Physics Commons^™

Establishment Of A Chebyshev-Dependent Inhomogeneous Second Order Differential Equation For The Applied Physics-Related Boubaker-Turki Polynomials, Micahel Dada, O. Bamidele Awojoyogbe, Maximilian Hasler, Karem B. Ben Mahmoud, Amine Bannour

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes Chebyshev-dependent inhomogeneous second order differential equation for the m-Boubaker polynomials (or Boubaker-Turki polynomials). This differential equation is also presented as a guide to applied physics studies. A concrete example is given through an attempt to solve the Bloch NMR flow equation inside blood vessels.

All-Optical Suppression Of Relativistic Self-Focusing Of Laser Beams In Plasmas, Serguei Y. Kalmykov, Sunghwan A. Yi, Gennady Shvets

Serge Youri Kalmykov

It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bi-envelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly …

Theoretical Result Of Deflection Of Light Under General Relativity Could Be Wrong, Jorge A. Franco

Jorge A Franco

Through the new definitions of relativistic mass, gravitational field and that of Energy, obtained in previous work was derived a very approximate value of Mercury’s precession. In present work we address the photon’s motion around a massive body by doing the same treatment done for any mass. The clue to do this is due to realizing that photon has a real mass (depending on its linear momentum, kinetic energy and its frequency) and thus, it is susceptible to be attracted by another mass. According to this work, this is a consistent, general and natural way to attack the problem of …

Peristaltic Pumping Of A Non-Newtonian Fluid, Amit Medhavi

Applications and Applied Mathematics: An International Journal (AAM)

The flow induced by sinusoidal peristaltic motion of the tube wall of a non-Newtonian fluid obeying Herschel-Bulkley equation (a general rheological equation that represents a powerlaw, Bingham and Newtonian fluid for particular choice of parameters) under long wavelength and low Reynolds number approximation is investigated. The results obtained for flow rate, pressure drop and friction force are discussed both qualitatively and quantitatively and compared with other related studies. It is found that the pressure drop increases with the flow rate and yield stress but decreases with the increasing amplitude ratio. The flow behaviour index shows significant impact on the magnitude …

Studies Of Laser Wakefield Structures And Electron Acceleration In Underdense Plasmas, Anatoly Maksimchuk, Steven A. Reed, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Takeshi Matsuoka, Christopher Mcguffey, Gerard Mourou, Natalia Naumova, John Nees, Pascal Rousseau, Victor Yanovsky, Karl Krushelnick, Nicholas H. Matlis, Serguei Y. Kalmykov, Gennady Shvets, Michael C. Downer, C. R. Vane, J. R. Beene, Daniel W. Stracener, David R. Schultz

Serge Youri Kalmykov

Experiments on electron acceleration and optical diagnostics of laser wakes were performed on the HERCULES facility in a wide range of laser and plasma parameters. Using frequency domain holography we demonstrated single shot visualization of individual plasma waves, produced by 40 TW, 30 fs laser pulses focused to the intensity of 10^{19} W/cm^2 onto a supersonic He gas jet with plasma densities n_e ~ 10^{19} cm^{−3}. These holographic “snapshots” capture the variation in shape of the plasma wave with distance behind the driver, and resolve wave front curvature seen previously only in simulations. High-energy quasimonoenergetic electron beams were generated using …

First Solutions To Gravitation And Orbital Precession Under Vectorial Relativity, Jorge A. Franco

Jorge A Franco

One of the reasons of the success of Einstein’s General Theory of Relativity (GTR) was that it allowed to calculate planet’s precession (rotation of the elliptical path axis with time, i.e.: Mercury Precession). The fact that its occurrence has been experimentally observed is not accounted by classic Kepler’s or Newton Laws because it is only applicable to constant masses. This work shows that planet’s precession is a direct consequence of considering variable planet’s mass inside accepted physical laws in our known three-dimensional space. According to us, this work positively confirms new definitions of mass and Energy obtained under Vectorial Relativity.

Grain Growth And Texture Development In Lithium Fluoride Thin Films, Hakkwan Kim, Alexander H. King

Alexander H. King

We have studied grain-growth and texture development in polycrystalline lithium fluoride thin films using dark-field transmission electron microscopy. We demonstrate that we can isolate the size distribution of 〈111〉 surface normal grains from the overall size distribution, based on simple and plausible assumptions about the texture. The {111} texture formation and surface morphology were also observed by x-ray diffraction and atomic force microscopy, respectively. The grain-size distributions become clearly bimodal as the annealing time increases, and we deduce that the short-time size distributions are also a sum of two overlapping peaks. The smaller grain-size peak in the distribution corresponds to …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Mikhail Khenner

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The adaptability principle of mechanical law and the scale-invariant principle of mechanical law in fractal space are proved by using parameter-space and scale-space transforms in renormalization groups.From the space-transform angle,the transform of mechanical law from fractal space to European space is the scale-invariant transform while the transform of mechanical law from European space to fractal space is the adaptability transform.Their deductions are that law of conservation of energy and vectorial resultant of force and displacement in fractal space hold the line in form and Carpinteri's dimensional formula of fractal space is also proved. Namely,the spilling dimension of volume in fractal …

Fractional Definite Integral, Yang Xiaojun

Xiao-Jun Yang

Fractional definite integral is that a value of the integral calculus over given interva1．Under the circumstance of fractional dimension，fractional definite integral is important to compute some value in given interva1．It is complied with starting introducing definition，the properties，leads into fractional integral function of definition and the properties，and then induces to basic theorems for fractional integral calculus

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mikhail Khenner

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mikhail Khenner

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov

Articles

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

Evolution Of Higher-Order Gray Hirota Solitary Waves, Tim Marchant

Tim Marchant

The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to detmine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary …

Mathematical Modelling Of Nematicons And Their Interactions, Prof. Tim Marchant

Tim Marchant

The mathematical modelling of guided wave (nematicon) propagation in liquid crystals is considered. Model equations are derived based on suitable trial functions in an averaged Lagrangian. These equations are used to model nematicon interactions.

Undular Bores And The Initial-Boundary Value Problem For The Modified Korteweg-De Vries Equation, Tim Marchant

Tim Marchant

Two types of analytical undular bore solutions, of the initial value problem for the modified Korteweg-de Vries (mKdV), are found. The first, an undular bore composed of cnoidal waves, is qualitatively similar to the bore found for the KdV equation, with solitons occurring at the leading edge and small amplitude linear waves occurring at the trailing edge. The second, a newly identified type of undular bore, consists of finite amplitude sinusiodal waves, which have a rational form. At the leading edge is the mKdV algebraic soliton, while, again, small amplitude linear waves occur at the trailing edge. The initial-boundary value …

Collisionless Shock Resolution In Nematic Liquid Crystals, Tim Marchant

Tim Marchant

The diffractive resolution on a collisionless shock formed along the spatial profile of a beam in a nematic liquid crystal is considered, this material being an example of a self-focusing, nonlocal medium. It is found that the shock is resolved through the formation of an undular bore structure which persists for experimentally relevant propagation distances due to nonlocality delaying the onset of modulational instability. Both 1+1 and 2+1 dimensional bores with circular symmetry are considered (termed line and circular bores, respectively). A semianalytical solution is developed for the line undular bore, approximating it as a train of uniform solitary waves. …

Semi-Analytical Solutions For A Gray-Scott Reaction-Diffusion Cell With An Applied Electric Field, Tim Marchant

Tim Marchant

An ionic version of the Gray–Scott chemical reaction scheme is considered in a reaction–diffusion cell, with an applied electric field, which causes migration of the reactant and autocatalyst in a preferred direction. The Galerkin method is used to reduce the governing partial differential equations to an approximate model consisting of ordinary differential equations. This is accomplished by approximating the spatial structure of the reactant and autocatalyst concentrations. Bifurcation analysis of the semi-analytical model is performed by using singularity theory to analyse the static multiplicity and a stability analysis to determine the dynamic multiplicity. The application of the electric field causes …

Nonlocal Validity Of An Asymptotic One-Dimensional Nematicon Solution, Tim Marchant

Tim Marchant

The propagation of coherent, polarized light in a nematic liquid crystal, governed by the nematicon equations, is considered. It is found that in the special case of 1 + 1 dimensions and the highly nonlocal limit, the nematicon equations have an asymptotic bulk solitary wave solution, termed a nematicon, which is given in terms of Bessel functions. This asymptotic solution gives both the ground state and the symmetric and antisymmetric excited states, which have multiple peaks. Numerical simulations of nematicon evolution, for parameters corresponding to experimental scenarios, are presented. It is found, for experimentally reasonable parameter choices, that the validity …

Dipole Soliton Formation In A Nematic Liquid Crystal In The Non-Local Limit, Tim Marchant

Tim Marchant

The interaction of two symmetric solitary waves, termed nematicons, in a liquid crystal is considered in the limit of nonlocal response of the liquid crystal. This nonlocal limit is the applicable limit for most experimentally available liquid crystals. In this nonlocal limit, two separate cases for the initial separation of the nematicons are considered, these being large and small separation. Both spinning and nonspinning nematicons are considered. It is found that in the case of large initial separation, the nematicons can form a spinning or nonspinning bound state with a finite steady separation, this being called a nematicon dipole, when …

Cascading Infrastructure Failures: Avoidance And Response, George H. Baker, Cheryl J. Elliott

George H Baker

No critical infrastructure is self-sufficient. The complexity inherent in the interdependent nature of infrastructure systems complicates planning and preparedness for system failures. Recent wide-scale disruption of infrastructure on the Gulf Coast due to weather, and in the Northeast due to electric power network failures, dramatically illustrate the problems associated with mitigating cascading effects and responding to cascading infrastructure failures once they have occurred.

The major challenge associated with preparedness for cascading failures is that they transcend system, corporate, and political boundaries and necessitate coordination among multiple, disparate experts and authorities. This symposium brought together concerned communities including government and industry …