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Full-Text Articles in Physical Sciences and Mathematics

Wave Motion Induced By Turbulent Shear Flows Over Growing Stokes Waves, Shahrdad Sajjadi, Serena Robertson, Rebecca Harvey, Mary Brown Dec 2016

Wave Motion Induced By Turbulent Shear Flows Over Growing Stokes Waves, Shahrdad Sajjadi, Serena Robertson, Rebecca Harvey, Mary Brown

Publications

The recent analytical of multi-layer analyses proposed by Sajjadi et al. (J Eng Math 84:73, 2014) (SHD14 therein) is solved numerically for atmospheric turbulent shear flows blowing over growing (or unsteady) Stokes (bimodal) water waves, of low-to-moderate steepness. For unsteady surface waves, the amplitude a(t)∝ekcita(t)∝ekcit, where kcikci is the wave growth factor, k is the wavenumber, and cici is the complex part of the wave phase speed, and thus, the waves begin to grow as more energy is transferred to them by the wind. This will then display the critical height to a point, where the thickness of the inner …


On Safety Assessment Of Novel Approach To Robust Uav Flight Control In Gusty Environments, Vladimir Golubev, Petr Kazarin, William Mackunis, Sherry Borener, Derek Hufty Sep 2016

On Safety Assessment Of Novel Approach To Robust Uav Flight Control In Gusty Environments, Vladimir Golubev, Petr Kazarin, William Mackunis, Sherry Borener, Derek Hufty

Publications

In a follow-up to our previous study, the current work examines the gust-induced “cone of uncertainty” in a small unmanned aerial vehicle’s (UAV) flight trajectory addressed in the context of safety assessments of UAV operations. Such analysis is a critical facet of the integration of unmanned aerial systems (UAS) into the National Airspace System (NAS), particularly in terminal airspace. The paper describes a predictive, robust feedback-loop flight control model that is applicable to various classes of UAVs and unsteady flight-path scenarios. The control design presented in this paper extends previous research results by demonstrating asymptotic (zero steady-state error) altitude regulation …


Aviation And Cybersecurity: Opportunities For Applied Research, Jon Haass, Radhakrishna Sampigethaya, Vincent Capezzuto Jul 2016

Aviation And Cybersecurity: Opportunities For Applied Research, Jon Haass, Radhakrishna Sampigethaya, Vincent Capezzuto

Publications

Aviation connects the global community and is moving more people and payloads faster than ever. The next decade will experience an increase in manned and unmanned aircraft and systems with new features and unprecedented applications. Cybertechnologies—including software, computer networks, and information technology—are critical and fundamental to these advances in meeting the needs of the aviation ecosystem of aircraft, pilots, personnel, passengers, stakeholders, and society. This article discusses current and evolving threats as well as opportunities for applied research to improve the global cybersecurity stance in the aviation and connected transportation industry of tomorrow.


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.


Plasma Density Analysis Of Cubesat Wakes In The Earth’S Ionosphere, Robert M. Albarran Ii, Aroh Barjatya Jan 2016

Plasma Density Analysis Of Cubesat Wakes In The Earth’S Ionosphere, Robert M. Albarran Ii, Aroh Barjatya

Publications

Spinning or tumbling CubeSats with Langmuir probes deployed on booms will render spin-modulated plasma densities as the probes move in and out of the spacecraft wake. It is traditionally assumed that the lower-density measurements from the spin cycle are made in the spacecraft wake, and the higher-density measurements are outside the wake. Although this assumption is valid for larger spacecraft in the Earth’s ionosphere, this paper scrutinizes its validity for CubeSats in similar conditions. Spacecraft–plasma interactions (surface charging, plasma sheaths, and wakes) are less understood for CubeSats, and the small CubeSat dimensions must be considered with respect to characteristic length …


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.


Direct Atmospheric Evidence For The Irreversible Formation Of Aqueous Secondary Organic Aerosol, Marwa M. El-Sayed, Yingqing Wang, Christopher J. Hennigan Jun 2015

Direct Atmospheric Evidence For The Irreversible Formation Of Aqueous Secondary Organic Aerosol, Marwa M. El-Sayed, Yingqing Wang, Christopher J. Hennigan

Publications

The reversible nature of aqueous secondary organic aerosol (aqSOA) formation was characterized for the first time through direct atmospheric measurements. Water-soluble organic carbon in the gas and particle phases (WSOCg and WSOCp) was measured simultaneously to quantify aqSOA formation in Baltimore, Maryland. During the nighttime, aqSOA formation was evident as WSOCg increasingly partitioned to the particle phase with increasing relative humidity (RH). To characterize the reversible/irreversible nature of this aqSOA, the WSOCp measurement was alternated through an unperturbed ambient channel and through a “dried” channel maintained at ~40% RH (with 7 s residence time) to mimic the natural drying particles …


Editorial: Special Issue: Safety & Efficiency Of Civil Aviation: Selected Papers From The World Conferences Of The Air Transport Research Society And The World Conference On Transport Society - 2013, Paul Hooper, Ian Douglas, Chunyan Yu, Stefano Paleari Jan 2015

Editorial: Special Issue: Safety & Efficiency Of Civil Aviation: Selected Papers From The World Conferences Of The Air Transport Research Society And The World Conference On Transport Society - 2013, Paul Hooper, Ian Douglas, Chunyan Yu, Stefano Paleari

Publications

The Air Transport Research Society (ATRS) is a Special Interest Group (SIG) of the World Conference on Transport Research Society (WCTRS). The ATRS annual World Conference was held at the University of Bergamo, Bergamo, Italy on 26-29 June 2013 and it attracted 266 papers from 37 countries. Also, the WCTRS triennial World Conference was held on 15- 18 July at Rio de Janeiro, Brazil, during which the ATRS organised several sessions devoted to air transport topics. This special issue of the Journal of Air Transport Studies has drawn upon all of this material to present four papers that promote improvements …


Potential And Technological Advancement Of Biofuels, Rajee Olaganathan, Fabian Ko Qui Shen, Lim Jun Shen Aug 2014

Potential And Technological Advancement Of Biofuels, Rajee Olaganathan, Fabian Ko Qui Shen, Lim Jun Shen

Publications

This scientific paper examines the feasibility of biofuels as a solution to the world‟s energy crisis. It studies the development of the four different generations of biofuel that have been discerned over the years, determining the pros and cons of each. The paper further investigates the issues concerning each generation, and determines how their successors have solved and improved on those problems. In order to give the reader an unbiased perspective, the paper studies both general advantages and disadvantages that encompasses social, economic and environmental impacts. Research and development on the first two generations of biofuels have matured, and case …


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

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. …


Is Biofuel A Feasible Long-Term Chief Energy Source? A Global Perspective, Rajee Olaganathan, Aston Lee, Debra Tong, Mameegate Zheng Jun Cheston, Zack Ho Xuan Yi Jun 2014

Is Biofuel A Feasible Long-Term Chief Energy Source? A Global Perspective, Rajee Olaganathan, Aston Lee, Debra Tong, Mameegate Zheng Jun Cheston, Zack Ho Xuan Yi

Publications

This scientific paper examines the feasibility of officiating biofuels as the future chief energy source of the world. It weighs the pros and cons of the four different generations of biofuels that have been discovered over time, explaining how the raw materials used in each generation determines each individual level of long-term sustainability. It then further analyses both general advantages and disadvantages, comprising of economic, social, health and environmental impacts; giving the reader an unbiased perspective. Few case studies have also been reviewed to better understand the implications of drawing energy from biofuels, as well as the current state of …


Reduction Of Transportation Greenhouse Gas Emissions To Mitigate Climate Change Impacts, Mary Snow, Richard Snow May 2014

Reduction Of Transportation Greenhouse Gas Emissions To Mitigate Climate Change Impacts, Mary Snow, Richard Snow

Publications

Weather affects almost all modes of transportation in a modern society, and likewise, transportation has an enormous impact on the weather. Transportation greenhouse gas emissions (GHG) impact climate change, which impacts transportation in return. Reduction of transportation impacts on climate change can mitigate the reverse climate change impacts on transportation. This paper examines the relationship between transportation and climate change and establishes prospective solutions to reduce transportation greenhouse gas emission impacts on climate change and mitigate the reverse climate change impacts on transportation.


Aircraft Access To System-Wide Information Management Infrastructure, Mohammad Moallemi, Remzi Seker, Mohamed Mahmoud, Jayson Clifford, John Pesce, Carlos Castro, Massood Towhidnejad, Jonathan Standley, Robert Klein May 2014

Aircraft Access To System-Wide Information Management Infrastructure, Mohammad Moallemi, Remzi Seker, Mohamed Mahmoud, Jayson Clifford, John Pesce, Carlos Castro, Massood Towhidnejad, Jonathan Standley, Robert Klein

Publications

Within the Federal Aviation Administration’s (FAA) NextGen project, System Wide Information Management (SWIM) program is the essential core in facilitating the collaborative access to the aviation information by various stakeholders. The Aircraft Access to SWIM (AAtS) initiative is an effort to connect the SWIM network to the aircraft to exchange the situational information between the aircraft and the National Airspace System (NAS). This paper summarizes the highlevel design and implementation of the AAtS infrastructure; namely the communication medium design, data management system, pilot peripheral, as well as the security of the data being exchanged and the performance of the entire …


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. Finally we …


Standoff Methods For The Detection Of Threat Agents: A Review Of Several Promising Laser-Based Techniques, J. Bruce Johnson, Susan D. Allen, Jonathan Merten, Lewis Johnson, Daniel Pinkham, Scott W. Reeve Jan 2014

Standoff Methods For The Detection Of Threat Agents: A Review Of Several Promising Laser-Based Techniques, J. Bruce Johnson, Susan D. Allen, Jonathan Merten, Lewis Johnson, Daniel Pinkham, Scott W. Reeve

Publications

Detection of explosives, explosive precursors, or other threat agents presents a number of technological challenges for optical sensing methods. Certainly detecting trace levels of threat agents against a complex background is chief among these challenges; however, the related issues of multiple target distances (from standoff to proximity) and sampling time scales (from passive mines to rapid rate of march convoy protection) for different applications make it unlikely that a single technique will be ideal for all sensing situations. A number of methods for spanning the range of optical sensor technologies exist which, when integrated, could produce a fused sensor system …


Differential Spectral Imaging Of The Cn Violet Band In Laser-Induced Plasmas On Tnt Simulant Molecules, J. Merten, M. Jones, S. Hoke, S. Allen Jan 2014

Differential Spectral Imaging Of The Cn Violet Band In Laser-Induced Plasmas On Tnt Simulant Molecules, J. Merten, M. Jones, S. Hoke, S. Allen

Publications

Dual channel emission imaging of m-nitrobenzoic acid and benzoic acid was performed in order to visualize the morphology of the CN violet band emission of a TNT analogue. The CN channel was corrected for continuum emission using a simultaneously imaged background channel. Simultaneous dual channel imaging alleviated problems with shot to shot variation in the plasma morphology due to the friable substrates and showed differences between plasmas formed on the two targets.


The 6th Mode Of Transportation, Robert O. Walton Jan 2014

The 6th Mode Of Transportation, Robert O. Walton

Publications

The five modes of freight transportation are normally characterized as motor carriers, railroads, airlines, water carriers, and pipelines. This paper will attempt to position the Internet as the sixth mode of transportation. This paper compares the strengths and weaknesses of the traditional five modes of transportation against the proposed 6th mode of the Internet. Without including the Internet as a mode of transportation, and tracking the economic value that it adds to the economy, the economic impact of the Internet as a mode is not considered. The recommendation of this study is that the Internet should be added to the …


Biofuel From Microalgae – A Review On The Current Status And Future Trends, Rajee Olaganathan, May Zaw Htet, Lim Yan Ling, Sek Hui Yun Aug 2013

Biofuel From Microalgae – A Review On The Current Status And Future Trends, Rajee Olaganathan, May Zaw Htet, Lim Yan Ling, Sek Hui Yun

Publications

The constant reliance on fossil fuel energy resources is unsustainable, due to both depleting world reserves and increasing green house gas emissions associated with their use and thus there are dynamic research at the global level envisioned at developing alternative renewable and potentially carbon neutral solid, liquid and gaseous biofuels as alternative energy resources. The contemporary knowledge and technology predictions have proved that among the third generation biofuels especially those derived from microalgae are considered the best reasonable alternative energy resource compared to undeniable drawbacks of first and second generation biofuels. Moreover, its efficiency to sequester carbon from the atmosphere …


Linear Model Estimation Of Nonlinear Systems Using Least-Squares Algorithm5, Alireza Rahrooh, Walter W. Buchanan, Remzi Seker Jun 2013

Linear Model Estimation Of Nonlinear Systems Using Least-Squares Algorithm5, Alireza Rahrooh, Walter W. Buchanan, Remzi Seker

Publications

This paper presents utilizes Least-Squares Algorithm to obtain more accurate linear models of nonlinear systems using parameter estimation. This approach generates an optimal linear model which is valid over a wide range of trajectories and converges to the desired steady-state value with no errors unlike the existing techniques. The proposed technique is very efficient and does not require storing the data. Therefore, it can easily be used and implemented with limited resources for undergraduate curriculum especially in underdeveloped countries. Most available techniques for linearization of nonlinear system are only valid about the operating point; furthermore, the knowledge of the operating …


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 macromotion …


Modelling And Hazard Analysis For Contaminated Sediments Using Stamp Model And Stpa Tool, Karim Hardy, Franck Guarnieri Mar 2013

Modelling And Hazard Analysis For Contaminated Sediments Using Stamp Model And Stpa Tool, Karim Hardy, Franck Guarnieri

Publications

The goal of this article is dual: first, introducing a new model of accident named STAMP (systems-theoretic accident modeling and processes); then applying the model to an innovative process for the treatment of contaminated substances and the re-use of treated substances. This article is a demonstration for a need of a new tool to take into account hazards and safety within socio-technical systems.


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 towards …


Heteroclinic And Homoclinic Connections Between The Sun-Earth Triangular Points And Quasi-Satellite Orbits For Solar Observations, Pedro J. Llanos, Gerald R. Hintz, Martin W. Lo, James K. Miller Jan 2013

Heteroclinic And Homoclinic Connections Between The Sun-Earth Triangular Points And Quasi-Satellite Orbits For Solar Observations, Pedro J. Llanos, Gerald R. Hintz, Martin W. Lo, James K. Miller

Publications

Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L4 and L5 and the collinear point L3 of the CRTBP (circular restricted three-body problem) in the Sun-Earth system. These trajectories could serve as channels through where material can be transported from L5 to L3 by performing small maneuvers at the departure of the Trojan orbit. …


Payload Charging Events In The Mesosphere And Their Impact On Langmuir Type Electric Probes, T. A. Bekkeng, Aroh Barjatya, U. P. Hoppe, M. Friedrich Jan 2013

Payload Charging Events In The Mesosphere And Their Impact On Langmuir Type Electric Probes, T. A. Bekkeng, Aroh Barjatya, U. P. Hoppe, M. Friedrich

Publications

Three sounding rockets were launched from Andøya Rocket Range in the ECOMA campaign in December 2010. The aim was to study the evolution of meteoric smoke particles during a major meteor shower. Of the various instruments onboard the rocket payload, this paper presents the data from a multi-Needle Langmuir Probe (m-NLP) and a charged dust detector. The payload floating potential, as observed using the m-NLP instrument, shows charging events on two of the three flights. These charging events cannot be explained using a simple charging model, and have implications towards the use of fixed bias Langmuir probes on sounding rockets …


The Influence Of Automation On Aviation Accident And Fatality Rates: 2000-2010, Nicholas A. Koeppen Jul 2012

The Influence Of Automation On Aviation Accident And Fatality Rates: 2000-2010, Nicholas A. Koeppen

Publications

The purpose of this project is to evaluate if technological advances and implementation of automation have produced a decrease in the number and severity of accidents in commercial aviation over the last decade. To accomplish this evaluation historical commercial aviation accident data from 2000 to 2010 will be examined. Commercial fixed wing and rotary wing data will be evaluated. No aviation incident data will be collected; the project will be limited in scope to commercial aviation accidents. Accidents highlighting major deficiencies involving automation will be discussed in detail. To further support the projects purpose, emphasis will be given to evaluate …


Asteroid Retrieval Feasibility Study, John Brophy, Fred Culick, Louis Friedman, Pedro Llanos, Et Al. Apr 2012

Asteroid Retrieval Feasibility Study, John Brophy, Fred Culick, Louis Friedman, Pedro Llanos, Et Al.

Publications

This report describes the results of a study sponsored by the Keck Institute for Space Studies (KISS) to investigate the feasibility of identifying, robotically capturing, and returning an entire Near-Earth Asteroid (NEA) to the vicinity of the Earth by the middle of the next decade. The KISS study was performed by people from Ames Research Center, Glenn Research Center, Goddard Space Flight Center, Jet Propulsion Laboratory, Johnson Space Center, Langley Research Center, the California Institute of Technology, Carnegie Mellon, Harvard University, the Naval Postgraduate School, University of California at Los Angeles, University of California at Santa Cruz, University of Southern …


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.