Energy conditions in f(R,G) gravity

Modified gravity is one of the most favorable candidates for explaining the current accelerating expansion of the Universe. In this regard, we study the viability of an alternative gravitational theory, namely $f(R,G)$ , by imposing energy conditions. We consider two forms of $f(R,G)$ , commonly discussed in the literature, which account for the stability of cosmological solutions. We construct the inequalities obtained by energy conditions and specifically apply the weak energy condition using the recent estimated values of the Hubble, deceleration, jerk and snap parameters to probe the viability of the above-mentioned forms of $f(R, G)$ .     

Renormalization aspects of \mathcal {N}=1 Super Yang–Mills theory in the Wess–Zumino gauge

The generalized $f(R)$ gravity with curvature–matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal space-like Killing vector field of 5D spacetime, and it can be reduced to the 4D formalism of FRW universe. This theory is quite general and can give the corresponding results for Einstein gravity, and $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give some new results besides previous ones given by Huang et al. in Phys Rev D 81:064003, 2010. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho $ , we not only discuss the constraints on the model parameters $m,n$ , but also illustrate the evolutionary trajectories of the scale factor $a(t)$ , the deceleration parameter $q(t)$ , and the scalar field $\epsilon (t),\phi (t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.     

The coincidence problem in f(R) gravity models

To explore possibilities of avoiding coincidence problem in $f(R)$ gravity we consider models in Einstein conformal frame which are equivalent to Einstein gravity with a minimally coupled scalar field. As the conformal factor determines the coupling term and hence the interaction between matter and dark energy, the function $f(R)$ can in principle be determined by choosing an appropriate function for the deceleration parameter only. Possible behavior of $f(R)$ to avoid coincidence problem are investigated in two such cases.     

Consequences of f(R) theories of gravity on gravitational leptogenesis

$f(R)$ f ( R ) -theories of gravity are reviewed in the framework of the matter-antimatter asymmetry in the Universe. The asymmetry is generated by the gravitational coupling of heavy (Majorana) neutrinos with the Ricci scalar curvature. In order that the mechanism works, a time varying non-zero Ricci curvature is necessary. The latter is provided by $f(R)$ f ( R ) cosmology, whose Lagrangian density is of the form $\mathcal{L}(R)\sim f(R)$ L ( R ) ～ f ( R ) , with $f(R)\sim R+\alpha R^n$ f ( R ) ～ R + α R n .     

Dark energy, cosmic coincidence and future singularity of the universe

Dark energy model with the equation of state $p_{DE} =-\rho _{DE} -A\rho _{DE}^\alpha $ , is characterised by four finite life time future singularity of the universe for different values of the parameter $A$ and $\alpha $ [Nojiri et al. in Phys Rev D 71:063004, 2005]. Since from the matter dominated era to the dark energy dominated era the ratio of the dark energy density to the matter energy density increases as the universe expand for these future singularities, the universe passes through a significant time when the dark energy density and the matter energy density are nearly comparable. Considering $\frac{1}{r_0 }<r=\frac{\rho _{DE} }{\rho _M }<r_0 $ , where $r_0$ is any fixed ratio, we calculate the fraction of total life time of the universe when the universe passes through the coincidental stage for these singularities. It has been found that the fractional time varies as $\alpha $ varies within the range for which these finite life time future singularities occur and the fraction is smaller for smaller values of $r_0 $ . Importance of the fractional time and observational limits onto the values of the parameter $A$ and $\alpha $ has also been discussed.     

Influence of temperature on the electric,dielectric and AC conductivity properties of nano-crystalline zinc substituted cobalt ferrite synthesized by solution combustion technique

Cobalt–zinc nanoferrites with formulae Co $_{1-x}$ Zn $_{x}$ Fe $_{2}$ O $_{4}$ , where x = 0.0, 0.1, 0.2 and 0.3, have been synthesized by solution combustion technique. The variation of DC resistivity with temperature shows the semiconducting behavior of all nanoferrites. The dielectric properties such as dielectric constant ( $\varepsilon $ ’) and dielectric loss tangent (tan $\delta )$ are investigated as a function of temperature and frequency. Dielectric constant and loss tangent are found to be increasing with an increase in temperature while with an increase in frequency both, $\varepsilon $ ’ and tan $\delta $ , are found to be decreasing. The dielectric properties have been explained on the basis of space charge polarization according to Maxwell–Wagner’s two-layer model and the hopping of charge between Fe $^{2+}$ and Fe $^{3+}$ . Further, a very high value of dielectric constant and a low value of tan $\delta $ are the prime achievements of the present work. The AC electrical conductivity ( $\sigma _\mathrm{AC})$ is studied as a function of temperature as well as frequency and $\sigma _\mathrm{AC}$ is observed to be increasing with the increase in temperature and frequency.     

Warm-intermediate inflationary universe model with viscous pressure in high dissipative regime

Warm inflation model with bulk viscous pressure in the context of “intermediate inflation” where the cosmological scale factor expands as $a(t)=a_0\exp (At^f)$ , is studied. The characteristics of this model in slow-roll approximation and in high dissipative regime are presented in two cases: 1—Dissipative parameter $\Gamma $ as a function of scalar field $\phi $ and bulk viscous coefficient $\zeta $ as a function of energy density $\rho $ . 2— $\Gamma $ and $\zeta $ are constant parameters. Scalar, tensor perturbations and spectral indices for this scenario are obtained. The cosmological parameters appearing in the present model are constrained by recent observational data (WMAP7).     

Mössbauer spectroscopy in the investigation of new mineral–related materials

New materials based on the composition of the mineral schafarzikite, FeSb $_{2}\textit {O}_{4}$ , have been synthesised. $^{57}$ Fe- and $^{121}$ Sb- Mössbauer spectroscopy shows that iron is present as Fe $^{2+}$ and that antimony is present as Sb $^{3+}$ . The presence of Pb $^{2+}$ on the antimony sites in materials of composition FeSb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ induces partial oxidation of Fe $^{2+}_{}$ to Fe $^{3+}$ . The quasi-one-dimensional magnetic structure of schafarzikite is retained in FeSb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ and gives rise to weakly coupled non-magnetic Fe $^{2+}$ ions coexisting with Fe $^{3+}$ ions in a magnetically ordered state. A similar model can be applied to account for the spectra recorded from the compound Co $_{0.5}$ Fe $_{0.5}$ Sb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ .     

An Algebraic Construction of Boundary Quantum Field Theory

We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras ${\mathcal A_V}$ on the Minkowski half-plane M ₊ starting with a local conformal net ${\mathcal A}$ of von Neumann algebras on ${\mathbb R}$ and an element V of a unitary semigroup ${\mathcal E(\mathcal A)}$ associated with ${\mathcal A}$ . The case V?=?1 reduces to the net ${\mathcal A_+}$ considered by Rehren and one of the authors; if the vacuum character of ${\mathcal A}$ is summable, ${\mathcal A_V}$ is locally isomorphic to ${\mathcal A_+}$ . We discuss the structure of the semigroup ${\mathcal E(\mathcal A)}$ . By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to ${\mathcal E(\mathcal A^{(0)})}$ with ${\mathcal A^{(0)}}$ the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mack-Todorov extension of ${\mathcal A^{(0)}}$ . A further family of models comes from the Ising model.     

Thermal width of quarkonium from holography

Nuclear effects in deep inelastic scattering at low $x$ are phenomenologically described changing the typical dynamical and/or kinematical scales characterizing the free nucleon case. In a holographic approach, this rescaling is an analytical property of the computed structure function $F_2(x,Q^2)$ . This function is given by the sum of a conformal term and of a contribution due to quark confinement, depending on IR hard-wall parameter $z_0$ and on the mean square distances, related to a parameter $Q^\prime $ , among quarks and gluons in the target. The holographic structure function per nucleon in a nucleus $A$ is evaluated showing that a rescaling of the typical nucleon size, $z_0$ and $Q^\prime $ , due to nuclear binding, can be reabsorbed in a $Q^2$ -rescaling scheme. The difference between neutron and proton structure functions and the effects of the longitudinal structure functions can also be taken into account. The obtained theoretical results favorably compare with the experimental data.     

An Averaging Theorem for FPU in the Thermodynamic Limit

Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\beta ^{-1}$ . Given a fixed $K$ , we construct $K$ packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order $\beta ^{1-a}$ , $a>0$ ) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $\beta $ . The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\rightarrow \infty $ , $\beta >0$ .     

Quantum billiards in multidimensional models with branes

A gravitational $D$ -dimensional model with $l$ scalar fields and several forms is considered. When a cosmological-type diagonal metric is chosen, an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed; the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions asymptotic solutions to WDW equation are found in the limit of the formation of the billiard walls which reduce the problem to the so-called quantum billiard on the $(D+ l -2)$ -dimensional Lobachevsky space. Two examples of quantum billiards are considered. The first one deals with $9$ -dimensional quantum billiard for $D = 11$ model with $330$ four-forms which mimic space-like $M2$ - and $M5$ -branes of $D=11$ supergravity. The second one deals with the $9$ -dimensional quantum billiard for $D =10$ gravitational model with one scalar field, $210$ four-forms and $120$ three-forms which mimic space-like $D2$ -, $D4$ -, $FS1$ - and $NS5$ -branes in $D = 10$ $II A$ supergravity. It is shown that in both examples wave functions vanish in the limit of the formation of the billiard walls (i.e. we get a quantum resolution of the singularity for $11D$ model) but magnetic branes could not be neglected in calculations of quantum asymptotic solutions while they are irrelevant for classical oscillating behavior when all $120$ electric branes are present.     

Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice

We consider a version of directed bond percolation on the triangular lattice such that vertical edges are directed upward with probability $y$ , diagonal edges are directed from lower-left to upper-right or lower-right to upper-left with probability $d$ , and horizontal edges are directed rightward with probabilities $x$ and one in alternate rows. Let $\tau (M,N)$ be the probability that there is at least one connected-directed path of occupied edges from $(0,0)$ to $(M,N)$ . For each $x \in [0,1]$ , $y \in [0,1)$ , $d \in [0,1)$ but $(1-y)(1-d) \ne 1$ and aspect ratio $\alpha =M/N$ fixed for the triangular lattice with diagonal edges from lower-left to upper-right, we show that there is an $\alpha _c = (d-y-dy)/[2(d+y-dy)] + [1-(1-d)^2(1-y)^2x]/[2(d+y-dy)^2]$ such that as $N \rightarrow \infty $ , $\tau (M,N)$ is $1$ , $0$ and $1/2$ for $\alpha > \alpha _c$ , $\alpha < \alpha _c$ and $\alpha =\alpha _c$ , respectively. A corresponding result is obtained for the triangular lattice with diagonal edges from lower-right to upper-left. We also investigate the rate of convergence of $\tau (M,N)$ and the asymptotic behavior of $\tau (M_N^-,N)$ and $\tau (M_N^+ ,N)$ where $M_N^-/N\uparrow \alpha _c$ and $M_N^+/N\downarrow \alpha _c$ as $N\uparrow \infty $ .     

Study of Alpha Decay Chains of Superheavy Nuclei and Magic Number Beyond Z = 82 and N = 126

We study various $\alpha $ -decay chains on the basis of the preformed cluster decay model. Our work targets the superheavy elements, which are expected to show extra stability at shell closure. Our computations identify the following combinations of proton and neutron numbers as the most stable nuclei: $Z=112$ , $N=161, 163$ ; $Z=114$ , $N=171, 178, 179$ ; and $Z=124$ , $N=194$ . We also investigate the alternative of heavy cluster emissions in the decay chain of ³⁰¹120, instead of $\alpha $ decay. Our study of cluster radioactivity shows that the half-life for ¹⁰Be decay in ²⁸⁹114 is larger, indicating enhanced stability at $Z=114$ , $N=175$ . Similar calculations concerning the emission of $\ ^{14}{\rm C}$ and $\ ^{34}{\rm Si}$ from ³⁰¹120 find the more stable combinations $Z=114$ , $N=173$ , and $Z=106$ , $N=161$ , respectively. From the same parent, ³⁰¹120, the emission of a $\ ^{49-51}{\rm Ca}$ cluster yielding a $Z=100$ , $N=152$ daughter is the most probable.     

Galton–Watson Trees with Vanishing Martingale Limit

We show that an infinite Galton–Watson tree, conditioned on its martingale limit being smaller than  $\varepsilon $ , agrees up to generation $K$ with a regular $\mu $ -ary tree, where $\mu $ is the essential minimum of the offspring distribution and the random variable $K$ is strongly concentrated near an explicit deterministic function growing like a multiple of $\log (1/\varepsilon )$ . More precisely, we show that if $\mu \ge 2$ then with high probability, as $\varepsilon \downarrow 0$ , $K$ takes exactly one or two values. This shows in particular that the conditioned trees converge to the regular $\mu $ -ary tree, providing an example of entropic repulsion where the limit has vanishing entropy. Our proofs are based on recent results on the left tail behaviour of the martingale limit obtained by Fleischmann and Wachtel [11].     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Analysis of the {3\over 2}^{+} heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the ${3\over 2}^{+}$ heavy and doubly heavy baryon states $\varXi^{*}_{cc}$ , $\varOmega^{*}_{cc}$ , $\varXi^{*}_{bb}$ , $\varOmega^{*}_{bb}$ , $\varSigma_{c}^{*}$ , $\varXi_{c}^{*}$ , $\varOmega_{c}^{*}$ , $\varSigma_{b}^{*}$ , $\varXi_{b}^{*}$ and $\varOmega_{b}^{*}$ by subtracting the contributions from the corresponding ${3\over 2}^{-}$ heavy and doubly heavy baryon states with the QCD sum rules, and we make reasonable predictions for their masses.     

Particle creation in a f(R) theory with cosmological constraints

The novel idea that spatial expansion of our universe can be regarded as the consequence of the emergence of space was proposed by Padmanabhan. By using of the basic law governing the emergence, which Padmanabhan called holographic equipartition, he also arrives at the Friedmann equation in a flat universe. When generalized to other gravity theories, the holographic equipartition need to be generalized with an expression of $f(\Delta N,N_{sur})$ . In this paper, we give general expressions of $f(\Delta N,N_{sur})$ for generalized holographic equipartition which can be used to derive the Friedmann equations of the Friedmann–Robertson–Walker universe with any spatial curvature in higher ( $\hbox {n}+1$ )-dimensional Einstein gravity, Gauss–Bonnet gravity and more general Lovelock gravity. The results support the viability of the perspective of holographic equipartition.     

Formation and crystallization kinetics of Nd–Fe–B-based bulk amorphous alloy

In order to improve the glass-forming ability (GFA) of Nd–Fe–B ternary alloys to obtain fully amorphous bulk Nd–Fe–B-based alloy, the effects of Mo and Y doping on GFA of the alloys were investigated. It was found that the substitution of Mo for Fe and Y for Nd enhanced the GFA of the Nd–Y–Fe–Mo–B alloys. It was also revealed that the GFA of the samples was optimized by 4 at.% Mo doping and increased with the Y content. The fully amorphous structures were all formed in the Nd $_{6-{x}}$ Y $_{{x}}$ Fe $_{68}$ Mo $_{4}$ B $_{22}$ (x $=$ 1–5) alloy rods with 1.5 mm-diameter. After subsequent crystallization, the devitrified Nd $_{3}$ Y $_{3}$ Fe $_{68}$ Mo $_{4}$ B $_{22}$ alloy rod exhibited a uniform distribution of grains with a coercivity of 364.1 kA/m. The crystallization behavior of Nd $_{3}$ Y $_{3}$ Fe $_{68}$ Mo $_{4}$ B $_{22}$ BMG was investigated in isothermal situation. The Avrami exponent n determined by JAM plot is lower than 2.5, implying that the crystallization is mainly governed by a growth of particles with decreasing nucleation rate.     

Charmonium rescattering effects in \psi(2S) \rightarrow \gamma \eta_{c}^{} decay

Charmonium rescattering effects in the M1 transition of $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ are investigated by modeling a $ \chi_{{cJ}}^{}$ or J/ $ \psi$ rescattering into a $ \eta_{c}^{}$ final state. The absorptive and dispersive part of the transition amplitudes for the rescattering loops of $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) and $ \gamma$ $ \chi$ ( $ \psi$ ) are separately evaluated. The numerical results show that the contribution from the $ \gamma$ $ \chi$ ( $ \psi$ ) rescattering process is negligible. Compared with the virtual D $ \bar{{D}}$ (D ^*) rescattering processes, the $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) process may be regarded as the next-leading order of the hadronic loop mechanism, which only offers the partial decay width of ～ 0.045 keV to the $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ .