Theoretical Results Research Articles

A novel parabolic model driven by double phase flux operator with variable exponents: Application to image decomposition and denoising

This work tackles a novel parabolic equation driven by a nonlinear operator with double variable exponents, aiming to decompose and denoise images. Our primary approach involves enhancing classical models based on variable exponent operators by considering a novel nonlinear operator having a double-phase flux with unbalanced growth. We begin initially by analyzing the theoretical solvability of our model. Employing the Musielak-Orlicz space, we establish a suitable functional framework for investigating the proposed model. Subsequently, we use the Faedo-Galerkin approach to establish the existence and uniqueness of a weak solution for our problem. Furthermore, we provide a demonstration showcasing how our model preserves solution positivity, emphasizing this as a consistent feature of the proposed model. To evaluate our theoretical results, we present various numerical simulations on some grayscale and medical images (Magnetic Resonance Images (MRI)). These simulations covered aspects like decomposition, robustness and behavior sensitivity of model parameters with visual and quantitative comparisons. The obtained numerical results strongly support the efficiency of the proposed model in preserving features, reducing artifacts and deleting noise in comparison to some well-known existing state-of-the-art models. Furthermore, the proposed model quantitatively surpasses the competitive models in terms of several well-known criteria, namely the Peak Signal-to-Noise Ratio (PSNR), the Structural Similarity Index (SSIM) and the Mean-Square Error (MSE).

Multicolor emissive hyperbranched polysiloxanes from enhanced spatial electronic communication for security encryption and bacteria imaging

Unconventional fluorescent polymers with long-wavelength emission have attracted considerable attention due to their facile preparation, good biocompatibility, and excellent processability. However, their emission at long-wavelength is relative low. Herein, a series of aromatic amino acids functionalized hyperbranched polysiloxanes with deep red to cyan fluorescence were prepared. Experimental and theoretical calculation results show that the long-wavelength emission comes from the spatial electronic delocalization among conjugated π bonds and electron-rich functional groups. The balance between rigidity and flexibility is favorable for the strong long-wavelength emission. Moreover, the polymers’ fluorescence is sensitive to Fe3+ and OH– ions; and these polymers show potential applications in security encryption, fluorescent stamp inks and bacteria multicolor fluorescence imaging. This work provides an efficient method for the development of long-wavelength emissive unconventional fluorescence polymers

Self-standing Z-scheme structured heterogeneous nanosheet arrays of ZnIn2S4/cobalt porphyrin sulfonate for bifunctional photocatalytic carbon dioxide reduction and antibacterial

Photocatalytic CO2 reduction for solar fuel generation and photocatalytic sterilization are highly desired green routes for sustainable environmental purification. Herein, a bifunctional self-standing nanosheet array of Z-scheme structured inorganic–organic heterojunction is synthesized via in-situ growth of ZnIn2S4 (ZIS) on carbon cloth (CC) followed by self-assembly with cobalt porphyrin (meso-tetra(4-sulfonatophenyl) porphyrin, CoTPPS). The obtained CC-ZIS-CoTPPS performed well in the photocatalytic CO2 reduction and antibacterial processes simultaneously in a portable photocatalytic system with a negligible amount of solution. Specifically, the optimized CC-ZIS-CoTPPS demonstrates more than 140 times enhanced CO evolution than pristine CoTPPS. Experimental and theoretical results imply that the enhanced photocatalytic CO2 reduction is associated with elevated light absorption, promoted charge separation, and improved CO2 activation in the inorganic–organic Z-scheme heterojunction. In addition, the self-standing nanosheet array possesses a mechanical cutting effect, which can kill bacteria adhering to the surface even in dark conditions. Moreover, CC-ZIS-CoTPPS achieved a 100 % killing rate under visible light irradiation by synergistically chemical and mechanical sterilization. Furthermore, CC-ZIS-CoTPPS exhibits efficient bifunctional photocatalytic photocatalytic CO2 reduction coupled with in-situ sterilization. This work presents an atomic perspective for developing innovative bifunctional photocatalysts, which hold great potential in portable devices to alleviate energy and environmental crises.

Preliminary investigation of the effects of high-temperature thermal activation on the activity of graphite tailings and the mechanical properties of graphite tailings mortar

The disposal of graphite tailings, a byproduct of graphite mining, poses significant recycling challenges. This study explores eco-friendly cement mortar by partially replacing sand with activated graphite tailings, focusing on waste utilization. Activating the pozzolanic properties of graphite tailings at various thermal activation temperatures converts them into high-quality binder materials. Quantitative assessments of graphite tailings' activity, conducted through ion leaching tests and raw material diffraction analysis, produce an activity index Ka, evaluating their performance under different thermal activation temperatures. Variable testing of substitution rates and activation temperatures examines changes in mechanical properties, microstructure, and pore distribution of the graphite tailings mortar. Optimum results reveal a 30 % substitution rate and a 750°C activation temperature. Graphite tailings, as pozzolanic binder materials, enhance mortar strength by improving particle size distribution, reducing "micro-area bleeding" and "boundary effects". After thermal activation, reactive minerals on the tailings' surface undergo secondary hydration reactions with cementitious products, modifying chemical structures and micro-morphology at the interface. Semi-quantitative XRD analysis and FT-IR spectroscopy characterize the ensuing chemical reactions, unveiling molecular bond and functional group changes. The superior performance of thermally activated graphite tailings primarily stems from increased active SiO2 and Al2O3 post-activation. The active SiO2 and Al2O3 reacts with cementitious products to form C-(A)-S-H gels, filling micro-pores at the tailings-mortar interface, which is the key characteristic that enables graphite tailings to serve as high-quality pozzolanic binder aggregates. A predictive model for compressive strength, utilizing reference models from solid waste mortar concrete, quantifies the positive impact of chemical activation. The theoretical results obtained from this predictive model closely align with the experimental findings.

A triple plasmon-induced transparency terahertz sensor based on graphene metamaterials

A metamaterial-based terahertz sensor design is presented in this paper. The metamaterial unit structure comprises a graphene cross and three sets of graphene strips, which collectively achieve a triple plasmon-induced transparency (PIT) in both polarization directions. The theoretical results based on the Lorentz resonance theoretical model are in good agreement with finite difference time domain (FDTD) simulations. The sensor is polarization-independent and changes in the angle of incidence between 0° and 10° have a negligible impact on the sensing performance. Furthermore, the sensor exhibits a notable slow-light effect, with a maximum sensitivity of 1.65 THz/RIU and a FOM value of 4.74/RIU for the triple PIT, which is superior to that of comparable devices.

Discontinuous Galerkin methods for magnetic advection-diffusion problems

We devise and analyze a class of the primal discontinuous Galerkin methods for magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we explore some terms related to convection under the vector case that provides more flexibility in constructing the schemes. Under a degenerate Friedrichs system, we show the stability and optimal error estimate, which boil down to two ingredients – the weight function and the special projection – that contain information of advection. Numerical experiments are provided to verify the theoretical results.

Synchronization of directly coupled complex networks with multiweights and multiple delays

This paper investigates the synchronization of directed and multiweighted dynamic networks (DMDNs) with different delay couplings. Time delays in this paper are assumed to exist between the communication process, so communication between different nodes can generate time delays, while communications between the same nodes do not need time delays. Using the normalized left eigenvectors (NLEigs) corresponding to the zero eigenvalue of the coupling matrix, we prove that if both the time delay and the Chebyshev distance between NLEigs are small enough, all coupling matrices can accelerate the synchronization. Moreover, we also investigate the consensus for directed and multiweighted multi-agents with arbitrary bounded/unbounded time delays. Furthermore, the corresponding pinning control synchronization and consensus problem are also investigated, and sufficient synchronization criteria are also obtained. Numerical simulations are presented to show the validity of obtained theoretical results.

Computational Screening Two-Dimensional Conjugated Microporous Polymer Applied in Perovskite Solar Cells.

A two-dimensional (2D) conjugated microporous polymer with a structure of 2D nanosheets has been synthesized. Theoretical calculations and experimental results reveal that the Fermi level of this 2D polymer aligns well with perovskite absorber, and its conduction band is high enough to block electron transport into the anode. This 2D polymer is used to modify the hole transport layer, significantly improving its photoelectric properties, including enhanced hole mobility, matched energy level, and reduced recombination. Furthermore, the 2D polymer exhibits a mesoporous structure, allowing perovskite to fill into its loose framework, increasing the hole export area and providing a large hole transport flux. As a result, the efficiency of inverted perovskite solar cells enhances to 24.64 % from 21.17 % of control device without 2D conjugated microporous polymer. Given that this material can be synthesized on a large scale, this work has significant implications for the future development of 2D polymers in perovskite solar cells, potentially accelerating industrialization.

On bench evaluation of intraocular lenses: performance of a commercial interferometer

NIMO-TEMPO is a metrology device that measures all types of intraocular lenses available in the ophthalmic market. Its technology, based on interferometry, captures the wavefront of the lens to compute optical results essential to evaluate its quality and understand its characteristics. This study aims to demonstrate the reliability of this device and its associated software, TEMPO-MENTOR, in measuring intraocular lenses. The analysis is based on comparing the theoretical results of the optical design and data computed by the device algorithm. Results provided with NIMO-TEMPO are also validated using another metrology device.

Chiral sensing via dielectric waveguide-nanoparticle array interactions

Identifying the handedness of chiral materials in small quantities remains a significant challenge in biochemistry. Nanophotonic structures offer a promising solution by enhancing weak chiroptical responses through increased optical chirality. Utilizing a silicon-based approach for chiral sensing on a photonic integrated platform is highly desirable. In this study, we explore the interaction between a dielectric waveguide and silicon nanoparticles for detecting the handedness of chiral analytes. A chiral core induces polarization rotation of wavefields traveling along a dielectric waveguide with a square cross-section. This polarization rotation affects waveguide coupling differently depending on the left- or right-handed arrangement of nanoparticles around the waveguide, enabling enantiomer detection through discernible transmission differences. From a basic design to more practical structures, we investigate configurations that maintain the same working principles. Theoretical results based on the transfer matrix method corroborate the numerical simulations.

Electron-impact ionization of water molecules at low impact energies.

The electron-impact ionization of water molecules at low impact energies is investigated using a theoretical approach named M3CWZ. In this model, which considers exchange effects and post-collision interaction, the continuum electrons (incident, scattered, and ejected) are all described by a Coulomb wave that corresponds to distance-dependent charges generated from the molecular target properties. Triple differential cross-sections for low impact energy ionization of either the 1b1 or 3a1 orbitals are calculated for several geometrical and kinematical configurations, all in the dipole regime. The M3CWZ model is thoroughly tested with an extensive comparison with available theoretical results and COLTRIMS measurements performed at projectile energies of Ei = 81eV [Ren et al., Phys. Rev. A 95, 022701 (2017)] and Ei = 65eV [Zhou et al., Phys. Rev. A 104, 012817 (2021)]. Similar to other theoretical models, an overall good agreement with both sets of measured data is observed for the angular distributions. Our calculated cross-sections' magnitudes are also satisfactory when compared to the other theoretical results, as well as to the cross-normalized relative scale data at 81eV impact energy. The 65eV set of data, measured on an absolute scale, offers a further challenging task for theoretical descriptions, and globally the M3CWZ performs fairly well and comparably to other theories. The proposed approach with variable charges somehow allows to capture the main multicenter distortion effects while avoiding high computational costs.

Study of electron and positron elastic scattering cross-sections of astro molecule H2S

Abstract The elastic, integrated, momentum transfer, viscosity, energy-dependent, and differential cross-sections and the Sherman function for electron and positron H2S scattering are reported at impact energies ranging from 1 eV to 1 MeV. The average orientations of the polar molecule H2S are considered, and the electron and positron elastic scattering cross-sections of H2S are typically calculated using single scattering-independent atom approximation. The relativistic Dirac equation is solved using the free atom optical potential, which includes the electrostatic interaction potential, exchange potential, correlation polarization potential, and imaginary absorption potential. The present computed cross-section results are compared with the available experimental and theoretical results, and a reasonable agreement is observed.

Singularities of worldsheets along framed particle trajectories in Minkowski three-space

Modeling the worldsheets along the trajectory (a string) of a point particle (a 0-brane) as two timelike surfaces in 3-subspace of Minkowskian spacetime, respectively, the work aims at analyzing the topological structures of these two worldsheets along the trajectory of the point particle from the view point of singularity theory. Different from the regular curves, the traveling trajectory (modeled as framed timelike curve) of the particle is allowed to be singular, two worldsheets are generated by the traveling trajectories of the particle. As applications of singularity theory, we classify the singularities of these two worldsheets along the traveling trajectory of the particle. Using the approach of the unfolding theory in singularity theory, we find two new geometric invariants which are useful for characterizing the local topological structures of singularities of these two worldsheets along the particle. It is revealed that there exist cuspidal edge type and swallowtail type of singularities for these two worldsheets under the appropriate conditions of geometric invariants. Meanwhile, it is also pointed out that the types of singularities of these two worldsheets have a close relationships to the order of contacts between these two worldsheets and two timelike planes, respectively. Finally, some examples are presented to interpret our theoretical results.

A unified approach to the construction of higher-order derivative-free iterative methods for solving systems of nonlinear equations

In this article, we introduce a unified approach to constructing a higher-order derivative-free scheme based on the approximations of F'(zk)-1. A family of order p=6,7 derivative-free method is proposed and compared to some well-known methods. The necessary and sufficient condition for p-th order of convergence are given in terms of parameter matrices τ(k) and α(k) . Some good choices of and are offered. Numerical experiments were carried out to confirm the theoretical results.

High‐contrast QPSK pattern recognition device consisting of a 4×$\times$4 MMI coupler

AbstractPattern recognition of optical label is utilized not only in packet switches but also in the field of data security due to its wide range of applications. In particular, pattern recognition using waveguide devices is highly valued because it eliminates the need for encoder processing. However, existing methods suffer from the problem of degraded contrast ratio because half of the input power are emitted from non‐target waveguides. In this article, a method is proposed to improve the contrast ratio employing a 44 multi‐mode interference (MMI) coupler with multiple input signals. The theoretical results reveal that the proposed method improves the contrast ratio from 3.0 dB to 9.5 dB and dB for the three‐input and four‐input cases, respectively, for quadrature phase‐shift keying (QPSK)‐modulated signal. Furthermore, numerical simulation was performed through the three dimension finite‐difference time‐domain (3D‐FDTD) method, and the proposed scheme successfully discriminated each QPSK pattern. The power value at all ports closely matches the theoretical value, and the ratios of 9.5 dB and 30.0 dB are numerically obtained.

Quantitative photothermal investigation of nonradiative recombination parameters in GaAs/InAs(QD)/GaAs quantum dot structures using a three-layer laser beam deflection model

In this paper, we developed a theoretical model for the photothermal deflection technique in order to investigate the electronic parameters of three-layer semiconductor structures. This model is based on the resolution of thermal and photogenerated carrier diffusion-wave equations in different media. Theoretical results show that the amplitude and phase of the photothermal deflection signal is very sensitive to the nonradiative recombination parameters. The theoretical model is applied to one layer of InAs quantum dots (QDs) inserted in GaAs matrix InAs/GaAs QDs in order to investigate the QD density effects on nonradiative recombination parameters in InAs through fitting the theoretical photothermal beam deflection signal to the experimental data. It was found that the minority carrier lifetime and the electronic diffusivity decrease as functions of increasing InAs QD density. This result is also related to the decrease in the mobility from 21.58 to 4.17 (±12.9%) cm2/V s and the minority carrier diffusion length from 0.62 (±5.8%) to 0.14 (±10%) μm, respectively. Furthermore, both interface recombination velocities S2/3 of GaAs/InAs (QDs) and S1/2 of InAs (QDs)/GaAs increase from 477.7 (±6.2%) to 806.5 (±4%) cm/s and from 75 (±7.8%) to 148.1 (±5.5%) cm/s, respectively.

Cluster formation tracking of networked perturbed robotic systems via hierarchical fixed-time neural adaptive approach

This paper investigates the fixed-time cluster formation tracking (CFT) problem for networked perturbed robotic systems (NPRSs) under directed graph information interaction, considering parametric uncertainties, external perturbations, and actuator input deadzone. To address this complex problem, a novel hierarchical fixed-time neural adaptive control algorithm is proposed based on a hierarchical fixed-time framework and a neural adaptive control strategy. The objective of this study is to achieve accurate CFT of NPRSs within a fixed time. Specifically, we design a distributed observer algorithm to estimate the states of the virtual leader within a fixed time accurately. By using these observers, a neural adaptive fixed-time controller is developed in the local control layer to ensure rapid and reliable system performance. Through the use of the Lyapunov argument, we derive sufficient conditions on the control parameters to guarantee the fixed-time stability of NPRSs. The theoretical results are eventually validated through numerical simulations, demonstrating the effectiveness and robustness of the proposed approach.

Rich dynamics of a hepatitis C virus infection model with logistic proliferation and time delays

AbstractIn this paper, we study a dynamic model of hepatitis C virus (HCV) infection with density‐dependent proliferation of uninfected and infected hepatocytes and two time delays, which is derived from a three‐dimensional model by the quasi‐steady‐state approximation. The model can exhibit forward bifurcation or backward bifurcation, and an explicit control threshold parameter is obtained for the case of backward bifurcation. It is shown that if the proliferation rate of infected hepatocytes is greater than the proliferation rate of uninfected hepatocytes by a certain amount, it becomes more difficult for the virus to be removed. The model has rich dynamical properties: (i) In some parameter regions, bistability can occur; (ii) both time delays (virus‐to‐cell delay) and (cell‐to‐cell delay) can lead to Hopf bifurcations; (iii) same length of time delays and can lead to at most one stability switch, but different time delays can lead to multiple stability switches. Several sufficient conditions for the global stability of the disease‐free equilibrium and the endemic equilibrium are obtained for both forward and backward bifurcation scenarios. In particular, several sharp results on global stability are obtained. Theoretical and numerical results portray the complexity of viral evolutionary dynamics in chronic HCV‐infected patients.

Dynamics of a Discrete Population Model

In order to explore the influences of the strong Allee effect on population evolution in two-patch environments, this paper constructs a population model with discrete diffusion and analyzes its dynamics. Using the center manifold theorem, we discuss the codimension-one bifurcation, such as flip bifurcation, of the model. The qualitative structures and stability of the model at the degenerate fixed point are obtained from the approximation of flow. Based on the theoretical analysis results, we investigate the influences of the strong Allee effect and diffusion on population evolution. The qualitative structures of degenerate fixed point and numerical simulation show that the strong Allee effect will make the population tend to a stable size when the two initial population patch sizes are equal and exceed a threshold. But the stable size of population does not exceed the carrying capacity, depending on the constant Allee effect and carrying capacity, which differ from the conclusion of logistic model that population size tends to the carrying capacity. However, if the two initial population patches are equal in size and below this threshold, or if the sizes of the initial population patches are unequal, the population size will decrease. The fixed point becomes degenerate with respect to the strong Allee effect causing the population tend to a stable size below carrying capacity, which exacerbates the complexity of population evolution.

Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.