Digital Commons Network^™

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, obtained by the regression model, …

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, S.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 CGLE …

Shifted One-Parameter Supersymmetric Family Of Quartic Asymmetric Double-Well Potentials, Haret C. Rosu, S.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, S.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, S.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, S.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 certain values of the parameter …

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. Finally we …

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

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

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 macromotion …

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.

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.

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 towards …

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

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

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 cross-cultural …

Multi-Disciplinary Hands-On Desktop Learning Modules And Modern Pedagogies, Bernard J. Van Wie, David B. Thiessen, Marc Compere, Ximena Toro, Jennifer C. Adam, Et Al.

Publications

Our team’s research focuses on fundamental problems in undergraduate education in terms of how to expand use of well researched, yet still “new”, teaching pedagogies of ‘sensing’ or ‘hands-on’, ‘active’ and ‘problem-based learning’ within engineering courses. It is now widely accepted that traditional lectures ARE NOT best for students – yet that is what the community almost universally does.

To address this issue we are developing new Desktop Learning Modules (DLMs) that contain miniaturized processes with a uniquely expandable electronic system to contend with known sensor systems/removable cartridges, as well as, unknown expansions to the project. We have shown that …

Two-Scale Microstructure Dynamics, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht

Publications

Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlin-type model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out.

Waves In Microstructured Solids: A Unified Viewpoint Of Modelling, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

The basic ideas for describing the dispersive wave motion in microstructured solids are discussed in the one-dimensional setting because then the differences between various microstructure models are clearly visible. An overview of models demonstrates a variety of approaches, but the consistent structure of the theory is best considered from the unified viewpoint of internal variables. It is shown that the unification of microstructure models can be achieved using the concept of dual internal variables.

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

Publications

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.

Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

The dispersive wave motion in solids with microstructure is considered in the one-dimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualisation, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory.

Deformation Waves In Microstructured Materials: Theory And Numerics, Juri Engelbrecht, Arkadi Berezovski, Mihhail Berezovski

Publications

A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macro-motion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches

Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski

Publications

As a preliminary study to more complex situations of interest in small-scale technology, this paper envisages the elementary propagation properties of elastic waves in one-spatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure space-like and time-like material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on …

Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski

Publications

The basic time scales for current-induced net transport of surface water and associated time scales of reaching the nearshore in the Gulf of Finland, the Baltic Sea, are analysed based on Lagrangian trajectories of water particles reconstructed from three-dimensional velocity fields by the Rossby Centre circulation model for 1987–1991. The number of particles reaching the nearshore exhibits substantial temporal variability whereas the rate of leaving the gulf is almost steady. It is recommended to use an about 3 grid cells wide nearshore area as a substitute to the coastal zone and about 10–15 day long trajectories for calculations of the …

Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht

Publications

Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model.

Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht

Publications

The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids. The basic governing equations are solved by means of a finite-volume scheme that is faithful, accurate, and conservative. Furthermore, this scheme is compatible with thermodynamics through the identification of the notions of numerical fluxes (a notion from numerics) and of excess quantities (a notion from irreversible thermodynamics). A selection of one-dimensional wave propagation problems is presented, the simulation of which exploits the designed numerical scheme. This selection of exemplary problems includes (i) waves in periodic media for weakly nonlinear waves with …

Spatiotemporal Structure Of Pulsating Solitons In The Cubic-Quintic Ginzburg-Landau Equation: A Novel Variational Formulation, S.C. Mancas, S. Roy Choudhury

Publications

Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic–quintic Ginzburg–Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. 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 …

On Nonlinear Generalizations Of The Kdv And Bbm Equations From Long Range Water Wave Theory, Timothy A. Smith

Publications

A generalization of the famous KdV and BBM equation are considered with a new nonlinear term. Sufficient conditions of solvability, existence and uniqueness are established.

Singular Superposition/Boundary Element Method For Reconstruction Of Multi-Dimensional Heat Flux Distributions With Application To Film Cooling Holes, Mahmood Silieti, Eduardo Divo, Alain J. Kassab

Publications

A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the walls of the cooling holes. The purpose of the inverse analysis is to determine the heat flux distribution along cooling hole surfaces. This is accomplished in an iterative process by distributing a set of singularities (sinks) inside the physical boundaries of the cooling hole (usually along cooling hole centerline) with a given …