Inverse Coefficient Research Articles

Turbulent transport of radiation in the solar convective zone

ABSTRACTA turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that the ratio of the effective penetration length to the mean penetration length of radiation increases 2.5 times in the vicinity of the solar surface. The main reasons for this are the compressibility effects that become important in the vicinity of the solar surface where temperature and density fluctuations increase towards the solar surface, enhancing fluctuations of the radiation absorption coefficient and increasing the effective penetration length of radiation.

Electrostriction-enhanced giant piezoelectricity via relaxor-like secondary crystals in extended-chain ferroelectric polymers

<h2>Summary</h2> Piezoelectricity in ferroelectric polymers originates from the electrostrictive effect coupled with a remanent polarization. However, its structural origin remains controversial, and it is not clear how modifying the electrostriction can further improve piezoelectricity for polymers. Here, we report that electrostriction can be significantly enhanced in poled poly(vinylidene fluoride-<i>co</i>-trifluoroethylene) [P(VDF-TrFE)] random copolymers containing extended-chain primary crystals and relaxor-like secondary crystals in the oriented amorphous fraction (SC_OAF). As a result of the high polarizability of dipoles and ferroelectric nanodomains in the SC_OAF, the inverse piezoelectric coefficient d₃₁ reaches as high as 77 ± 5 pm/V for the P(VDF-TrFE) 55/45 copolymer at 55°C. This finding not only extends our understanding of piezoelectricity in polymers but also provides guidance for further enhancing the piezoelectricity of ferroelectric polymers in the future.

Indicators of cosmonaut locomotor functions stability: A new method for ground-reaction forces analysis

The paper introduces a new method for ground-reaction forces (GRF) analysis for the evaluation of cosmonaut locomotor functions stability after a long-duration spaceflight (LDSF). The method is based on the analysis of GRF profiles obtained before and after LDSF by standard БД-2 treadmill reaction force data readings. Following probabilistic indicators were introduced: distributions of step and step-phase duration probabilities, their extremums, standard deviations and inverse coefficients of variety; step structure variability; the non-stationarity index for step durations arrays; GRF pattern, its width and maximum. Every indicator of one cosmonaut pilot study has changed drastically after LDSF. The new statistics provided appeared to be promising indicators of locomotor function state. A further trial of the new method may provide new knowledge of human movement strategies alterations after LDSF and may establish it as a standard analytical procedure for personalized flight assistance after its reliability verification.

Coefficients of the inverse of functions for the subclass of the class $$\varvec{{\mathcal {U}} (\lambda )}$$

Coefficients of the inverse of functions for the subclass of the class $$\varvec{{\mathcal {U}} (\lambda )}$$

Wettability Changes Due to Nanomaterials and Alkali-A Proposed Formulation for EOR.

We investigated the usage of two silica nanomaterials (surface-modified) and alkali in enhanced oil recovery through Amott spontaneous imbibition tests, interfacial tension (IFT) measurements, and phase behavior. We evaluated the wettability alteration induced by the synergy between nanomaterials and alkali. Moreover, numerical analysis of the results was carried out using inverse Bond number and capillary diffusion coefficient. Evaluations included the use of Berea and Keuper outcrop material, crude oil with different total acid numbers (TAN), and Na2CO3 as alkaline agent. Data showed that nanomaterials can reduce the IFT, with surface charge playing an important role in this process. In synergy with alkali, the use of nanomaterials led to low-stable IFT values. This effect was also seen in the phase behavior tests, where brine/oil systems with lower IFT exhibited better emulsification. Nanomaterials’ contribution to the phase behavior was mainly the stabilization of the emulsion middle phase. The influence of TAN number on the IFT and phase behavior was prominent especially when combined with alkali. Amott spontaneous imbibition resulted in additional oil recovery ranging from 4% to 50% above the baseline, which was confirmed by inverse Bond number analysis. High recoveries were achieved using alkali and nanomaterials; these values were attributed to wettability alteration that accelerated the imbibition kinetics as seen in capillary diffusion coefficient analysis.

Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. The aim of this note is to point out a new connection between inverse coefficient problems and semidefinite programming that may help addressing these challenges. We show that an inverse elliptic Robin transmission problem with finitely many measurements can be equivalently rewritten as a uniquely solvable convex non-linear semidefinite optimization problem. This allows to explicitly estimate the number of measurements that is required to achieve a desired resolution, to derive an error estimate for noisy data, and to overcome the problem of local minima that usually appears in optimization-based approaches for inverse coefficient problems.

On the Uniqueness of the Solution of the Inverse Coefficient Problem for the Helmholtz Equation in a Phaseless Spatially Nonoverdetermined Statement

On the Uniqueness of the Solution of the Inverse Coefficient Problem for the Helmholtz Equation in a Phaseless Spatially Nonoverdetermined Statement

Теплофизические характеристики теплозащитного пакета корпуса ракетного двигателя при программированном нагреве

An experimental determination of the temperature dependences of the thermophysical characteristics of the MFP-92 multifunctional coating in the operating temperature range under thermal loading, simulating standard flight conditions, has been carried out. Heating was carried out with a jet of an industrial oxygen-propane burner mounted on a tripod with the possibility of varying the distance to the surface of the sample. The programs of the material operating modes include two peaks of heating to a temperature of ~1400 ° C with a heating and cooling rate of 20 - 40 deg / s. Under such conditions, thermal degradation of the MFP-92 material occurs, which changes its phase composition, structure, and, accordingly, thermophysical characteristics (TPС). The main transformations in the MFP-92 material occur in the temperature range up to 1000 °C, therefore, the heat transfer in it for given heating programs can be described using a simplified TРС model. This model assumes the existence of material in two states - initial (phase A) and annealed with completely completed transformation processes (phase B), each of which is assigned its own set of TPC. To determine the TPC of the MFP-92 material in its samples during thermal testing, temperature fields were recorded, which were then processed using the method of solving the inverse (coefficient) problem of thermal conductivity on a computer model. As a result, the temperature dependences of the specific heat and the coefficient of thermal conductivity of phases A and B were obtained, as well as the value of the most powerful thermal effect of the phase transition at 110 °C in phase A. The remaining phase transitions were taken into account by the corresponding changes in the specific heat. During material testing, the emissive of the material is also determined. Verification of the two-phase model of the MFP-92 material and the obtained values of its TPC was carried out based on the temperature fields obtained during the thermal tests of the samples of the three-layer thermal protection package "MFP-92 material-thermal insulation-steel substrate" under heating conditions according to the operating mode program confirmed their adequacy.

Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions

We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse coefficient problem of determining a spatially varying potential and the order of the time-fractional derivative by Dirichlet data at one end point of the spatial interval. The imposed Neumann conditions are required to be within the correct Sobolev space of order α. Our proof is based on a representation formula of solution to an initial boundary value problem with non-zero boundary data. Moreover, we apply such a formula and prove the uniqueness in the determination of boundary value at another end point by Cauchy data at one end point.

Evaluation of proper sensor position for classification of sheep behaviour through accelerometers

Automated classification and identification of feeding behaviour through sensors, has the potential to allow improvements in animal health and welfare. Sensor position, as well as epoch setting of segmented signal data, affects classification accuracy in behavioural activity discrimination. The aim of this study was to evaluate the effects of position, at different time epoch setting, of a tri-axial accelerometer-based device (BEHARUM) on the classification of behaviour types such as grazing, ruminating and other activities in sheep grazing a chicory-based sward. Sheep were video recorded, during accelerometer deployment, by fixed camera. Mean, variance and inverse coefficient of variation (i.e., mean/ standard deviation), of the raw acceleration data for each axis, as well as the resultant variance and inverse coefficient of variation values of the three axes, were calculated for the following positions: mouth, nape, collar and epoch settings: 5 s, 10 s, 30 s, 60 s, 120 s, 180 s, 300 s. Video recordings were coded manually assigning to each position and epoch the prevailing behaviour. Multivariate discriminant analysis (DA) was used to distinguish between the three behaviour types. To evaluate the performance of DA in discriminating the three activities, overall accuracy and Coehn’s k coefficient were calculated, based on the error distribution in assignment. Mouth position recorded the highest accuracies and Coehn’s k coefficient in 300 s time epoch setting (88 % and 0.8 respectively), as well as collar position (90 % and 0.8 respectively), while nape position showed the best performance in 180 and 300 s (80 % and 0.6 respectively). Overall, the best performance of DA was obtained using collar position in particular at 300 s time epoch.

Adoption and impact of super granulated urea (guti urea) technology on farm productivity in Bangladesh: A Heckman two-stage model approach

We aimed to determine the impact of farmers’ guti urea technology adoption on farm productivity in the Rajbari District of Bangladesh. The multi-stage sampling techniques were used to obtain a total 400 samples where 181 (45.25%) adopters and 219 (54.75%) non-adopters. The pre-canvassing structured survey schedule was used during the personal interviews. In addition, FGDs and KIIs were conducted to obtain qualitative information. To analyze the collected data, descriptive statistics, probit regression, and Heckman's two-stage model were used. Firstly, a binary regression model was used to examine the factors determining the participation of farmers in the use of guti urea technology. Secondly, treatment effect was assessed by the Heckman's two-stage model to identify the impact of the farmers’ participation on the adoption of guti urea technology. The inverse Mill's ratio coefficient indicates the presence of selection bias and the efficacy of applying the two-stage Heckman model. The results show that the involvement of farmers in the use of guti urea technology has a significantly positive impact on farm productivity. The analysis also shows that a 1% increase in adoption of guti urea technology contributes to a significant increase in farm productivity when other factors remain the same. We conclude that there is room for further increases in farm productivity through planned guti urea technology adoption in crop production. We recommend that the policy makers and authority expand the use and ensure the accessibility of guti urea as well as disseminate knowledge through the development of training opportunities for farmers to increase and enhance the reach of guti urea adoption amongst farmers. The results imply that the provision of complementary services is necessary in addition to the adoption of guti urea to achieve the aim of improving productivity.

An Inverse Problem Solution for Thermal Conductivity Reconstruction

This work deals with the inverse problem of reconstructing the thermal conductivity coefficient of the (2+1)D heat equation from over–posed data at the boundaries. The proposed solution uses a variational approach for identifying the coefficient. The inverse problem is reformulated as a higher–order elliptic boundary–value problem for minimization of a quadratic functional of the original equation. The resulting system consists of a well–posed fourth–order boundary–value problem for the temperature and an explicit equation for the unknown thermal conductivity coefficient. The existence and uniqueness of the resulting higher–order boundary–value problem are investigated. The unique solvability of the inverse coefficient problem is proven. The numerical algorithm is validated and applied to problems of reconstructing continuous nonlinear coefficient and discontinuous coefficients. Accurate and stable numerical solutions are obtained.

Simultaneously improving piezoelectric properties and temperature stability of Na0.5K0.5NbO3 (KNN)-based ceramics sintered in reducing atmosphere

It is a very difficult work to sinter K0.5Na0.5NbO3 (KNN)-based materials with good reduction resistance in strong reducing atmosphere. 0.945K0.48Na0.52Nb0.96Ta0.04O3−0.055BaZrO3 + 0.03ZrO2 + y mol%MnO (KNNT−0.055BZ + 0.03Zr + yMn) ceramics sintered in reducing atmosphere were prepared successfully by conventional solid-state reaction methods. MnO dopant increases grain size at y = 5–8 due to strong lattice distortion and then decreases grain size at y = 9 due to much Mn4Nb2O9 accumulated at the grain boundary. MnO dopant as an excellent sintering aid can effectively reduce volatilization of alkali metal by decreasing the sintering temperature (Tsinter). Reducing alkali metal volatilization can greatly reduce oxygen vacancies and improve piezoelectric properties. MnO dopant can improve the anti-reduction properties. The KNNT−0.055BZ + 0.03Zr + yMn ceramics at y = 6–9 show outstanding anti-fatigue of unipolar piezoelectric strain under the synergistic effect of reduced oxygen vacancies due to reduced volatilization and increased grain size. Piezoelectric properties and temperature stability of KNNT−0.055BZ + 0.03Zr ceramics sintered in reducing atmosphere are improved simultaneously by MnO dopant. Optimum inverse piezoelectric coefficient (d33*) of ceramics at y = 8 reaches up to 480 pm/V under low driving electric field E = 20 kV/cm at room temperature, and its temperature stability of d33* reaches 158 °C. It will be an excellent lead-free material candidate for the preparation of multilayer piezoelectric actuators co-fired with nickel electrode.

Two-step sintering of 0.93Bi0.5Na0.5TiO3-0.07BaTiO3 lead-free piezoelectric material

Two-step sintering (TSS) as an efficient sintering method for obtaining dense microstructure while preventing excess grain growth was used for sintering 0.93Bi0.5Na0.5TiO3-0.07BaTiO3 composition which is located near the morphotropic phase boundary of this binary system. In order to compare the obtained microstructure and piezoelectric properties, conventional single step sintering (SSS) was also examined. Microstructure evolution during sintering at different temperatures was investigated to find the optimum sintering temperature. Ferroelectric hysteresis loop as well as unipolar strain behavior of optimally sintered ceramics was studied. According to density measurement and microstructure studies of the prepared ceramics, TSS resulted in finer and more dense and uniform microstructure compared to SSS method. As a result remnant polarization of TSSed ceramic was increased by 35% and its coercive field was decreased by 16%. The inverse piezoelectric coefficient of the SSSed and TSSed was obtained 220 and 300 p.m./V, respectively. These values are high enough for practical applications such as actuators. The obtained results clearly showed that TSS is capable of sintering 0.93Bi0.5Na0.5TiO3-0.07BaTiO3 at temperatures lower than which is required for SSS method. Therefore the composition stoichiometry is maintained after sintering and denser microstructure without abnormal grain growth is obtained which is responsible for improved electrical properties of the piezoceramics.

Full-Band EEG Recordings Using Hybrid AC/DC-Divider Filters.

Full-band DC recordings enable recording of slow electrical brain signals that are severely compromised during conventional AC recordings. However, full-band DC recordings may be limited by the amplifier's dynamic input range and the loss of small amplitude high-frequency signals. Recently, Neuralynx has proposed full-band recordings with inverse filtering for signal reconstruction based on hybrid AC/DC-divider RRC filters that enable only partial suppression of DC signals. However, the quality of signal reconstruction for biological signals has not yet been assessed. Here, we propose a novel digital inverse filter based on a mathematical model describing RRC filter properties, which provides high computational accuracy and versatility. Second, we propose procedures for the evaluation of the inverse filter coefficients, adapted for each recording channel to minimize the error caused by the deviation of the real values of the RRC filter elements from their nominal values. We demonstrate that this approach enables near 99% reconstruction quality of high-potassium-induced cortical spreading depolarizations (SDs), endothelin-induced ischemic negative ultraslow potentials (NUPs), and whole-cell recordings of membrane potential using RRC filters. The quality of the reconstruction was significantly higher than with the existing inverse filtering procedures. Thus, RRC filters with inverse filtering are optimal for full-band EEG recordings in various applications.

Piezoelectric Properties of (1 – X)BiScO3 – XPbTiO3 System for Actuator Applications

ABSTRACTIn this research, the crystalline and piezoelectric properties of (1 – X )BiScO3–XPbTiO3 (X = 0.60, 0.62, 0.64, 0.66 and 0.68) ceramics were investigated to determine the optimized composition for energy harvester and sensor applications. BS-PT ceramics have strong merits in terms of their high Curie temperature and piezoelectric charge coefficient. Devices of the (1 – X )BS-XPT ceramics were fabricated by a conventional mixed-oxide sintering process with nano-powders. By employing the X-ray diffraction patterns, the morphotropic phase boundary (MPB) region of the monoclinic and tetragonal phases was identified at X = 0.64. Near the MPB region, the piezoelectric and dielectric properties of BS-PT ceramics were improved compared with those of other composition. By optimizing the compositions of the BS-PT ceramics, the maximum values of the dielectric constant (εr), piezoelectric charge coefficient (d33), electromechanical coupling factor (kp) and remanent polarization (Pr) were obtained, with values of 1387, 417 pC/N, 51.4% and 44.8 µC/cm2, respectively. Moreover, a high Curie temperature of 399.2 °C and inverse piezoelectric charge coefficient of 574 pm/V were observed for the 0.36BS–0.64PT composition, which can be a huge merit for actuator applications. These high piezoelectric charge coefficients and inverse piezoelectric charge coefficients can be the strong merits for energy harvester and actuator applications.

Numerical Solution Methods for a Nonlinear Operator Equation Arising in an Inverse Coefficient Problem

We consider the inverse problem of determining two unknown coefficients in a linearsystem of partial differential equations using additional information about one of the solutioncomponents. The problem is reduced to a nonlinear operator equation for one of the unknowncoefficients. The successive approximation method and the Newton method are used to solve thisoperator equation numerically. Results of calculations illustrating the convergence of numericalmethods for solving the inverse problem are presented.

Determination of a time-dependent potential in a Rayleigh-Love equation with non-classical boundary condition

Mathematical model of the longitudinal vibration of bars includes higher-order derivatives in the equation of motion under considering the effect of the lateral motion of a relatively thick bar. This paper considers such an inverse coefficient problem of determining time-dependent potential of a linear source together with the unknown longitudinal displacement from a Rayleigh-Love equation (containing the fourth-order space derivative) by using an additional measurement. Existence and uniqueness theorem of the considered inverse coefficient problem is proved for small times by using contraction principle.

Calculation of the gradient of Tikhonov’s functional in solving coefficient inverse problems for linear partial differential equations

Abstract A fast algorithm for calculating the gradient of the Tikhonov functional is proposed for solving inverse coefficient problems for linear partial differential equations of a general form by the regularization method. The algorithm is designed for problems with discretized differential operators that linearly depend on the desired coefficients. When discretizing the problem and calculating the gradient, it is possible to use the finite element method. As an illustration, we consider the solution of two inverse problems of elastography using the finite element method: finding the distribution of Young’s modulus in biological tissue from data on its compression and a similar problem of determining the characteristics of local oncological inclusions, which have a special parametric form.

Electroelastic waveguide: Analysis of the effect of prestresses

The paper considers the direct problem for an orthotropic electroelastic waveguide in the presence of a homogeneous field of preliminary stresses. Dispersion curves for the given parameters of the material are constructed using numerical methods. The influence of the distribution laws of variable characteristics of an electroelastic waveguide and preliminary stresses on the change in the dispersion set of curves is analyzed. On the basis of the results obtained, practical recommendations are given for studying the inverse coefficient problem of restoring the level of prestressing.