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.

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.

Bayesian analysis of nuclear equation of state at high baryon density

Bayesian analysis was employed to constrain the equation of state(EoS)of nuclear matter with a baryon density of up to six times the nuclear saturation density,using data from heavy-ion collisions at beam energies√S_(NN)=2-10GeV.The resulting EoS excellently agrees with that constrained by astrophysical observations.

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.

The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound

In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.

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.

Calculation of Viscosities of Liquid Mixtures Using Eyring's Theory in Combination with Cubic Equations of State

Cubic equations of state (EOS) have been combined with the absolute rate theory of Eyring to calculate viscosities of liquid mixtures. A modified Huron-Vidal gE-mixing rule is employed in the calculation and in comparison with the van Laar and the Redlich-Kister-type mixing rule. The EOS method gives an accurate correlation of liquid viscosities with an overall average deviation less than 1% for 67 binary systems including aqueous solutions. It is also successful in extrapolating viscosity data over a certain temperature range using parameters obtained from the isotherm at a given temperature and in predicting viscosities of ternary solutions from binary parameters for either polar or associated systems.

Astrophysical constraints on a parametric equation of state for neutron-rich nucleonic matter

Extracting the equation of state(EOS) and symmetry energy of dense neutron-rich matter from astrophysical observations is a long-standing goal of nuclear astrophysics. To facilitate the realization of this goal, the feasibility of using an explicitly isospin-dependent parametric EOS for neutron star matter was investigated recently in [1–3]. In this contribution, in addition to outlining the model framework and summarizing the most important findings from [1–3], we report a few new results regarding constraining parameters characterizing the highdensity behavior of nuclear symmetry energy. In particular,the constraints on the pressure of neutron star matter extracted from combining the X-ray observations of the neutron star radius, the minimum–maximum mass M=2:01 M_⊙, and causality condition agree very well with those extracted from analyzing the tidal deformability data by the LIGO ? Virgo Collaborations. The limitations of using the radius and/or tidal deformability of neutron stars to constrain the high-density nuclear symmetry energy are discussed.

Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.

Calculation of Viscosities of Liquid Mixtures Using Eyring’s Theory in Combination with Cubic Equations of State

Cubic equations of state EOS have been combined with the absolute rate theory of Eyring to calculate viscosities of liquid mixtures. A modified Huron-Vidal gE-mixing rule is employed in the calculation and in com- parison with the van Laar and the Redlich-Kister-type mixing rule. The EOS method gives an accurate correlation of liquid viscosities with an overall average deviation less than 1% for 67 binary systems including aqueous solu- tions. It is also successful in extrapolating viscosity data over a certain temperature range using parameters obtained from the isotherm at a given temperature and in predicting viscosities of ternary solutions from binary parameters for either polar or associated systems.

Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.

Bianchi Type-V Cosmological Model with Linear Equation of State in Brans-Dicke Theory of Gravitation

A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field &oslash;and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.

Theoretical Models of Highly Magnetic White Dwarf Stars with Non-Polytropic Equation of State

Super-massive white dwarf (WD) stars in the mass range 2.4 - 2.8 solar masses are believed to be the progenitors of “super-luminous” Type Ia supernovae according to a hypothesis proposed by some researchers. They theorize such a higher mass of the WD due to the presence of a very strong magnetic field inside it. We revisit their first work on magnetic WDs (MWDs) and present our theoretical results that are very different from theirs. The main reason for this difference is in the use of the equation of state (EoS) to make stellar models of MWDs. An electron gas in a magnetic field is Landau quantized and hence, the resulting EoS becomes non-polytropic. By constructing models of MWDs using such an EoS, we highlight that a strong magnetic field inside a WD would make the star super-massive. We have found that our stellar models do indeed fall in the mass range given above. Moreover, we are also able to address an observational finding that the mean mass of MWDs are almost double that of non-magnetic WDs. Magnetic field changes the momentum-space of the electrons which in turn changes their density of states (DOS), and that in turn changes the EoS of matter inside the star. By correlating the magnetic DOS with the non-polytropic EoS, we were also able to find a physical reason behind our theoretical result of super-massive WDs with strong magnetic fields. In order to construct these models, we have considered different equations of state with at most three Landau levels occupied and have plotted our results as mass-radius relations for a particular chosen value of maximum Fermi energy. Our results also show that a multiple Landau-level system of electrons leads to such an EoS that gives multiple branches in the mass-radius relations, and that the super-massive MWDs are obtained when the Landau-level occupancy is limited to just one level. Finally, our theoretical results can be explained solely on the basis of quantum and statistical mechanics that warrant no assumptions regarding stars.

Correlation of the mean activity coefficient of aqueous electrolyte solutions using an equation of state

Accurate calculation of thermodynamic properties of electrolyte solution is essential in the design and optimization of many processes in chemical industries. A new electrolyte equation of state is developed for aqueous electrolyte solutions. The Carnahan-Starling repulsive model and an attractive term based on square-well potential are adopted to represent the short range interaction of ionic and molecular species in the new electrolyte EOS. The long range interaction of ionic species is expressed by a simplified version of Mean Spherical Approximation theory （MSA）. The new equation of state also contains a Born term for charging free energy of ions. Three adjustable parameters of new eEOS per each electrolyte solution are size parameter, square-well potential depth and square-well potential interaction range. The new eEOS is applied for correlation of mean activity coefficient and prediction of osmotic coefficient of various strong aqueous electrolyte solutions at 25℃ and 0.1 MPa. In addition, the extension of the new eEOS for correlation of mean activity coefficient and solution density of a few aqueous electrolytes at temperature range of 0 to 100℃ is carried out.

A NOTE ON THE UNIQUENESSTHEOREM FOR STEADY-STATESEMICONDUCTOR EQUATIONS

In this note we investigate one-dimensional steady-state semicon-ductor devices. We proved the uniqueness of the solution to the unipolar de-vice problem with non-constant mobility.

Extension of LCVM-type mixing rule to three-parameter equations of state for vapor-liquid equilibria of mixtures

In this paper, the LCVM mixing rule is extended to the multi-parameter equations of state by combining infi- nite-pressure and zero-pressure mixing rule models. The new LCVM-type mixing rule, coupled with Patel-Teja equation of state (EOS) is applied for vapor-liquid equilibria of different polar and non-polar systems in which the NRTL activity coefficient model is used to calculate the excess Gibbs free energy. The tested results agree well with existing experimental data within a wide range of temperatures and pressures. In comparison with the Van der Waals mixing rule, the new mixing rule gives much better corre- lations for the vapor-liquid equilibria of non-polar and polar systems.

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.