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In the conventional seesaw models of neutrino masses, leptogenesis occurs at a very high scale. Three approaches have been discussed in the literature to lower the scale of leptogenesis making them testable: mass degeneracy, hierarchy of couplings and three-body decays. We advocate yet another approach to a testable leptogenesis, whereby the decaying particles could go out of equilibrium at an accessible scale due to kinematics, although their couplings to the decay products are larger for generating a desired CP asymmetry. We demonstrate this new possibility for the testable leptogenesis in a two-Higgs doublet model where the neutrino masses originate from a one-loop diagram.

Comparisons of the positive and negative halves of the distributions of parity-odd event variables in particle-physics experimental data can provide sensitivity to sources of nonstandard parity violation. Such techniques benefit from lacking first-order dependence on simulations or theoretical models, but have hitherto lacked systematic means of enumerating all discoverable signals. To address that issue this paper seeks to construct sets of parity-odd event variables which may be proved to be able to reveal the existence of any Lorentz-invariant source of nonstandard parity violation which could be visible in data consisting of groups of real nonspace-like four-momenta exhibiting certain permutation symmetries.

The equilibrium of globular and galaxy clusters is analyzed using a gravitomagnetic (GM) model for a fluid in stationary, axially-symmetric motion. An oblique change of coordinates leads to a free-fall nonlinear force balance equation relating the GM flux function and the gravitational potential. An approximate internal solution of the force balance is obtained introducing trial functions in the form of a sedimentation equilibrium. The internal solution defines the tangential component of the GM field acting on the surface of the cluster. This GM component constitutes the boundary condition that must be used to obtain a self-consistent solution together with Gauss’ and Ampère’s laws. The complete solution is postponed for future work, but a simple application to the classic Coma Cluster problem indicates that the rotating velocity on the surface of the cluster is within the range of observed values, without introducing dark matter.

We support, with new fitting instruments and the analysis of more recent experimental data, the proposal of a relationship between the mass of a Supermassive Black Hole (SMBH) and the kinetic energy of random motions in the host elliptical galaxy. The first results obtained in a previous paper with 13 elliptical galaxies are now confirmed by the new data and an enlarged sample. We find M_BH ∝ (M_Gσ²/c²)^β with 0.8 ≤ β ≤ 1 depending on the different fitting methods and samples used. The meaningful case β = 1 is carefully analyzed. Furthermore, we test the robustness of our relationship, including in the sample also lenticular and spiral galaxies and we show that the result does not change. Finally, we find a stronger correlation between the mass of the galaxy and the corresponding velocity dispersion that allows us to connect our relationship to the M_BH ∝ σ^α law. With respect to this law, our relationship has the advantage of having a smaller scatter.

In this paper, we provide a new derivation of the Dirac equation which promptly generalizes to higher spins. We apply this idea to spin-half Elko dark matter.

We consider collision of two geodesic particles near the lightlike surface (black hole horizon or naked singularity) of such an axially symmetric rotating or static metric that the coefficient $g_{\varphi \varphi }\to 0$ on this surface. It is shown that the energy in the center of mass frame $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$ is indefinitely large even without fine-tuning of particles’ parameters. Kinematically, this is the collision between two rapid particles that approach the horizon almost with the speed of light but at different angles (or they align along the normal to the horizon too slowly). The latter is the reason why the relative velocity tends to that of light, hence to high $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$. Our approach is model-independent. It relies on general properties of geometry and is insensitive to the details of material source that supports the geometries of the type under consideration. For several particular models (the stringy black hole, the Brans–Dicke analogue of the Schwarzschild metric and the Janis–Newman–Winicour one) we recover the results found in literature previously.

Origami-inspired structures have found many innovative applications in engineering fields. The expressive volume changes intrinsically related to their geometry is very useful for different purposes. Nevertheless, the mathematical description of origami structures is complex, which makes the design a challenging topic. This work deals with the use of reduce-order models for the origami description. A cylindrical origami structure with waterbomb pattern, called origami stent, is of concern. A reduced-order model (ROM) is developed based on kinematics and symmetry hypotheses. Afterward, a finite element analysis (FEA) is developed based on a nonlinear bar-and-hinge model. Numerical simulations are carried out evaluating the ROM validity range. Rigid and non-rigid situations are investigated showing that ROM is able to be employed for origami description.

Redundant manipulators allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The results reveal fundamental properties of the chaotic phenomena and give a deeper insight towards the development of superior trajectory control algorithms.

It is desirable to understand the movement of both matter and energy in the universe based upon fundamental principles of space and time. Time dilation and length contraction are features of Special Relativity derived from the observed constancy of the speed of light. Quantum Mechanics asserts that motion in the universe is probabilistic and not deterministic. While the practicality of these dissimilar theories is well established through widespread application inconsistencies in their marriage persist, marring their utility, and preventing their full expression. After identifying an error in perspective the current theories are tested by modifying logical assumptions to eliminate paradoxical contradictions. Analysis of simultaneous frames of reference leads to a new formulation of space and time that predicts the motion of both kinds of particles. Proper Space is a real, three-dimensional space clocked by proper time that is undergoing a densification at the rate of c. Coordinate transformations to a familiar object space and a mathematical stationary space clarify the counterintuitive aspects of Special Relativity. These symmetries demonstrate that within the local universe stationary observers are a forbidden frame of reference; all is in motion. In lieu of Quantum Mechanics and Uncertainty the use of the imaginary number i is restricted for application to the labeling of mass as either material or immaterial. This material phase difference accounts for both the perceived constant velocity of light and its apparent statistical nature. The application of Proper Space Kinematics will advance more accurate representations of microscopic, macroscopic, and cosmological processes and serve as a foundation for further study and reflection thereafter leading to greater insight.