Physical Sciences and Mathematics Commons^™

Why Was Nicholson's Theory So Successful: An Explanation Of A Mysterious Episode In 20 Century Atomic Physics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the early 1910s, John Nicholson suggested that all atoms are formed by four basic elementary particles. This theory had a spectacular match with observations: it explained, with an unbelievable accuracy of 0.1, the atomic weights of all 92 elements known at that time. Specifically, it was shown that every atomic weight can be represented, with this accuracy, as an integer combination of four basic atomic weights. However, in a few years, this theory turned out to be completely wrong: atoms consist of protons, neutrons, and electrons, not of Nicholson's particles. This mysterious episode seems to contradict the usual development …

Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.

Why Physical Processes Are Smooth Or Almost Smooth: A Possible Physical Explanation Based On Intuitive Ideas Behind Energy Conservation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While there are some non-smooth (and even discontinuous) processes in nature, most processes are smooth or almost smooth. This smoothness help estimate physical quantities, but a natural question is: why are physical processes smooth or almost smooth? Are there any fundamental reasons for this ubiquitous smoothness? In this paper, we provide a possible physical explanation for emirical smoothness: namely, we show that smoothness naturally follows from intuitive ideas behind energy conservation.

A Possible (Qualitative) Explanation Of The Hierarchy Problem In Theoretical Physics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the important open problem in theoretical physics is the hierarchy problem: how to explain that some physical constant are many orders of magnitude larger than others. In this paper, we provide a possible qualitative explanation for this phenomenon.

Why Strings, Why Quark Confinement: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this pedagogical article, we recall the infinities problem of modern physics, and we show that the natural way to overcome this problem naturally leads to strings and to quark confinement.

Can We Preserve Physically Meaningful "Macro" Analyticity Without Requiring Physically Meaningless "Micro" Analyticity?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Physicists working on quantum field theory actively used "macro" analyticity -- e.g., that an integral of an analytical function over a large closed loop is 0 -- but they agree that "micro" analyticity -- the possibility to expand into Taylor series -- is not physically meaningful on the micro level. Many physicists prefer physical theories with physically meaningful mathematical foundations. So, a natural question is: can we preserve physically meaningful "macro" analyticity without requiring physically meaningless "micro" analyticity? In the 1970s, an attempt to do it was made by using constructive mathematics, in which only objects generated by algorithms are …

Need For Simplicity And Everything Is A Matter Of Degree: How Zadeh's Philosophy Is Related To Kolmogorov Complexity, Quantum Physics, And Deep Learning, Vladik Kreinovich, Olga Kosheleva, Andres Ortiz-Muñoz

Departmental Technical Reports (CS)

Many people remember Lofti Zadeh's mantra -- that everything is a matter of degree. This was one of the main principles behind fuzzy logic. What is somewhat less remembered is that Zadeh also used another important principle -- that there is a need for simplicity. In this paper, we show that together, these two principles can generate the main ideas behind such various subjects as Kolmogorov complexity, quantum physics, and deep learning. We also show that these principles can help provide a better understanding of an important notion of space-time causality.

Mathematical Modeling Of Microemulsification Processes, Numerical Simulations And Applications To Drug Delivery, Ogochukwu Nneka Ifeacho

Open Access Theses & Dissertations

Microemulsion systems are a great pharmaceutical tool for the delivery of formulations containing multiple hydrophilic and hydrophobic ingredients of varying physicochemical properties. These systems are gaining popularity because of its long shelf life, improved drug solubilisation capacity, easy preparation and improvement of bioavailability. Despite the advantages associated with the use of microemulsion systems in pharmaceutical industries, the major challenge impeding their use has been and continues to be the lack of understanding of these systems.

Microemulsions can be mathematically modeled by an initial boundary value problem involving a sixth order nonlinear time dependent equation. In this Thesis, we present a …

Density Functional Calculations On Single Molecular (1d) And Van Der Waals Bi -Layered (2d) Magnets., Md Shamsul Alam

Open Access Theses & Dissertations

Low-dimensional magnetic materials show novel properties that is not seen in bulk magnets. The weak interactions such as spin-orbit interactions, electron correlation, van der Waals interaction in case magnetic bi-layers, play an important role in determining the properties of the system. Using density functional theory, we computationally investigated two categories of magnetic material- 1: Single Molecular Magnets (SMM) 2: Van der Waals layered Cr-Halide magnets. We used different classes of density functionals to examine the spin ordering and magnetic anisotropy barriers in several single molecule magnets - Mn12, Co4, Ni4, V15. We find that the magnetic anisotropy barrier significantly depends …

Some Fermi-Lowdin Orbital Self-Interaction Correction Studies On Atomic Systems, Christopher Alexis Ibarra

Open Access Theses & Dissertations

Density Function Theory (DFT) is a popular quantum chemistry calculation method with many appeals but also deficiencies. Many modification and additions to the method have been made over the years, such as self-interaction corrections and new density functional approximations. We review here the theoretical background needed for a basic understanding of quantum chemistry calculations. In addition, we present the quantum chemistry calculation method used in this paper called Fermi-Lowdin Self-Interaction Correction (FLOSIC), including the base code it was implemented on, the Naval Research Laboratory Molecular Orbital Library (NRLMOL) Code, and the resulting modified code simply called FLOSIC. Furthermore, we explore …

Development Of Software Tools And Experimental In Situ Electron Spin Resonance For Characterizing The Magnetic And Electrocatalytic Properties Of Transition Metal Chalcogenide Crystals, Jose Armando Delgado

Open Access Theses & Dissertations

Studying the magnetic properties and crystal defects of transition metal chalcogenide crystals is of paramount importance for utilizing them for next generation spintronics devices and hydrogen evolution reaction catalysts. Hydrothermally grown transition metal chalcogenide nanocrystals (MoS2, Ru2S3, Rh2S3, Co2S8) were chosen as catalysts for the hydrogen evolution reaction due to their low dimensionality and previous utilization as catalysts for hydrodesulfurization. The relationship between crystal defect sites and catalytic activity must be discerned to maximize the efficiency of hydrogen production during the hydrogen evolution reaction. ESR spectroscopy was utilized as a spin sensitive technique to study the defects and local changes …

Comparative Experimental And Theoretical Study Of Dopamine And Serotonin Interaction, Jose A. Guerrero

Open Access Theses & Dissertations

To accurately identify and measure the concentrations of dopamine (DA) and serotonin (5-HT) in mixtures of these neurotransmitters without labeling, a comprehensive, comparative computational and Raman experimental analysis is provided. While the distinction between these two analytes may be accomplished for concentrations in the millimolar range of these mixtures, their accurate quantification remains unattainable. As shown for the first time in this study, potential creation of a new composite resulting from their interactions with each other could be a reason for this lack of quantification.

Although this new hydrogen-bonded complex greatly complicates future analyte differentiation and quantification at concentrations typical …

Independent And Simultaneous Control Of Electromagnetic Wave Properties In Self-Collimating Photonic Crystals Using Spatial Variance, Jesus Javier Gutierrez

Open Access Theses & Dissertations

Photonic crystals are engineered periodic structures that provide great control over electromagnetic waves. One of these mechanisms is self-collimation, in which the electromagnetic wave travels through the photonic crystal along an axis of the lattice without diffracting or spreading. This mechanism of self-collimation is a dispersion phenomenon, which is dependent on the unit cell's physical and geometrical characteristics. An algorithm for generating spatially variant lattices (SVL) was developed that can change geometrical properties in photonic crystals as a function of position, like unit cell orientation, fill fraction, symmetry, and others in a manner that is smooth, continuous, and virtually free …

Development And Assesment Of Local Scaled Self-Interaction Corrected Density Functional Method With Simple Scaling Factor, Selim Romero

Open Access Theses & Dissertations

The Hohenberg-Kohn-Sham (HKS) density functional theory (DFT) is widely used to compute electronic structures of atoms, molecules, and solids. It is an exact theory in which ground state electron density plays the role of basic variable, same as the wavefunction does in quantum mechanics. The total ground state energy is a functional of electron density. The practical application of HKS DFT require approximation to the exchange-correlation energy functional. Many density functional approximations (DFAs) with various degree of sophistication and complexities have been developed. Depending on the complexity, these functionals include electron density, density gradients, density Laplacian, kinetic energy densities, Hartree-Fock …

Planar Motion Control Of A Cube Satellite Using Cold Gas Thrusters, Christian Lozoya

Open Access Theses & Dissertations

This Thesis presents a mathematical model developed for the computational simulation ofCubeSat movement using four thrusters that permit uniaxial translation and rotation. Arbitrary functions are fit to boundary conditions to simulate the force, acceleration, velocity, and displacement of the CubeSat along a plane. The model is used to derive a motion control algorithm assuming constant pressure and mass. A single model describes both translation and rotation. This Thesis also explores the relationship between propellant consumption and the time required to complete a displacement implied by the model.