A New Alpha-function for the Peng-Robinson Equation of State： Application to Natural Gas

Cubic equations of state(EOSs) are simple and easy at calculation. One way of improving the accuracy of a cubic EOS is through the modification of temperature-dependent energy parameter by using alpha-function.The industrial applications of natural gas are very wide and as a result, prediction of thermodynamic properties and phase behavior of natural gas is an important part of design for such processes. In this work we develop a newα-function for the Peng-Robinson(PR) EOS with the parameters optimized especially for natural gas components.The parameters are generalized as a linear function of acentric factor. The results are compared to the predictions from original PR EOS and other α-functions in literature. It is shown that the new α-function presents a good accuracy with the average deviation of 1.42% for natural gas components.

Numerical method of the Riemann problem for two-dimensional multi-fluid flows with general equation of state

Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional （2D） multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.

Equation of state for warm dense lithium： A first principles investigation

The quantum molecular dynamics based on the density functional theory has been adopted to simulate the equation of state for the shock compressed lithium. In contrary to some earlier experimental measurement and theoretical simulation,there is not any evidence of the ‘kink＇ in the Hugoniot curve in our accurate simulation. Throughout the shock compression process, only a simple solid-to-liquid melting behavior is demonstrated, instead of complicated solid–solid phase transitions. Moreover, the x-ray absorption near-edge spectroscopy has been predicted as a feasible way to diagnose the structural evolution of warm dense lithium in this density region.

Anisotropic Standard Decelerating Cosmological Model with Quadratic Equation of State

Spatially homogeneous and anisotropic Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been diagnosed in general theory of relativity. To obtain a deterministic solution, we have used a relation between metric potentials. The exact solution of Einstein’s field equations thus obtained represents an expanding and decelerating universe. The physical and kinematical parameters of the model have also been analyzed with certain constrained between the parameters of the quadratic equation of state.

Generalization of vdW Type of Equations of State

1 INTRODUCTIONBecause of importance of equations of state (EOS)in science and industry,hundreds forms of EOS havebeen presented since latter 19th century.It seems impossible to develop a general equation covering vari-ous kinds of EOS.But for cubic EOS,several generalequations have been reported already. Martin presented the first general equation whichis following p=RT/V-α(T)/(υ+β)(υ+γ)+δ(T)/υ(υ+β)(υ+γ) (1) Kumar et a1.presented an equation called the most general form of a density-cubic or, alterna tively,volume-cubic mathematical equation,the form of which is as

An Interface-Capturing Method for Resolving Compressible Two-Fluid Flows with General Equation of State

In this study,a stable and robust interface-capturing method is developed to resolve inviscid,compressible two-fluid flows with general equation of state(EOS).The governing equations consist of mass conservation equation for each fluid,momentum and energy equations for mixture and an advection equation for volume fraction of one fluid component.Assumption of pressure equilibrium across an interface is used to close the model system.MUSCL-Hancock scheme is extended to construct input states for Riemann problems,whose solutions are calculated using generalized HLLC approximate Riemann solver.Adaptive mesh refinement(AMR)capability is built into hydrodynamic code.The resulting method has some advantages.First,it is very stable and robust,as the advection equation is handled properly.Second,general equation of state can model more materials than simple EOSs such as ideal and stiffened gas EOSs for example.In addition,AMR enables us to properly resolve flow features at disparate scales.Finally,this method is quite simple,time-efficient and easy to implement.

Effects of Total Intravenous Anesthesia and Static Aspiration Combined General Anesthesia on Postoperative Cognitive Function and Psychological State of Elderly Patients with Esophageal Cancer

Objective: To compare the effects of total intravenous anesthesia and static aspiration combined general anesthesia on postoperative cognitive function and psychological state of elderly esophageal cancer patients. Methods: From July 2020 to April 2021, 180 elderly patients who underwent radical esophageal cancer surgery in our hospital were randomly divided into 90 cases in the control group and 90 in the observation group. The control group used static aspiration compound general anesthesia, and the patients in the observation group used intravenous anesthesia to compare the cognitive function and psychological state of the two groups of patients. Results: There was no statistical difference in the cognitive function score of patients in the observation group 30 minutes before anesthesia, 1 h and 24 hours after anesthesia compared with that in the control group, P > 0.05;there was no statistical difference between the Hamilton Anxiety Scale (HAMA) scores 30 minutes before and 24 hours after anesthesia in the observation group compared with the control group, P > 0.05;the cognitive function score of patients in the observation group of 4 h after surgery and 12 h after operation was significantly higher than that of the control group;the HAMA scores of patients in the observation group of 1 h, 4 h and 12 h after surgery were significantly lower than that of the control group, P Conclusion: The application of total intravenous anesthesia in elderly patients with esophageal cancer surgery can reduce the impact of anesthesia on their cognitive function and psychological state, which is worth popularizing and applying in clinical practice.

Parallelizable Calculation of Observables Values on Analog Quantum Computer

The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.

GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.

Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schrödinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.

Fluid State of Dirac Quantum Particles

In our previous works, we suggest that quantum particles are composite physical objects endowed with the geometric and topological structures of their corresponding differentiable manifolds that would allow them to imitate and adapt to physical environments. In this work, we show that Dirac equation in fact describes quantum particles as composite structures that are in a fluid state in which the components of the wavefunction can be identified with the stream function and the velocity potential of a potential flow formulated in the theory of classical fluids. We also show that Dirac quantum particles can manifest as standing waves which are the result of the superposition of two fluid flows moving in opposite directions. However, for a steady motion a Dirac quantum particle does not exhibit a wave motion even though it has the potential to establish a wave within its physical structure, therefore, without an external disturbance a Dirac quantum particle may be considered as a classical particle defined in classical physics. And furthermore, from the fact that there are two identical fluid flows in opposite directions within their physical structures, the fluid state model of Dirac quantum particles can be used to explain why fermions are spin-half particles.

A state space solution for the bending problem of thick laminated piezoelectric open cylindrical shells

Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.

Exact bound state solutions of the Klein-Gordon particle in Hulthn potential

In this paper, the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly. The corresponding bound state solutions are expressed in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints.

A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).

All Meromorphic Solutions of Some Algebraic Differential Equations

In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.

On the Non-Trivial Zeros of Dirichlet Functions

The purpose of this research is to extend to the functions obtained by meromorphic continuation of general Dirichlet series some properties of the functions in the Selberg class, which are all generated by ordinary Dirichlet series. We wanted to put to work the powerful tool of the geometry of conformal mappings of these functions, which we built in previous research, in order to study the location of their non-trivial zeros. A new approach of the concept of multiplier in Riemann type of functional equation was necessary and we have shown that with this approach the non-trivial zeros of the Dirichlet function satisfying a Reimann type of functional equation are either on the critical line, or they are two by two symmetric with respect to the critical line. The Euler product general Dirichlet series are defined, a wide class of such series is presented, and finally by using geometric and analytic arguments it is proved that for Euler product functions the symmetric zeros with respect to the critical line must coincide.

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of PercusYevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.

Coherent States and Uncertainty Product of the Harmonic Oscillator with Position-Dependent Mass

In this work, we applied the invariant method to calculate the coherent state of the harmonic oscillator with position-dependent mass, which in modern physics has great application. We also obtain the calculation of Heisenberg’s uncertainty principle, and we will show that it is verified.

Simplified Criterion of Steady-State Stability of Electric Power Systems

In the paper the simplified criterion of a steady-state stability of electric power systems (EPS) is justified on the basis of Lyapunov functions in a quadratic form ensuring necessary and sufficient conditions of its performance. Upon that, the use of the node-voltage equations allows reducing study of a steady-state stability of complex EPS to study of the generator-bus system. The obtained results facilitate studies of a steady-state stability of the complex systems and have practical importance.