Incompressibility of Nuclear Matter in a Quark-Meson Coupling Model

The quark meson coupling model is used to investigate the correlation between thenuclear incompressibility K and the third order derivitive K′ of the nuclear matter saturationcurve,the temperature and entropy dependence of the nuclear

The New Determination of the Criteria of Compressibility and Incompressibility of Medium

It is shown that the criterion of incompressibility applicable to any medium, contradicts to the real meaning of this term. On the basis of expression of speed of sound in inhomogeneous medium and generalized equation of continuity of mass obtained in papers [1,2] respectively, it is proved that so called internal gravitation waves do not exist in nature. This concept appeared as a result of incorrect interpretation of incompressibility of medium. Correct understanding of criteria of compressibility or incompressibility leads to qualitatively new understanding of homogeneity or heterogeneity of medium, in particular—only strongly inhomogeneous medium can be incompressible while weakly inhomogeneous medium is always compressible. Besides, it is shown that in inhomogeneous media additional terms are added to known hydrodynamic (gas dynamic) correlations applicable to any medium which disappear at transfer to homogeneous model of medium.

Why the Central Monster in M87 Should Be a Massive DEO Rather than a SMBH?

In this paper, we show that massive envelopes made of highly compressed normal matter surrounding dark objects (DEOs) can curve the surrounding spacetime and make the systems observationally indistinguishable from their massive black hole counterparts. DEOs are new astrophysical objects that are made up of entropy-free incompressible supranuclear dense superfluid (SuSu-matter), embedded in flat spacetimes and invisible to outside observers, practically trapped in false vacua. Based on highly accurate numerical modelling of the internal structures of pulsars and massive neutron stars, and in combination with using a large variety of EOSs, we show that the mass range of DEOs is practically unbounded from above: it spans those of massive neutron stars, stellar and even supermassive black holes: thanks to the universal maximum density of normal matter, , beyond which normal matter converts into SuSu-matter. We apply the scenario to the Crab and Vela pulsars, the massive magnetar PSR J0740 6620, the presumably massive NS formed in GW170817, and the SMBHs in Sgr A* and M87*. Our numerical results also reveal that DEO-Envelope systems not only mimic massive BHs nicely but also indicate that massive DEOs can hide vast amounts of matter capable of turning our universe into a SuSu-matter-dominated one, essentially trapped in false vacua.

CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.

The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation

Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.

Why the Energy Density of the Universe Is Lower and Upper-Bounded? Relaxing the Need for the Cosmological Constant

Recently, it was argued that the energy density of the supranuclear dense matter inside the cores of massive neutron stars must have reached the , beyond which supranuclear dense matter becomes incompressible entropy-free gluon-quark superfluid. As this matter is also confined and embedded in flat spacetime, it is Lorentz invariant and could be treated as vacuum. The lower bound of matter in the universe may be derived using the following observational constraints: 1) The average energy density of the observable universe is erg/cc, 2) The observable universe is remarkably flat, and 3) the Hubble constant is a slowly decreasing function of cosmic time. Based thereon, I argue that the energy density in nature should be bounded from below by the average density of our vast and flat parent universe, , which is, in turn, comparable to the vacuum energy density , and amounts to erg/cc. When the total energy density is measured relative to , then both GR and Newtonian field equations may consistently model the gravitational potential of the parent universe without invoking cosmological constants. Relying on the recently proposed unicentric model of the observable universe, UNIMOUN, the big bang must have warped the initially flat spacetime into a curved one, though the expansion of the fireball doomed the excited energy state to diffuse out and return back to the ground energy state that governs the flat spacetime of our vast parent universe.

Foundation of the Unicentric Model of the Observable Universe—UNIMOUN

In view of the growing difficulties of ΛCDM-cosmologies to compete with recent highly accurate cosmological observations, I propose the alternative model: the Unicentric Model of the Observable UNiverse (UNIMOUN). The model relies on employing a new time-dependent -metric for the GR field equations, which enables reversible phase transitions between normal compressible fluids and incompressible quantum superfluids, necessary for studying the cosmic evolution of the observable universe. The main properties of UNIMOUN read: 1) The observable universe was born in a flat spacetime environment, which is a tiny fraction of our infinitely large and flat parent universe, 2) Our big bang (BB) happened to occur in our neighbourhood, thereby endowing the universe the observed homogeneity and isotropy, 3) The energy density in the universe is upper-bounded by the universal critical density , beyond which matter becomes purely incompressible, rendering formation of physical singulareties, and in particular black holes, impossible, 4) Big bangs are neither singular events nor invoked by external forces, but rather, they are common self-sustaining events in our parent universe, 5) The progenitors of BBs are created through the merger of cosmically dead and inactive neutron stars and/or through “supermassive black holes” that are currently observed at the centres of most massive galaxies, 6) The progenitors are made up of purely incompressible entropy-free superconducting gluon- quark superfluids with (SuSu-matter), which endows these giant objects measurable sizes, 7) Spacetimes embedding SuSu-matter are conformally flat. It is shown that UNIMOUN is capable of dealing with or providing answers to several fundamental open questions in astrophysics and cosmology without invoking inflation, dark matter or dark energy.

Hubble Tension versus the Cosmic Evolution of Hubble Parameter in the Unicentric Model of the Observable Universe

Recently, a unicentric model of the observable universe (UNIMOUN) was proposed. Accordingly, big bangs are common events in our infinitely large, flat, homogeneous and isotropic parent universe. Their progenitors are clusters of cosmically dead and massive neutron stars that merged after reaching the ultimate lowest quantum energy state, where the matter is in an incompressible superconducting gluon-quark superfluid state and zero-entropy, hence granting the resulting progenitors measurable sizes and immunity to collapsing into black holes. Our big bang happened to occur in our neighbourhood, thereby enduing the universe, the observed homogeneity and isotropy. As the enclosed mass of the progenitor was finite, the dynamically expanding curved spacetimes embedded the fireball started flattening to finally diffuse into the flat spacetime of the parent universe. By means of general relativistic numerical hydrodynamical calculations, we use the H-metric to follow the time-evolution of the spacetime embedding the progenitor during the hadronization and the immediately following epochs. Based thereon, we find that the kinetic energy of newly created normal matter increases with distance in a self-similar manner, imitating thereby outflows of nearly non-interacting particles. On cosmic time scales, this behaviour yields a Hubble parameter, H(t), which decreases slowly with the distance from the big bang event. Given the sensitivity of the data of the Cosmic Microwave Background (CMB) from Planck to the underlying cosmological model, we conclude that UNIMOUN is a viable alternative to ΛCMD-cosmologies.

The EOSs and the Blatant Discrepancy in Modelling Massive Neutron Stars: Origin and a Possible Solution Method

Exploring the state of ultra-cold supranuclear dense matter that makes up the cores of massive neutron stars is one of the greatest unresolved problems in modern physics. In this letter, we show that when the interiors of pulsars are made of compressible and dissipative normal matter, the commonly used solution procedures combined with the known EOSs yield widely scattered solutions and poorly determined radii. A remarkable agreement emerges, however, if pulsars harbour cores that are made of incompressible entropy-free superfluids (SuSu-matter) embedded in flat spacetimes. Such supranuclear dense matter should condensate to form false vacua as predicated by non-perterbative QCD vacuum. The solutions here are found to be physically consistent and mathematically elegant, irrespective of the object’s mass. Based thereon, we conclude that the true masses of massive NSs may differ significantly from those revealed by direct observation.

Evidence for False Vacuum States inside the Cores of Massive Pulsars and the Ramification on the Measurements of Their True Masses

Based on the theory and observations of glitching pulsars, we show that the ultra-cold supranuclear dense matter inside the cores of massive pulsars should condensate in vacua, as predicated by non-perturbative QCD. The trapped matter here forms false vacuums embedded in flat spacetimes and completely disconnected from the outside world. Although the vacuum expectation value here vanishes, the masses and sizes of these incompressible superfluid cores are set to grow with cosmic times, in accord with the Onsager-Feynman superfluidity analysis. We apply our scenario to several well-studied pulsars, namely the Crab, Vela, PSR J0740+6620 and find that the trapped mass-contents in their cores read {0.15,0.55,0.64}, implying that their true masses are {1.55,2.35,2.72} , respectively. Based thereon, we conclude that: 1) The true masses of massive pulsars and neutron stars are much higher than detected by direct observations and, therefore, are unbounded from above, 2) The remnant of the merger event in GW170817 should be a massive NS harbouring a core with 1.66 .

具有非线性边界条件的不可压MHD-Boussinesq方程组初边值问题的整体适定性

The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD-Boussinesq equation with the given pressure-velocity’s relation boundary condition for the fluid field,one generalized perfectly conducting boundary condition for the magnetic field and one density/temperature-velocity’s relation boundary condition for the density/temapture at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven.

Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows

In this paper, the problem of finding exact solutions to the magnetohydrodynamic(MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation(PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.

TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID

In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.

CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW

In this paper,we justify the convergence from the two-species Vlasov-PoissonBoltzmann(VPB,for short)system to the two-fluid incompressible Navier-Stokes-FourierPoisson(NSFP,for short)system with Ohm’s law in the context of classical solutions.We prove the uniform estimates with respect to the Knudsen numberεfor the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions.Consequently,we prove the convergence to the two-fluid incompressible NSFP asεgoes to 0.

Finite deformation analysis of the rotating cylindrical hollow disk composed of functionally-graded incompressible hyper-elastic material

The deformations and stresses of a rotating cylindrical hollow disk made of incompressible functionally-graded hyper-elastic material are theoretically analyzed based on the finite elasticity theory.The hyper-elastic material is described by a new micro-macro transition model.Specially,the material shear modulus and density are assumed to be a function with a power law form through the radial direction,while the material inhomogeneity is thus reflected on the power index m.The integral forms of the stretches and stress components are obtained.With the obtained complicated integral forms,the composite trapezoidal rule is utilized to derive the analytical solutions,and the explicit solutions for both the stretches and the stress components are numerically obtained.By comparing the results with two classic models,the superiority of the model in our work is demonstrated.Then,the distributions of the stretches and normalized stress components are discussed in detail under the effects of m.The results indicate that the material inhomogeneity and the rotating angular velocity have significant effects on the distributions of the normalized radial and hoop stress components and the stretches.We believe that by appropriately choosing the material inhomogeneity and configuration parameters,the functionally-graded material(FGM)hyper-elastic hollow cylindrical disk can be designed to meet some unique requirements in the application fields,e.g.,soft robotics,medical devices,and conventional aerospace and mechanical industries.

VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN

In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary conditions.It is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth domain.In particular,we establish the uniform estimate of the strong solutions for when the boundary is flat.Furthermore,we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero(i.e.,(ε,χ,γ,κ)→0).

Impact of Artificial Compressibility on the Numerical Solution of Incompressible Nanofluid Flow

The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.

Incompressible Limit of the Oldroyd-B Model with Density-Dependent Viscosity

This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ Rd, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.

ON THE LARGE DEFORMATION RUBBER-LIKE MATERIALS: CONSTITUTIVE LAWS AND FEM

This paper mainly discusses the constitutive Iaws of incompressible rubber-like materialsand the aaaociated finite element analysis method.By a multiplicative decomposition of the deformationgradient into distortional and dilatational parts,the YEOH mode type constitutive laws of rubber-likematerials and their numerical implementation are presented.In order to deal with incompressible prob-lends,a three-field variational principle is developed in which deformation,Jacobian and pressure fieldare treated independently.The connection between the three-field principle and the Hu-Wasizhu gener-alized variational principle is established.It is shown that the approach proposed can be degenerated tothe B-bar method in the linear case.The detailed FE formulation is given in which deformation is ap-proximated by isoparametric conforming element,and Jacobian and pressure by discontinuous approxi-mation.Finally,two numerical examples are presented to show the effectiveness and reliability of themethod proposed.The work in this paper provides a corner stone of FEA of this kind of problem.This paper features the combination of the muhiplicative decomposition,the three-field principleand YEOH model of rubber like materials,especially under Lagrangian description,giving an effec-tive way for solving this kind of problems.The Lagrangian description is compatible with usually geo-metrically nonlinear FEM and the constitutive laws are expressed by the second Kirchhoff stress and theGreen strain.

Why the Spacetime Embedding Incompressible Cores of Pulsars Must Be Conformally Flat?

The multi-messenger observations of the merger event in GW170817 did not rule out the possibility that the remnant might be a dynamically stable neutron star with . Based on this and other recent events, I argue that the universal maximum density hypothesis should be revived. Accordingly, the central densities in the cores of ultra-compact objects must be upper-limited by the critical density number ncr, beyond which supranuclear dense matter becomes purely incompressible. Based on the spacetime-matter coupling in GR, it is shown that the topology of spacetime embedding incompressible quantum fluids with n=ncr must be Minkowski flat, which implies that spacetime at the background of ultra-compact objects should be bimetric.