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Full-Text Articles in Physical Sciences and Mathematics

Spacetime Groups, Ian M. Anderson, Charles G. Torre Jan 2019

Spacetime Groups, Ian M. Anderson, Charles G. Torre

Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to ...


Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek Jul 2018

Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek

Publications

In the paper, the finite element method and the finite volume method are used in parallel for the simulation of a pulse propagation in periodically layered composites beyond the validity of homogenization methods. The direct numerical integration of a pulse propagation demonstrates dispersion effects and dynamic stress redistribution in physical space on example of a one-dimensional layered bar. Results of numerical simulations are compared with analytical solution constructed specifically for the considered problem. Analytical solution as well as numerical computations show the strong influence of the composition of constituents on the dispersion of a pulse in a heterogeneous bar and ...


Stability Of Solitary And Cnoidal Traveling Wave Solutions For A Fifth Order Korteweg-De Vries Equation, Ronald Adams, Stefan C. Mancas Mar 2018

Stability Of Solitary And Cnoidal Traveling Wave Solutions For A Fifth Order Korteweg-De Vries Equation, Ronald Adams, Stefan C. Mancas

Publications

We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.


Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski Feb 2018

Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski

Publications

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also ...


Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal Nov 2017

Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal

Publications

No abstract provided.


A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith, Alcuin Rajan Sep 2017

A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith, Alcuin Rajan

Publications

In finance, regression models or time series moving averages can be used to determine the value of an asset based on its underlying traits. In prior work we built a regression model to predict the value of the S&P 500 based on macroeconomic indicators such as gross domestic product, money supply, produce price and consumer price indices. In this present work this model is updated both with more data and an adjustment in the input variables to improve the coefficient of determination. A scheme is also laid out to alternately define volatility rather than using common tools such as ...


Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski Jul 2017

Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.


Traveling Wave Solutions To Kawahara And Related Equations, Stefan C. Mancas Jun 2017

Traveling Wave Solutions To Kawahara And Related Equations, Stefan C. Mancas

Publications

Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the tanh-method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave ...


Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas Apr 2017

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas

Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.


Numerical Simulation Of Acoustic Emission During Crack Growth In 3-Point Bending Test, Mihhail Berezovski, Arkadi Berezovski Jan 2017

Numerical Simulation Of Acoustic Emission During Crack Growth In 3-Point Bending Test, Mihhail Berezovski, Arkadi Berezovski

Publications

Numerical simulation of acoustic emission by crack propagation in 3-point bending tests is performed to investigate how the interaction of elastic waves generates a detectable signal. It is shown that the use of a kinetic relation for the crack tip velocity combined with a simple crack growth criterion provides the formation of waveforms similar to those observed in experiments.


Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, Stefan C. Mancas Sep 2016

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, Stefan C. Mancas

Publications

From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.


Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski Feb 2016

Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in ...


Signal Flow Graph Approach To Efficient Dst I-Iv Algorithms, Sirani M. Perera Jan 2016

Signal Flow Graph Approach To Efficient Dst I-Iv Algorithms, Sirani M. Perera

Publications

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having (n�1) points signal flow graph for DST-I and n points signal flow graphs for DST II-IV.


An Economic Regression Model To Predict Market Movements, Timothy A. Smith, Andrew Hawkins Dec 2015

An Economic Regression Model To Predict Market Movements, Timothy A. Smith, Andrew Hawkins

Publications

In finance, multiple linear regression models are frequently used to determine the value of an asset based on its underlying traits. We built a regression model to predict the value of the S&P 500 based on economic indicators of gross domestic product, money supply, produce price and consumer price indices. Correlation between the error in this regression model and the S&P’s volatility index (VIX) provides an efficient way to predict when large changes in the price of the S&P 500 may occur. As the true value of the S&P 500 deviates from the predicted value ...


Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski Oct 2015

Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski

Publications

Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.


Pulses And Snakes In Ginzburg-Landau Equation, Stefan C. Mancas, Roy S. Choudhury Jan 2015

Pulses And Snakes In Ginzburg-Landau Equation, Stefan C. Mancas, Roy S. Choudhury

Publications

Using a variational formulation for partial differential equations combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the ...


Shifted One-Parameter Supersymmetric Family Of Quartic Asymmetric Double-Well Potentials, Haret C. Rosu, Stefan C. Mancas, Pisin Chen Oct 2014

Shifted One-Parameter Supersymmetric Family Of Quartic Asymmetric Double-Well Potentials, Haret C. Rosu, Stefan C. Mancas, Pisin Chen

Publications

Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014) 87-102), we define supersymmetric partner potentials through a particular Riccati solution of the form F (x) = (x - c)^2 - 1, where c is a real shift parameter, and work out the quartic double-well family of one-parameter isospectral potentials obtained by using the corresponding general Riccati solution. For these parametric double well potentials, we study how the localization properties of the two wells depend on the parameter of the potentials for various values of the shifting parameter.


Variable Viscosity Condition In The Modeling Of A Slider Bearing, Kedar Nath Uprety, Stefan C. Mancas Jul 2014

Variable Viscosity Condition In The Modeling Of A Slider Bearing, Kedar Nath Uprety, Stefan C. Mancas

Publications

To reduce tear and wear of machinery lubrication is essential. Lubricants form a layer between two surfaces preventing direct contact and reduce friction between moving parts and hence reduce wear. In this short letter the lubrication of two slider bearings with parallel and nonparallel is studied. First, we show that bearings with parallel plates cannot support any load. For bearings with nonparallel plates we are interested on how constant and temperature dependent viscosity affects the properties of the bearings. Also, a critical temperature for which the bearings would fail due to excess in temperature is found for both latter cases ...


Ermakov-Lewis Invariants And Reid Systems, Stefan C. Mancas, Haret C. Rosu Jun 2014

Ermakov-Lewis Invariants And Reid Systems, Stefan C. Mancas, Haret C. Rosu

Publications

Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.


One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, Stefan C. Mancas, Pisin Chen Apr 2014

One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, Stefan C. Mancas, Pisin Chen

Publications

In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F∘f)(x)=F(f(x)) and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for ...


A Fast Algorithm For The Inversion Of Quasiseparable Vandermonde-Like Matrices, Sirani M. Perera, Grigory Bonik, Vadim Olshevsky Jan 2014

A Fast Algorithm For The Inversion Of Quasiseparable Vandermonde-Like Matrices, Sirani M. Perera, Grigory Bonik, Vadim Olshevsky

Publications

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having O(n2) complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials ...


Computational Models For Nanosecond Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades Jan 2014

Computational Models For Nanosecond Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Laser ablation in an ambient environment is becoming increasingly important in science and technology. It is used in applications ranging from chemical analysis via mass spectroscopy, to pulsed laser deposition and nanoparticle manufacturing. We describe numerical schemes for a multiphase hydrodynamic model of nanosecond laser ablation expressing energy, momentum, and mass conservation in the target material, as well as in the expanding plasma plume, along with collisional and radiative processes for laser-induced breakdown (plasma formation). Numerical simulations for copper in a helium background gas are presented and the efficiency of various ODE integrators is compared.


Dispersive Waves In Microstructured Solids, A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets, Mihhail Berezovski Jun 2013

Dispersive Waves In Microstructured Solids, A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets, Mihhail Berezovski

Publications

The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler–Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a one-dimensional case.


Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski May 2013

Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski

Publications

Numerical simulations of the thermoelastic response of a microstructured material on a thermal loading are performed in the one-dimensional setting to examine the influence of temperature gradient effects at the microstructure level predicted by the thermoelastic description of microstructured solids (Berezovski et al. in J. Therm. Stress. 34:413–430, 2011). The system of equations consisting of a hyperbolic equation of motion, a parabolic macroscopic heat conduction equation, and a hyperbolic evolution equation for the microtemperature is solved by a finite-volume numerical scheme. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the coupling of equations of the ...


Hydrodynamic Modeling Of Ns-Laser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal Jan 2013

Hydrodynamic Modeling Of Ns-Laser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal

Publications

Laser ablation is a versatile and widespread technique, applied in an increasing number of medical, industrial and analytical applications. A hydrodynamic multiphase model describing nanosecond-laser ablation (ns- LA) is outlined. The model accounts for target heating and mass removal mechanisms as well as plume expansion and plasma formation. A copper target is placed in an ambient environment consisting of helium and irradiated by a nanosecond-laser pulse. The effect of variable laser settings on the ablation process is explored in 1-D numerical simulations.


Time-Stepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades Jan 2013

Time-Stepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Nanosecond laser ablation is a popular technique, applied in many areas of science and technology such as medicine, archaeology, chemistry, environmental and materials sciences. We outline a computational model for radiative and collisional processes occurring during ns-laser ablation, and compare the performance of various low and high order time-stepping algorithms.


Project Haiti 2012: Providing An Experiential Learning Experience Through The Design And Delivery Of A Water Purifier In Haiti, Yung Wong, Johnathon Camp, Shavin Pinto, Kyle Fennesy, Marc Compere, Yan Tang Jan 2013

Project Haiti 2012: Providing An Experiential Learning Experience Through The Design And Delivery Of A Water Purifier In Haiti, Yung Wong, Johnathon Camp, Shavin Pinto, Kyle Fennesy, Marc Compere, Yan Tang

Publications

In this paper, we share our experiences and lessons learned from Project Haiti 2012, a project to design and install a water purification system serving 20,000 people per day in the largest tent city in Haiti. Project Haiti 2012 was the third and largest system we have built for Haitians and represents a huge success for all participants and stakeholders. This paper discusses the unique experiential learning opportunity involved in the design and delivery of the water purifier in a foreign developing country. Multiple positive educational, social, and economic outcomes were achieved including students applying knowledge gained from coursework ...


On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski Feb 2012

On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski

Publications

Abstract

The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.

Research highlights

The Mindlin-type microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlin-type microstructure model with weakly non-convex free energy resolves this discrepancy. It is shown that the improved model with weakly non-convex free energy is asymptotically stable for short waves.


Wave Propagation And Dispersion In Microstructured Solids, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski Jan 2012

Wave Propagation And Dispersion In Microstructured Solids, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

A series of numerical simulations is carried on in order to understand the accuracy of dispersive wave models for microstructured solids. The computations are performed by means of the finite-volume numerical scheme, which belongs to the class of wave-propagation algorithms. The dispersion effects are analyzed in materials with different internal structures: microstructure described by micromorphic theory, regular laminates, laminates with substructures, etc., for a large range of material parameters and wavelengths.


High Tech High Touch: Lessons Learned From Project Haiti 2011, Yan Tang, Marc Compere, Yung Lun Wong, Jared Anthony Coleman, Matthew Charles Selkirk Jan 2012

High Tech High Touch: Lessons Learned From Project Haiti 2011, Yan Tang, Marc Compere, Yung Lun Wong, Jared Anthony Coleman, Matthew Charles Selkirk

Publications

In this paper, we will share our experiences and lessons learned from a design project for providing clean water to a Haitian orphanage (Project Haiti 2011). Supported by funds from a renewable energy company and the university president’s office, five engineering students and two faculty members from Embry-Riddle Aeronautical University successfully designed and installed a solar powered water purification system for an orphanage located in Chambellan, Haiti. This paper discusses the unique educational experiences gained from unusual design constraints, such as ambiguity of existing facilities due to limited communication, logistics of international construction at a remote village location, and ...