The solution of the cosmological constant problem from the inhomogeneous equation of state — a hint from modified gravity?

The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown that, in a proper parameter regime, the expansion of the universe with a large absolute value of the cosmological constant may asymptotically tend to de Sitter space corresponding to a small effective positive cosmological constant. It is argued that such a behavior can be regarded as a solution of the cosmological constant problem in this model. The mechanism behind the relaxation of the cosmological constant is discussed. A connection with modified gravity theories is discussed and an example of a possible realization of the cosmological constant relaxation in f(R) modified gravity is described.     

Nonlocal symmetry and exact solutions of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation

In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the(2+1)-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion(CRE) solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions.     

Differential-geometric structures associated with the Lagrangian and a nonvariational interpretation of the Euler equations and Nöther’s theorem

Differential-geometry structures associated with Lagrangians are studied. A relative invariant E embraced by an extension of fundamental object is constructed (in the paper, E is referred to as the Euler relative invariant) such that the equation E = 0 is an invariant representation of the Euler equation for the variational functional. For this reason, a nonvariational interpretation of the Euler equations becomes possible, because the Euler equations need not be connected with the variational problem, and one can regard the equations from the very beginning as an equation arising when equating the Euler relative invariant to zero. Local diffeomorphisms between two structures associated with Lagrangians are also discussed. The theorem concerning conditions under which the vanishing condition for the Euler relative invariant of one of these structures leads to vanishing of the Euler invariant relative of the other structure can be treated as a nonvariational interpretation of Nöther’s theorem.     

Tautomerization and solvent effects on the absorption and emission properties of the Schiff base N,N′-bis(salicylidene)-p-phenylenediamine – A TDDFT study

Time-dependent density functional theory combined with a polarized continuum model has been applied to study solvent effects on the geometrical and energetic properties, as well as the absorption and emission properties, of three tautomeric forms of N,N′-bis(salicylidene)-p-phenylenediamine (BSP). The calculated properties are in agreement with the available experimental data. It was observed that the solvent environment does not affect the vertical excitation energies significantly, whereas tautomerization strongly affects both the absorption and emission spectra of BSP.     

Observation of B(s)(0) → D(s)(*)+ D(s)(*)- using e+ e- collisions and a determination of the B(s)-B(s) width difference ΔΓ(s)

We have made the first observation of B(s)(0)→D(s)(*)+ D(s)(*)- decays using 23.6 fb(-1) of data recorded by the Belle experiment running on the Υ(5S) resonance. The branching fractions are measured to be B(B(s)(0)→D(s)+ D(s)-)=(1.03(-0.32-0.25)(+0.39+0.26))%, B(B(s)(0)→D(s)(*±) D(s)(?))=(2.75(-0.71)(+0.83)±0.69)%, and B(B(s)(0)→D(s)*+ D(s)*-)=(3.08(-1.04-0.86)(+1.22+0.85))%; the sum is B[B(s)(0)→D(s)(*)+ D(s)(*)-]=(6.85(-1.30-1.80)(+1.53+1.79))%. Assuming B(s)(0)→D(s)(*)+ D(s)(*)- saturates decays to CP-even final states, the branching fraction determines the ratio ΔΓ(s)/cosφ, where ΔΓ(s) is the difference in widths between the two B(s)-B(s) mass eigenstates, and φ is a CP-violating weak phase. Taking CP violation to be negligibly small, we obtain ΔΓ(s)/Γ(s)=0.147(-0.030)(+0.036)(stat)(-0.041)(+0.042)(syst), where Γ(s) is the mean decay width.     

Optical solitons and periodic solutions of the (2 + 1)-dimensional nonlinear Schrödinger's equation

In this Letter, we consider the $(2+1)$-dimensional nonlinear Schrödinger's equation. With the aid of the Jacobian elliptic equation, we derive the exact bright soliton, dark soliton, singular soliton and periodic solutions of this equation expressed in terms of trigonometric functions, hyperbolic functions and Jacobian elliptic functions, respectively. Finally, for certain parametric values, we plot three dimensional graphics of modulus, real and imaginary parts of some solutions, which can help one better understand their dynamical behavior via their graphics analysis.     

Exact self-similar wave solutions for the generalized (3 + 1)-dimensional cubic–quintic nonlinear Schröinger equation with distributed coefficients

In this paper, a similarity transformation is presented to reduce the generalized (3 + 1)-dimensional cubic–quintic nonlinear Schrödinger equation with distributed coefficients to the related constant-coefficients one. Then a number of spatiotemporal self-similar wave solutions are constructed. Under the specific choice of the dispersion, cubic and quintic nonlinearities, phase modulation and the gain/loss, we investigate the dynamical behaviors of those spatiotemporal self-similar waves in an inhomogeneous optical fiber media.     

Studies on the growth and characterization of tris (glycine) calcium(ΙΙ) dichloride—a nonlinear optical crystal

A systematic characterization of a novel nonlinear optical material tris (glycine) calcium(ΙΙ) dichloride (TGCC) is performed. The solubility and metastable zone width of TGCC were studied. TGCC single crystal of dimensions 34×23×5 mm³ was grown by the slow evaporation technique. Single crystal X-ray diffraction studies reveal that the crystal belongs to orthorhombic system. Energy dispersive X-ray analysis confirms the presence of elements in the crystal. Structural perfection of the as-grown single crystal was studied through multicrystal X-ray diffraction analysis. The thermal characteristics of TGCC were analyzed by thermogravimetric and differential thermal analysis and differential scanning calorimetry. The transmittance of TGCC crystal has been used to calculate the optical band gap of the crystal. Chemical etching studies of TGCC crystal was carried out. The dielectric and mechanical behavior of the crystals were analyzed. The second harmonic conversion property of TGCC was identified by the Kurtz and Perry powder technique and was observed to be higher than that of KDP.     

Interplay of the doped Ge atoms and the N vacancies with the negative thermal expansion of M3(Cu1−x Ge x )N1−y

The giant negative thermal expansion (NTE) found in the anti-perovskite manganese nitride could be controlled by the content of the doped Ge and the vacancies of N. In this paper, the origin of such a tunable thermal expansion behavior is systematically studied. Our calculations indicate that the doped Ge atoms enhance the NTE property of the compound, and the existing N vacancies have a weak influence on the NTE property. Furthermore, the change of the exchange parameters between Mn ions with the content of the doped Ge as well as with the N vacancies in the compound is revealed, from which the relative stabilities of different magnetic phases in the concerned compounds can be explained.     

New method of determining the young’s Modulus of (Ga,Mn)As nanowhiskers with a scanning electron microscope

Arrays of (Ga,Mn)As nanowhiskers have been grown by molecular-beam epitaxy. The scanning electron microscopy study of the surface morphology of the samples has revealed the appearance of mechanical vibrations of individual nanowhiskers. To describe the vibrations, a model has been developed for the determination of the Young’s modulus of (Ga,Mn)As nanowhiskers.     

Structure and Magnetic Properties of (Ni1 – xZnx)Fe2O4 Ceramics with a Spatial Change in the Composition

Physics of the Solid State - Samples of homogeneous (x = 0, 0.1, and 0.2) and multilayer ceramics based on solid solutions of nickel–zinc ferrites (Ni1 – xZnx)Fe2O4...     

Preliminary results of the cross-section measurement of e<Superscript>+</Superscript>e<Superscript>−</Superscript> → φ(1020)η process with the CMD-3 detector at VEPP-2000 collider

We report preliminary results on the cross section of the process e⁺e^? → φ(1020)η measured at 30 center-of-mass energy points in the range from 1.59 up to 2.0 GeV. Data analysis is based on the integrated luminosity of 22 pb^?1 collected with the CMD-3 detector in 2011–2012. The obtained cross section agrees with the BaBar measurement and has better statistical accuracy.     

Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state <Emphasis Type="Italic">p</Emphasis> = <Emphasis Type="Italic">w</Emphasis><Emphasis Type="Italic">ρ</Emphasis>

We systematically study the evolution of the Friedmann–Robertson–Walker (FRW) universe coupled with a cosmological constant Λ and a perfect fluid that has the equation of state p = w ρ, where p and ρ denote, respectively, the pressure and energy density of the fluid, and w is an arbitrary real constant. Depending on the specific values of w, Λ, and the curvature k of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the existence of big bang, big crunch, and big rip singularities. In some cases, errors in classification and interpretation appearing in standard textbooks have been corrected.     

Parton structure of the Pomeron in hard single-Pomeron exchange process with μ<Superscript>+</Superscript>μ<Superscript>−</Superscript> pair production on the CMS (LHC)

Process of the μ⁺μ⁻ pair production in hard single-Pomeron exchange is studied on the CMS (LHC) at the energy range $ \sqrt s $ \sqrt s = 7 and 14 TeV. Using H1(DESY) data for quark/antiquark parton distributions in the single-Pomeron, calculations were performed to predict the quark/antiquark component of the parton distribution. The estimations show that the quark/antiquark contribution does not exceed ∼5%. Using CMSSW package the events of the process were reconstructed. The method for estimation of the valent quark/antiquark contribution in the parton structure of the single-Pomeron is developed. This method could be used at the experimental data performance obtained on the CMS detector.     

Remote substituent effects on homolytic Fe?C bond energies of p‐G‐C6H4CH2Fe(CO)2(η5‐C5H5) and p‐G‐C6H4(H)(CN)CFe(CO)2(η5‐C5H5) studied by Hartree–Fock and density functional theory methods

In general, both stoichiometric and catalytic reactions of organometallic complexes involve breaking and forming metal–ligand bonds. Therefore, an evaluation of the thermodynamics of such reactions requires the knowledge of metal–ligand bond energies (BDEs). The homolytic Fe? C bond dissociation energies [i.e., ΔH_homo(Fe? C)s] of 12 para‐substituted benzyldicarbonyl(η⁵‐cyclopentadienyl)iron, p‐G‐C₆H₄CH₂Fp [1,G = NO₂, CN, COMe, CO₂Me, CF₃, Br, Cl, F, H, Me, MeO, NMe₂; Fp = (η⁵‐C₅H₅)(CO)₂Fe] and 12 para‐substituted α‐cyanobenzyldicarbonyl (η⁵‐cyclopentadienyl)iron, p‐G‐PANFp [2,PAN = C₆H₄CH(CN)] were studied using Hartree–Fock (HF) and density functional theory (DFT) methods with large basis sets. The results show that BP86 and TPSSTPSS can provide the best price/performance ratio and more accurate predictions in the study of ΔH_homo(Fe? C)s. The B3LYP method satisfactorily predicts the α and remote substituent effects on ΔH_homo(Fe? C)s [ΔΔH_homo(Fe? C)s]. The fair correlations [r = 0.97 (g, 1), 0.99(g, 2)] of ΔΔH_homo(Fe? C)s of series 1 and 2 with the substituent σ constants imply that the para substituent effects on ΔH_homo(Fe? C)s originate mainly from polar effects, but those on radical stability originate from both spin delocalization and polar effects. The molecule stabilization effects (MEs) causes that not only the magnitude of ΔΔH_homo(Fe? C)s(1) varies significantly but also the direction changes from S‐pattern to O‐pattern. ΔΔH_homo(Fe? C)s(2) were found to conform to the Capto‐dative Principle. The detailed knowledge of the factors that determine the Fp? C bond strengths would greatly aid in understanding reactivity patterns in many processes. Copyright © 2010 John Wiley & Sons, Ltd.     

N-Chlorosuccinimide (NCS)–N,N-dimethylformamide (DMF), a reagent for the oxidation of benzylic alcohols to aldehydes and ketones

Molecular Diversity - The oxidation of benzylic alcohol to corresponding aldehyde and ketone using N-chlorosuccinimide (NCS)–N,N-dimethylformamide (DMF) has been described. This method gives...