Heavy neutrino-antineutrino oscillations in quantum field theory

It has been proposed that the coherent propagation of long-lived heavy neutrino mass eigenstates can lead to an oscillating rate of lepton number conserving (LNC) and violating (LNV) events, as a function of the distance between the production and displaced decay vertices. We discuss this phenomenon, which we refer to as heavy neutrino-antineutrino oscillations, in the framework of quantum field theory (QFT), using the formalism of external wave packets. General formulae for the oscillation probabilities and the number of expected events are derived and the coherence and localisation conditions that have to be satisfied in order for neutrino-antineutrino oscillations to be observable are discussed. The formulae are then applied to a low scale seesaw scenario, which features two nearly mass degenerate heavy neutrinos that can be sufficiently long lived to produce a displaced vertex when their masses are below the W boson mass. The leading and next-to-leading order oscillation formulae for this scenario are derived. For an example parameter point used in previous studies, the kinematics of the considered LNC/LNV processes are simulated, to check that the coherence and localisation conditions are satisfied. Our results show that the phenomenon of heavy neutrino-antineutrino oscillations can indeed occur in low scale seesaw scenarios and that the previously used leading order formulae, derived with a plane wave approach, provide a good approximation for the considered example parameter point.

Measuring the criticality of a Hopf bifurcation

This work is based on the observation that the first Poincaré–Lyapunov constant is a quadratic function of the coefficients of the two-dimensional vector field at a Hopf bifurcation. From a given parameter point, we find the distance to the “Hopf quadric.” This distance provides a measure of the criticality of the Hopf bifurcation. The viability of the approach is demonstrated through numerical examples.

Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps

We consider a family of one-dimensional discontinuous invertible maps from an application in engineering. It is defined by a linear function and by a hyperbolic function with real exponent. The presence of vertical and horizontal asymptotes of the hyperbolic branch leads to particular codimension-two border collision bifurcation (BCB) such that if the parameter point approaches the bifurcation value from one side then the related cycle undergoes a regular BCB, while if the same bifurcation value is approached from the other side then a nonregular BCB occurs, involving periodic points at infinity, related to the asymptotes of the map. We investigate the bifurcation structure in the parameter space. Depending on the exponent of the hyperbolic branch, different period incrementing structures can be observed, where the boundaries of a periodicity region are related either to subcritical, or supercritical, or degenerate flip bifurcations of the related cycle, as well as to a regular or nonregular BCB. In particular, if the exponent is positive and smaller than one, then the period incrementing structure with bistability regions is observed and the corresponding flip bifurcations are subcritical, while if the exponent is larger than one, then the related flip bifurcations are supercritical and, thus, also the regions associated with cycles of double period are involved into the incrementing structure.

Major Information from a “Minor Parameter”: Point of Contact in Sign Language Phonology

Proceedings of the Eighth Annual Meeting of the Berkeley Linguistics Society (1982)

Generative reproduction of Vaccinium myrtillus in laboratory conditions and the influence of zinc-smelter emissions on it

The germination of <em>Vaccinium myrtillus</em> seeds and the development of the seedlings in laboratory conditions are described. The dynamics, the power of germinaltion and Pieper coefficients for the seeds were strongly influenced by the intensity of zinc-,smelter pollution of the forest stand from which they originated. The rates of survival were also estimated for seedlings transferred from filter-;paper into polluted and unpolluted samples of soil and litter. The differences noticed in the latter parameter point to the possibility of formation in the polluted stand of ecotypes more resistant to the influence of pollution than the original ones.

Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation

In this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.

Modal and Nonmodal Symmetric Perturbations. Part II: Nonmodal Growths Measured by Total Perturbation Energy

Maximum nonmodal growths of total perturbation energy are computed for symmetric perturbations constructed from the normal modes presented in Part I. The results show that the maximum nonmodal growths are larger than the energy growth produced by any single normal mode for a give optimization time, and this is simply because the normal modes are nonorthogonal (measured by the inner product associated with the total perturbation energy norm). It is shown that the maximum nonmodal growths are produced mainly by paired modes, and this can be explained by the fact that the streamfunction component modes are partially orthogonal between different pairs and parallel within each pair in the streamfunction subspace. When the optimization time is very short (compared with the inverse Coriolis parameter), the nonmodal growth is produced mainly by the paired fastest propagating modes. When the optimization time is not short, the maximum nonmodal growth is produced almost solely by the paired slowest propagating modes and the growth can be very large for a wide range of optimization time if the parameter point is near the boundary and outside the unstable region. If the parameter point is near the boundary but inside the unstable region, the paired slowest propagating modes can contribute significantly to the energy growth before the fastest growing mode becomes the dominant component. The maximum nonmodal growths produced by paired modes are derived analytically. The analytical solutions compare well with the numerical results obtained in the truncated normal mode space. The analytical solutions reveal the basic mechanisms for four types of maximum nonmodal energy growths: the PP1 and PP2 nonmodal growths produced by paired propagating modes and the GD1 and GD2 nonmodal growths produced by paired growing and decaying modes. The PP1 growth is characterized by the increase of the cross-band kinetic energy that excessively offsets the decrease of the along-band kinetic and buoyancy energy. The situation is opposite for the PP2 growth. The GD1 (or GD2) growth is characterized by the reduction of the initial cross-band kinetic energy (or initial along-band kinetic and buoyancy energy) due to the inclusion of the decaying mode.