Kaniadakis deformed κ-mathematics is an area of mathematics that has found relevance in the analysis of complex systems. Specifically, the mathematical framework in the context of a first-order decay κ-differential equation is investigated, facilitating an in-depth examination of the κ-mathematical structure. This framework serves as a foundational platform, representing the simplest non-trivial setting for such inquiries which are demonstrated for the first time in the literature. Finally, additional avenues of study are discussed.

The Maximum Entropy (MaxEnt) technique is applied to the derivation of the Gaussian Dispersion Plume Model as well as to more complex transport phenomena such as the one-dimensional advection equation, the one-dimensional diffusion equation, the one dimensional advection-diffusion equation, and finally to the multi-dimensional advection-diffusion equation. Further application is discussed.

This work explores the hyperbolic cosine and hyperbolic secant functions within the framework of the maximum entropy principle, deriving these probability distribution functions from first principles. The resulting maximum entropy solutions are applied to various physical systems, including the repulsive oscillator and solitary wave solutions of the advection equation, using the method of moments. Additionally, a different moment analysis using experimental and theoretical inputs is employed to address non-linear systems described by the non-linear Schrödinger equation, non-linear diffusion equation, and Korteweg–de Vries equation, demonstrating the versatility of this approach. These findings demonstrate the broad applicability of maximum entropy methods in solving different differential equations, with potential implications for future research in non-linear dynamics and transport physics.

The problem of an electrically charged pendulum above a grounded conducting surface is examined using traditional analyses, such as forces, energy, and torque. The system was numerically modelled using a finite difference method and analysed. A number of classroom activities have been suggested.

There are indications that the Newtonian gravitational constant may not be a constant but may vary with respect to some other physical parameter. Various possible characterizations of Newton’s gravitational parameter as a function of the cosmic scale parameter are proposed and studied within the framework of classical Newtonian cosmology. A number of toy cosmologies with varying Newtonian gravitational parameters are developed and analyzed. The numerical solutions to the temporal evolution of the universe from the Friedmann equation are examined and discussed as well as kinematic observables. Finally, other avenues of research are addressed.

Good approximate eigenstates of a Hamiltionian operator which poesses a point as well as a continuous spectrum have beeen obtained using the Lanczos algorithm. Iterating with the bare Hamiltonian operator yields spurious solutions which can easily be identified. The rms radius of the ground state eigenvector, for example, is calculated using the bare operator.

In order to highlight time-varying constants such as the universal gravitation constant and to elucidate the effects of higher dimensions on cosmological parameters in the universe, we developed a toy cosmological model based upon an anisotropic n-dimensional spatial universe within an (n + 1)-dimensional spacetime. A dynamical power law model for dark energy is considered. The observational parameters of this cosmology are predicted and discussed. Considerable attention is devoted to the application of the extra-dimensional n-dimensional anisotropic cosmology model resulting in a universe consistent with current observations.

The SNO+ experiment is located 2 km underground at SNOLAB in Sudbury, Canada. A low background search for neutrinoless double beta (0νββ) decay will be conducted using 780 tonnes of liquid scintillator loaded with 3.9 tonnes of natural tellurium, corresponding to 1.3 tonnes of ^130Te. This paper provides a general overview of the SNO+ experiment, including detector design, construction of process plants, commissioning efforts, electronics upgrades, data acquisition systems, and calibration techniques. The SNO+ collaboration is reusing the acrylic vessel, PMT array, and electronics of the SNO detector, having made a number of experimental upgrades and essential adaptations for use with the liquid scintillator. With low backgrounds and a low energy threshold, the SNO+ collaboration will also pursue a rich physics program beyond the search for 0νββ decay, including studies of geo- and reactor antineutrinos, supernova and solar neutrinos, and exotic physics such as the search for invisible nucleon decay. The SNO+ approach to the search for 0νββ decay is scalable: a future phase with high ^130Te-loading is envisioned to probe an effective Majorana mass in the inverted mass ordering region.

A liquid scintillator consisting of linear alkylbenzene as the solvent and 2,5-diphenyloxazole as the fluor was developed for the SNO+ experiment. This mixture was chosen as it is compatible with acrylic and has a competitive light yield to pre-existing liquid scintillators while conferring other advantages including longer attenuation lengths, superior safety characteristics, chemical simplicity, ease of handling, and logistical availability. Its properties have been extensively characterized and are presented here. This liquid scintillator is now used in several neutrino physics experiments in addition to SNO+.

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

Quadcopters, or drones, have come into wide use recently for a variety of applications including video inspection of otherwise inaccessible areas, real estate sales, and entertainment. Students are interested in them and in some cases own their own. The combination of high mobility, relatively low price, and autonomous operation is quite compelling. Besides just flying around on Earth, could drones be useful in planetary exploration? Being able to avoid getting stuck (as the Mars rover Spirit did, although after far exceeding its life expectancy) while covering far more of a planet than a ground-based rover would be attractive.

A search has been performed for neutrinos from two sources, the hep reaction in the solar pp fusion chain and the upsilon e component of the diffuse supernova neutrino background (DSNB), using the full dataset of the Sudbury Neutrino Observatory with a total exposure of 2.47 kton-years after fiducialization. The hep search is performed using both a single-bin counting analysis and a likelihood fit. We find a best-fit flux that is compatible with solar model predictions while remaining consistent with zero flux, and set a onesided upper limit of Phi(hep) < 30 x 10(3) cm(-2) s(-1) [90% credible interval (CI)]. No events are observed in the DSNB search region, and we set an improved upper bound on the nu(e) component of the DSNB flux of Phi(DSNB)(nu e) < 19 cm(-2) s(-1) (90% CI) in the energy range 22.9 < E-nu < 36.9 MeV.

Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions. Systems subject to conservative forces have also been considered. In this approach, determining the solutions to the transport equations no longer requires solving a partial differential equation but instead experimentally determining the low-lying moments and potentials. (C) 2020 Elsevier B.V. All rights reserved.

Neutrons produced in nuclear interactions initiated by cosmic-ray muons present an irreducible background to many rare-event searches, even in detectors located deep underground. Models for the production of these neutrons have been tested against previous experimental data, but the extrapolation to deeper sites is not well understood. Here we report results from an analysis of cosmogenically produced neutrons at the Sudbury Neutrino Observatory. A specific set of observables are presented, which can be used to benchmark the validity of GEANT4 physics models. In addition, the cosmogenic neutron yield, in units of 10(-4) cm(2)/(g.mu), is measured to be 7.28 +/- 0.09(stat)(-1.12)(+1.59)(syst) in pure heavy water and 7.30 +/- 0.07(stat)(-1.02)(+1.40)(syst) in NaCl-loaded heavy water. These results provide unique insights into this potential background source for experiments at SNOLAB.

Neutron production in giga electron volt-scale neutrino interactions is a poorly studied process. We have measured the neutron multiplicities in atmospheric neutrino interactions in the Sudbury Neutrino Observatory experiment and compared them to the prediction of a Monte Carlo simulation using GENIE and a minimally modified version of GEANT4. We analyzed 837 days of exposure corresponding to Phase I, using pure heavy water, and Phase II, using a mixture of Cl in heavy water. Neutrons produced in atmospheric neutrino interactions were identified with an efficiency of 15.3% and 44.3%, for Phases I and II respectively. The neutron production is measured as a function of the visible energy of the neutrino interaction and, for charged current quasielastic interaction candidates, also as a function of the neutrino energy. This study is also performed by classifying the complete sample into two pairs of event categories: charged current quasielastic and non charged current quasielastic, and nu(mu) and nu(e). Results show good overall agreement between data and Monte Carlo for both phases, with some small tension with a statistical significance below 2 sigma for some intermediate energies.

This paper reports results from a search for nucleon decay through invisible modes, where no visible energy is directly deposited during the decay itself, during the initial water phase of SNO+. However, such decays within the oxygen nucleus would produce an excited daughter that would subsequently deexcite, often emitting detectable gamma rays. A search for such gamma rays yields limits of 2.5 x 10(29) y at 90% Bayesian credibility level (with a prior uniform in rate) for the partial lifetime of the neutron, and 3.6 x 10(29) y for the partial lifetime of the proton, the latter a 70% improvement on the previous limit from SNO. We also present partial lifetime limits for invisible dinucleon modes of 1.3 x 10(28) y for nn, 2.6 x 10(28) y for pn and 4.7 x 10(28) y for pp, an improvement over existing limits by close to 3 orders of magnitude for the latter two.

The long baseline between Earth and the Sun makes solar neutrinos an excellent test beam for exploring possible neutrino decay. The signature of such decaywould be an energy-dependent distortion of the traditional survival probability which can be fit for using well-developed and high-precision analysis methods. Here a model including neutrino decay is fit to all three phases of B-8 solar neutrino data taken by the SudburyNeutrino Observatory (SNO). This fit constrains the lifetime of neutrino mass state nu(2) to be > 8.08 x 10(-5) s/eV at 90% confidence. An analysis combining this SNO result with those from other solar neutrino experiments results in a combined limit for the lifetime of mass state nu(2) of > 1.92 x 10(-3) s/eV at 90% confidence.

In recent years, the Lie group SU(7) has been featured prominently in a number of grand unification proposals involving the Standard Model as a low energy effective theory. This note investigates the framework of the SU(7) group. The antisymmetric and symmetric structure constants for the Lie algebra su (7) have been explicitly calculated from the generators for the fundamental representation of SU(7), which are also cataloged.

Experimental tests of Lorentz symmetry in systems of all types are critical for ensuring that the basic assumptions of physics are well founded. Data from all phases of the Sudbury Neutrino Observatory, a kiloton-scale heavy water Cherenkov detector, are analyzed for possible violations of Lorentz symmetry in the neutrino sector. Such violations would appear as one of eight possible signal types in the detector: six seasonal variations in the solar electron neutrino survival probability differing in energy and time dependence and two shape changes to the oscillated solar neutrino energy spectrum. No evidence for such signals is observed, and limits on the size of such effects are established in the framework of the standard model extension, including 38 limits on previously unconstrained operators and improved limits on 16 additional operators. This makes limits on all minimal, Dirac-type Lorentz violating operators in the neutrino sector available for the first time.

Although we may consider the power outlets in our homes to be nearly ideal voltage sources, a variety of influences in and around the home can cause departures from the nominal 60 Hz, 110–120 V root-mean-square (rms) of the North American grid. Even without instrumentation, we can see that a large motor starting from rest can be sufficient to cause lights to dim momentarily (voltage sag). This dimming is due to the inrush current drawn by a stationary motor, which may be several times the current drawn at operating speed. We prepared a voltage monitoring system using a voltage divider, the construction details of which we omit in the interest of safety.