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We study an asymptotic model for the motion of capillary-gravity waves in a fluid with non-Newtonian viscosity (known as odd viscosity). This model was one of three which were introduced recently by Granero-Belinchón and Ortega; they showed that two of their models were well-posed in Sobolev spaces and one was well-posed in analytic function spaces. For the model previously shown to have analytic solutions, we improve the theory to establish well-posedness in Sobolev spaces. This is accomplished through careful use of commutator estimates. We discuss related applications of our approach using these commutator estimates. [ABSTRACT FROM AUTHOR]

We study a three-dimensional model Volterra-type integral equation with boundary weakly singular, singular, and strongly singular kernels in the domain , , which can be called a rectangular pipe. In the case that the coefficients of the equation are connected with each other, a solution to the equation is sought in the class of continuous functions in vanishing with a specified asymptotic behavior on special domains. We prove under some conditions that the problem of finding a solution to a three-dimensional integral Volterra-type equation with boundary weakly singular, singular, and strongly singular kernels reduces to solving one-dimensional integral Volterra-type equations with special boundary kernels. Solving the given integral equations, we employ connections of the latter equations with first-order differential equations with weakly singular, singular and strongly singular coefficients. Also, we establish that there is no need to require the differentiability of a solution and a right-hand side. It suffices that the right-hand side of the three-dimensional integral equation with boundary singular weakly singular, and strongly singular kernels is continuous and vanishes with a specified asymptotics on special domains. We prove that, depending on the sign of the coefficients of the equation, the explicit solution to a three-dimensional model Volterra-type integral equation with singular kernels can contain from one to three arbitrary functions of two variables. We also describe the case that there is a unique solution to the integral equation. [ABSTRACT FROM AUTHOR]

A novel image analysis method was developed to determine the volume expansion ratio of cooked rice, and study the kinetics of the volume expansion ratio changes of rice as a function of the cooking time. The correlation between volume expansion ratio and various physicochemical factors has been studied to elucidate the key factors affecting the changes in cooked rice volume. The results demonstrated that the image analysis method is capable of both visually and quantitatively analyzing the volume expansion properties of rice throughout the cooking process. This method revealed that five models can effectively simulate (with a correlation coefficient R2 > 0.95) the changes in the volume expansion ratio for Koshihikari and Thai Jasmine rice as a function of cooking time. These models consider cooking time as a variable. Consequently, a linear equation based solely on cooking time was derived, which can predict the volume expansion ratio of rice during the cooking process. The correlation analysis suggested that the apparent amylose content, protein content and grain length had significantly (P < 0.05) negative correlation with the volume expansion ratio; while starch content and grain width had significantly (P < 0.05) positive correlation with the volume expansion ratio; the pasting properties parameters had different relationships with the volume expansion ratio of cooked rice. [ABSTRACT FROM AUTHOR]

For sample return missions from deep space, a thin aeroshell capsule was proposed aimed at mitigating the aerodynamic heating during its reentry into the earth's atmosphere. The functional requirements of the capsule mandate that it aerodynamically decelerate sufficiently and land in the appropriate attitude without a parachute. To evaluate its motion attitude during transonic conditions in a wind tunnel, we employed the 1-degree of freedom (1-DOF) oscillation method. Furthermore, to predict its motion during an actual flight based on the wind tunnel test results, we examined the impact of the moment of inertia (MOI) on the motion. In all the MOI cases investigated, the limit cycle oscillation (LCO) was observed with a constant amplitude of angle. The variations in the MOI resulted in differences in the amplitude of the angle and time to reach the LCO. This study focused on the growth phase until the LCO and evaluated the characteristics on the phase plane. Consequently, a gradual approach to acceleration attributed to the static moment was observed in the growth history. A new modeling approach, centered on the nullcline during the growth phase, was adopted. Here, an approximation using a third-order function of angular velocity was applied to reproduce the nullcline obtained from the experiment. Upon non-dimensionalization of this model equation using the motion period, it was confirmed that the non-dimensional parameters were affected by the motion period, while this model focused solely on the growth phase. Furthermore, upon parameter tuning to replicate the amplitude of the angle and time to reach the LCO, and using these parameters, we predicted the impact of the MOI. The predicted results qualitatively reproduced larger MOI leading to larger amplitudes of angle and longer times to reach the LCO, which was consistent with the experimental results.

Based on the model equation for homogeneous particles, we propose a model equation for just suspension speed for mixed particles. If the correlation equation of Zwietering holds, the just suspension speed of mixed particles [njs,mix(XT)] is given as a function of the volume fraction of particle i (φi) and the just suspension speed of uniform particle i [njs,i(XT)]. [Graphic: see text]njs,mix(XT)=[∑injs,i(XT)20/3φi∑injs,i(XT)10/3φi]3/10 The calculated values using the proposed model equation were in close agreement with the experimental data. Furthermore, the results were in good agreement with the literature data for mixed particles containing four-component system. The study also confirmed the usefulness of the proposed model equation, since the existing correlation equation did not correlate well with the experimental data.

The paper is devoted to the investigation of some classes of first-order integro-differential equation with singular kernel and its conjugate equation. The kernel of non-conjugate equation has singularity at the point , and the kernel of conjugate equation has singularity at the point . First, two conjugate classes of functions are introduced and then in these classes of functions the model equations are investigated. Further in three cases, in depending of the roots of the characteristic equation, the solution of studied equations were found in an explicit form. It is shown that the general solution of investigated equations contains some number of arbitrary constants. Also, there were found the case when the model equations has only unique solutions. Also in this work we studied the non-model equation. When the roots of the corresponding characteristic equation are real and different the solution of the non-model equation were found through the resolvent of corresponding Volterra-type integral equation. [ABSTRACT FROM AUTHOR]

The paper presents the prediction of bearing capacity equation of E-shaped footing subjected to a vertical concentric load and resting on layered sand using machine learning techniques and the data used in the analysis has been extracted from finite element modelling of the same footing. The input variables used in the developed neural network model were the bearing capacity of square footing, thickness ratio, friction angle ratio and the output were the bearing capacity of E-shaped footing on layered sand. Multiple layer perceptron (MLP) and multiple linear regression (MLR) prediction models were used for the determination of error metrics and the ultimate bearing capacity of E-shaped footing resting on layered sand. Finally, for the ANN model development, a model equation was developed with the assistance of weights and biases, based on the MLP and MLR model using open-source WEKA and Anaconda software respectively. Sensitivity analysis has been performed on the data sets which correlates the various input variables with the output variable of both the models. The coefficient of determination (R2) comes out to be 0.99 and 0.98 for the MLP and MLR models respectively indicating that both the models were able to predict the bearing capacity for the E shaped footing with acceptable accuracy.

To evaluate the concentration of natural radionuclides and to carry out geophysical interpretation of part of Igarra area, Southern Nigeria, an integrated geophysical approach was adopted involving radiometric, gravity, and magnetic methods. The RS-230 Super-Spec spectrometer, G-512 Lacoste and Romberg gravimeter, and the GSM-19v7.0 Overhauser instrument were used for the radiometric, gravity, and magnetic data acquisitions, respectively, along a specified traverse within the area. The datasets were processed using Oasis Montaj, Grav-Master, and Ms-Excel software. Gravity results show that the mean free air and Bouguer anomalies in the area are − 67.42 and − 84.22 mGal, while magnetic survey indicates that the mean corrected magnetic field intensity in this area is 32218.49 nT. Radiometric survey results show that the mean radioactivity concentrations of thorium ( 232 Th ) , uranium ( 238 U ), and potassium ( 40 K ) are 31.81 Bq/kg, 26.48 Bq/kg, and 167.33 Bq/kg, respectively. Further analysis also revealed that the mean radioactivity equivalent of the area is 84.86 Bq/kg; absorbed dose rate is 72.74nGy/h, while the mean external hazard index is 0.30. A novel model equation for estimating absorbed dose rate from radioactivity equivalent was also obtained and validated. The gravity and magnetic survey results indicate the presence of low-density and high magnetic basement rocks underlying this area, while radiometric results reveal that radiations in this area did not exceed acceptable standards of 370 Bq/kg for radioactivity equivalent, 84 nGy/h for absorbed dose rate, and unity which corresponds to 370 Bq/kg for external hazard index as recommended by the United Nations Scientific Committee on the Effects of Atomic Radiation and the International Atomic Energy Agency. [ABSTRACT FROM AUTHOR]

The paper presents the prediction of bearing capacity equation of E-shaped footing subjected to a vertical concentric load and resting on layered sand using machine learning techniques and the data used in the analysis has been extracted from finite element modelling of the same footing. The input variables used in the developed neural network model were the bearing capacity of square footing, thickness ratio, friction angle ratio and the output were the bearing capacity of E-shaped footing on layered sand. Multiple layer perceptron (MLP) and multiple linear regression (MLR) prediction models were used for the determination of error metrics and the ultimate bearing capacity of E-shaped footing resting on layered sand. Finally, for the ANN model development, a model equation was developed with the assistance of weights and biases, based on the MLP and MLR model using open-source WEKA and Anaconda software respectively. Sensitivity analysis has been performed on the data sets which correlates the various input variables with the output variable of both the models. The coefficient of determination (R2) comes out to be 0.99 and 0.98 for the MLP and MLR models respectively indicating that both the models were able to predict the bearing capacity for the E shaped footing with acceptable accuracy. [ABSTRACT FROM AUTHOR]

Nano- $g$ accelerometers are widely used in space exploration and measurement of the earth’s gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this article, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison to the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultralow frequency. [ABSTRACT FROM AUTHOR]

In this paper for a new class of model and non-model partial integro-differential equations with singularity in the kernel, we obtained integral representation of family of solutions by aid of arbitrary functions. Such type of integro-differential equations are different from Cauchy-type singular integro-differential equations. Cauchy-type singular integro-differential equations are studied by the methods of the theory of analytic functions. In the process of our research the new types of singular integro-differential operators are introduced and main property of entered operators are learned. It is shown that the solution of studied equation is equivalent to the solution of system of two equations with respect to x and y, one of which is integral equation and the other is integro-differential equation. Further, non-model integro-differential equations are studied by regularization method. This regularization method for non-model equation is based on selecting and analysis of a model part of the equation and reduced to the solution of two second kind Volterra type integral equations with weak singularity in the kernel. It is shown that the presence of a non-model part in the equation does not affect to the general structure of the solutions. From here investigation of the model equations for given class of the integro-differential equations becomes important. In the cases, when the solution of given integro-differential equation depends on any arbitrary functions, a Cauchy type problems are investigated.

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This paper carried out simulations of a channel flow experiment and a case study of granular avalanche flow using two kinds of methods, depth-integrated continuum method and discrete element method. In the simulation of the channel flow experiment, we presented a method for calculating normal force and bending moment of the rigid wall based on the depth-integrated continuum method. Although the peak value of the normal force and bending moment cannot be obtained using the depth-integrated continuum method, the residual value can be obtained rapidly and accurately. Then, Frank landslide in Canada was simulated using the two methods. Calculation results of the extent and duration of the granular avalanche were in good agreement with actual situation, which validated the correctness and effectiveness of the two methods. The velocity process, energy process, and risk zoning of the granular avalanche were obtained. Calculation results showed that the maximum average velocity of the granular avalanche was about 68 m/s at 20 s. The computational efficiency of the depth-integrated continuum method was better than that of the discrete element method, while the energy process of the granular avalanche could be better traced using the discrete element method. Detailed comparison and discussion were carried out in the simulations of the experiment and the case study which can provide a scientific reference and basis for the simulation of the granular avalanche flow. [ABSTRACT FROM AUTHOR]

• Strategy developed for calibrating nano-g accelerometer's nonlinearity by shaking. • Systematic errors identified and eliminated for calibrating on a horizontal shaker. • Small measurement uncertainty of accelerometer's second-order coefficient achieved. Nano- g accelerometers are utilized extensively in high precision applications, such as gravity measurements on moving bases, which often face strong motion disturbances. Accurately-calibrated coefficients are crucial for suppressing their high-order error effects, but challenging to measure using conventional calibration methods. This paper presents an investigation into calibration of the nonlinearity coefficient of nano- g accelerometers on a horizontal shaker driven by a dual frequency signal. A nonlinear output component occurring at the low difference frequency, with a high signal-to-noise ratio, is utilized. The calibration principle and strategy are investigated, along with an analysis of the potential experimental error sources. Two critical accompanying systematical errors, arising from shaker's movement distortion along the primary vibration direction and gravity coupling of input acceleration caused by the guide rail deflection, are identified and eliminated through a proposed procedure. Experimental tests demonstrate an uncertainty level two orders of magnitude better than the traditional method based on the dividing head. [ABSTRACT FROM AUTHOR]

Based on the urban shantytown renovation project in Hongguang Town, Helan County, Ningxia, in Northwest China, the influence of fly ash and silica fume admixture on the mechanical properties of Self-compacting Concrete (SCC) was tested and analyzed in this work. The experimental tests including compressive strength, splitting strength, triaxial strength and an ultrasonic nondestructive test. Furthermore, the Back Propagation (BP) neural network algorithms were established. The results show that there is an obvious difference between the development law of compressive strength of SCC and that of ordinary concrete. The splitting pressure ratio of SCC is 1/10 to 1/8, while that of ordinary concrete is 1/13 to 1/10. Moreover, the peak strain, peak stress and initial stiffness of SCC increase with the increase of the confining pressure when compressed from three directions. In addition, the ultrasonic amplitude of SCC can reflect the changing laws of its compressive strength. As a conclusion, the addition of fly ash and silica fume increases the splitting pressure ratio of SCC. More importantly, the compressive strength formula for SCC with silica fume and a low content of fly ash is proposed, and the model equation between the amplitude and compressive strength is given. This study provides a reference for the mixture ratio of fly ash and silica fume in the application of SCC.

Establishing a model equation with high accuracy and high computational efficiency is very important for the estimation of battery state of charge (SOC). To ensure better SOC estimation results, most studies have focused on the improvement of the algorithm, while the impact of the model equation which may offset the benefits of advanced algorithms has been overlooked. To address this problem, this paper studies the widely used model equations and presents a new model equation based on a Gaussian function that improves the SOC estimation accuracy and computational efficiency. With the Worldwide harmonized Light Vehicles Test Cycle (WLTC) which is highly dynamic and more realistic than any other driving cycles, the proposed model equation is applied to different filtering algorithms to validate its performance in SOC estimation. The results indicate that the proposed model equation can greatly improve the accuracy of SOC estimation without an increase of computation. In addition, for the traditional polynomial-based model equations, the 6th-order power function polynomial has better performance in SOC estimation than polynomials with other orders.

We consider a problem of factoring the scattering matrix for Schrödinger equation on the real axis. We find the elementary factorization blocks in both the finite and infinite cases and establish a relation to the matrix conjugation problem. We indicate a general scheme for constructing a large class of scattering matrices admitting a quasirational factorization. [ABSTRACT FROM AUTHOR]

We consider the nonlinear Boltzmann equation in the framework of the Shakhov model for the classical problem of gas flow in a plane layer. The problem reduces to a system of nonlinear integral equations. The nonlinearity of the studied system can be partially simplified by passing to a new argument depending on the solution of the problem itself. We prove the existence theorem for a unique solution of the linear system and the existence theorem for a positive solution of the nonlinear Urysohn equation. We determine the temperature jumps on the lower and upper walls in the linear and nonlinear cases, and it turns out that the difference between them is rather small. [ABSTRACT FROM AUTHOR]

A mathematical model for the prediction of shelling efficiency of an impact snake gourd seed decorticator was presented using dimension analysis based on the Buckingham's pi theorem. Experimental verification of the models was conducted comparing the theoretical predictions with estimates from the representation of conventional methods. A high coefficient of determination was found between the predicted and the experimental value (98.45% for effect of moisture content on decortication efficiency; 99.69% for effect of hammer diameter on decortications efficiency and 97.35% for effect of hammer speed on the decortications efficiency) showing that the model is appropriate. [ABSTRACT FROM AUTHOR]

A stable high-order Runge-Kutta discontinuous Galerkin (RKDG) scheme that strictly preserves positivity of the solution is designed to solve the Boltzmann kinetic equation with model collision integrals. Stability is kept by accuracy of velocity discretization, conservative calculation of the discrete collision relaxation term, and a limiter. By keeping the time step smaller than the local mean collision time and forcing positivity values of velocity distribution functions on certain points, the limiter can preserve positivity of solutions to the cell average velocity distribution functions. Verification is performed with a normal shock wave at a Mach number 2.05, a hypersonic flow about a two-dimensional (2D) cylinder at Mach numbers 6.0 and 12.0, and an unsteady shock tube flow. The results show that, the scheme is stable and accurate to capture shock structures in steady and unsteady hypersonic rarefied gaseous flows. Compared with two widely used limiters, the current limiter has the advantage of easy implementation and ability of minimizing the influence of accuracy of the original RKDG method. [ABSTRACT FROM AUTHOR]