Experimental study on the size effect on the equation of state of concretes under shock loading

Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.

A-high-order Accuraqcy Implicit Difference Scheme for Solving the Equation of Parabolic Type

In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.

Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Extension of Tao-Mason Equation of State to Heavy n-Alkanes

In our previous paper we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. This is a continuation for evaluating TM EOS in predicting PVT properties of heavy n-alkanes. Liquid density of long-chain n-alkane systems from C 9 to C 20 have been calculated using an analytical equation of state based on the statistical-mechanical perturbation theory. The second virial coefficients of these n-alkanes are scarce and there is no accurate potential energy function for their theoretical calculation. In this work the second virial coefficients are calculated using a corresponding state correlation based on surface tension and liquid density at the freezing point. The deviation of calculated densities of these alkanes is within 0.5% from experimental data. The densities of n-alkanes obtained from the TM EOS are compared with those calculated from Ihm-Song-Mason equation of state and the corresponding-states liquid densities (COSTALD). Our results are in favor of the preference of the TM EOS over other two equations of state.

CALCULATIONS OF THE PHASE EQUILIBRIA AND CRITICAL CURVES WITH THE EQUATION OF STATE FOR BINARY MIXTURES

A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.

The Estimates L_(1)-L_(∞) for the Reduced Radial Equation of Schrodinger

Estimates of the type L1-L∞ for the Schrödinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schrödinger Equation and are the essential elements in the study of the problems of initial values, the asymptotic times for large solutions and Scattering Theory for the Schrödinger equation and non-linear in general;for other equations of Non-linear Evolution. In general, the estimates Lp-Lp' express the dispersive nature of this equation. And its study plays an important role in problems of non-linear initial values;likewise, in the study of problems nonlinear initial values;see [1] [2] [3]. On the other hand, following a series of problems proposed by V. Marchenko [4], that we will name Marchenko’s formulation, and relate it to a generalized version of Theorem 1 given in [1], the main theorem (Theorem 1) of this article provides a transformation operator W?that transforms the Reduced Radial Schrödinger Equation (RRSE) (whose main characteristic is the addition a singular term of quadratic order to a regular potential V(x)) in the Schrödinger Equation on Half-Line (RSEHL) under W. That is to say;W?eliminates the singular term of quadratic order of potential V(x) in the asymptotic development towards zero and adds to the potential V(x) a bounded term and a term exponentially decrease fast enough in the asymptotic development towards infinity, which continues guaranteeing the uniqueness of the potential V(x) in the condition of the infinity boundary. Then the L1-L∞ estimates for the (RRSE) are preserved under the transformation operator , as in the case of (RSEHL) where they were established in [3]. Finally, as an open question, the possibility of extending the L1-L∞ estimates for the case (RSEHL), where added to the potential V(x) an analytical perturbation is mentioned.

Gas seepage equation of deep mined coal seams and its application

In order to obtain a gas seepage law of deep mined coal seams, according to the properties of coalbed methane seepage in in-situ stress and geothermal temperature fields, the gas seepage equation of deep mined coal seams with the Klinkenberg effect was obtained by confirming the coatbed methane permeability in in-situ stress and geothermal temperature fields. Aimed at the condition in which the coal seams have or do not have an outcrop and outlet on the ground, the application of the gas seepage equation of deep mined coal seams in in-situ stress and geothermal temperature fields on the gas pressure calculation of deep mined coal seams was investigated. The comparison between calculated and measured results indicates that the calculation method of gas pressure, based on the gas seepage equation of deep mined coal seams in in-situ stress and geothermal temperature fields can accu- rately be identical with the measured values and theoretically perfect the calculation method of gas pressure of deep mined coal seams.

Modeling and simulation of JWL equation of state for reactive Al/PTFE mixture

An analytical method is presented to fit parameters of Jones-Wilkins-Lee （JWL） equation of state （EOS） for the chemical process of aluminum-polytetrafluoroethylene （ AI/PTFE ） mixture. Subroutine codes for both strength model and EOS were developed in explicit-FE code AUTODYN. Firstly, the shock Hugoniot data of reactive A1/PTFE mixture was analytically derived by implemen- ting this methodology. The JWL EOS was verified to fit shock Hugoniot data of both reacted and un- reacted A1/PTFE mixture, which gives reasonable results. Furthermore, to numerically ascertain the reaction phases of ignition and growth and quasi detonation of A1/PTFE mixture, characterized ex- periment was setup to validate the reaction phases and coefficients of JWL EOS for A1/PTFE mix- ture. From the test, a promising example of reactive mixture A1/PTFE is capable to enhance lethality of weapons, the status computation in clude quasi-detonation pressure and temperature of A1/PTFE mixture in different chemical reaction phases is validated.

Basic quantities of the equation of state in isospin asymmetric nuclear matter

Based on the Hugenholtz-Van Hove theorem six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k),the isospin symmetric and asymmetric parts of the single-nucleon potentials U_(0)(ρ,k)and U_(sym,i)(ρ,k).The six basic quantities include the quadratic symmetry energy E_(sym,2)(ρ),the quartic symmetry energy E_(sym,4)(ρ),their corresponding density slopes L_(2)(ρ)and L_(4)(ρ),and the incompressibility coefficients K_(2)(ρ)and K_(4)(ρ).By using four types of well-known effective nucleon-nucleon interaction models,namely the BGBD,MDI,Skyrme,and Gogny forces,the density-and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density q_(0)are explicitly given.The contributions to these quantities from t(k)U_(0)(ρ,k),and U_(sym,i)(ρ,k)are also analyzed at the norma nuclear density q_(0).It is clearly shown that the first-order asymmetric term U_(sym,1)(ρ,k)(also known as the symmetry potential in the Lane potential)plays a vital role in determining the density dependence of the quadratic symmetry energy E_(sym,2)(ρ).It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials(U_(sym,i)(ρ,k)with i>1)cannot be neglected in the calculations of the other five basic quantities Moreover,by analyzing the properties of asymmetric nuclear matter at the exact saturation densityρ_(sat)(δ),the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation K_(sat,2)=K_(2)(ρ_(0))-4.14L_(2)(ρ_(0))

Representation of Phase Behavior of Ionic Liquids Using the Equation of State for Square-well Chain Fluids with Variable Range

An equation of state （EOS） for square-well chain fluids with variable range （SWCF-VR） developed based on statistical mechanics for chemical association was employed for the calculations of pressure-volume-temperature （pVT） and phase equilibrium of pure ionic liquids （ILs） and their mixtures. The new molecular parameters for 23 ILs were obtained by fitting their experimental density data over a wide temperature and pressure ranges. The mo- lecular parameters of ILs composed of homologous organic cation and an identical anion such as [Cxmim][NTf2] are good linear with respect to their molecular weight, indicating that the molecular parameters of homologous substances, subsequently p VT and vapor-liquid equilibria vapor-liquid equilibria （VLE） can be predicted using the generalized parameter when no experimental data were available. The new set of parameters were satisfactorily used for calculations of the property of solvent and ILs mixture and the solubility of gas in various ILs at low pressure only using one temperature-independent binary interaction parameter.

Validation for equation of state in wide regime:Copper as prototype

In this paper we introduce the wide regime equation of state(WEOS)developed in Institute of Applied Physics and Computational Mathematics(IAPCM).A semi-empirical model of the WEOS is given by a thermodynamically complete potential of the Helmholtz free energy which combines several theoretical models and has some adjustable parameters calibrated via some experimental and theoretical data.The validation methods of the equation of state in wide regime are presented using copper as a prototype.The results of the WEOS are well consistent with the available theoretical and experimental data,including ab initio cold curve under compression,isotherm,Hugoniot,off-Hugoniot and sound velocity data.It enhances our confidence in the accuracy of the WEOS,which is very important for the validation and verification of equation of state in high temperature and pressure technology.

A Modification of α in SRK Equation of State and Vapor-Liquid Equilibria Prediction

Based on results of saturated vapor pressures of pure substances calculated by SRK equation of state, the factor a in attractive pressure term was modified. Vapor-liquid equilibria of mixtures were calculated by original and modified SRK equation of state combined with MHV1 mixing rule and UNIFAC model, respectively. For 1447 saturated pressure points of 37 substance including alkanes; organics containing chlorine, fluorine, and oxygen; inorganic gases and water, the original SRK equation of state predicted pressure with an average deviation of 2.521% and modified one 1.673%. Binary vapor-liquid equilibria of alcohols containing mixtures and water containing mixtures also indicated that the SRK equation of state with the modified a had a better precision than that with the original one.

Friedmann Cosmology with a Generalized Equation of State and Bulk Viscosity

The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state （endowed some deviation from the conventionally assumed cosmic perfect fluid model）. We assume the bulk viscosityis a linear combination of two terms： one is constant, and the other is proportional to the scalar expansion 0 = 3a/a. The equation of state is described as p = （γ - 1）p ＋ po, where po is a parameter. In this framework we demonstrate that this model can be used to explain the dark energy dominated universe, and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolution： no future singularity, big rip, or Type-Ⅲ singularity as presented in IS. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71 （2005） 063004].

A compositional model for CO_(2) ooding including CO_(2) equilibria between water and oil using the Peng–Robinson equation of state with the Wong–Sandler mixing rule

This paper presents a three-dimensional, three-phase compositional model considering CO2 phase equilibrium between water and oil. In this model, CO2 is mutually soluble in aqueous and hydrocarbon phases, while other components, except water,exist in hydrocarbon phase. The Peng–Robinson(PR) equation of state and the Wong–Sandler mixing rule with non-random two-liquid parameters are used to calculate CO2 fugacity in the aqueous phase. One-dimensional and three-dimensional CO2 flooding examples show that a significant amount of injected CO2 is dissolved in water. Our simulation shows 7% of injected CO2 can be dissolved in the aqueous phase, which delays oil recovery by 4%. The gas rate predicted by the model is smaller than the conventional model as long as water is undersaturated by CO2, which can be considered as 'lost' in the aqueous phase. The model also predicts that the delayed oil can be recovered after the gas breakthrough, indicating that delayed oil is hard to recover in field applications. A three-dimensional example reveals that a highly stratified reservoir causes uneven displacement and serious CO2 breakthrough. If mobility control measures like water alternating gas are undertaken, the solubility e ects will be more pronounced than this example.

Improvement on the Carnahan-Starling Equation of State for Hard-sphere Fluids

Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.

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.

Synchronization of networked multibody systems using fundamental equation of mechanics

From the analytical dynamics point of view, this paper develops an optimal control framework to synchronize networked multibody systems using the fundamental equation of mechanics. A novel robust control law derived from the framework is then used to achieve complete synchronization of networked identical or non-identical multibody systems formulated with Lagrangian dynamics. A distinctive feature of the developed control strategy is the introduction of network structures into the control requirement. The control law consists of two components, the first describing the architecture of the network and the second denoting an active feedback control strategy. A corresponding stability analysis is performed by the algebraic graph theory. A representative network composed of ten identical or non-identical gyroscopes is used as an illustrative example. Numerical simulation of the systems with three kinds of network structures, including global coupling, nearest-neighbour, and small-world networks, is given to demonstrate effectiveness of the proposed control methodology.

Derivation of Martin-Hou Equation of State from Hard-particle Perturbation Theory

In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderson hard-particle perturbation theory including high-order terms. In the derivation, a theoretical form of Martin-Hou equation was obtained. It had a similar form and the same capability to predict P-V-T properties as the Martin-Hou equation and no additional data were required for evaluating the constants. The characteristic constants of the theoretical expression have certain relationships with the molecular parameters.

Thermal equation of state for lattice Boltzmann gases

The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar-Gross-Krook equation （LBGKE） induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.

A New General Equation of State

A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous general equations is that it is in simple form, and is easy to manipulate mathematically.