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 Wave propagation (8)
 Microstructured solids (7)
 Cubicquintic GinzburgLandau equation (5)
 Internal Variable (4)
 Phototransduction (4)

 Dispersion (3)
 Numerical simulation (3)
 Evolution equations (2)
 Nonlinear (2)
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 Abel equation (2)
 Dissipation Inequality (2)
 Laser ablation (2)
 Asymptotic stability (2)
 EmdenFowler equation (2)
 KdV (2)
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 Parabolic system (2)
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Articles 1  30 of 57
FullText Articles in Physical Sciences and Mathematics
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Publications
A spacetime group is a connected 4dimensional 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 NewmanPenrose 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 4dimensional 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
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 onedimensional 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 KortewegDe Vries Equation, Ronald Adams, Stefan C. Mancas
Stability Of Solitary And Cnoidal Traveling Wave Solutions For A Fifth Order KortewegDe 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 Kortewegde Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wavetrains 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
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 (nonmechanical) 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 quasinil 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
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
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
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
Traveling Wave Solutions To Kawahara And Related Equations, Stefan C. Mancas
Publications
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Kortewegde Vries (KdV) equation are found by using an elliptic function method which is more general than the tanhmethod. 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 ThomasFermi Equations As The Lampariello Class Of EmdenFowler Equations, Haret C. Rosu, Stefan C. Mancas
Generalized ThomasFermi Equations As The Lampariello Class Of EmdenFowler Equations, Haret C. Rosu, Stefan C. Mancas
Publications
A oneparameter family of EmdenFowler equations defined by Lampariello’s parameter p which, upon using ThomasFermi boundary conditions, turns into a set of generalized ThomasFermi equations comprising the standard ThomasFermi 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 ThomasFermi equation and perform its phaseplane analysis. The results of the latter analysis are similar for the whole class.
Numerical Simulation Of Acoustic Emission During Crack Growth In 3Point Bending Test, Mihhail Berezovski, Arkadi Berezovski
Numerical Simulation Of Acoustic Emission During Crack Growth In 3Point Bending Test, Mihhail Berezovski, Arkadi Berezovski
Publications
Numerical simulation of acoustic emission by crack propagation in 3point 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 CamassaHolm Waves, Haret C. Rosu, Stefan C. Mancas
Ermakov Equation And CamassaHolm 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 CamassaHolm 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 CamassaHolm equation.
Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski
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 IIv Algorithms, Sirani M. Perera
Signal Flow Graph Approach To Efficient Dst IIv 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, rotationreflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST IIV. 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 DSTI and n points signal flow graphs for DST IIIV.
An Economic Regression Model To Predict Market Movements, Timothy A. Smith, Andrew Hawkins
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
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 selfimaging 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 GinzburgLandau Equation, Stefan C. Mancas, Roy S. Choudhury
Pulses And Snakes In GinzburgLandau 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 cubicquintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and nonintegrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulsetype structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the ...
Shifted OneParameter Supersymmetric Family Of Quartic Asymmetric DoubleWell Potentials, Haret C. Rosu, Stefan C. Mancas, Pisin Chen
Shifted OneParameter Supersymmetric Family Of Quartic Asymmetric DoubleWell Potentials, Haret C. Rosu, Stefan C. Mancas, Pisin Chen
Publications
Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014) 87102), 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 doublewell family of oneparameter 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
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 ...
ErmakovLewis Invariants And Reid Systems, Stefan C. Mancas, Haret C. Rosu
ErmakovLewis Invariants And Reid Systems, Stefan C. Mancas, Haret C. Rosu
Publications
Reid's mthorder 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 higherorder 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.
OneParameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, Stefan C. Mancas, Pisin Chen
OneParameter 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 oneparameter 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 VandermondeLike Matrices, Sirani M. Perera, Grigory Bonik, Vadim Olshevsky
A Fast Algorithm For The Inversion Of Quasiseparable VandermondeLike Matrices, Sirani M. Perera, Grigory Bonik, Vadim Olshevsky
Publications
The results on Vandermondelike 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 Vandermondelike matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and wellfree Vandermondelike matrices having O(n2) complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2term and 3term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and wellfree polynomials ...
Computational Models For Nanosecond Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades
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 laserinduced 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
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 onedimensional case.
Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski
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 onedimensional 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 finitevolume numerical scheme. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the coupling of equations of the ...
Hydrodynamic Modeling Of NsLaser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal
Hydrodynamic Modeling Of NsLaser 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 nanosecondlaser 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 nanosecondlaser pulse. The effect of variable laser settings on the ablation process is explored in 1D numerical simulations.
TimeStepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades
TimeStepping 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 nslaser ablation, and compare the performance of various low and high order timestepping 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
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
On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski
Publications
Abstract
The asymptotic stability of solutions of the Mindlintype 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 nonconvex free energy dependence on microdeformation.
Research highlights
The Mindlintype microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlintype microstructure model with weakly nonconvex free energy resolves this discrepancy. It is shown that the improved model with weakly nonconvex free energy is asymptotically stable for short waves.
Wave Propagation And Dispersion In Microstructured Solids, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski
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 finitevolume numerical scheme, which belongs to the class of wavepropagation 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
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 EmbryRiddle 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 ...