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.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

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.

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.

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

EQUATION OF STATE BASED HYDRATE MODEL FOR NATURAL GAS SYSTEMS CONTAINING BRINE AND POLAR INHIBITOR

A new thermodynamic model for gas hydrates was established by combining the modified Patel-Teja equation of state proposed for aqueous electrolyte systems and the simplified Holder -John multi -shell hydrate model. The new hydrate model is capable of predicting the hydrate formation/dissociation conditions of natural gas systems containing pure water/formation water (brine) and polar inhibitor without using activity coefficient model. Extensive test results indicate very encouraging results.

Strangeness to increase the density of finite nuclear systems in constraining the high-density nuclear equation of state

As the high-density nuclear equation of state(EOS) is not very well constrained, we suggest that the structural properties from the finite systems can be used to extract a more accurate constraint. By including the strangeness degrees of freedom, the hyperon or anti-kaon, the finite systems can then have a rather high-density core which is relevant to the nuclear EOS at high densities directly. It is found that the density dependence of the symmetry energy is sensitive to the properties of multi-K hypernuclei, while the high-density EOS of symmetric matter correlates sensitively to the properties of kaonic nuclei.

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.

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.

The pressure compensation technology of deep-sea sampling based on the real gas state equation

Compressed gas is usually used for the pressure compensation of the deep-sea pressure-maintaining sampler.The pressure and volume of the recovered fluid sample are highly related to the precharged gas. To better understand the behavior of the gas under high pressure, we present a new real gas state equation based on the compression factor Z which was derived from experimental data. Then theoretical calculation method of the pressure and volume of the sample was introduced based on this empirical gas state equation. Finally, the proposed calculation method was well verified by the high-pressure vessel experiment of the sampler under 115 MPa.

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.

Ground states for asymptotically periodic quasilinear Schrdinger equations with critical growth

For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.

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.

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 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.

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.

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.