Ordinary Versus Novel Particle With the Example of Their Spontaneous Transition

The bicubic equation of particle limiting velocity formalism yields three solutions c1, c2 and c3, (primary, secondary and tertiary) limiting velocities in terms of the congruent parameter  which is defined in terms of m, v, and E, respectively being particle mass, velocity and energy. The bicubic equation discriminant D is given in terms of the congruent parameter z(m). When one has z2(m) ≤ 1 with the discriminant satisfying D ≤ 0 then we are talking about limiting velocities of ordinary particles. Good examples are the relativistic particles such as electron, neutrino,etc., with luminal limiting velocity c3 = c and calculated superluminal c2, and imaginary superluminal c1, all corresponding to the real particle energy. On the specific level, the situations like these, we discuss in the muon neutrino velocities with the OPERA detector and the electron velocities from the 2010 Grab Nebula Flare. The z(m) = 1 value separates the ordinary particles from novel particles, associated with D ⪰ 0 and z2 ⪰ 1 with new novel particle limiting velocity solutions c1, c2 and c3 which depend, in addition to z(m), also on the congruent angle α(m), nonlinearly related to z(m). These solutions are discussed on the newly defined sterile neutrino which here is modeled as an ordinary particle with z2 ⪯ 1 spontaneously transiting via z(m) = 1 into the modeled novel sterile neutrino with z2 ⪰ 1. All ordinary and novel particles limiting velocities carry real particle energies; the ordinary particle limiting velocity solutions being in quadratic forms, while the novel particle limiting velocity solutions being respectively, in quadratic complex form, linear complex form, and just congruent angle α complex quadratic form.

Fully Correlated Stochastic Inter-Particle Collision Model for Euler–Lagrange Gas–Solid Flows

In Lagrangian stochastic collision models, a fictitious particle is generated to act as a collision partner, with a velocity correlated to the velocity of the real colliding particle. However, most often, the fluid velocity seen by this fictitious particles is not accounted for in the generation of the fictitious particle velocity, leading to a de-correlation between the fictitious particle velocity and the local fluid velocity, which, after collision, leads to an unrealistic de-correlation of the real particle velocity and the fluid velocity as seen by the particle. This de-correlation, in turn, causes a spurious decrease of the particle kinetic energy, even though the collisions are assumed perfectly elastic. In this paper, we propose a new model in which the generated fictitious particle velocity is correctly correlated to both the real particle velocity and the local fluid velocity at the particle, hence preventing the spurious loss of the total particle kinetic energy. The model is suitable for small inertial particles. Two algorithms for integrating the collision frequency are also compared to each other. The models are validated using large eddy simulation (LES) of mono-dispersed particle-laden stationary homogeneous isotropic turbulence. Simulations are conducted with spherical particles with different turbulent Stokes number, $$St_t = [0.75 - 5.8]$$ S t t = [ 0.75 - 5.8 ] , and volume fractions, $$\alpha _p = [0.014 - 0.044]$$ α p = [ 0.014 - 0.044 ] , and are compared to the results of the LES using a deterministic discrete particle simulation model.

Simulation of Angular Flow in a Shallow Basin Triggered by a Rotating Vertical Cylinder by SPH Method

A simple numerical model has been generated for developing a code of Smoothed Particle Hydrodynamics (SPH) method. Those will be modified and used for future research. In this computational research domain is a square that consists of a real particle and virtual particle as the boundary treatment. In the initial condition, particle occupies a certain position. Circular flow has been generated by a rotating vertical cylinder to produce shear velocity to the real particle. The particles movement has been observed during time integration. A physical model has been constructed to compare the numerical model. The movement of real particles on the numerical model agrees with the movement of water particles on the physical model.