Nature of the $$\Omega (2012)$$ through its strong decays

We extend our previous analysis on the mass of the recently discovered \(\Omega (2012)\) state by investigation of its strong decays and calculation of its width employing the method of light cone QCD sum rule. Considering two possibilities for the quantum numbers of \(\Omega (2012)\) state, namely 1P orbital excitation with \(J^P=\frac{3}{2}^-\) and 2S radial excitation with \(J^P=\frac{3}{2}^+\), we obtain the strong coupling constants defining the \(\Omega (1P/2S)\rightarrow \Xi K\) decays. The results of the coupling constants are then used to calculate the decay width corresponding to each possibility. Comparison of the obtained results on the total widths in this work with the experimental value and taking into account the results of our previous mass prediction on the \(\Omega (2012)\) state, we conclude that this state is 1P orbital excitation of the ground state \(\Omega \) baryon, whose quantum numbers are \(J^P=\frac{3}{2}^-\).     

Coupled channels dynamics in the generation of the $$\Omega (2012)$$ resonance

We look into the newly observed \(\Omega (2012)\) state from the molecular perspective in which the resonance is generated from the \(\bar{K} \Xi ^*\), \(\eta \Omega \) and \(\bar{K} \Xi \) channels. We find that this picture provides a natural explanation of the properties of the \(\Omega (2012)\) state. We stress that the molecular nature of the resonance is revealed with a large coupling of the \(\Omega (2012)\) to the \(\bar{K} \Xi ^*\) channel, that can be observed in the \(\Omega (2012) \rightarrow \bar{K} \pi \Xi \) decay which is incorporated automatically in our chiral unitary approach via the use of the spectral function of \(\Xi ^*\) in the evaluation of the \(\bar{K} \Xi ^*\) loop function.     

Field theory,curdling, limit cycles,and cellular automata

It is suggested that the process of curdling is an important question for the science of fractals. A field equation which displays nucleation (curdling) of particles out of a pure radiation field is discussed. The particle formation arises naturally from the nonlinear character of the equation rather than from imposed quantization conditions. The relativistically invariant equation is $$div(\rho ^\mu (r,t,\Omega _1 )) = \int {[\rho _\mu (r,t,\Omega ),\rho ^\mu (r,t,\Omega _2 )]d} \Omega _2 $$ where ¦, ¦ denotes commutator.ρ ^μ (r,t,Ω) is both a 4-vector and a 2×2 matrix. It represents substance atr, t traveling with the velocity of light in direction Ω. A unique feature is that the scattering ofρ(Ω ₁) byρ(Ω ₂) as determined by the right-hand side of the above equation results in fields that persist at a given place even thoughρ itself represents substance traveling always at the speed of light. Explicit solutions are given for the case of one dimension. Fields representing particles are obtained and shown to have specially oscillatory structure with incipient fractal character.     

Motions of vortex patches

An evolution equation describing the motion of vortrex patches is established. The existence of steady solutions of this equation is proved. These solutions arem-fold symmetric regions of constant vorticity ω₀ and are uniformly rotating with angular velocity Ω in the range $$\tilde \Omega _{m - 1}< \tilde \Omega \leqslant \tilde \Omega _m (\tilde \Omega = \Omega /\omega _0 ,m \geqslant 2)$$ where \(\tilde \Omega _m = (m - 1)/2m\) . We call this class, ofm-fold symmetric rotating regionsD, the class of them-waves of Kelvin. Any may be regarded as a simply connected region which is a stationary configuration of the Euler equations in two dimensions. If then any magnification, rotation or reflection is also in with the same angular velocity Ω ofD. The angular velocity \(\Omega _m = \tilde \Omega _m \omega _0 \) corresponds only to the circle solution, which is a trivial member of every class ,m?2. The class corresponds to the rotating ellipses of Kirchoff. Other properties of the class are established.     

Convection and cracking stability of spheres in general relativity

In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativistic spheres. We show that a density profile \(\rho (r)\), monotonous, decreasing and concave , i.e. \(\rho ' < 0\) and \(\rho '' < 0\), will be stable against convection, if the radial sound velocity monotonically decreases outward. We also studied the cracking instability scenarios and found that isotropic models can be unstable, when the reaction of the pressure gradient is neglected, i.e. \(\delta \mathcal {R}_p = 0\); but if it is considered, the instabilities may vanish and this result is valid, for both isotropic and anisotropic matter distributions.     

Complex Vector Formalism of Harmonic Oscillator in Geometric Algebra: Particle Mass,Spin and Dynamics in Complex Vector Space

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed.     

Semi-leptonic charm baryon decays in the relativistic spectator quark model

We calculate the exclusive semi-leptonic charm baryon decays of the lowest lying charm baryon states into the ground state strangeness baryons using the covariant spectator quark model approach. We present results on rates,q ²- andE _l -spectra as well as on the angular decay distribution in the cascade decay \(\Omega _c \to \Omega ( \to \Xi \pi ,\Lambda {\rm K})\) .     

Abelian cosmic string in the extended Starobinsky model of gravity

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by \(f(R) = R - 2\Lambda + \eta R^2 + \rho R^m\), with \(m > 2\). As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters \(\eta \) and \(\rho \) increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant.     

Ableitung verallgemeinerter Ginzburg-Landau-Gleichungen für reine Supraleiter aus einem Variationsprinzip

It is shown that generalized Ginzburg-Landau equations follow from the expression

$$\Omega = \user2{Sp}\rho (H + T\ln \rho ) + \frac{1}{{2\mu _0 }}\int {(B - B_a )^2 d^3 r}$$     

An interacting dark energy model in a non-flat universe

In this paper, an interacting dark energy model in a non-flat universe is studied, with taking interaction form $C=\alpha H\rho _{de}$ C = α H ρ d e . And in this study a property for the mysterious dark energy is aforehand assumed, i.e. its equation of state $w_{\Lambda }=-1$ w Λ = - 1 . After several derivations, a power-law form of dark energy density is obtained $\rho _{\Lambda } \propto a^{-\alpha }$ ρ Λ ∝ a - α , here $a$ a is the cosmic scale factor, $\alpha $ α is a constant parameter introducing to describe the interaction strength and the evolution of dark energy. By comparing with the current cosmic observations, the combined constraints on the parameter $\alpha $ α is investigated in a non-flat universe. For the used data they include: the Union2 data of type Ia supernova, the Hubble data at different redshifts including several new published datapoints, the baryon acoustic oscillation data, the cosmic microwave background data, and the observational data from cluster X-ray gas mass fraction. The constraint results on model parameters are $\Omega _{K}=0.0024\,(\pm 0.0053)^{+0.0052+0.0105}_{-0.0052-0.0103}, \alpha =-0.030\,(\pm 0.042)^{+0.041+0.079}_{-0.042-0.085}$ Ω K = 0.0024 ( ± 0.0053 ) - 0.0052 - 0.0103 + 0.0052 + 0.0105 , α = - 0.030 ( ± 0.042 ) - 0.042 - 0.085 + 0.041 + 0.079 and $\Omega _{0m}=0.282\,(\pm 0.011)^{+0.011+0.023}_{-0.011-0.022}$ Ω 0 m = 0.282 ( ± 0.011 ) - 0.011 - 0.022 + 0.011 + 0.023 . According to the constraint results, it is shown that small constraint values of $\alpha $ α indicate that the strength of interaction is weak, and at $1\sigma $ 1 σ confidence level the non-interacting cosmological constant model can not be excluded.     

Nonlinear generation of vorticity in thin smectic films

The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems that contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli–de Gennes–Matricon branches with different approach zero energy level at p_z → 0. The density of states of the bound fermions diverges at zero energy giving rise to the \(\sqrt \Omega \) dependence of the density of states in the polar phase of superfluid ³He rotating with the angular velocity Ω and to the \(\sqrt B \) dependence of the density of states for superconductors in the (d_xz + id_yz)-wave pairing state.     

Rigorous treatment of metastable states in the van der Waals-Maxwell theory

We consider a classical system, in a ν-dimensional cube Ω, with pair potential of the formq(r) + γ ^v φ(γr). Dividing Ω into a network of cells ω₁, ω₂,..., we regard the system as in a metastable state if the mean density of particles in each cell lies in a suitable neighborhood of the overall mean densityρ, withρ and the temperature satisfying $$f_0 (\rho ) + \tfrac{1}{2}\alpha \rho ^2 > f(\rho ,0 + )$$ and $$f''_0 (\rho ) + 2\alpha > 0$$ wheref(ρ, 0+) is the Helmholz free energy density (HFED) in the limit γ→ 0; α = ∫ φ(r)d ^v r andf ₀ (ρ) is the HFED for the caseφ = 0. It is shown rigorously that, for periodic boundary conditions, the conditional probability for a system in the grand canonical ensemble to violate the constraints at timet > 0, given that it satisfied them at time 0, is at mostλt, whereλ is a quantity going to 0 in the limit $$|\Omega | \gg \gamma ^{ - v} \gg |\omega | \gg r_0 \ln |\Omega |$$ Here,r ₀ is a length characterizing the potentialq, andx ? y meansx/y → +∞. For rigid walls, the same result is proved under somewhat more restrictive conditions. It is argued that a system started in the metastable state will behave (over times ?λ ^?1) like a uniform thermodynamic phase with HFED f₀(ρ) + 1/2αρ², but that having once left this metastable state, the system is unlikely to return.     

N-Vortex Equilibria for Ideal Fluids in Bounded Planar Domains and New Nodal Solutions of the sinh-Poisson and the Lane-Emden-Fowler Equations

We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain ${\Omega\subset\mathbb{R}^2}We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain W ì \mathbbR²{\Omega\subset\mathbb{R}^2} , which is not necessarily simply connected. On an arbitrary bounded domain we obtain new equilibria for N = 3 or N = 4. If Ω has an axial symmetry we obtain a symmetric equilibrium for each N ? \mathbbN{N\in\mathbb{N}} . We also obtain new stream functions solving the sinh-Poisson equation -Dy = rsinhy{-\Delta\psi=\rho\sinh\psi} in Ω with Dirichlet boundary conditions for ρ > 0 small. The stream function y_r{\psi_\rho} induces a stationary velocity field v_r{v_\rho} solving the Euler equation in Ω. On an arbitrary bounded domain we obtain velocitiy fields having three or four counter-rotating vortices. If Ω has an axial symmetry we obtain for each N a velocity field v_r{v_\rho} that has a chain of N counter-rotating vortices, analogous to the Mallier-Maslowe row of counter-rotating vortices in the plane. Our methods also yield new nodal solutions for other semilinear Dirichlet problems, in particular for the Lane-Emden-Fowler equation -Du=|u|^p-1u{-\Delta u=|u|^{p-1}u} in Ω with p large.     

Exploring interacting holographic dark energy in a perturbed universe with parameterized post-Friedmann approach

The model of holographic dark energy in which dark energy interacts with dark matter is investigated in this paper. In particular, we consider the interacting holographic dark energy model in the context of a perturbed universe, which was never investigated in the literature. To avoid the large-scale instability problem in the interacting dark energy cosmology, we employ the generalized version of the parameterized post-Friedmann approach to treating the dark energy perturbations in the model. We use the current observational data to constrain the model. Since the cosmological perturbations are considered in the model, we can then employ the redshift-space distortions (RSD) measurements to constrain the model, in addition to the use of the measurements of expansion history, which has never been done in the literature. We find that, for both the cases with \(Q=\beta H\rho _\mathrm{c}\) and with \(Q=\beta H_0\rho _\mathrm{c}\), the interacting holographic dark energy model is more favored by the current data, compared to the holographic dark energy model without interaction. It is also found that, with the help of the RSD data, a positive coupling \(\beta \) can be detected at the \(2.95\sigma \) statistical significance for the case of \(Q=\beta H_0\rho _\mathrm{c}\).     

Phase separation dynamics in binary systems containing mobile particles with variable Brownian motion

In this paper, we consider a particular form of coupling, namely \(B=\sigma (\dot{\rho _m}-\dot{\rho _\phi })\) in spatially flat (\(k=0\)) Friedmann–Lemaitre–Robertson–Walker (FLRW) space–time. We perform phase-space analysis for this interacting quintessence (dark energy) and dark matter model for different numerical values of parameters. We also show the phase-space analysis for the ‘best-fit Universe’ or concordance model. In our analysis, we observe the existence of late-time scaling attractors.     

Der Quartett-Zustand desR-Zentrums in Kaliumchlorid-Kristallen

Optical absorption and paramagnetic resonance of KCl crystals containing preferentiallyR-centers have been studied during and after excitation with 430 mμ or 365 mμ light at 90 °K. A partly metastable, partly stable state has been detected and identified as the quartet state of theR-center, which proves to be an association of threeF-centers forming an equilateral triangle in the (111) plane of the crystal as proposed byvan Doorn andHaven andPick. — The crystals used were additively colored to 6.6·10¹⁷ F-centers/cm³ and illuminated withF-band light at room temperature until theR/M-ratio reached its maximum value. During light excitation the optical spectrum in the region of theR-bands shows characteristic small changes. A part of these changes disappears spontaneously with a time constant τ=14.5 sec when the light excitation is removed (“temporary bleaching”). The remaining part has a similar spectral distribution. It is completely stable in the dark, but can be bleached within a few seconds by illumination with 840 mμ light. — Electron spin resonance of the crystal under light excitation shows in addition to theF-center line a seven-line spectrum with strong angular dependence, if the field is rotated in a (110) plane. The maximum splitting is 674 G, the width of the individual lines 35.5 G. The angular dependence of the spectrum can be fitted to a fine-structure spin Hamiltonian

$$H = g\mu _B \vec H_0 \vec S + D[S_z^2 - \tfrac{1}{3}S(S + 1)]$$     

Searching a systematics for nonfactorizable contributions to hadronic decays ofD 0 andD + mesons

We investigate nonfactorizable contributions to charm meson decays in $D \to \bar K\pi /\bar K\rho /\bar K*\pi /\bar Ka_1 /\bar K*\rho $ modes. Obtaining the contributions from spectator-quark diagrams forN _c=3, we determine nonfactorizable isospin 1/2 and 3/2 amplitudes required to explain the data for these modes. We observe that ratio of these amplitudes seem to follow a universal value.     

A class of exact solutions to the force-free,axisymetric, stationary magnetosphere of a Kerr black hole

We analyze the constraint equation giving allowed solutions describing fields and currents in a force-free magnetosphere around a rotating black hole. Utilizing the divergence properties of the energy and angular-momentum fluxes, for physically allowed solutions with nonzero energy and angular momentum extraction, we conclude that poloidal surfaces are independent of the radial coordinate for large values of r. Imposing this requirement and the Znajek regularity condition, we explicitly derive all possible exact solutions admitted by the constraint equation for r independent poloidal surfaces which are given in terms of the electromagnetic angular velocity function , where a is the angular momentum per unit mass of the black hole. Further, we show that for the class of solutions we have developed there is no electromagnetic extraction of energy. G. M. acknowledges funding through a Troy University sabbatical. The work of C. D. D. is supported by the Office of Naval Research. This research was also supported through NASA GLAST Science Investigation No. DPR-S-1563-Y.     

A unified theory of matter. II. Derivation of the fundamental physical law

The equation for the fundamental field quantity ? is obtained. It is Div \(\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } \) ,where h is an arbitrary function oft andr, and [,]_? is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ?.(2) Relativistic covariance of the equations governing ?.(3) Principle of continguous action.(4) Conservation of total amount of ?. The equation appears to be unique. It is suggested that the physical world corresponds to ? being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential A^μ is identified with ε ρ^μ dΩ. Conservation laws on various measures of ? are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ? to the metric is made via Einstein's gravitational equation G_μυ =_KT_μυ.