Search Results (54)

Highly scattering media have garnered significant interest in recent years, ranging from potential applications in solar cells, photocatalysis, and other novel photonic devices to research on fundamental topics such as topological photonics, enhanced light–matter coupling and light confinement. Here, we report measurements of spectrally and time-resolved delayed luminescence (DL) in highly scattering rutile TiO₂ films. The complex emission kinetics manifests in the non-exponential decay of photon density and the temporal evolution of the spectral composition. We found that while the energy levels of TiO₂ nanoparticles broadly set the spectral regions of excitation and emission, our results demonstrate that the DL intensity and duration are strongly influenced by the inherent multiple elastic and inelastic processes determined by the mesoscale inhomogeneous structure of random media. We show that the lifetime of DL increases up to 6 s for the largest redshift detected, which is associated with multiple reabsorption processes. We outline a simple model for spectrally resolved DL emission from dense scattering media that can guide the design and characterization of composite materials with specific spectral and temporal properties. Full article

Ultrasonic pulse velocity (UPV) is a widely used technique for diagnosis and structural safety assessment of existing buildings. The main difficulties in UPV tests on-site are due to one-sided accessibility of materials and degraded/irregular surfaces. Pulse-echo ultrasonic tomography (PE-UT) can overcome the problem. Though it has been widely applied for detecting inhomogeneities within concrete, few works use the instrument to assess UPV. The present paper aims to fill the gap by comparing PE-UT results with those of through-transmission ultrasonic tests (TT-UT) commonly used for UPV characterization. TT-UT measurements were performed with cylindrical and exponential transducers. The latter are used on irregular surfaces or when coupling gel is forbidden. Few data are in the literature comparing exponential and cylindrical transducers’ results. This is a further element of novelty of the paper. PE-UT and TT-UT results were compared considering the effect of material compositeness, water, transmission mode, and transducer type. It was found that PE-UT allows for reliable and rapid one-sided measurements on concrete and stone in different conditions. The differences between PE-UT and TT-UT results were between 1 and 3%. Exponential transducers gave reliable results on fine-grained stone in direct transmission, with differences lower than 4% with cylindrical transducer results. Full article

Markov chain perturbation theory is a rapidly developing subfield of the theory of stochastic processes. This review outlines emerging applications of this theory in the analysis of stochastic models of chemical reactions, with a particular focus on biochemistry and molecular biology. We begin by discussing the general problem of approximate modeling in stochastic chemical kinetics. We then briefly review some essential mathematical results pertaining to perturbation bounds for continuous-time Markov chains, emphasizing the relationship between robustness under perturbations and the rate of exponential convergence to the stationary distribution. We illustrate the use of these results to analyze stochastic models of biochemical reactions by providing concrete examples. Particular attention is given to fundamental problems related to approximation accuracy in model reduction. These include the partial thermodynamic limit, the irreversible-reaction limit, parametric uncertainty analysis, and model reduction for linear reaction networks. We conclude by discussing generalizations and future developments of these methodologies, such as the need for time-inhomogeneous Markov models. Full article

This work develops a unified size-dependent shear deformation theory (SDSDT) to analyze the free vibration behavior of a functionally graded (FG) magneto-electro-elastic (MEE) microplate under fully simply supported conditions, open- or closed-circuit surface conditions, biaxial compression, magnetic and electric potentials, and uniform temperature changes based on consistent couple stress theory (CCST). The FG-MEE microplate is composed of BaTiO₃ (a piezoelectric material) and CoFe₂O₄ (a magnetostrictive material). Various CCST-based SDSDTs, considering couple stress and thickness stretching effects, can be reproduced by employing a generalized shape function that characterizes shear deformation distributions along the thickness direction within the unified SDSDT. These CCST-based SDSDTs encompass the size-dependent classical plate theory (CPT), first-order shear deformation theory (SDT), Reddy’s refined SDT, exponential SDT, sinusoidal SDT, and hyperbolic SDT. The unified SDSDT is validated by comparing its solutions with relevant three-dimensional solutions available in the literature. After validation and comparison studies, we conduct a parametric study, whose results indicate that the effects of thickness stretching, material length-scale parameter, inhomogeneity index, and length-to-thickness ratio, as well as the magnitude of biaxial compressive forces, electric potential, magnetic potential, and uniform temperature changes significantly impact the microplate’s natural frequency. Full article

This manuscript studies the M-fractional Landau–Ginzburg–Higgs (M-fLGH) equation in comprehending superconductivity and drift cyclotron waves in radially inhomogeneous plasmas, especially for coherent ion cyclotron wave propagation, aiming to explore the soliton solutions, the parameter’s effect, and modulation instability. Here, we propose a novel approach, namely a newly improved Kudryashov’s method that integrates the combination of the unified method with the generalized Kudryashov’s method. By employing the modified F-expansion and the newly improved Kudryashov’s method, we investigate the soliton wave solutions for the M-fLGH model. The solutions are in trigonometric, rational, exponential, and hyperbolic forms. We present the effect of system parameters and fractional parameters. For special values of free parameters, we derive some novel phenomena such as kink wave, anti-kink wave, periodic lump wave with soliton, interaction of kink and periodic lump wave, interaction of anti-kink and periodic wave, periodic wave, solitonic wave, multi-lump wave in periodic form, and so on. The modulation instability criterion assesses the conditions that dictate the stability or instability of soliton solutions, highlighting the interplay between fractional order and system parameters. This study advances the theoretical understanding of fractional LGH models and provides valuable insights into practical applications in plasma physics, optical communication, and fluid dynamics. Full article

In this paper, we investigate differential equations with generalized piecewise constant delay, DEGPCD in short, and establish the existence and stability of a unique almost periodic solution that is exponentially stable. Our results are derived by utilizing the properties of the $({\mu }_1,{\mu }_2)$-exponential dichotomy, Cauchy and Green matrices, a Gronwall-type inequality for DEGPCD, and the Banach fixed point theorem. We apply these findings to derive new criteria for the existence, uniqueness, and convergence dynamics of almost periodic solutions in both the linear inhomogeneous and quasilinear DEGPCD systems through the $({\mu }_1,{\mu }_2)$-exponential dichotomy for difference equations. These results are novel and serve to recover, extend, and improve upon recent research. Full article

The hydrogen embrittlement (HE) phenomenon occurring in drawn pearlitic steel wires sometimes results in dangerous delayed fracture and has been an important issue for a long time. HE is very sensitive to the amount of plastic deformation applied in the drawing process. Hydrogen (H) atom diffusion is affected by ambient thermal and mechanical conditions such as stress, pressure, and temperature. In addition, the influence of stress gradient (SG) on atomic diffusion is supposed to be crucial but is still unclear. Metallic materials undergoing plastic deformation naturally have SG, such as residual stresses, especially in inhomogeneous regions (e.g., surface or grain boundary). In this study, we performed molecular dynamics (MD) simulation using EAM potentials for Fe and H atoms and investigated the behavior of H atoms diffusing in pure iron (α-Fe) with the SG condition. Two types of SG conditions were investigated: an overall gradient established by a bending deformation of the specimen and an atomic-scale local gradient caused by the grain boundary (GB) structure. A bi-crystal model with H atoms and a GB structure was subjected to bending deformation. For a moderate flexure, bending stress is distributed linearly along the thickness of the specimen. The diffusion coefficient of H atoms in the bulk region increased with an increase in the SG value. In addition, it was clearly observed that the direction of diffusion was affected by the existence of the SG. It was found that diffusivity of the H atom is promoted by the reduction in its cohesive energy. From these MD results, we recognize an exponential relationship between the amount of H atom diffusion and the intensity of the SG in nano-sized bending deformation. Full article

The acoustoelectric (AE) effect induced by the absorption of ultraviolet (UV) light at 365 nm in piezoelectric ZnO films was theoretically and experimentally studied. c-ZnO films 4.0 µm thick were grown by the RF reactive magnetron sputtering technique onto fused silica substrates at 200 °C. A surface acoustic wave (SAW) delay line was fabricated with two split-finger Al interdigital transducers (IDTs) photolithographically implemented onto the ZnO-free surface to excite and reveal the propagation of the fundamental Rayleigh wave and its third harmonic at about 39 and 104 MHz. A small area of a few square millimeters on the surface of the ZnO layer, in between the two IDTs, was illuminated by UV light at different light power values (from about 10 mW up to 1.2 W) through the back surface of the SiO₂ substrate, which is optically transparent. The UV absorption caused a change of the ZnO electrical conductivity, which in turn affected the velocity and insertion loss (IL) of the two waves. It was experimentally observed that the phase velocity of the fundamental and third harmonic waves decreased with an increase in the UV power, while the IL vs. UV power behavior differed at large UV power values: the Rayleigh wave underwent a single peak in attenuation, while its third harmonic underwent a further peak. A two-dimensional finite element study was performed to simulate the waves IL and phase velocity vs. the ZnO electrical conductivity, under the assumption that the ZnO layer conductivity undergoes an in-depth inhomogeneous change according to an exponential decay law, with a penetration depth of 325 nm. The theoretical results predicted single- and double-peak IL behavior for the fundamental and harmonic wave due to volume conductivity changes, as opposed to the AE effect induced by surface conductivity changes for which a single-peak IL behavior is expected. The phenomena predicted by the theoretical models were confirmed by the experimental results. Full article

Sprite halos are diffuse glow discharges in the D-region ionosphere triggered by the quasi-electrostatic (QES) fields of lightning discharges. A three-dimensional (3D) QES model is adopted to investigate the effect of ionospheric electron density on sprite halos. The electron density is described by an exponential formula, parameterized by reference height (h’) and sharpness (β), and the local inhomogeneity has a Gaussian density distribution. Simulation results indicate that the reference height and steepness of the nighttime electron density affect the penetration altitudes and amplitudes of normalized electric fields, as well as the altitudes and intensities of the corresponding sprite halos optical emissions. A comparison of the daytime and nighttime conditions demonstrates that the daytime electron density profile is not favorable for generating sprite halos emissions. Furthermore, the pre-existing electron density inhomogeneities lead to enhanced local electric fields and optical emissions, potentially offering a plausible explanation for the horizontal displacement between sprites and their parent lightning, as well as their clustering. Full article

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions. Full article

This paper investigates the inhomogeneous version of the pantograph equation. The current model includes the exponential function as the inhomogeneous part of the pantograph equation. The Maclaurin series expansion (MSE) is a well-known standard method for solving initial value problems; it may be easier than any other approaches. Moreover, the MSE can be used in a straightforward manner in contrast to the other analytical methods. Thus, the MSE is extended in this paper to treat the inhomogeneous pantograph equation. The solution is obtained in a closed series form with an explicit formula for the series coefficients and the convergence of the series is proved. Also, the analytic solutions of some models in the literature are recovered as special cases of the present work. The accuracy of the results is examined through several comparisons with the available exact solutions of some classes in the relevant literature. Finally, the residuals are calculated and then used to validate the accuracy of the present approximations for some classes which have no exact solutions. Full article

The wave–current–seabed interaction problem is studied by using a coupled-mode system developed for modeling wave scattering by non-homogeneous, sheared currents in variable bathymetry regions. The model is based on a modal series expansion of wave velocity based on vertical eigenfunctions, dependent on local depth and flow parameters, including propagating and evanescent modes. The latter representation is able to accurately satisfy the wave flow continuity condition and the no-entrance boundary condition on the sloping parts of the seabed. A new derivation of a simplified nonlinear system is introduced using decomposition to a mean flow and a perturbative wave field. To force the system to consider incoming waves at the inlet, boundary knowledge of periodic, travelling nonlinear water waves over a flat bottom is required. For this purpose, specific solutions are derived using the semi-analytical method based on the stream function formulation, for cases of water waves propagating above linearly and exponentially sheared currents. Results obtained by the application of the CMS concerning the propagation of waves and currents—in particular, examples characterized by depth inhomogeneities—are presented and discussed, illustrating the applicability and performance of the method. Full article

As is well known, magnetic fields in space are distributed very inhomogeneously. Sometimes, field distributions have forms of filaments with high magnetic field values. As many observations show, such a filamentation takes place in convective cells in the Sun and other astrophysical objects. This effect is associated with the frozenness of the magnetic field into a medium with high conductivity that leads to the compression of magnetic field lines and formation of magnetic filaments. We analytically show, based on the general analysis, that the magnetic field intensifies in the regions of downward flows in both two-dimensional and three-dimensional convective cells. These regions of the hyperbolic type in magnetic fields play the role of a specific attractor. This analysis was confirmed by numerical simulations of 2D roll-type convective cells. Without dissipation, the magnetic field grows exponentially in time and does not depend on the aspect ratio between the horizontal and vertical scales of the cell. An increase due to compression in the magnetic field of highly conductive plasma is saturated due to the natural limitation associated with dissipative effects when the maximum magnitude of a magnetic field is of the order of the root of the magnetic Reynolds number Re_m. For the solar convective zone, the mean kinetic energy density exceeds the mean magnetic energy density for at least two orders of magnitude, which allows one to use the kinematic approximation of the MHD induction equation. In this paper, based on the stability analysis, we explain why downward flows influence magnetic filaments, making them flatter with orientation along the interfaces between convective cells. Full article

Ultrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge for modeling. Due to the inhomogeneity, nonlinear interactions, and high porosity of cement materials, the motion of particles on their surfaces satisfies the conditions for ultrafast diffusion. The investigation of the diffusion behavior in cementitious materials is crucial for predicting the mechanical properties of cement. In this study, we first attempted to investigate the dynamic of ultrafast diffusion in cementitious materials underlying the Riemann–Liouville nonlocal structural derivative. We constructed a Riemann–Liouville nonlocal structural derivative ultrafast diffusion model with an exponential function and then extended the modeling strategy using the Mittag–Leffler function. The mean square displacement is analogous to the integral of the corresponding structural derivative, providing a reference standard for the selection of structural functions in practical applications. Based on experimental data on cement mortar, the accuracy of the Riemann–Liouville nonlocal structural derivative ultrafast diffusion model was verified. Compared to the power law diffusion and the exponential law diffusion, the mean square displacement with respect to the Mittag–Leffler law is closely tied to the actual data. The modeling approach based on the Riemann–Liouville nonlocal structural derivative provides an efficient tool for depicting ultrafast diffusion in porous media. Full article

This contribution quantifies the birefringence within injection-molded cyclic olefin copolymer plates and discusses its impact on the mechanical properties of the plates. It also focuses on the impact of birefringence on integrated waveguides and Bragg gratings and provides fabrication guidelines for such structures. The anisotropy in all three dimensions of the workpiece is examined by means of polarimetry and a prism coupler. It is found that the birefringence is inhomogenously distributed within the workpieces, whereas the maximum birefringence not only varies locally, but also depends on the observation direction. Overall, a maximum birefringence of 10 × 10⁻⁴ is found at the plate’s surface near the injection gate. The anisotropy then reduces exponentially towards the center of the workpiece and saturates at 1.8 × 10⁻⁴, in a depth of 0.4 mm. Thus, the birefringence strongly affects near-surface photonic structures. It is found that, depending on their orientation and the local birefringence of the substrate, waveguides and Bragg gratings fabricated with comparable parameters behave completely differently in terms of polarization-dependent optical attenuation, cross-sectional intensity distribution and Bragg reflection signal. For example, the support of the TM mode can vary between total loss and an optical attenuation of 0.9 dB × cm⁻¹. In consequence, this study underlines the importance of quantifying the birefringent state of an injection-molded cyclic olefin copolymer workpiece if it is supposed to serve as a substrate for integrated photonic structures. The study furthermore demonstrates that birefringence effects can be omitted by burying the photonic structures deeper into the volume of the thermoplastic. Full article