Physics Commons^™

A New Algorithm For Solving Shortest Path Problem On A Network With Imprecise Edge Weight, Amit Kumar, Manjot Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Nayeem and Pal (Shortest path problem on a network with imprecise edge weight, Fuzzy Optimization and Decision Making 4, 293-312, 2005) proposed a new algorithm for solving shortest path problem on a network with imprecise edge weight. In this paper the shortcomings of the existing algorithm, (Nayeem and Pal, 2005) are pointed out and to overcome these shortcomings a new algorithm is proposed. To show the advantages of the proposed algorithm over existing algorithm the numerical examples presented in (Nayeem and Pal, 2005) are solved using the proposed algorithm and obtained results are discussed.

Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright

John B. Geddes

We study theoretically the effect of transverse boundary conditions on the traveling waves foundin infinitely extended and positively detuned laser systems. We find that for large-aspect-ratiosystems, well above threshold and away from the boundaries, the traveling waves persist. Sourceand sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defectscan also exist away from the boundaries. The transverse size of the sink defect, relative to the sizeof the transverse domain, is important in determining the final pattern observed, and so, close tothreshold, standing waves are always observed.

Solutions To Quasi-Relativistic Multi-Configurative Hartree-Fock Equations In Quantum Chemistry, Carlos Argáez García, Michael Melgaard

Articles

We establish existence of infinitely many distinct solutions to the multi-configurative Hartree-Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy for the n th electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge Z of K nuclei is greater than N-1 and that Z is smaller than a critical charge. The proofs are based on a new application of the Lions-Fang-Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert-Riemann manifold.

Six Types Of Multistability In A Neuronal Model Based On Slow Calcium Current, Tatiana Malashchenko, Andrey Shilnikov, Gennady Cymbalyuk

Neuroscience Institute Faculty Publications

Background: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/Principal Findings: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics …

Applications Of Local Fractional Calculus To Engineering In Fractal Time-Space: Local Fractional Differential Equations With Local Fractional Derivative, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.

A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent’s series of complex functions in complex fractal space, and generalized residue theorems are investigated.

Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.

A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun

Xiao-Jun Yang

It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.

Similarity Solution For Flow Of A Micro-Polar Fluid Through A Porous Medium, Kh. S. Mekheimer, R. E. Abo-Elkhair, S. Z. -A. Husseny, A. T. Ali

Applications and Applied Mathematics: An International Journal (AAM)

The equations of two dimensional incompressible steady micro-polar fluid flows through a porous medium are studied. Lie group analysis is employed and the solutions corresponding to the translational symmetry are developed. A boundary value problem is investigated and the results are sketched graphically. The effect on the flow of the porosity coefficient of the porous medium and the micro-polar parameters are observed.

Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid

Applications and Applied Mathematics: An International Journal (AAM)

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is …

Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed

Applications and Applied Mathematics: An International Journal (AAM)

The nonlinear propagation of small but finite amplitude dust-acoustic solitary waves (DAWs) in magnetized collision less dusty plasma has been investigated. The fluid model is a four component magnetized dusty plasma, consisting of positive and negative dust species, isothermal electrons and ions in the presence of an external magnetic field. A reductive perturbation method was employed to obtain the Zakharov Kuznetsov (ZK) equation for the first-order potential. The effects of the presence of positively charged dust fluid, the external magnetic field, and the obliqueness are obtained. The results of the present investigation may be applicable to some plasma environments, such …

The Quantum Dialectic, Logan Kelley

Pitzer Senior Theses

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …

On The Behavior Of The Asymptotics Of Robertson-Walker Cosmologies As A Function Of The Cosmological Constant, Noah Thomas Schaefferkoetter

Masters Theses

An analysis of the Einstein Field Equations within a Robertson-Walker Cosmology. More specifically, what values of the cosmological constant will result in a Big Bang.

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

Virginia Journal of Science

Abstracts for the Astronomy, Mathematics, and Physics with Materials Science Section for the 89th Annual Meeting of the Virginia Academy of Science, May 25-27, 2011, University of Richmond, Richmond VA.

Epistemic Strategies For Solving Two-Dimensional Physics Problems, Mary Elyse Hing-Hickman

Physics Theses & Dissertations

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.

In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply the …

Local Fractional Functional Analysis And Its Applications, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional functional analysis is a totally new area of mathematics, and a totally new mathematical world view as well. In this book, a new approach to functional analysis on fractal spaces, which can be used to interpret fractal mathematics and fractal engineering, is presented. From Cantor sets to fractional sets, real line number and the spaces of local fractional functions are derived. Local fractional calculus of real and complex variables is systematically elucidated. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach's spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental …

Local Fractional Laplace’S Transform Based Local Fractional Calculus, Yang Xiaojun

Xiao-Jun Yang

In this paper, a new modeling for the local fractional Laplace’s transform based on the local fractional calculus is proposed in fractional space. The properties of the local fractional Laplace’s transform are obtained and an illustrative example for the local fractional system is investigated in detail.

Fundamentals Of Local Fractional Iteration Of The Continuously Nondifferentiable Functions Derived Form Local Fractional Calculus, Yang Xiaojun

Xiao-Jun Yang

A new possible modeling for the local fractional iteration process is proposed in this paper. Based on the local fractional Taylor’s series, the fundamentals of local fractional iteration of the continuously non-differentiable functions are derived from local fractional calculus in fractional space.

Local Fractional Integral Transforms, Yang X

Xiao-Jun Yang

Over the past ten years, the local fractional calculus revealed to be a useful tool in various areas ranging from fundamental science to various engineering applications, because it can deal with local properties of non-differentiable functions defined on fractional sets. In fractional spaces, a basic theory of number and local fractional continuity of non-differentiable functions are presented, local fractional calculus of real and complex variables is introduced. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach’s spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental introduction to Yang-Fourier transforms, Yang-Laplace transforms, local …

Termodynamika Procesowa (Dla Me Aparatura Procesowa) Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

The Analysis Of Heat Transfer In A Gas-Gas Heat Exchanger Operated Under A Heat-Recirculating Mode, Mariusz Salaniec, Wojciech M. Budzianowski

Wojciech Budzianowski

The present paper presents the analysis of heat transfer in a gas-gas heat exchanger operated in a heat-recirculating mode.

An Overview Of Technologies For Upgrading Of Biogas To Biomethane, Wojciech M. Budzianowski

Wojciech Budzianowski

The present contribution presents an overview of technologies available for upgrading of biogas to biomethane. Technologies under study include pressure swing adsorption (PSA), high-pressure water wash (HPWW), reactive absorption (RA), physical absorption (PA), membrane separation (MS) and cryogenic separation (CS).

Influence Of Energy Policy On The Rate Of Implementation Of Biogas Power Plants In Germany During The 2001-2010 Decade, Izabela Chasiak, Wojciech M. Budzianowski

Wojciech Budzianowski

The current article describes energy policy tools, which caused intensive development of biogas-based power generation in Germany during the 2001-2010 decade. The German system of financial support to biogas power plants is presented in details. It is shown that in Germany, i.e. in a country characterised by similar climate and potentials to renewable energy to Poland, biogas power plants cover 10,7% of electricity demands in 2010, while all renewable energy sources cover only 5,4% of electricity demands. It is emphasised that under favourable Polish energy policy, the development of biogas energy can be very rapid.

Problems In Classical Potential Theory With Applications To Mathematical Physics, Erik Lundberg

USF Tampa Graduate Theses and Dissertations

In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters.

Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem).

Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is …

Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff

All HMC Faculty Publications and Research

A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by …

Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu

Pomona Faculty Publications and Research

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …

Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero

CGU Theses & Dissertations

There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for …

Numerics Of The Lattice Boltzmann Method: Effects Of Collision Models On The Lattice Boltzmann Simulations, Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, Wei Zhang

Mathematics & Statistics Faculty Publications

We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of …