor structure based on the cobalt and 2D material MXene (Ti3C2Tx). The performance of a silver (Ag)-cobalt (Co) (bimetallic)-based SPR sensor is numerically investigated by the transfer matrix method (TMM) for the analysis of light propagation through the proposed layers. Additionally, the electric field intensity and penetration depth (PD) are analyzed by the finite element method (FEM) using COMSOL Multiphysics. The cobalt confirms the large magneto-optical activity suitable for plasmonics. The optimization of the Ag-Co metals and MXene thickness enhances the sensitivity of the proposed sensor with the minimum reflectance (Rmin). Two-dimensional (2D) material of MXene enhances the sensitivity and protects the bimetals (Ag-Co) from oxidation. The highest sensitivity of 272.38°/RIU is achieved with the proposed sensor, and it is convenient in the medical and life science field to detect biomolecules. [ABSTRACT FROM AUTHOR]

The stability of a current-carrying beam in an external magnetic field is studied in this paper. The beam rests on periodic supports and is modeled as an Euler-Bernoulli elastic beam. Based on the linearized stability equation and propagator transfer matrix approach for a multi-span finite-length beam, the stability equation and solutions of the several boundary value problems are obtained. While the Floquet-Bloch theory is widely used in the dynamic problem of phononic and photonic structure conditions, its application to the solution of infinite length beam static stability problem is novel. The stability values of the periodic infinite beam model are in very good agreement with one of the finite-length multi-span beams. [ABSTRACT FROM AUTHOR]

Pneumatic artificial muscle (PAM) has attracted significant attention owing to its safe and compliant physical properties in industrial manipulators, along with advanced service technologies. Since PAM is prone to large deformation problems, actuation control, and dynamic identification is required to perceive considering precise and fast computation. This article presents a methodology for accurate dynamic modeling and analysis of a planar robotic arm in the presence of large deformations caused by the artificial muscle. This novel planar robotic arm with pneumatic actuation and spring loaded in an antagonistic form is designed and fabricated. This article deals with the displacement analysis of a new type of PAM-actuated mechanism for large deformation. The aim is to find an accurate mathematical model of this robotic arm with motion nonlinearity. Since vibration can be generated in the articulating operations according to the dynamic behavior of PAM, a transfer-matrix method is proposed to explore the effect of flexibility undergoing planar flexural deformation. An explanation of the procedure through presenting its general formulation is employed to experiment. The discrete method is analyzed beside the rich datasets generated for actuator identification in the preliminary experimental study. The transfer matrices are determined considering the flexibilities whereas results are verified using MSC.ADAMS©. Experimental validation and numerical modeling confirm that the presented modeling methods help to improve the performance of the pneumatic muscle drives in high-precision manipulators. This study leaves room for further development of this algorithmic framework with a more complicated mechanism with soft pneumatic network actuators for various designs. [ABSTRACT FROM AUTHOR]

Curve beams are widely used in structural engineering like civil engineering and aircraft structures. Due to their coupling effects of bending, shear, and torsion, curve beams have a significant role in wave propagation fields as complete bandgaps can be generated. With the miniaturization of devices, it becomes increasingly imperative to investigate wave characteristics of curve beams at the nanoscale, taking into account the flexoelectric effect. In this study, a theoretical model for the periodic flexoelectric curve beams is established under the strain-gradient electro-elasticity theory. Subsequently, a customized state-space-based transfer matrix method for flexoelectric curve beam is specifically proposed, referred to as FCB-TMM. According to the Floquet-Bloch theorem, the dispersion relations for the periodic flexoelectric curve beams with intriguing coupling characteristics can be obtained and verified. Additionally, the influence of the flexoelectric effect and strain gradient effect on its complete bandgaps is analyzed. The results indicate that the flexoelectric effect plays a vital role in wave propagation at small scales, causing a shift in the bandgaps towards higher frequencies. Ultimately, the synergistic effects of significant geometric and material parameters combined with the flexoelectric effect on the bandgaps are systematically discussed. It is discovered that changing flexoelectric coefficients may alter the pattern of bandgap variation with these geometric and material parameters, while the influence of flexoelectric coefficients on bandgaps varies depending on the values of these parameters. Our investigation offers an insight into understanding the wave propagation of the curve nanobeams, and thus further guides the application and development of flexoelectric wave components in MEMS/NEMS. • A state-space-based transfer matrix method is proposed for the flexoelectric curve nanobeams. • Complex band properties of the periodic flexoelectric curve nanobeams are investigated. • The synergistic effect between flexoelectric effect and significant parameters are systematically discussed. • The findings benefit the application and development of flexoelectric wave components in MEMS/NEMS. [ABSTRACT FROM AUTHOR]

• Analytical solution of viscoelastic laminated beams in hygro-thermo-mechanical condition is proposed. • The proposed solution is more accurate than simplified solutions and is efficient over finite element counterpart. • A superposition principle for viscoelastic laminated beams in hygro-thermo-mechanical condition is derived. In order to predict the creep and recovery behaviors of for viscoelastic laminated beam in hygro-thermo-mechanical (HTM) coupled condition, an exact analytical solution is proposed. This solution considers two effect mechanisms: temperature and humidity, including the expansion difference and the variation of viscoelastic properties. In the analytical model, the stresses and displacements of each lamina are described based on the hygro-thermo-elasticity theory combined with the Boltzmann superposition. By employing series expansion, the transfer matrix method, and Laplace transform, the solution is determined analytically. Notably, the entire process of Laplace inverse transformation is carried out analytically without relying on any numerical approximations. The comparison analysis indicates that the proposed solution is more computationally efficient than the finite element counterpart and is more accurate than the solutions based on transverse shear deformation assumption. By analyzing the components of the proposed solution, a modified superposition principle applicable to HTM coupled conditions and a superposition principle for creep recovery are derived. In the end, the HTM coupled behavior, the bending creep and recovery as well as the optimization of expansion coefficient are investigated in detail. [ABSTRACT FROM AUTHOR]

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4 × 4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ± p 1 , ± p 2 , with p 1 ≠ p 2 , and b) its off-diagonal 2 × 2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4 × 4 matrix and provide an algorithm to compute the N th power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z -axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z -axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity. [ABSTRACT FROM AUTHOR]

Identifying brain-tissue types holds significant research value in the biomedical field of non-contact brain-tissue measurement applications. In this paper, a layered metastructure is proposed, and the second harmonic generation (SHG) in a multilayer metastructure is derived using the transfer matrix method. With the SHG conversion efficiency (CE) as the measurement signal, the refractive index ranges that can be distinguished are 1.23~1.31 refractive index unit (RIU) and 1.38~1.44 RIU, with sensitivities of 0.8597 RIU−1 and 1.2967 RIU−1, respectively. It can distinguish various brain tissues, including gray matter, white matter, and low-grade glioma, achieving the function of a second harmonic mode sensor (SHMS). Furthermore, temperature has a significant impact on the SHG CE, which can be used to define the switch signal indicating whether the SHMS is functioning properly. When the temperature range is 291.4~307.9 Kelvin (K), the temperature switch is in the "open" state, and the optimal SHG CE is higher than 0.298%, indicating that the SHMS is in the working state. For other temperature ranges, the SHG CE will decrease significantly, indicating that the temperature switch is in the "off" state, and the SHMS is not working. By stimulating temperature and using the response of SHG CE, the temperature-switch function is achieved, providing a new approach for temperature-controlled second harmonic detection. [ABSTRACT FROM AUTHOR]

In this study, we investigated the morphological and mechanical properties of hybrid composites with a polyamide 6 (PA6) matrix and reinforced with basalt fibers (BFs) and halloysite nanotubes (HNTs). The presence of reinforcing materials fundamentally changed the behavior of the molecules, which was morphologically manifested in the change in the ratio of the rigid and the mobile amorphous phase. The x‐ray diffraction and transmission electron microscopic images showed the crystal nucleating effect of the halloysite nanotubes. Based on these, we concluded that around the basalt fibers, an interphase is formed, while around the nanoparticles, a two‐layer interphase is created, the inner layer of which is semicrystalline, while the outer layer is rigid amorphous (RA). The nanoparticles are surrounded by a semicrystalline interphase, which is surrounded by an RA interphase. This overlaps with the interphase of the basalt fibers, therefore the halloysite nanotubes can effectively help the stress transfer from the matrix to the basalt fibers. The mechanical properties of the samples also reflected this: the hybrid composites had a significantly higher tensile modulus, tensile strength, and an unchanged elongation at break compared to the composite reinforced with only basalt fiber. Highlights: Environmentally friendly polyamide 6 matrix hybrid composites were prepared.Uniform distribution of halloysite nanotubes was achieved.Enhanced mechanical properties were observed for hybrid composites.Halloysite nanotubes aid stress transfer from matrix to basalt fibers.Halloysite nanotubes act as crystalline nucleating agents. [ABSTRACT FROM AUTHOR]

Many animals, plants or gems exhibit iridescent material appearance in nature. These are due to specific geometric structures at scales comparable to visible wavelengths, yielding so‐called structural colors. The most vivid examples are due to photonic crystals, where a same structure is repeated in one, two or three dimensions, augmenting the magnitude and complexity of interference effects. In this paper, we study the appearance of 1D photonic crystals (repetitive pairs of thin films), also called Bragg mirrors. Previous work has considered the effect of multiple thin films using the classical transfer matrix approach, which increases in complexity when the number of repetitions increases. Our first contribution is to introduce a more efficient closed‐form reflectance formula [Yeh88] for Bragg mirror reflectance to the Graphics community, as well as an approximation that lends itself to efficient spectral integration for RGB rendering. We then explore the appearance of stacks made of rough Bragg layers. Here our contribution is to show that they may lead to a ballistic transmission, significantly speeding up position‐free rendering and leading to an efficient single‐reflection BRDF model. [ABSTRACT FROM AUTHOR]

We study the transport properties of Dirac fermions in ABC trilayer graphene (ABC-TLG) superlattices. More specifically, we analyze the impact of varying the physical parameters-the number of cells, barrier/well width, and barrier heights-on electron tunneling in the ABC-TLG. In the initial stage, we solved the eigenvalue equation to determine the energy spectrum solutions for the ABC-TLG superlattices. Subsequently, we applied boundary conditions to the eigenspinors and employed the transfer matrix method to calculate transmission probabilities and conductance. For the two-band model, we identified the presence of Klein tunneling, with a notable decrease as the number of cells increased. The introduction of interlayer bias opened a gap as the number of cells increased, accompanied by an asymmetry in scattered transmission. Increasing the barrier/well width and the number of cells resulted in an amplified number of gaps and oscillations in both two-band and six-band cases. We observed a corresponding decrease in conductance as the number of cells increased, coinciding with the occurrence of a gap region. Our study demonstrates that manipulating parameters such as the number of cells, the width of the barrier/well, and the barrier heights provides a means of controlling electron tunneling and the occurrence of gaps in ABC-TLG. Specifically, the interplay between interlayer bias and the number of cells is identified as a crucial factor influencing gap formation and transmission asymmetry. [ABSTRACT FROM AUTHOR]

Standard beams are mainly used for the calibration of strain sensors using their load reconstruction models. However, as an ill-posed inverse problem, the solution to these models often fails to converge, especially when dealing with dynamic loads of different frequencies. To overcome this problem, a piecewise Tikhonov regularization method (PTR) is proposed to reconstruct dynamic loads. The transfer function matrix is built both using the denoised excitations and the corresponding responses. After singular value decomposition (SVD), the singular values are divided into submatrices of different sizes by utilizing a piecewise function. The regularization parameters are solved by optimizing the piecewise submatrices. The experimental result shows that the MREs of the PTR method are 6.20% at 70 Hz and 5.86% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits MREs of 28.44% and 29.61% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates MREs of 29.98% and 18.42% at the same frequencies. Furthermore, the PREs of the PTR method are 3.54% at 70 Hz and 3.73% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits PREs of 27.01% and 26.88% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates PREs of 29.50% and 15.56% at the same frequencies. All in all, the method proposed in this paper can be extensively applied to load reconstruction across different frequencies. [ABSTRACT FROM AUTHOR]

We discuss the growth of the singular values of symplectic transfer matrices associated with ergodic discrete Schrödinger operators in one dimension, with scalar and matrix-valued potentials. While for an individual value of the spectral parameter the rate of exponential growth is almost surely governed by the Lyapunov exponents, this is not, in general, true simultaneously for all the values of the parameter. The structure of the exceptional sets is interesting in its own right, and is also of importance in the spectral analysis of the operators. We present new results along with amplifications and generalisations of several older ones, and also list a few open questions. Here are two sample results. On the negative side, for any square-summable sequence |$p_{n}$| there is a residual set of energies in the spectrum on which the middle singular value (the |$W$| -th out of |$2W$|⁠) grows no faster than |$p_{n}^{-1}$|⁠. On the positive side, for a large class of cocycles including the i.i.d. ones, the set of energies at which the growth of the singular values is not as given by the Lyapunov exponents has zero Hausdorff measure with respect to any gauge function |$\rho (t)$| such that |$\rho (t)/t$| is integrable at zero. The employed arguments from the theory of subharmonic functions also yield a generalisation of the Thouless formula, possibly of independent interest: for each |$k$|⁠ , the average of the first |$k$| Lyapunov exponents is the logarithmic potential of a probability measure. [ABSTRACT FROM AUTHOR]

One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underlying this is a factorization formula for L-operators (solutions of the Yang–Baxter equation associated to particular infinite-dimensional representations). To extend such a formalism to open spin chains, one needs a factorization identity for solutions of the reflection equation (boundary Yang–Baxter equation) associated to these representations. In the case of quantum affine sl 2 and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras. [ABSTRACT FROM AUTHOR]

Surface plasmon resonance (SPR) has gained attention as a promising method for effective label-free biosensing. Immunoglobulin (IgG) detection is very important to understand the past infection and immunity of any individual. Thus, this study aims to develop a SPR sensor with better sensitivity for detecting IgG. It emphasizes the utilization of a high-performance planar waveguide-based SPR sensor to detect IgG by analyzing a suitable sensor topology. The sensor configuration consists of five distinct layers: silver (Ag), silicon nitride ( Si 3 N 4 ), black phosphorus (BP), an enzyme, and a sensing medium. Silver (Ag) stimulates surface plasmons, while Si3N4 and BP are utilized to enhance absorption capabilities and serve as the bio-molecular recognition element, respectively. The proposed sensor simulation employs the transfer matrix method and an angular interrogation scheme. To assess this proposed sensor's impact, the sensing region is assessed while considering three layers: Ag, Ag-BP, and Ag–Si3N4. Initially, the thickness of the Ag layer is optimized by recording its transmittance and achieving a minimum transmittance of 0.0027 at a thickness of 50 nm. Subsequently, the performance parameters are assessed using four different structures with slight variations in the IgG samples. The results depict the maximum achieved sensitivities as follows: 192 ∘ / RIU for conventional SPR, 203 ∘ / RIU for BP-based SPR, 287 ∘ / RIU for Si3N4-based SPR, and 352 ∘ / RIU for the proposed structure. This comparative study demonstrates that the proposed SPR configuration significantly enhances sensitivity, quality factor, and detection accuracy performance. [ABSTRACT FROM AUTHOR]

The boundary conditions of the moving layered medium are analyzed and the expressions of electromagnetic field are deduced. The reflection and transmission coefficients in fixed coordinates are obtained by using the covariance characteristic of Maxwell Equations. It is very complicated to apply boundary conditions many times in analyzing a multi-layer slab. In this paper, the results obtained from the boundary conditions of single-layer slab are analogous with those obtained by the transfer matrix method. Through improvement and generalization, the transfer matrix method can be used to calculate the moving multi-layer slabs. It can be applied to calculate the reflection and transmission coefficients of one-dimensional moving photonic crystal as well as deal with TM and TE polarization for the oblique incident. The zero reflection points of TM and TE polarization for layered slab are calculated. The results calculated in this study are matching well with the reference. It shows that the reflection oscillation enhances with the increase of β and layer number, while the changing rule of reflections about TM polarization is relatively complex. The reflections of both TE wave and TM wave are all related to the incidence angle. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotics of resonances in the semiclassical limit |$h\to 0^{+}$| for two-by-two matrix Schrödinger operators in one dimension. We study the case where the two underlying classical Hamiltonian trajectories cross tangentially in the phase space. In the setting that one of the classical trajectories is a simple closed curve whereas the other one is non-trapping, we show that the imaginary part of the resonances is of order |$h^{(m_{0}+3)/(m_{0}+1)}$|⁠ , where |$m_{0}$| is the maximal contact order of the crossings. This principal order comes from the subprincipal term of the transfer matrix at crossing points, which describes the propagation of microlocal solutions from one trajectory to the other. In addition, we compute explicitly the leading coefficient of the resonance widths. [ABSTRACT FROM AUTHOR]

In the present study, an ultra-sensitive surface plasmon resonance biosensor is developed. The device is composed of a CaF2-prism, silver, silicon nitride, nickel, and black phosphorus have been deposited. The setup is grounded in the Kretschmann configuration and theoretically analyzed by means of transfer matrix method and Fresnel equations. For selective diagnosis of liver tissue and its mutation in terms of variation in RI, the biosensor provides an ultrahigh angular sensitivity of 383.62°/RIU for MET tissue and 403.92°/RIU for HCC tissue. The optimization of angular sensitivity and other sensor parameters in terms of thickness and number of layers has also been utilized. To validate the reflectance curve, electric field intensity enhancement factor and phase interrogation have also been conducted. The acquired results state that the proposed biosensor yields an enhanced sensitivity when compared to other reported results. Due to its advantage of fast, accurate and early-stage detection of liver mutations with a very small number of samples, this report may expedite a sensing device for commercial applications. [ABSTRACT FROM AUTHOR]

Until now, Surface Plasmon Resonance (SPR) biosensors still rely on gold as their transducer element, and this makes cheap analytical devices difficult to achieve. On the other hand, lossy mode resonance (LMR) sensors offer transducers with more alternative materials due to their flexibility, which can be excited in p‐ and s‐polarized light. In this research it is carried out a numerical investigation using the transfer matrix method on LMR sensor composed of molybdenum disulfide (MoS2) as lossy layer and Cytop as matching layer. The reflectance curves for different thicknesses of MoS2 and Cytop are numerically investigated. The results obtained show that the chip consisting of 250 nm Cytop and 4 layers of MoS2 has a penetration depth 3 times higher than conventional SPR chips. If sensors with two types of polarization are compared, sensors with s‐polarized light have shown higher sensitivity reaching 72.13°/RIU with a wider dynamic range starting from a refractive index of 1.331 to 1.401. In this refractive index range, this sensor has displayed good signal stability where the reduction in resonance dip depth is only ≈6%. These computational results make the proposed structure very promising to be applied in the quantification of biological materials. [ABSTRACT FROM AUTHOR]

Sensors and actuators frequently encounter unexpected deviations from their optimal operating conditions, making their reliability an essential topic in many electric motor drives. In this paper, a comparison of structured residual synthesis methods for actuator and sensor additive fault detection and isolation (FDI) in a permanent magnet (PM) DC motor, applying two different approaches to the design of primary residuals, is presented. The first method involves a standard approach and is based on system transfer matrix synthesis. The second, more convenient approach involves the synthesis of primary residuals based on the analysis of subsystems that describe the observed system. Both methods are applicable for linear and time-invariant (LTI) systems but were successfully applied to a laboratory system that shows nonlinear behavior, time-variant properties, and is affected by a constant disturbance, thanks to the proposed technique of residual translation with the previous design of internal residuals. With the proposed method, all important performance characteristics of the residual generators such as fault sensitivity, reaction speed, and robustness are achieved. The technique can be applied to all mechatronic systems in general, whose behavior can be with satisfactory accuracy described by an LTI model. Given the transfer functions and state-space model of the system in the presence of faults in the Z domain with reduced order, presented technique is computationally efficient for embedded systems. Also, in addition to fault detection and isolation, the system can identify faults by analyzing fault sensitivities, nominal faults, and stationary residual values, making it superior for most FDI applications. A real-time experiment performed on a laboratory setup, which consists of a DC motor, an amplifier designed in the form of a linear electronic circuit, and a Compact RIO 9075 real-time processor is used to develop the FDI system, to generate residuals and confirm advantages of the proposed FDI technique. [ABSTRACT FROM AUTHOR]

The paraxial propagation of a higher-order cosine-hyperbolic-Gaussian beam (HOChGB) in a chiral medium is investigated theoretically. Analytical expression of the HOChGB passing through a chiral medium is derived based on the Huygens-Fresnel Integral and the ABCD transfer matrix. From the obtained formula, the propagation properties of this beam in a chiral medium are analyzed with numerical illustrative examples. The obtained results show that the evolution of the intensity pattern of HOChGB depends strongly on the chiral factor, the beam order, and the decentered parameter. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically investigate the transmission properties of a structure composed of a topological one-dimensional photonic crystal (1D PhC) heterostructure and a conventional 1D PhC containing indium-antimonide (InSb) as a defect layer using the transfer matrix method. The phenomenon of Fano resonance can be achieved by coupling the defect mode with the topological edge state mode, which is supported by the topological PhC. The numerical results show that a narrow Fano resonance is observed in the transmission spectrum of the structure in the presence of the external magnetic field applied to the InSb defect layer. The optical properties of the InSb defect layer, and, therefore, the Fano resonance, can be dynamically controlled by changing the applied external magnetic field. The results obtained with the proposed structure reveal that the magnetic field has the greatest influence on controlling the optical properties of the Fano resonance. These findings could be beneficial for optical devices such as optical filters, sensors, and optical switches. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to investigate a one-dimensional photonic crystal containing N-doped germanium semiconductor as a nonlinear defect layer with an intensity-dependent refractive index, silica (SiO2) and zinc selenide (ZnSe) as crystal cells. Bistability of the TE polarization of the transmission spectrum due to the nonlinear property of the defect layer is investigated by the transfer matrix method (TMM). The refractive index of the germanium nonlinear semiconductor layer is simultaneously depending on the doping density and the intensity of the irradiated light. The changes in both factors are investigated. The impact on the transmission spectrum of the bistability threshold due to the change in the thickness of the defect layer, the thickness of other layers of crystal cells, and the angle of incident light are investigated. The nonlinear effect caused by light intensity as well as doped density effect on the germanium nonlinear semiconductor medium is used simultaneously. As a result, the nonlinear effect caused by the light intensity to create bistability is more than the doping density. [ABSTRACT FROM AUTHOR]

This work presents an innovative platform of a multi-channel one-dimensional photonic crystal (1-DPC) based on blood refractive index data of different patients in the aspect of the main protein components like hemoglobin. This photonic crystal (PC) contains a defect center infiltrated with plasma using a microorder size syringe. When binary silica and III–V semiconductor (InSb) materials are combined, they increase the refractive index difference between the alternate layers of the composite material, resulting in a wide photonic band gap (PBG). We use the well-known transfer matrix method (TMM) to observe the reflectance of various blood samples that were previously published. We assess and contrast the influence of different refractive index data on the dynamic shift in PBG calculation for novel superior and resourceful sensor in the prevention of microscopic organisms such as SARS-CoV-2, the virus linked with COVID-19. Yet, the performance of this PC has more moral content and unlimited casting efficacy in the face of an incurable virus. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the theoretical framework underlying our proposed methodology of verification and validation (V&V) for quantum mechanical emission models using analogous macroscopic electromagnetic systems. We derive the correspondence between quantum mechanics and electromagnetism using the transfer matrix approach and describe the electromagnetic analog that will be used to anchor the atomistic quantum tunneling simulations. Finally, we illustrate this correspondence by comparing the quantum mechanical and electromagnetic systems for some simple, analytically soluble examples and outline future V&V work based on the framework presented here. [ABSTRACT FROM AUTHOR]

The issue of counting independent sets of a graph, G, represented as i (G) , is a significant challenge within combinatorial mathematics. This problem finds practical applications across various fields, including mathematics, computer science, physics, and chemistry. In chemistry, i (G) is recognized as the Merrifield–Simmons (M-S) index for molecular graphs, which is one of the most relevant topological indices related to the boiling point in chemical compounds. This article introduces an innovative algorithm designed for tallying independent sets within grid-like structures. The proposed algorithm is based on the 'branch-and-bound' technique and is applied to compute i (G m , n) for a square grid formed by m rows and n columns. The proposed approach incorporates the widely recognized vertex reduction rule as the basis for splitting the current subgraph. The methodology involves breaking down the initial grid iteratively until outerplanar graphs are achieved, serving as the 'basic cases' linked to the leaf nodes of the computation tree or when no neighborhood is incident to a minimum of five rectangular internal faces. The time complexity of the branch-and-bound algorithm speeds up the computation of i (G m , n) compared to traditional methods, like the transfer matrix method. Furthermore, the scope of the proposed algorithm is more general than the algorithms focused on grids since it could be applied to process general mesh graphs. [ABSTRACT FROM AUTHOR]

Utilizing multi-modal data, as opposed to only hyperspectral image (HSI), enhances target identification accuracy in remote sensing. Transformers are applied to multi-modal data classification for their long-range dependency but often overlook intrinsic image structure by directly flattening image blocks into vectors. Moreover, as the encoder deepens, unprofitable information negatively impacts classification performance. Therefore, this paper proposes a learnable transformer with an adaptive gating mechanism (AGMLT). Firstly, a spectral–spatial adaptive gating mechanism (SSAGM) is designed to comprehensively extract the local information from images. It mainly contains point depthwise attention (PDWA) and asymmetric depthwise attention (ADWA). The former is for extracting spectral information of HSI, and the latter is for extracting spatial information of HSI and elevation information of LiDAR-derived rasterized digital surface models (LiDAR-DSM). By omitting linear layers, local continuity is maintained. Then, the layer Scale and learnable transition matrix are introduced to the original transformer encoder and self-attention to form the learnable transformer (L-Former). It improves data dynamics and prevents performance degradation as the encoder deepens. Subsequently, learnable cross-attention (LC-Attention) with the learnable transfer matrix is designed to augment the fusion of multi-modal data by enriching feature information. Finally, poly loss, known for its adaptability with multi-modal data, is employed in training the model. Experiments in the paper are conducted on four famous multi-modal datasets: Trento (TR), MUUFL (MU), Augsburg (AU), and Houston2013 (HU). The results show that AGMLT achieves optimal performance over some existing models. [ABSTRACT FROM AUTHOR]

A pulse-Doppler (PD) radar has the advantage of strong anti-interference ability, and it is often used as a solution for maneuvering target tracking. In the application of target monitoring and tracking in PD radars, the interacting multiple model algorithm (IMM) has become the main and preferred choice due to its flexibility and high accuracy. However, the probability transfer matrix in classical IMM algorithms generally depends on constant prior knowledge, and if a PD radar is tracking a strong maneuvering target, it is inevitable to encounter some limitations, such as the possibility of target tracking trajectory deviation, and even a loss of the target. The Markov probability transfer matrix is proposed with an adaptive modification ability in real time to overcome the above problems in this paper. Additionally, for improving the speed of switching between the models, the fuzzy control system for secondary updating of model probability is adopted. By this means, the tracking accuracy of maneuvering targets is enhanced. Compared with the classical IMM algorithm, the corresponding simulation results for the PD radar indicate that the overall tracking accuracy of the proposed adaptive IMM algorithm is improved by 19.6%. In conclusion, the continuity and accuracy of the target trajectory can be effectively improved with the proposed adaptive IMM algorithm in PD radar cases. [ABSTRACT FROM AUTHOR]

As an affordable form of public transit, the metro still faces first- and last-mile problems. Integration of dockless bike sharing (DBS) and the metro offers a reasonable solution to this problem. However, an in-depth exploration of the spatio-temporal characteristics and determinants of DBS–metro integration, especially meteorological indicators, is lacking. The spatiotemporal characteristics of the transfer volume on weekdays and weekends in Beijing were analyzed. Geographically weighted regression was utilized to investigate the effects of the significant determinants on the spatial variation of the transfer volume. The results indicate that the transfer volume is concentrated within the Fifth Ring Road in Beijing. The effects of education services and metro station density were negatively correlated with transfer volume. As expected, population density and enterprises positively affect transfer volume, whereas wind speed and relative humidity have negative effects. These findings provide new insights into the promotion of DBS–metro integration. [ABSTRACT FROM AUTHOR]

Incorporating dispersion into time-varying media not only holds practical significance but also profoundly transforms the electromagnetic characteristics of such dynamic media. In this work, we have developed a temporal transfer matrix method (TTMM) tailored for time-varying media exhibiting a specific type of dispersion, namely, Lorentzian dispersion. The conventional TTMM for nondispersive time-varying media can be regarded as an approximation of this developed TTMM in the nondispersive limit by ignoring the unobservable infinite-frequency modes. By using this developed TTMM, we have investigated the Floquet bands of Lorentzian dispersive media with time-periodic plasmon frequencies or resonant frequencies. Under temporal modulations, certain degenerate points of the Floquet bands will be lifted, creating bandgaps, while others will give rise to two types of exceptional point (EP) pairs. This sharply contrasts with the well-known Floquet bands of nondispersive time-varying media, where only one type of EP pair exists. Our developed TTMM serves as a powerful tool for investigating the phenomena within the realm of dispersive time-varying media. [ABSTRACT FROM AUTHOR]

We present mathematical theory for self-similarity induced spectral gaps in the spectra of systems generated by generalised Fibonacci tilings. Our results characterise super band gaps, which are spectral gaps that exist for all sufficiently large periodic systems in a Fibonacci-generated sequence. We characterise super band gaps in terms of a growth condition on the traces of the associated transfer matrices. Our theory includes a large family of generalised Fibonacci tilings, including both precious mean and metal mean patterns. We apply our analytic results to characterise spectra in three different settings: compressional waves in a discrete mass-spring system, axial waves in structured rods and flexural waves in multi-supported beams. The theory is shown to give accurate predictions of the super band gaps, with minimal computational cost and significantly greater precision than previous estimates. It also provides a mathematical foundation for using periodic approximants (supercells) to predict the transmission gaps of quasicrystalline samples, as we verify numerically. [ABSTRACT FROM AUTHOR]

Presently, noise pollution in ducts is considered seriously, and numerous studies concerning sound absorption in pipes are ongoing globally. Aiming at the difficulty to eliminate the low-frequency noise in pipeline, a multi-resonant cavity duct metamaterial is proposed. The acoustic properties of the metamaterial are calculated using the energy method based on the Hamilton principle and the transfer matrix methodology. The result demonstrates that the duct metamaterial, due to its band gaps and negative bulk modulus, obtains several sound absorption peaks and is advantageous to sound elimination in low frequency. The good acoustic characteristics of the duct metamaterial for sound insulation can be attributed to the plate-cavity interaction. Parametric analysis of the proposed structure is also carried out. This study demonstrates the application prospects of duct metamaterials for multi-frequency sound absorption in engineering practice. [ABSTRACT FROM AUTHOR]

Fabric-reinforced cementitious matrix (FRCM) materials are increasingly common for strengthening existing masonry structures. The constitutive behaviour of these materials is complex to model due to the inner complex mechanisms that develop in composite mechanics, such as stress transfer between matrix and fabric, mortar cracking, friction at the matrix-to-fabric interface, and bonding with the substrate. This paper aims to address these phenomena by presenting a numerical approach able to predict the bond behaviour of FRCM-to-masonry systems through the use of simple truss elements and nonlinear springs to simulate the fabric-to-matrix and composite-to-substrate interactions. The model was implemented in an open-source environment and allowed direct sensitivity analysis to assess the role of the constitutive variables. The comparisons between the results of the numerical approach and experimental responses show that the proposed methodology is an effective and easy tool to predict the mechanical behaviour of FRCM composites, with a reduced computational effort. [ABSTRACT FROM AUTHOR]

The hitting time, which refers to the time required to find the marked element in the search algorithm, is one of the most interesting properties of quantum walk. In this paper we briefly analyze the hitting time on a finite 2D lattice in the classical case, focusing on the quantum version of the hitting time and give specific expressions for each. It is well known that the quantum hitting time has the same order as the square of the classical case, and our work also happens to verify this particular property. [ABSTRACT FROM AUTHOR]

The effect of a single-layer anti-reflective coating (ARC) on ZnO-based dye-sensitized solar cells (DSSCs) is theoretically predicted and verified by experimental fabrication. By the transfer matrix method (TMM), the absorption of the DSSC with and without the single-layer ARC is calculated and the improvement in short-circuit current density (∆Jsc%) is estimated. The optimized thickness of the ARC required to obtain maximum improvement in the short-circuit current density (∆Jsc%) is determined. By employing ARC with the calculated optimized thickness, the fabrication of spin-coated ZnO-based DSSCs is carried out. The structural and optical parameters are studied using XRD analysis and UV absorption spectra. The efficiency of the DSSC with and without the ARC is measured by intensity-modulated photocurrent and photovoltage spectroscopy. The theoretically predicted efficiency of the DSSC with and without ARC agrees well with the experimental values that provide insights about improving the electrical performance of the DSSC by the ARC. [ABSTRACT FROM AUTHOR]

A transversely isotropic elastic medium with a vertical axis of symmetry is considered. We obtain dispersion equations in real terms for guided Love and Rayleigh waves in a such a medium consisting of horizontal layers sandwiched between two half‐spaces by brief modifications of the available literatures on dispersion equations in elastic layered media through transfer matrix. To illustrate the applicability, dispersion curves of guided waves are computed for three‐ and five‐layered symmetric models with transversely isotropic coal seam in the middle. The Airy phase is marked by a minimum or maximum of group velocity in a dispersion curve, and this phase is important to get seam structure for mining safety. For the first three modes, the effect of Thomsen anisotropy parameters γ, ε and δ of a coal seam on frequency (fA) and group velocity (UA) of the Airy phase is similar in three‐ and five‐layered models. For guided Love waves, fA and UA have nearly a uniform increase with the increase of γ. For guided Rayleigh waves, the increase of ε causes fA and UA to increase; however, the increase of δ causes fA and UA to decrease. [ABSTRACT FROM AUTHOR]

Numerical methods generally need analytical solutions as test cases and validations in simplified problems. This work provides Laplace-domain explicit analytic solutions for fluid–structure interaction (FSI) water hammer waves within a pipe. Rather than applying the transfer matrix method (TMM) to the FSI four equations, it is transposed to the equivalent two-wave propagating problem considered instead. Using the classical wave matrix diagonalization approach permits decoupling the waves' propagation while at the same time coupling boundary conditions in the diagonal base. This approach permits the transfer matrix for coupled waves boundary conditions to be provided so as to obtain a Laplace-domain solution for the pressure/stress vector solution. This solution is written in a general framework that can be adapted for general applied boundary conditions for a single pipe. Three sets of boundary conditions are considered as examples and illustrations from solving the inverse Laplace transform of the considered explicit solutions. Consistent results with recently proposed time-domain solutions are found, and a one-to-one mapping between Laplace-domain and time-domain approaches is also established. This permits finding the discrete spectrum of FSI water hammer wave mode decomposition from TMM solutions. [ABSTRACT FROM AUTHOR]