Singularities and Entropy in Bulk Viscosity Dark Energy Model

In this paper bulk viscosity is introduced to describe the effects of cosmic non-perfect fluid on the cosmos evolution and to build the unified dark energy (DE) with (dark) matter models. Also we derive a general relation between the bulk viscosity form and Hubble parameter that can provide a procedure for the viscosity DE model building. Especially, a redshift dependent viscosity parameterζ∝λ₀ +λ₁(1+z)ⁿ proposed in the previous work [X.H. Meng and X. Dou, Commun. Theor. Phys. 52 (2009) 377] is investigated extensively in this present work. Further more we use the recently released supernova dataset
(the Constitution dataset) to constrain the model parameters. In order to differentiate the proposed concrete dark energy models from the well known $\Lambda$CDM model, statefinder diagnostic method is applied to this bulk viscosity model, as a complementary to the Om parameter diagnostic and the deceleration parameter analysis performed by us before. The DE model evolution behavior and tendency are shown in the plane of the statefinder diagnostic parameter pair {r,s} as axes where the fixed point represents theΛCDM model. The possible singularity property in this bulk viscosity
cosmology is also discussed to which we can conclude that in the different parameter regions chosen properly, this concrete viscosity DE model can have various late evolution behaviors and the late time singularity could be avoided. We also calculate the cosmic entropy in the bulk viscosity dark energy frame, and find that the total entropy in the viscosity DE model increases monotonously with respect to the scale factor evolution, thus this monotonous
increasing property can indicate an arrow of time in the universe evolution, though the quantum version of the arrow of time is still very puzzling.     

AN INFLATIONARY MODEL OF KALUZA-KLEIN TYPE

Assuming an equation of state as p₁=ρ/3 and p₂=ρ/D, an inflationary model of Kaluza-Klein type is studied. By solving the horizon and entropy problems, it is found that the dimension of the extra subspace should be as large as 35 to 70, if the ratio of R₂(max) to Planck length is taken as 10² to 10⁴. However, the substantial period of the inflation happens at time much larger than the Planck time if we take the ratio as 10³ or even a larger number.     

Using Energy Conditions to Distinguish Brane Models and Study Brane Matter

Current universe (assumed here to be normal matter on the brane) is pressureless from observations. In this case the energy condition is ρ₀≥0 and p₀=0. By using this condition, brane models can be distinguished. Then, assuming arbitrary component of matter in DGP model, we use four known energy conditions to study the matter on the brane. If there is nonnormal matter or energy (for example dark energy with w<-1/3) on the brane, the universe is accelerated.     

Friedmann Cosmology with Bulk Viscosity: A Concrete Model for Dark Energy

The universe content is considered as a non-perfect fluid with bulk viscosity and can be described by a general equation of state (endowed some deviation from the conventionally assumed cosmic perfect fluid model). An explicitly bulk viscosity dark energy model is proposed to confront consistently with the current observationaldata sets by statistical analysis and is shown consistent with (not deviated away much from) the concordant Λ Cold Dark Matter (CDM) model by comparing the decelerating parameter. Also we compare our relatively simple viscosity dark energy model with a more complicated one by contrast with the concordant ΛCDM modeland find our model improves for the viscosity dark energy model building. Finally we discuss the perspectives of dark energy probes for the coming years with observations.     

Viscous Cosmological Model with Variable Gravitational and Cosmological Constants

We have considered some cosmological solutions with variable gravitational and cosmological constants with bulk viscosity. It is found that the solutions are singularity free and the deceleration parameter is in general not a constant unless we assume perfect fluid with equation of state in the standard cosmologies. Moreover, the deceleration parameter is a function of the scale factor and changes sign with evolution, so our solution is a generalization of those obtained by Arbab I. Arbab. The introduction of viscosity not only free from singularity but also give the deceleration parameter a freedom to vary with scale factor. Thus, a viscous cosmological fluid gives a more general situation in the early universe.     

A Modified Approach for Calculating Dressed Quark Propagator at Finite Chemical Potential

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the full inverse quark propagator at finite chemical potential is analytic in the neighborhood of μ = 1, it is proved that the dressed quark propagator at finite chemical potential μ can be written as G0^-1 [μ] =iγ·p↑-A（p↑-^2） ＋B（p↑-^2） with p↑-μ= （p↑-p4 ＋iμ）. From the dressed quark propagator at finite chemical potential in Munczek model the bag constant of a baryon and the scalar quark condensate are evaluated. A comparison with previous results is given.     

Bulk viscous L.R.S. Bianchi type V tilted stiff fluid cosmological model in general relativity

Locally rotationally symmetric (L.R.S.) Bianchi type V bulk viscous tilted stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have also assumed a condition A=Bⁿ between metric potentials A, B where n is the constant. The behaviour of the model in presence and absence of bulk viscosity and singularities in the model are also discussed. In general, the models represent accelerating, shearing, tilted and non-rotating universe. The models have point type singularity in presence and absence of bulk viscosity both.     

The Hubble parameter in the early universe with viscous QCD matter and finite cosmological constant

The evolution of a flat, isotropic and homogeneous universe is studied. The background geometry in the early phases of the universe is conjectured to be filled with causal bulk viscous fluid and dark energy. The energy density relations obtained from the assumption of covariant conservation of energy‐momentum tensor of the background matter in the early universe are used to derive the basic equation for the Hubble parameter H. The viscous properties described by ultra‐relativistic equations of state and bulk viscosity taken from recent heavy‐ion collisions and lattice QCD calculations have been utilized to give an approximate solution of the field equations. The cosmological constant is conjectured to be related to the energy density of the vacuum. In this treatment, there is a clear evidence for singularity at vanishing cosmic time t indicating the dominant contribution from the dark energy. The time evolution of H seems to last for much longer time than the ideal case, where both cosmological constant and viscosity coefficient are entirely vanishing.     

Line shape and lifetime in argon 2p electron spectroscopy

The argon 2p photoelectron spectrum and the argon L₃M₂₃M₂₃ ¹S₀ Auger spectrum have been measured at several photon energies between 6 and 80 eV above the 2p_3/2 threshold with an instrumental line width significantly smaller then the natural line width. The spectra are described well by the theory of van der Straten et al. [Z. Phys. D 8 (1988) 35] provided that allowance is made for the instrumental resolution and measurements are made at a sufficiently low pressure. The lifetime (Lorentzian) line width determined from these measurements for the core-ionized atom is 112±3 meV, in good agreement with the line width for the 2p_3/2→4s core-excited state, 114±2 meV, indicating that the 4s electron has little influence on the Auger decay rate. Remeasurement of the line width for the carbon 1s hole in carbon dioxide gives values in good agreement with the previous measurement of 99 meV.     

Cosmological model with viscosity media (dark fluid) described by an effective equation of state

A generally parameterized equation of state (EOS) is investigated in the cosmological evolution with bulk viscosity media modelled as dark fluid, which can be regarded as a unification of dark energy and dark matter. Compared with the case of the perfect fluid, this EOS has possessed four additional parameters, which can be interpreted as the case of the non-perfect fluid with time-dependent viscosity or the model with variable cosmological constant. From this general EOS, a completely integrable dynamical equation to the scale factor is obtained with its solution explicitly given out. (i) In this parameterized model of cosmology, for a special choice of the parameters we can explain the late-time accelerating expansion universe in a new view. The early inflation, the median (relatively late time) deceleration, and the recently cosmic acceleration may be unified in a single equation. (ii) A generalized relation of the Hubble parameter scaling with the redshift is obtained for some cosmology interests. (iii) By using the SNe Ia data to fit the effective viscosity model we show that the case of matter described by p=0$p=0$ plus with effective viscosity contributions can fit the observational gold data in an acceptable level.     

Quenching of the 2p1/2−2p3/2 proton spin-orbit splitting in the Sr−Zr region

The constancy in excitation energy of the lowest 2⁺ state in the Sr isotopes across sthe N=56 subshell closure is shown to result from a reduction in the 2p_1/2−2p_3/2 proton spin-orbit splitting as the 2d_5/2 neutron orbital is filled     

Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex ⁴=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.     

MBBA和CC混合物的螺距测量及螺距与温度关系经验公式

我们用布喇格散射法测定了混合液晶MBBA:CC=22.7:77.3(重量比)在不同温度下的螺距。从测得的结果,结合文献中对其它材料所测的数据,我们提出一个螺距p随温度T变化的经验公式:p=p₀-b/(T-T₀)对左旋材料螺距p<0,对右旋材料p>0。除接近相变温度或旋向翻转温度附近外,公式不但适用于单体螺旋状液晶也适用于混合液晶。对一些材料,从实验数据中定出了与它们相对应的常数p₀,b和T₀。 关键词：     

XPS investigation of preferential sputtering of S from MoS2 and determination of MoSx stoichiometry from Mo and S peak positions

The preferential sputtering of S from bulk MoS₂ standard samples exposed to 3 keV Ar⁺ ion bombardment has been studied by XPS. The MoS_x stoichiometry decreases from MoS₂ to MoS_1.12 with a concomitant reduction in the Mo 3d_5/2 binding energy from 229.25 to 228.35 eV. The altered layer extends to a depth of 3.8 nm and is proposed to consist of a single amorphous MoS_x phase in which Mo has a varying number of nearest neighbour S atoms. Using peak positions alone it is possible to determine the MoS_x stoichiometry to an accuracy of x±0.1 from a plot of MoS_x stoichiometry against (Mo 3d_5/2–S 2p_3/2) binding energy. The results are of strong current interest for coating analysis applications as MoS₂ is a compound capable of providing low friction properties when incorporated into hard coatings.     

One- and Two-Mode Combination Squeezing Operator for Two Harmonic Oscillators with Coordinate-Momentum Coupling

By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinate- momentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H=p^21/2m1＋m1ω^21x^21/2＋p^222m2＋m2ω^22x^22/2-λx2p1 so its ground state is a one- and two-mode combination squeezed state. Quantum fluctuation in the ground state is calculated.     

Emergent universe in brane world scenario with Schwarzschild–de Sitter bulk

A model of an emergent universe is obtained in brane world. Here the bulk energy is in the form of cosmological constant, while the brane consists of a fluid satisfying an equation of state of the form , which is effectively a radiation equation of state at high energies. It is shown that with the positive bulk cosmological constant, one of our models represents an emergent universe.     

The osgood criterion and finite‐time cosmological singularities

In this paper, we apply Osgood's criterion from the theory of ordinary differential equations to detect finite‐time singularities in a spatially flat FLRW universe in the context of a perfect fluid, a perfect fluid with bulk viscosity, and a Chaplygin and anti‐Chaplygin gas. In particular, we applied Osgood's criterion to demonstrate singularity behaviour for Type 0/big crunch singularities as well as Type II/sudden singularities. We show that in each case the choice of initial conditions is important as a certain number of initial conditions leads to finite‐time, Type 0 singularities, while other precise choices of initial conditions which depend on the cosmological matter parameters and the cosmological constant can avoid such a finite‐time singularity. Osgood's criterion provides a powerful and yet simple way of deducing the existence of these singularities, and also interestingly enough, provides clues of how to eliminate singularities from certain cosmological models.     

Exact solutions in Brans-Dicke theory with bulk viscosity

The effect of bulk viscosity on the evolution of the homogeneous and isotropic cosmological models in the Brans-Dicke theory of gravitation is studied. Solutions are found, with a baratropic equation of state, a time-independent bulk viscosity, the gravitational constant inversely proportional to the age of the universe, and the mass of the universe (in the closed model) proportional to the square of its age; the expansion factor is a linear function of the cosmological time. For flat space, power law expansions are found, among them one that is related to extended inflation.     

利用直接核反应研究轻丰中子核的奇特结构

直接核反应(包括弹性散射、非弹性散射、转移反应等)是研究丰中子核奇特结构的常用实验手段之一。以6,8He、11Li、11,12Be、14,15B、15,16C等N=8附近核的结构研究为例,综述了如何利用这几种反应从实验上研究丰中子核的奇特结构。利用6,8He,11Be等晕核在质子和氘靶上的弹性散射数据,拟合得到了这些反应体系的有效相互作用(光学势)。利用16C在质子和氘靶上的非弹性散射数据,抽取了16C 的形变参数,结果表明16C的形变不可忽略。利用单核子转移反应,定量研究了8He, 11,12Be等丰中子核基态及低占据态中的p-,s-,以及d-波成分的强度。结果表明:8He基态中的4个价中子,除了可以构成正常的 (0p_3/2)4 组态外,还有一定的几率构成($ 0 p_{3/2} $)2(0p_1/2)2组态;12Be的基态以d波闯入为主,而其临近的11Be的基态以s波闯入为主。