A Fundamental Equation of State for Chloroethene for Temperatures from the Triple Point to 430 K and Pressures to 100 MPa

A fundamental equation of state in terms of the Helmholtz energy is presented for chloroethene (vinyl chloride). Due to its fundamental nature, it can be used to consistently calculate all thermodynamic state properties in the fluid region. Based on the underlying experimental database, it is valid from the triple-point temperature 119.31 K to 430 K with a maximum pressure of 100 MPa. In addition to the accurate reproduction of experimental data, correct extrapolation behavior during the development of the equation was attained. This enables the equation to be applied in modern mixture frameworks.

Citation Trend of Indian Physics and Astronomy Research during 2005 2020 through the Lens of Some New Indicators

The indicator Citation Swing Factor (CSF) has recently been developed to quantitatively measure the diffusion process from h-core zone to h-core excess zone. This paper calculated CSF for Indian physics and astronomy research output appeared in selective Indian journals since 2005 to 2020. The theoretical values of CSF are also calculated on the basis of its fundamental equation and same was compared it with the respective observed values. The average error over entire time span is found 2.26 per cent indicating close proximity between theoretically expected and practically observed values. Besides, three other scientometric indicators are introduced here, viz. Time-Normalised Total Cited Ratio (TC), Time-Normalised Cited Uncited Ratio (CU) and Time-Normalised Total Uncited Ratio (TU). Of these four indicators, the variation of TC is highest (1.76), followed by TU (0.53), CU (0.37) and CSF(E) (0.09), as evident from the values of respective Coefficients of Variations. The numerical values of these indicators are found out for the same sample and the temporal variations along with their mutual interrelationships are determined by regression analysis. It is observed that the three indicators, TC, CU and TU are mutually interrelated through the following linear regression equations, i.e. TC = -0.76 + 1.88*TU and CU = -0.201 + 0.34*TU.

Application of the nonlinear optimisation in regional gravity field modelling using spherical radial base functions

The gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.

Theoretical Solutions to The Problem of Seepage and Consolidation in Saturated Clay Based on The Spatial Axisymmetric Model

The series solutions to the problem of spatial axisymmetric consolidation are deduced under non-homogeneous boundary conditions. Firstly, differentiable step function is introduced to construct the homogeneous operation function. Secondly, the operation function is used to superimpose the non-homogeneous boundaries to obtain homogeneous boundaries, non-homogeneous fundamental equation and new initial condition. Finally, the method of variables separation is used to construct the eigenfunction, and due to the mathematical justification of complete orthogonality of the eigenfunction, the series expansions of the fundamental equation and initial condition are carried out to obtain solutions for the seepage and consolidation in saturated clay with a borehole boundary. The correctness of the theoretical solutions are verified by the strict mathematical and mechanics derivation and the law of space-time variation in seepage flow.

Gerber-Shiu Function in a Discrete-time Risk Model with Dividend Strategy

In this paper, a discrete-time risk model with dividend strategy and a general premium rate is considered. Under such a strategy, once the insurer’s surplus hits a constant dividend barrier , dividends are paid off to shareholders at instantly. Using the roots of a generalization of Lundberg’s fundamental equation and the general theory on difference equations, two difference equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results obtained are utilized to derive the probability of ultimate ruin when the claim sizes is a mixture of two geometric distributions. Numerical examples are also given to illustrate the applicability of the results obtained.

Thermodynamic Properties of Methyl Diethanolamine

The homogeneous density of the liquid phase is experimentally investigated for methyl diethanolamine. Data are obtained along five isotherms in a temperature range between 300 K and 360 K for pressures up to 95 MPa. Two different apparatuses are used to measure the speed of sound for the temperatures between 322 K and 450 K with a maximum pressure of 95 MPa. These measurements and literature data are used to develop a fundamental equation of state for methyl diethanolamine. The model is formulated in terms of the Helmholtz energy and allows for the calculation of all thermodynamic properties in gaseous, liquid, supercritical, and saturation states. The experimental data are represented within their uncertainties. The physical and extrapolation behavior is validated qualitatively to ensure reasonable calculations outside of the range of validity. Based on the experimental datasets, the equation of state is valid for temperatures from 250 K to 750 K and pressures up to 100 MPa.

Method for constructing the fundamental equation of state that takes into account the peculiarities of the substance behaviour in a wide vicinity of the critical point

On the basis of the phenomenological theory of the critical point and the Benedek hypothesis, an expression for the Helmholtz free energy F with scale functions in the density-temperature variables has been developed. The proposed free energy equation has been tested on the example of constructing the fundamental equation of state of 2,3,3,3-tetrafluoropropene (R1234yf). By comparison with the known experimental data on the equilibrium properties of R1234yf – density and pressure on the phase equilibrium line, p-ρ-T-data in the single-phase region, the second and third virial coefficients, isochoric heat capacity, isobaric heat capacity and the sound velocity – the operating range of the equation of state of R1234yf has been established according to temperature from 220 K to 420 K and pressure up to 20 MPa.

Constraint-Following Servo Control for the Trajectory Tracking of Manipulator with Flexible Joints and Mismatched Uncertainty

Trajectory tracking is a common application method for manipulators. However, the tracking performance is hard to improve if the manipulators contain flexible joints and mismatched uncertainty, especially when the trajectory is nonholonomic. On the basis of the Udwadia–Kalaba Fundamental Equation (UKFE), the prescribed position or velocity trajectories are creatively transformed into second-order standard differential form. The constraint force generated by the trajectories is obtained in closed form with the help of UKFE. Then, a high-order fractional type robust control with an embedded fictitious signal is proposed to achieve practical stability of the system, even if the mismatched uncertainty exists. Only the bound of uncertainty is indispensable, rather than the exact information. A leakage type of adaptive law is proposed to estimate such bound. By introducing a dead-zone, the control will be simplified when the specific parameter enters a certain area. Validity of the proposed controller is verified by numerical simulation with two-link flexible joint manipulator.