Identifying an unknown potential term in the fourth-order Boussinesq–Love equation from mass measurement

PurposeThe inverse problem of identifying the time-dependent potential coefficient along with the temperature in the fourth-order Boussinesq–Love equation (BLE) with initial and boundary conditions supplemented by mass measurement is, for the first time, numerically investigated. From the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data.Design/methodology/approachFor the numerical discretization, the authors apply the Crank–Nicolson finite difference method along with the Tikhonov regularization for finding a stable and accurate approximate solution. The resulting nonlinear minimization problem is solved using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted.FindingsThe present computational results demonstrate that obtained solutions are stable and accurate.Originality/valueThe inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical identification has been studied yet. Therefore, the main aim of the present work is to undertake the numerical realization. The von Neumann stability analysis is also discussed.

An inverse problem of determining the time-dependent potential in a higher-order Boussinesq-Love equation from boundary data

PurposeThe paper aims to numerically solve the inverse problem of determining the time-dependent potential coefficient along with the temperature in a higher-order Boussinesq-Love equation (BLE) with initial and Neumann boundary conditions supplemented by boundary data, for the first time.Design/methodology/approachFrom the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, the authors apply the generalized finite difference method (GFDM) for solving the BLE along with the Tikhonov regularization to find stable and accurate numerical solutions. The regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. The stability analysis of solution of the BLE is proved using the von Neumann method.FindingsThe present numerical results demonstrate that obtained solutions are stable and accurate.Practical implicationsSince noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Originality/valueThe knowledge of this physical property coefficient is very important in various areas of human activity such as seismology, mineral exploration, biology, medicine, quality control of industrial products, etc. The originality lies in the insight gained by performing the numerical simulations of inversion to find the potential co-efficient on time in the BLE from noisy measurement.

Exergy: Mechanical Nuclear Physics Measures Pressure, Viscosity and X-Ray Resonance in K-Shell in a Classical Way

First, the liquid drop model assumes a priori; to the atomic nucleus composed of protons and neutrons, as an incompressible nuclear fluid that should comply with the Navier–Stokes 3D equations (N-S3D). Conjecture, not yet proven, however, this model has successfully predicted the binding energy of the nuclei. Second, the calculation of nuclear pressure p0∈1.42,1.94]1032Pa and average viscosity η=1.71×1024fm2/s, as a function of the nuclear decay constant k=p02η=1T1/2, not only complements the information from the National Nuclear Data Center, but also presents an analytical solution of (N- S3D). Third, the solution of (N-S3D) is a Fermi Dirac generalized probability function Pxyzt=11+ep02ηt−μx2+y2+z21/2, Fourth, the parameter μ has a correspondence with the Yukawa potential coefficient μ=αm=1/r, Fifth, using low energy X-rays we visualize and measure parameters of the nuclear surface (proton radio) giving rise to the femtoscope. Finally, we obtain that the pressure of the proton is 8.14 times greater than the pressure of the neutron, and 1000 times greater than the pressure of the atomic nucleus. Analyzed data were isotopes: 9≤Z≤92 and 9≤N≤200.

Compressibility Characteristics of Soft Clays Treated by Graphene Oxide

Changing the soft soils' characteristics is difficult by directly incorporating Graphene oxide due to underlying soil properties. Therefore the stability of treated soils used for cementitious materials can be improved by treatment with Graphene oxide. Consistency and compression tests were used to study the mechanical behavior of the new compound Graphene mixture from fine, stable Graphene oxide. The soft clay used in this study has a shear strength of 33.0 kPa. It was stabilized with 0.1% Graphene oxide and cured for one day and some samples for seven days. It was concluded that the void ratio decreased with the addition of Graphene oxide under a given consolidation pressure. The other soil properties: swelling potential, coefficient of volume compressibility (mv), and coefficient of consolidation (Cv) decrease with increasing Graphene oxide under curing periods.

Forecasting Sales Volumes of Small and Medium-Sized Machine-Building Enterprises

In the article, the authors considered the possibilities of forecasting sales based on the use of ABC analysis tools, the customer potential coefficient and the degree of customization of orders. The object of the study was five medium-sized machine-building enterprises. The method is based on static grouping and analysis of actual sales volumes in the context of customers and the range of orders. The peculiarity of these enterprises is the presence of a large pool of customers with low repeatability of orders. The analysis showed that the majority of Group A customers have low customer potential and stable or declining demand. The largest increase in orders was observed among the customers of Group B. The level of customization of the order increases customer loyalty, but increasing the level of customization reduces the economic efficiency of the activity. The authors suggest direct planning of the basic part of the sales volume based on the achieved level of orders by customers of Groups A and B with the customer potential above 1. The additional part of the sales volume determined by the goals of the enterprise, its resources and planned based on an increase in the level of customization.

Streaming Potential Coefficient Measurements in Porous Rocks Saturated by Divalent Electrolytes

Streaming potential in a water-rock system is generated by the relative motion between water and solid surfaces and is directly related to the existence of an electric double layer between water and solid grain surfaces of porous media. The streaming potential measurements have great potential in geophysical applications. Most porous rocks are filled by ground water containing various types of electrolytes. Therefore, it is important to understand the variation of the streaming potential with types of electrolytes for specific rocks. In this work, we have carried out streaming potential measurements for three consolidated rocks saturated by three divalent electrolytes at different electrolyte concentrations. The experimental result shows that the streaming potential coefficient in magnitude of all samples decreases with increasing electrolyte concentration. Additionally, an empirical relation between the streaming potential coefficient and the electrolyte concentration is obtained and it has a similar form to those available in literature for monovalent electrolytes.