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The Standard Model of particle physics describes neutrinos as massless, chargeless elementary particles that come in three different flavours. However, recent experiments indicate that neutrinos not only have mass, but also have multiple…
Interacting-Particle Reaction Dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enable a wide range of…
When neutrinos travel through matter with a periodic density profile, the neutrino oscillation probability can be enhanced if certain conditions are satisfied. In a two-neutrino framework, the condition for parametric resonance is known.…
These notes present a critique of the standard three-flavor neutrino oscillation framwork. The design proposal of the MINOS at Fermilab based on a two mass eigenstate framework may require serious reconsideration if there is strong mixing…
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
The Phase Response Curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper we present a new approach to PRCs…
Periodic relativity (PR), uses a flat metric without weak field approximation. PR satisfies Einstein's field equations. PR proposes a definite connection between the proper time interval of an object and Doppler frequency shift of its…
We present a review of the description of hadron properties along an invariant mass operator in the point form of Poincar\'e-invariant relativistic dynamics. The quark-quark interaction is furnished by a linear confinement, consistent with…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
Rigidity conditions for a body considered as a discrete system of relativistic particles are proposed. They by themselves do not yet determine an evolution of the system, and some second-order equations must be added to them.…
Multi-parameter regression (MPR) modelling refers to the approach whereby covariates are allowed to enter the model through multiple distributional parameters simultaneously. This is in contrast to the standard approaches where covariates…
Previous studies from the astrophysics and laser physics communities have identified an interesting phenomenon wherein ultrarelativistic charged particles experiencing strong radiation reaction tend to move along special directions fixed by…
It has been firmly established, that neutrinos change their flavour during propagation. This feature is attributed to the fact, that each flavour eigenstate is a superposition of three mass eigenstates, which propagate with different…
Observation of ultra-high energy astrophysical neutrinos and identification of their flavors have been proposed for future neutrino telescopes. The flavor ratio of astrophysical neutrinos observed on the Earth depends on both the initial…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
Relativistic Newtonian Dynamics (RND) was introduced in a series of recent papers by the author, in partial cooperation with J. M. Steiner. RND was capable of describing non-classical behavior of motion under a central attracting force. RND…
Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require…