Inverse Coefficient Research Articles

Inverse coefficient problems for one-dimensional time-fractional diffusion equations

We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one end point of the spatial interval.

Low-field-driven large strain in lead zirconate titanium-based piezoceramics incorporating relaxor lead magnesium niobate for actuation

Studies on the piezoelectric materials capable of efficiently outputting high electrostrains at low electric fields are driven by the demand for precise actuation in a wide range of applications. Large electrostrains of piezoceramics in operation require high driving fields, which limits their practical application due to undesirable nonlinearities and high energy consumption. Herein, a strategy is developed to enhance the electrostrains of piezoceramics while maintaining low hysteresis by incorporating lead magnesium niobate relaxors into lead zirconate titanium at the morphotropic phase boundary. An ultrahigh inverse piezoelectric coefficient d33*\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{33}^{*}$$\\end{document} of 1380 pm/V with a reduced hysteresis of 11.5% is achieved under a low electric field of 1 kV/mm, outperforming the major lead-based piezoelectric materials. In situ synchrotron X-ray diffraction and domain wall dynamics characterization with sub-microsecond temporal resolution reveal that the outstanding performances originate from facilitated domain wall movement, which in turn is due to reduced lattice distortion and miniaturized domain structures. These findings not only address the pending challenges of effective actuation under reduced driving conditions but also lay the foundation for a more systematic approach to exploring the origin of large electrostrains.

Global Lipschitz stability for an inverse coefficient problem for a mean field game system

For an inverse coefficient problem of determining a state‐varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an arbitrarily chosen subdomain over a time interval. The proof is based on Carleman estimates with different norms.

Sharp coefficient bounds for a class of symmetric starlike functions involving the balloon shape domain

Recent research has extensively explored classes of starlike and convex functions across various domains. This study introduces a novel class of symmetric starlike functions with respect to symmetric points and associated with the balloon shape domain. We establish the explicit representation of all functions in this class. We determine the sharp bounds for the initial four coefficients, the sharp Fekete-Szegö inequality, and the sharp bound for the second Hankel determinant for every function in the newly defined class. Furthermore, we present the new findings on the inverse and logarithmic coefficients sharp bounds for all functions belonging to this class.

Inverse coefficient problem for a partial differential equation with multi-term orders fractional Riemann–Liouville derivatives

This work studies direct initial boundary value and inverse coefficient determination problems for a one-dimensional partial differential equation with multi-term orders fractional Riemann–Liouville derivatives. The unique solvability of the direct problem is investigated and a priori estimates for its solution are obtained in weighted spaces, which will be used for studying the inverse problem. Then, the inverse problem is equivalently reduced to a nonlinear integral equation. The fixed-point principle is used to prove the unique solvability of this equation.

Inverse problem for semilinear wave equation with strong damping

The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using an additional integral type overdetermination condition.

High-performance PSZT-PSMI-PSZS ceramics: Piezoelectric and ferroelectric insights for advanced applications

High-performance ferroelectric materials have garnered increased attention due to their exceptional dielectric, piezoelectric, and electrostrictive properties. A solid-state reaction method was used to prepare the perovskite Pb(1-x)Smx[(Zr0.52Ti0.48)0.9(Mo1/3In2/3)0.05(Zn1/3Sb2/3)0.05]O3 (where x = 0, 0.02, 0.04, 0.06, and 0.08) ceramics, abbreviated PSZT-PSMI-PSZS. Energy-dispersive X-ray spectroscopy (EDX) and Fourier-transform infrared (FT-IR) spectroscopy were employed to verify the elemental composition and molecular structure, respectively. The results showed good agreement between nominal and measured compositions, and indicated structural changes post-calcination, suggesting successful formation of the perovskite phase. Piezoelectric properties were evaluated, revealing the highest piezoelectric coefficient (d33 = 310 pC/N) at x = 0.02, attributed to optimal morphological features and the morphotropic phase boundary effect. This sample also demonstrated the highest electromechanical coupling factors (kp = 60 %, k31 = 35 %) and the largest impedance resonance frequency difference (Δf = 15.05 kHz). Ferroelectric testing indicated excellent ferroelectric characteristics, with the maximum remanent polarization (Pr = 17.71 μC/cm2) and saturation polarization (Ps = 22.75 μC/cm2) observed at x = 0.02, along with the lowest coercive field (Ec = 10.16 kV/cm). Additionally, this composition exhibited the highest unipolar strain (Smax = 0.17 %) and the inverse piezoelectric coefficient (d∗33 = 427.57 p.m./V). This comprehensive analysis emphasizes the potential of Sm-doped PZT-PMI-PZS ceramics for advanced piezoelectric and ferroelectric applications, particularly at a doping concentration of x = 0.02, where the materials exhibited excellent electrical and mechanical properties.

On the inverse problem of time dependent coefficient in a time fractional diffusion problem by sinc wavelet collocation method

The object of this study is to establish the unknown function in a time fractional diffusion problem and the solution as well by utilizing Sinc wavelet collocation method (SWCM) and residual power series method (RPSM) together. SWCM enables us to convert time fractional diffusion problem into a system of fractional ordinary differential and algebraic equations. At this stage, the unknown function and the solution are constructed in the series form by employing RPSM. The novelty of this study is that the combination of SWCM and RPSM is utilized to establish the solution of inverse coefficient problem for the first time. Demonstrative examples are presented to articulate the implementation and importance of the proposed method.

Oxygen-defective electrostrictors for soft electromechanics.

Electromechanical metal oxides, such as piezoceramics, are often incompatible with soft polymers due to their crystallinity requirements, leading to high processing temperatures. This study explores the potential of ceria-based thin films as electromechanical actuators for flexible electronics. Oxygen-deficient fluorites, like cerium oxide, are centrosymmetric nonpiezoelectric crystalline metal oxides that demonstrate giant electrostriction. These films, deposited at low temperatures, integrate seamlessly with various soft substrates like polyimide and PET. Ceria thin films exhibit remarkable electrostriction (M33 > 10-16 m2 V-2) and inverse pseudo-piezo coefficients (e33 > 500 pmV-1), enabling large displacements in soft electromechanical systems. Our study explores resonant and off-resonant configurations in the low-frequency regime (<1 kHz), demonstrating versatility for three-dimensional and transparent electronics. This work advances the understanding of oxygen-defective metal oxide electromechanical properties and paves the way for developing versatile and efficient electromechanical systems for applications in biomedical devices, optical devices, and beyond.

Identification of Time-Wise Thermal Diffusivity, Advection Velocity on the Free-Boundary Inverse Coefficient Problem

This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.

Genetic network analysis uncovers spatial variation in diversity and connectivity of a species presenting a continuous distribution

The conservation of genetic diversity and connectivity is essential for the long-term persistence and adaptive ability of a species. Recent calls have been made for the inclusion of genetic diversity and differentiation measures in the assessment, management, and conservation of species. However, the literature often lacks direction on how to do so for species with continuous distributions or no distinct breaks in genetic connectivity. There are many considerations to overcome when investigating genetic diversity and connectivity of such species. We combine multiple genetic network methodologies with more traditional population genetic analyses within a single framework to address the challenges of investigating population structure and quantifying variation in genetic diversity and connectivity of wide-ranging species with continuous distributions. We demonstrate the efficacy and applicability of our framework through a study on woodland caribou (Rangifer tarandus) occupying the boreal forest of Canada; a species of significant conservation concern. The dataset consisted of 4911 unique individuals genotyped at 9 microsatellite loci, which were subsequently partitioned into 103 spatial nodes to create a population-based genetic network. The Walktrap community detection algorithm was used to detect hierarchical population genetic structure within the study area and node-based network metrics such as mean inverse edge weight and clustering coefficient were used to quantify the variation in genetic connectivity across the range. Lastly, genetic diversity was assessed by calculating allelic richness and heterozygosity of the nodes making up the network. The community detection analysis identified two communities at the coarsest scale to nine communities at the optimal partition. A strong pattern of Isolation by Distance (IBD) was found across the range at multiple scales. Furthermore, signs of genetic erosion along the study area’s southern boundaries were depicted by nodes presenting low genetic diversity and low centrality values. These results are important to the species status assessments in providing previously unavailable information on connectivity and diversity within and beyond the current local population units used in management. Our approach to quantify the patterns and extent of connectivity across the boreal range is comprehensive and could easily be adapted to other species. The results are robust and provide a solid foundation for the continued monitoring and recovery of the species.

Synthesis-Dependent Structural and Magnetic Properties of Monodomain Cobalt Ferrite Nanoparticles

This research examines the structural and magnetic properties of monodomain cobalt ferrite nanoparticles with the formula (Co1−xFex)A[Fe2−xCox]BO4. The particles were synthesized using various methods, including coprecipitation (with and without ultrasonic assistance), coprecipitation followed by mechanochemical treatment, microemulsion, and microwave-assisted hydrothermal techniques. The resulting materials were extensively analyzed using X-ray diffraction (XRD) and magnetic measurements to investigate how different synthesis methods affect the structure and cation distribution in nanoscale CoFe2O4. For particles ranging from 15.8 to 19.0 nm in size, the coercivity showed a near-linear increase from 302 Oe to 1195 Oe as particle size increased. Saturation magnetization values fell between 62.6 emu g−1 and 74.3 emu g−1, primarily influenced by the inversion coefficient x (0.58–0.85). XRD analysis revealed that as the larger Co2+ cations migrate from B- to A-sites (decreasing x), the lattice constants and inter-cation hopping distances increase, while the average strength of super-exchange interactions decreases. This study establishes a connection between the magnetic properties of the synthesized samples and their structural features. Importantly, this research demonstrates that careful selection of the synthesis method can be used to control the magnetic properties of these nanoparticles.

An Empirical Study on the Impact of Digital Economy Development Level on the Efficiency of Green and Low Carbon Transition in Chinese Cities

&lt;p&gt;As China's economic and social development enters a new growth stage, urban green transformation has gradually become an important means to promote high-quality development. In order to explore the effective methods of the impact of China's digital economy development level on the efficiency of urban green low-carbon transition, this paper, based on the statistical data of 263 prefectural-level cities in China during the period of 2012-2021, adopts Peking University's financial inclusion index as well as the five selected control variables, measures the efficiency of urban green low-carbon transition by using the SBM model and examines the impact of driving factors on urban green low-carbon transition by using the spatial Durbin lagged panel fixed-effects model. the influence of driving factors on the efficiency of green low-carbon transition in Chinese cities. It was found that: the digital economy index showed a positive correlation with urban green transition efficiency, and the corresponding positive influence coefficient was 0.523, and the influence of control variables on urban green transition efficiency showed differentiation characteristics, among which: the investment rate in environmental pollution control, the contribution rate of GDP in the service industry, and the professional investment rate in green transition showed a positive correlation with urban green transition efficiency, and the corresponding influence coefficients were 0.437, 0.304 and 0.348; the contribution rate of urban industrial GDP and urbanization level show inverse correlation with the efficiency of urban green transformation, and the corresponding inverse impact coefficients are -0.412 and -0.276, respectively. The conclusions of this paper are of great practical value for the formulation of policies to improve the efficiency of urban green transformation.&lt;/p&gt;

Giant field-induced strain with excellent fatigue performance in (Al0.5Nb0.5)4+-modified 0.85Bi0.5Na0.5TiO3-0.11Bi0.5K0.5TiO3-0.04BaTiO3 piezoelectric ceramics

Utilizing a conventional solid-state reaction procedure, (Al0.5Nb0.5)4+-modified 0.85Bi0.5Na0.5TiO3-0.11Bi0.5K0.5TiO3-0.04BaTiO3 (BNKT-BT) samples were synthesized. The impact of (Al0.5Nb0.5)4+ on the crystal structure, ferroelectric, dielectric, and AC impedance properties was systematically investigated. The XRD patterns demonstrate that the crystal structures of all samples exhibit typical pseudo-cubic features. According to the XPS, the doping of (Al0.5Nb0.5)4+ reduces the concentration of oxygen vacancies inside the ceramics, which significantly affects the relaxation properties. This substitution successfully triggers a change from a non-ergodic relaxor (NR) state to an ergodic relaxor (ER) state, which is ascribed to the weakening of the pinning effect of the oxygen vacancies on the polar nanoregions (PNRs). The ceramics exhibit an enormous monopolar strain of 0.468 % under 60 kV/cm, accompanied by an inverse piezoelectric coefficient (d33*) of 780 pm/V, surpassing the performance of numerous other BNT-based piezoelectric ceramics. After 1×104 switching cycles, the strain value changes slightly, indicating excellent fatigue performance. The considerable strain arises from a reversible transformation of the ER phase to the ferroelectric phase induced by an electric field. This research suggests that (Al0.5Nb0.5)4+-doped BNKT-BT ceramics have good prospects for application in actuators and sensors.

Initial Boundary Value and Inverse Coefficient Problems for One-Dimensional Fractional Diffusion Equation in a Half-Line

Initial Boundary Value and Inverse Coefficient Problems for One-Dimensional Fractional Diffusion Equation in a Half-Line

Inverse Coefficient Problem for the 2D Wave Equation with Initial and Nonlocal Boundary Conditions

In this paper, we consider direct and inverse problems for the two-dimensional wave equation. The direct problem is an initial boundary value problem for this equation with nonlocal boundary conditions. In the inverse problem, it is required to find the time-variable coefficient at the lower term of the equation. The classical solution of the direct problem is presented in the form of a biorthogonal series in eigenvalues and associated functions, and the uniqueness and stability of this solution are proven. For solution to the inverse problem, theorems of existence in local, uniqueness in global, and an estimate of conditional stability are obtained. The problems of determining the right-hand sides and variable coefficients at the lower terms from initial boundary value problems for second-order linear partial differential equations with local boundary conditions have been studied by many authors. Since the nonlinearity is convolutional, the unique solvability theorems in them are proven in a global sense. In the works, the method of separation of variables is used to find the classical solution of the direct problem in the form of a biorthogonal series in terms of eigenfunctions and associated functions. The nonlocal integral condition is used as the overdetermination condition with respect to the solution of the direct problem. The direct problem reduces to equivalent integral equations of the Fourier method. To establish integral inequalities, the generalized Gronwall-Bellman inequality is used. We obtain an a priori estimate of the solution in terms of an unknown coefficient, that are useful for studying the inverse problem.

Certain sharp estimates of Ozaki close-to-convex functions

The goal of this paper is to establish the sharp estimates on coefficient functionals like Hermitian–Toeplitz determinant of second-order involving logarithmic coefficients, initial logarithmic inverse coefficients as well as sharp bounds on initial order Schwarzian derivatives of the Ozaki close-to-convex functions.

Spatial diffusion of potentially toxic elements in soils around non-ferrous metal mines

This study focuses on the diffusion patterns of principal ore-forming elements (Pb and Zn) and associated elements (Cd, Cu, Cr, and As) in lead-zinc ore. Sampling points in upwind and downwind directions of lead-zinc ore areas at various densities (1 N/km2 – 4 N/km2) were categorized. This study analyzed the statistical relationship between the content of PTEs in the soil around lead-zinc ore and the source strength and dominant wind direction, constructed one-dimensional and two-dimensional diffusion model, and simulated the EER scope caused by PTEs. The findings indicate that: (1) concerning source strength, the content of PTEs in soils of high-density ore aggregation areas is significantly higher than in low-density ore aggregation areas. However, the impact of source strength decreases with decreasing ore grade, with a difference in Pb content of 1.71 times among principal ore-forming elements and almost consistent Cd content among associated elements. (2) Regarding the transport pathways, for most PTEs, the inverse proportion coefficients downwind are higher than upwind, approximately 1.18–3.63 times, indicating greater migration distances of PTEs downwind due to atmospheric dispersion. (3) By establishing a two-dimensional risk diffusion model, the study simulates the maximum radius of risk diffusion (r = 5.7 km), the 50% probability radius (r = 3.1 km), and the minimum radius (r = 0.8 km) based on the maximum, median, and minimum values statistically obtained from the EER. This study provides a scientific basis for implementing preventive measures for PTEs accumulation in soil within different pollution ranges. Different risk prevention and control measures should be adopted for PTEs accumulation in soil within the three ranges after cutting off pollution sources. Subsequent research should further investigate the impact and contribution of atmospheric transmission and surface runoff on the diffusion of PTEs in areas with high risk near lead-zinc ore.

Ultra-high electrostrain in flux-grown (Bi0.5Na0.5)TiO3-0.06BaTiO3-0.03(K0.5Na0.5)NbO3 single crystals around the nonergodic/ergodic crossover region

In this study, we successfully grew large-sized single crystals (12 × 11 × 8 mm³) of 0.91Bi0.5Na0.5TiO3-0.06BaTiO3-0.03(K0.5Na0.5)NbO3 (BNT-6BT-3KNN) with a <100>c orientation using the flux growth method. This marks the first instance of achieving such crystals. The single crystals display double hysteresis loops, featuring a maximum polarization of ∼64.6 μC/cm2. Capitalizing on the nonergodic/ergodic boundary, the single crystals exhibit a substantial strain (Sm) of 0.91% at the maximum electric field of 20 kV/cm and an exceptionally high inverse piezoelectric coefficient d33* of 4550 pm/V. The creation of long-range domains from needle-like nanodomains and polar-nano regions under the application of an electric field was confirmed through bright-field transmission electron microscopy and piezoresponse force microscopy analyses. The phase diagram for BNT-6BT-3KNN single crystals was constructed by analyzing the temperature dependence of dielectric, ferroelectric, and electrostrain behaviors.

FDS-MOMEDA: optimization-blind deconvolution in finite high-dimensional spaces for extracting pulse signal in rolling bearing fault diagnosis

Rolling bearing fault diagnosis is crucial for ensuring the safe and reliable operation of mechanical equipment. Detecting faults directly from measurement signals is challenging due to severe noise and interference. Blind deconvolution (BD), as a preferred method, effectively recovers periodic pulses from the measured vibration signals of faulty bearings. This study introduces a simulated annealing-based BD approach to enhance the pulse signal components reflecting faults in vibration signals measured on rolling bearings. This method iteratively searches for the optimal coordinates in a high-dimensional orthogonal optimization space, where the optimal coordinates reflect the combination of the inverse filter coefficients. Compared to the generalized spherical optimization space used in the ‘Optimization-Blind Deconvolution’ method in previous works, the proposed finite high-dimensional optimization space helps overcome the problem of inverse filter coefficient convergence, allowing for the design of inverse filters without limit of its shape. To better accommodate the cyclostationarity characteristics of bearing signal measured in reality, the proposed method employs a target vector that allows for uncertainty in pulse occurrence instants, thus overcomes challenges introduced by pseudo-periodic phenomena resulting from bearing slippage. Numerical simulations and experimental results on real bearing vibration signals confirm that the proposed method can design more flexible filters to enhance pulse-like patterns in signals, effectively utilize limited filter resources. Its capacity to tolerate inaccurate fault period estimates, high background noise, and pulse randomness enables it to effectively address vibration measurement signals in real-world scenarios.