Narrow Results

We present some recurrence results in the context of ergodic theory and dynamical systems. The main focus will be on smooth dynamical systems, in particular, those with some chaotic/hyperbolic behavior. The aim is to compute recurrence rates, limiting distributions of return times, and short returns. We choose to give the full proofs of the results directly related to recurrence, avoiding as much as possible to hide the ideas behind technical details. This drove us to consider as our basic dynamical system a one-dimensional expanding map of the interval. We note, however, that most of the arguments still apply to higher dimensional or less uniform situations, so that most of the statements continue to hold. Some basic notions from the thermodynamic formalism and the dimension theory of dynamical systems will be recalled.

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

Microelectroosmotic flow is usually restricted to low Reynolds number regime, and mixing in these microfluidic systems becomes problematic due to the negligible inertial effects. To gain an improved understanding of mixing enhancement in microchannels patterned with heterogeneous surface charge, the lattice Boltzmann method has been employed to obtain the electric potential distribution in the electrolyte, the flow field, and the species concentration distribution, respectively. The simulation results show that heterogeneous surfaces can significantly disturb the streamlines leading to apparently substantial improvements in mixing. However, the introduction of such a feature can reduce the mass flow rate in the channel. The reduction in flow rate effectively prolongs the available mixing time when the flow passes through the channel and the observed mixing enhancement by heterogeneous surfaces partly results from longer mixing time.

Compound channels are a common hydraulic section of many alluvial and fluvial systems, serving as conduits for the flow of water and sediment. The proper design of these structures requires an understanding of the entrainment and mixing mechanisms in them. This paper presents a three-dimensional numerical study of lock-exchange flow in a compound channel covering the Reynolds numbers (Re) range of 17000–39000. This study investigates flow structures and mixing patterns for various geometries and flow characteristics. The results show that the entrainment coefficient decreases as the dense flow progresses, and the amplitude of instantaneous mixing fluctuations decreases with an increase in the width of the floodplain and reduced gravity. The averaged flux entrainment profiles show a minimum at $\mathrm{\text{Re}}=27000$ at different times in the front area. In the head area also, a downward concavity can be seen in the profiles around $\mathrm{\text{Re}}=27000$. This study also reveals that changes in floodplain height do not affect the establishment of lobe-and-cleft instability. The wider the floodplain channel, the larger the lobe-and-cleft instability created. Small-scale mixing dominates at high Reynolds numbers, leading to higher fluid mixing.

We investigate how the anticipated neutral current rate from SNO will sharpen our understanding of the solar neutrino anomaly. Quantitative analyses are performed with representative values of this rate in the expected range of 0.8–1.2. This would provide a 5–10σ signal for ν_e transition into a state containing an active neutrino component. Assuming this state to be purely active one can estimate both the ⁸B neutrino flux and the ν_e survival probability to a much higher precision than currently possible. Finally the measured value of the NC rate will have profound implications for the mass and mixing parameters of the solar neutrino oscillation solution.

A non-Abelian extension of electric-magnetic duality implies that dual to confined colour SU(3), there also ought to be a broken threefold symmetry which can play the role of fermion generations. A model constructed on these premises not only gives a raison d'être for 3 and only 3 generations as observed but also offers a natural explanation for the distinctive fermion mass and mixing patterns seen in experiment. A calculation to one-loop order in this model with only 3 fitted parameters already gives correct values, all within present experimental errors, for the following quantities: the mass ratios m_c/m_t, m_s/m_b, m_μ/m_τ, all 9 matrix elements of the CKM mixing matrix |V_rs| for quarks, plus the lepton MNS mixing matrix elements |U_μ3| and |U_e3| studied in neutrino oscillation experiments with respectively atmospheric and reactor neutrinos.

Based on possible, albeit tiny, admixtures of mirror matter in ordinary mesons we study the K_L→γγ transition. We find that this process can be described with a small SU(3) symmetry breaking of only 3%. We also determine the η–η' mixing angle and the pseudoscalar decay constants. The results for these parameters are consistent with those obtained in the literature. They favor three recent determinations; the first is based on two analytical constraints, the second one based on next-to-leading order power corrections, and the third one on a phenomenological determination of the mixing parameters in the framework of the quark-flavor mixing scheme.

We investigate the J^p = 1/2^- baryons in the octets based on flavor SU(3) symmetry. Since baryons with same quantum numbers can mix with each other, we consider the mixing between two octets before their mixing with the singlet. Most predicted decay widths are consistent with the experimental data, and meanwhile we predict two possible Ξ mass ranges of the two octets.

Motivated by the chiral suppression in the mixing between a scalar glueball and quarkonia, we have investigated the mixing of three important candidates of glueballs: f₀(1370), f₀(1500) and f₀(1710), with their latest two-body pseudoscalar meson decay data in a simple decay model. In our work, we utilize a general mass matrix, in which the chiral suppression parameter a and the direct mixing r between |S〉 and |N〉 are introduced as free parameters. The most hopeful result in our fits suggests that the f₀(1710) is mainly the mixing of |G〉 and |S〉, the f₀(1370) has almost equal |G〉, |S〉 and |N〉 components, and the f₀(1500) is mainly the mixing of |S> and |N> with sizable glueball component. We find that r is reasonably small as expected, the chiral suppression parameter a can be small which suggests the chiral suppression in the mixing between glueball and quarkonia is necessary to be considered, and the SU(3) symmetry is respected in decay processes.

Studies of hadrons composed of charm quarks attend a growing attention in recent years due to both, experimental accessibility and theoretical motivation. In this paper we review selected results on charm hadron studies carried out with the Belle detector at the electron positron collider KEKB in Japan.

The most important open problems of the today's neutrino physics are the absolute values of the neutrino masses, the determination of the Dirac or the Majorana character and better measurements of the mixing matrix elements. Results of the neutrino oscillations experiments strongly confirm that the neutrinos have nonzero masses. Experiments give information about the differences between the squares of the masses but not any knowledge on their absolute values. Similarly neutrino oscillation phenomena does not help us to understand their Dirac or Majorana character. One of the processes that could clarify this important point is the double beta decay and the search is still going on but not yielded any positive results due to the big experimental difficulties. Also the inverse of this decay, e^-e^- → W^-W^- is another process that could be tested at the accelerators. This process is possible only if the neutrinos have masses and they are Majorana particles. Since neutrinos could have very tiny masses and the cross section of the above process is proportional to the square of the effective neutrino mass it is an extremely rare process. Also it violates total lepton number by two units, Δ = 2. In the literature the inverse neutrinoless double beta scattering have been extensively studied, in this article we obtain the relevant helicity amplitudes, investigate the effects of the neutrino mixing matrix elements, especially the roles of the CP violating phases and the possible CP asymmetries.

Neutral mesons exhibit a phenomenon called flavour mixing. As a consequence of a second order weak process the flavour eigenstates corresponding to the meson and its anti-meson are superpositions of two mass eigenstates. A meson produced in a flavour state changes into an anti-meson and back again as a function of time. Such flavour oscillations are considered sensitive probes of physics beyond the Standard Model. In this brief review I summarize the status of experimental constraints on mixing parameters in the meson system.

Considering the constraints from the current experiment results, we analyze mixing with a Higgs boson around 125 GeV, and discuss the influence of M_A, tanβ to the m_h and Δm_B in the Minimal Supersymmetric Standard Model (MSSM). We find these constraints have a strong impact to the parameters of M_A and tanβ, they almost exclude the small M_A and large tanβ, to have a obvious correction to the mass difference Δm_B we argue that the M_A should not too large, it is possible to observe the M_A boson with a mass 300 ~ 400 GeV in the future.

The approximately symmetric form of the PMNS matrix suggests that there could exist a hidden symmetry which makes the PMNS matrix different from the CKM matrix for quarks. In literature, all the proposed fully symmetric textures exhibit an explicit $\mu -\tau$ symmetry in addition to other symmetries which may be different for various textures. Observing obvious deviations of the practical PMNS matrix elements from those in the symmetric textures, there must be a mechanism to distort the symmetry. It might be due to the existence of light sterile neutrinos. As an example, we study the case of the Tribimaximal (TB) texture and propose that its apparent symmetry disappears due to the existence of a sterile neutrino.

We study the renormalizable singlet–doublet fermionic extension of the Standard Model (SM). In this model, the new vector-like fermions couple to the gauge bosons and to the Higgs via new Yukawa couplings that allow for nontrivial mixing in the new sector, providing a stable, neutral dark matter candidate. Approximate analytic formulae are given for the mass spectrum around the blind spots, where the dark matter candidate coupling to h or Z vanishes. We calculate the two particle scattering amplitudes in the model, impose the perturbative unitarity constraints and establish bounds on the Yukawa couplings.

One of the most robust relationships predicted by binary tetrahedral $(T^{\prime })$ flavor symmetry relates the reactor neutrino angle ${𝜃}_{13}$ to the atmospheric neutrino angle ${𝜃}_{23}$, independently of ${𝜃}_{12}$. It has the form ${𝜃}_{13}=\sqrt{2}|\frac{\pi }{4}-{𝜃}_{23}|$. When this prediction first appeared in 2008, ${𝜃}_{13}$ was consistent with zero and ${𝜃}_{23}$ with $\pi /4$. Nonzero ${𝜃}_{13}$ was established by Daya Bay in 2012. Nonzero $|\frac{\pi }{4}-{𝜃}_{23}|$ is now favored by the NO$\nu$A experiment and, for ${𝜃}_{23}$, the aforementioned $T^{\prime }$ relation selects the second octant $({𝜃}_{23}>\frac{\pi }{4})$ over the first octant $({𝜃}_{23}<\frac{\pi }{4})$. This analysis initially assumes CP conservation in the lepton sector, but leptonic CP violation is discussed and it is shown that this specific $T^{\prime }$ relationship is invariant.

Considering corrections due to SU(3) flavor symmetry breaking, non-ideal ω - ϕ mixing, double OZI and electromagnetic amplitudes of J/ψ decays into a vector and a pseudo-scalar meson, and three-gluon-annihilation amplitudes of radiative decays of J/ψ into a pseudoscalar meson, we investigate two-photon decays of pseudoscalar mesons, radiative decays between pseudoscalar and vector mesons, decays of J/ψ into a vector and a pseudoscalar meson, and radiative decays of J/ψ into a pseudoscalar meson. The quarkonia-glueball structure of η, η′ and η(1440) is phenomenologically deduced from the fit to the updated world average data concerning the above mentioned decays. We find that η (η′) contains about 48.7%, 47.6%, 3.7% (32.9%, 48.8%, 18.3%) non-strange quarkonium, strange quarkonium and glueball components, respectively, and that η(1410) is mainly a glueball state (about 78% glueball component), mixed with 18.5% non-strange quarkonium and 3.5% strange quarkonium. We predict that Br(J/ψ→γη) : Br(J/ψ→γη′) : Br (J/ψ→γη(1410)) = 1.0:5.2:8.0, which can be tested at BEPC/BES with 50 million J/ψ events.

Encouraged by the phenomenological success of the tri-bimaximal hypothesis, we postulate that the neutrino mass matrix in the lepton flavour basis is an S3 group matrix in the natural representation of S3. This immediately requires one neutrino to be trimaximally mixed, as suggested by the solar neutrino data. We go on to postulate that the charged-lepton mass matrix in the neutrino mass-basis is an S3 class matrix in the natural representation of the S3 class-algebra, leading to exact tri-bimaximal mixing which is compatible with data overall. The above two postulates are mutually consistent, and imply that the neutrino mass matrix in the flavour basis is an S3⊃S2 class operator, in the natural representation of the S3 group (the S2 being associated with mu-tau interchange). Thus the tri-bimaximal mixing matrix is seen to be closely related to the S3 group characters, and may be properly regarded as simply the table of induction coefficients for the [2]×[1]=[3]+[21] induced representation of S3.

In the model III 2HDM there are new CP violating phases which would affect the mixing. In this paper, we calculate the new physics contributions to the neutral B meson mass splitting ΔM_Bq (q=d,s) at the next-to-leading order (NLO) level. Using the high accuracy data and other relevant data, we draw the constraints on the parameter space of the model III 2HDM. Moreover, we calculate the new physics corrections to the ratio q/p. It is found that the phase of (q/p)_n for B_d which is due to the new contributions is very small and consequently in agreement with the measurements of the time dependent CP asymmetry S_J/ψK in B→J/ψK_S. On the contrary, the phase of (q/p)_n for B_s is large enough to give significant effects on CP violation in the neutral B_s system.

We present preliminary measurements from a combined analysis of lifetimes and transversity amplitudes for and and present the first direct measurement of the width difference in system using 260 pb^-1 CDF Run II data. For , we obtain , , . The decay amplitudes and lifetime are also measured.