Elastodynamics of Inorganic and Polymer Sculptured Thin Films

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Elastodynamics of Inorganic and Polymer Sculptured Thin Films Akhlesh Lakhtakia Nano. MM –– Nanoengineered

Elastodynamics of Inorganic and Polymer Sculptured Thin Films Akhlesh Lakhtakia Nano. MM –– Nanoengineered Metamaterials Group Department of Engineering Science and Mechanics Pennsylvania State University 7 th Iberian Vacuum Meeting 5 th European Topical Conference on Hard Coatings Caparica, Portugal June 25, 2008

Elastodynamics of Inorganic and Polymer Sculptured Thin Films Akhlesh Lakhtakia Nano. MM –– Nanoengineered

Elastodynamics of Inorganic and Polymer Sculptured Thin Films Akhlesh Lakhtakia Nano. MM –– Nanoengineered Metamaterials Group Department of Engineering Science and Mechanics Pennsylvania State University 7 th Iberian Vacuum Meeting 5 th European Topical Conference on Hard Coatings Caparica, Portugal June 25, 2008

 • Nanotechnology • Metamaterials • Sculptured Thin Films

• Nanotechnology • Metamaterials • Sculptured Thin Films

 • Nanotechnology

• Nanotechnology

A. Lakhtakia Nanotechnology: The term Norio Tanaguchi (1974): ‘Nano-technology’ mainly consists of the processing

A. Lakhtakia Nanotechnology: The term Norio Tanaguchi (1974): ‘Nano-technology’ mainly consists of the processing of separation, consolidation, and deformation of materials by one atom or one molecule. N. Taniguchi, On the Basic Concept of 'Nano-Technology', Proc. Intl. Conf. Prod. Eng. Tokyo, Part II, Japan Society of Precision Engineering, 1974.

A. Lakhtakia Nanotechnology: The term US Patents and Trademarks Office (2006): “Nanotechnology is related

A. Lakhtakia Nanotechnology: The term US Patents and Trademarks Office (2006): “Nanotechnology is related to research and technology development at the atomic, molecular or macromolecular levels, in the length of scale of approximately 1 -100 nanometer range in at least one dimension; that provide a fundamental understanding of phenomena and materials at the nanoscale; and to create and use structures, devices and systems that have novel properties and functions because of their small and/or intermediate size. ”

A. Lakhtakia Nanotech Economy Total worldwide R&D funding = Governments (2005): Established Corporations (2005):

A. Lakhtakia Nanotech Economy Total worldwide R&D funding = Governments (2005): Established Corporations (2005): Venture Capitalists (2005): $0. 5 B Source: Lux Research, The Nanotech Report, 4 th Ed. (2006). $ 9. 6 B in 2005 $4. 6 B $4. 5 B

A. Lakhtakia Nanotech Economy: Scope Source: Meridian Institute, Nanotechnology and the Poor: Opportunities and

A. Lakhtakia Nanotech Economy: Scope Source: Meridian Institute, Nanotechnology and the Poor: Opportunities and Risk (2005)

A. Lakhtakia Nanotechnology promises to be • pervasive • ubiquitous

A. Lakhtakia Nanotechnology promises to be • pervasive • ubiquitous

A. Lakhtakia Source: Nanotechnology & Life

A. Lakhtakia Source: Nanotechnology & Life

A. Lakhtakia Nanotechnologies?

A. Lakhtakia Nanotechnologies?

 • Metamaterials

• Metamaterials

A. Lakhtakia Engineers and Composite Materials

A. Lakhtakia Engineers and Composite Materials

A. Lakhtakia Evolution of Materials Research • Material Properties (< ca. 1970) • Design

A. Lakhtakia Evolution of Materials Research • Material Properties (< ca. 1970) • Design for Functionality (ca. 1980) • Design for System Performance (ca. 2000)

A. Lakhtakia Evolution of Materials Research • Material Properties (< ca. 1970) • Design

A. Lakhtakia Evolution of Materials Research • Material Properties (< ca. 1970) • Design for Functionality (ca. 1980) • Design for System Performance (ca. 2000)

A. Lakhtakia Evolution of Materials Research • Material Properties (< ca. 1970) • Design

A. Lakhtakia Evolution of Materials Research • Material Properties (< ca. 1970) • Design for Functionality (ca. 1980) • Design for System Performance (ca. 2000)

A. Lakhtakia Multifunctionality

A. Lakhtakia Multifunctionality

Multifunctionality A. Lakhtakia

Multifunctionality A. Lakhtakia

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. Light weight (for fuel efficiency)

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. Light weight (for fuel efficiency) 2. High stiffness (resistance to deformation) 3. High strength (resistance to rupture)

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. Light weight (for fuel efficiency)

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. Light weight (for fuel efficiency) 2. High stiffness (resistance to deformation) 3. High strength (resistance to rupture) 4. High acoustic damping (quieter cabin) 5. Low thermal conductivity (less condensation; 6. more humid cabin)

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. Light weight (for fuel efficiency)

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. Light weight (for fuel efficiency) 2. High stiffness (resistance to deformation) 3. High strength (resistance to rupture) 4. High acoustic damping (quieter cabin) 5. Low thermal conductivity (less condensation; 6. more humid cabin)

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. 2. 3. 4. 5. Light

Multifunctionality A. Lakhtakia Performance Requirements on the Fuselage 1. 2. 3. 4. 5. Light weight (for fuel efficiency) High stiffness (resistance to deformation) High strength (resistance to rupture) High acoustic damping (quieter cabin) Low thermal conductivity (less condensation; more humid cabin) Future: Conducting & other fibers for (i) reinforcement (ii) antennas (iii) environmental sensing (iv) structural health monitoring (iv) morphing

A. Lakhtakia Metamaterials Rodger Walser SPIE Press (2003)

A. Lakhtakia Metamaterials Rodger Walser SPIE Press (2003)

A. Lakhtakia Walser’s Definition (2001/2) • macroscopic composites having a manmade, three-dimensional, periodic cellular

A. Lakhtakia Walser’s Definition (2001/2) • macroscopic composites having a manmade, three-dimensional, periodic cellular architecture designed to produce an optimized combination, not available in nature, of two or more responses to specific excitation

A. Lakhtakia “Updated” Definition composites designed to produce an optimized combination of two or

A. Lakhtakia “Updated” Definition composites designed to produce an optimized combination of two or more responses to specific excitation

Cellularity

Cellularity

Nanoengineered Metamaterials A. Lakhtakia Cellularity Multifunctionality

Nanoengineered Metamaterials A. Lakhtakia Cellularity Multifunctionality

Nanoengineered Metamaterials A. Lakhtakia Cellularity Multifunctionality Morphology Performance

Nanoengineered Metamaterials A. Lakhtakia Cellularity Multifunctionality Morphology Performance

Nanoengineered Metamaterials A. Lakhtakia Multi-component system = Assembly of different components Component: Simple action

Nanoengineered Metamaterials A. Lakhtakia Multi-component system = Assembly of different components Component: Simple action Assembly of components: Complex action

Nanoengineered Metamaterials A. Lakhtakia Energy harvesting cell Energy storage cell Chemisensor cell Force-sensor cell

Nanoengineered Metamaterials A. Lakhtakia Energy harvesting cell Energy storage cell Chemisensor cell Force-sensor cell Energy distributor cell RFcomm cell IRcomm cell Shape-changer cell Light-source cell

Nanoengineered Metamaterials A. Lakhtakia Supercell

Nanoengineered Metamaterials A. Lakhtakia Supercell

Nanoengineered Metamaterials A. Lakhtakia Periodic Arrangement of Supercells Fractal Arrangement of Supercells Functionally Graded

Nanoengineered Metamaterials A. Lakhtakia Periodic Arrangement of Supercells Fractal Arrangement of Supercells Functionally Graded Arrangement of Supercells

Nanoengineered Metamaterials A. Lakhtakia Biomimesis

Nanoengineered Metamaterials A. Lakhtakia Biomimesis

Nanoengineered Metamaterials A. Lakhtakia Biomimesis

Nanoengineered Metamaterials A. Lakhtakia Biomimesis

Nanoengineered Metamaterials A. Lakhtakia Fabrication 1. Self-assembly 2. Positional assembly 3. Lithography 4. Etching

Nanoengineered Metamaterials A. Lakhtakia Fabrication 1. Self-assembly 2. Positional assembly 3. Lithography 4. Etching 5. Ink-jet printing 6. …. 7. …. 8. Hybrid techniques

Nanoengineered Metamaterials A. Lakhtakia Fabrication 1. Self-assembly 2. Positional assembly 3. Lithography 4. Etching

Nanoengineered Metamaterials A. Lakhtakia Fabrication 1. Self-assembly 2. Positional assembly 3. Lithography 4. Etching 5. Ink-jet printing 6. …. 7. …. 8. Hybrid techniques

 • Sculptured Thin Films

• Sculptured Thin Films

A. Lakhtakia Sculptured Thin Films Assemblies of Parallel Curved Nanowires/Submicronwires Controllable Nanowire Shape

A. Lakhtakia Sculptured Thin Films Assemblies of Parallel Curved Nanowires/Submicronwires Controllable Nanowire Shape

A. Lakhtakia Sculptured Thin Films Assemblies of Parallel Curved Nanowires/Submicronwires Controllable Nanowire Shape

A. Lakhtakia Sculptured Thin Films Assemblies of Parallel Curved Nanowires/Submicronwires Controllable Nanowire Shape

A. Lakhtakia Sculptured Thin Films Morphological Change

A. Lakhtakia Sculptured Thin Films Morphological Change

A. Lakhtakia Sculptured Thin Films Assemblies of Parallel Curved Nanowires/Submicronwires Controllable Nanowire Shape 2

A. Lakhtakia Sculptured Thin Films Assemblies of Parallel Curved Nanowires/Submicronwires Controllable Nanowire Shape 2 -D morphologies 3 -D morphologies vertical sectioning Nanoengineered Materials (1 -3 nm clusters) Controllable Porosity (10 -90 %)

A. Lakhtakia Sculptured Thin Films Antecedents: (i) Young and Kowal - 1959 (ii) Niuewenhuizen

A. Lakhtakia Sculptured Thin Films Antecedents: (i) Young and Kowal - 1959 (ii) Niuewenhuizen & Haanstra - 1966 (iii) Motohiro & Taga - 1989 Conceptualized by Lakhtakia & Messier (1992 -1995) Optical applications (1992 -1995) Biological applications (2003 -)

A. Lakhtakia Sculptured Thin Films Research Groups (i) (iii) (iv) (vi) (viii) (ix) (xi)

A. Lakhtakia Sculptured Thin Films Research Groups (i) (iii) (iv) (vi) (viii) (ix) (xi) (xiii) (xiv) (xvi) Imperial College, London Penn State (xvii) University of Glasgow Edinboro University of Pennsylvania (xviii)University of Edinburgh Lock Haven University of Pennsylvania (xix)University of Leipzig Millersville University (xx) ENSMM, Besançon Rensselaer Polytechnic University (xxi) Toyota R&D Labs University of Arkansaa, Little Rock (xxii) Kyoto University of Toledo (xxiii) Hanyang University of Georgia (xxiv) University of Otago University of South Carolina (xxv) University of Canterbury University of Nebraska at Lincoln (xxvi) Ben Gurion University of the Pacific Northwest National Laboratory Negev University of Alberta (xxvii) University of Campinas Queen’s University of Moncton National Autonomous University of Mexico

A. Lakhtakia Physical Vapor Deposition

A. Lakhtakia Physical Vapor Deposition

A. Lakhtakia Physical Vapor Deposition (Columnar Thin Films)

A. Lakhtakia Physical Vapor Deposition (Columnar Thin Films)

A. Lakhtakia Physical Vapor Deposition (Sculptured Thin Films) Rotate about y axis for nematic

A. Lakhtakia Physical Vapor Deposition (Sculptured Thin Films) Rotate about y axis for nematic morphology Rotate about z axis for helicoidal morphology Combined rotations for complex morphologies

A. Lakhtakia Sculptured Thin Films Optical Devices: Polarization Filters Bragg Filters Ultranarrowband Filters Fluid

A. Lakhtakia Sculptured Thin Films Optical Devices: Polarization Filters Bragg Filters Ultranarrowband Filters Fluid Concentration Sensors Bacterial Sensors Biomedical Applications: Tissue Scaffolds Surgical Cover Sheets Other Applications: Photocatalysis (Toyota) Thermal Barriers (Alberta) Energy Harvesting (Penn State, Toledo)

A. Lakhtakia Optics of Chiral STFs

A. Lakhtakia Optics of Chiral STFs

Chiral STFs: Circular Bragg Phenomenon

Chiral STFs: Circular Bragg Phenomenon

A. Lakhtakia Chiral STF as CP Filter

A. Lakhtakia Chiral STF as CP Filter

A. Lakhtakia Spectral Hole Filter

A. Lakhtakia Spectral Hole Filter

A. Lakhtakia Fluid Concentration Sensor

A. Lakhtakia Fluid Concentration Sensor

A. Lakhtakia Optical Modeling of STFs Dielectric Materials

A. Lakhtakia Optical Modeling of STFs Dielectric Materials

A. Lakhtakia Optical Modeling of STFs Locally Orthorhombic Continuums

A. Lakhtakia Optical Modeling of STFs Locally Orthorhombic Continuums

A. Lakhtakia Optical Modeling of STFs Homogenize a collection of parallel ellipsoids to get

A. Lakhtakia Optical Modeling of STFs Homogenize a collection of parallel ellipsoids to get Sherwin and Lakhtakia (2001 -2003): Bruggeman formalism Mathematica Program

A. Lakhtakia Optical Modeling of STFs Wave Propagation Mathematica Program

A. Lakhtakia Optical Modeling of STFs Wave Propagation Mathematica Program

A. Lakhtakia LIGHT EMITTERS • Luminophores inserted in a chiral STF • Co- and

A. Lakhtakia LIGHT EMITTERS • Luminophores inserted in a chiral STF • Co- and contra-wound photonic source filaments • Calculations using Maxwell equations - volume fraction of filaments - wavelength - co/contra-wound

A. Lakhtakia LIGHT EMITTERS • Co/contra-wound: Clear differences in (i) polarization state (ii) emission

A. Lakhtakia LIGHT EMITTERS • Co/contra-wound: Clear differences in (i) polarization state (ii) emission bandwidth • Dependence on tilt angle Lakhtakia, Microw. Opt. Technol. Lett. 37, 37 (2003)

A. Lakhtakia LIGHT EMITTERS • Quantum dots inserted in a cavity between two left-handed

A. Lakhtakia LIGHT EMITTERS • Quantum dots inserted in a cavity between two left-handed chiral STFs Zhang et al. , Appl. Phys. Lett. 91, 023102 (2007).

A. Lakhtakia LIGHT EMITTERS • Quantum dots inserted in a cavity between two left-handed

A. Lakhtakia LIGHT EMITTERS • Quantum dots inserted in a cavity between two left-handed chiral STFs LCP Emission Peak Spectral Hole

A. Lakhtakia Polymeric STFs

A. Lakhtakia Polymeric STFs

A. Lakhtakia PARYLENE-C STFs: COMBINED CVD+PVD TECHNIQUE Pursel et al. , Polymer 46, 9544

A. Lakhtakia PARYLENE-C STFs: COMBINED CVD+PVD TECHNIQUE Pursel et al. , Polymer 46, 9544 (2005)

A. Lakhtakia PARYLENE-C STFs: COMBINED CVD+PVD TECHNIQUE 1. Vaporize the dimer at 150 deg

A. Lakhtakia PARYLENE-C STFs: COMBINED CVD+PVD TECHNIQUE 1. Vaporize the dimer at 150 deg C 2. Monomerize at 680 deg C and 0. 5 Torr 3. Release the monomer vapor through a nozzle towards a substrate 4. Polymerization into STFs

A. Lakhtakia PARYLENE-C STFs: COMBINED CVD+PVD TECHNIQUE Nanoscale Morphology Ciliary Structure

A. Lakhtakia PARYLENE-C STFs: COMBINED CVD+PVD TECHNIQUE Nanoscale Morphology Ciliary Structure

A. Lakhtakia BIOSCAFFOLDS

A. Lakhtakia BIOSCAFFOLDS

A. Lakhtakia BIOSCAFFOLDS Lakhtakia et al. , Adv. Solid State Phys. 46, 295 (2008).

A. Lakhtakia BIOSCAFFOLDS Lakhtakia et al. , Adv. Solid State Phys. 46, 295 (2008).

A. Lakhtakia • • • Applications of Parylene STFs Cell-culture substrates Coatings for prostheses

A. Lakhtakia • • • Applications of Parylene STFs Cell-culture substrates Coatings for prostheses (e. g. stents) Coatings for surgical equipment (e. g. , catheters) Biosensors Tissue engineering for controlled drug release Volumetric functionalization Optical monitoring

A. Lakhtakia STFs WITH TRANSVERSE ARCHITECTURE

A. Lakhtakia STFs WITH TRANSVERSE ARCHITECTURE

A. Lakhtakia STFs WITH TRANSVERSE ARCHITECTURE Metal STFs on Topographic Substrates Chromium Aluminum Molybdenum

A. Lakhtakia STFs WITH TRANSVERSE ARCHITECTURE Metal STFs on Topographic Substrates Chromium Aluminum Molybdenum Horn et al. , Nanotechnology 15, 303 (2004).

A. Lakhtakia STFs WITH TRANSVERSE ARCHITECTURE Dielectric STFs on Topographic HCP array of Si.

A. Lakhtakia STFs WITH TRANSVERSE ARCHITECTURE Dielectric STFs on Topographic HCP array of Si. Ox nanocolumns. Substrates BCC array of Si. Ox nanocolumns 1 um x 1 um mesh of Si. Ox nanolines

A. Lakhtakia MECHANICAL CHARACTERISTICS

A. Lakhtakia MECHANICAL CHARACTERISTICS

MECHANICAL CHARACTERISTICS A. Lakhtakia 1. Structural Integrity 2. Mechanical Tuning of Optical Properties Pressure

MECHANICAL CHARACTERISTICS A. Lakhtakia 1. Structural Integrity 2. Mechanical Tuning of Optical Properties Pressure Sensors Temperature Sensors 3. Acoustic Devices Shear Wave Filters

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Si. O Chiral STFs Seto et al. ,

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Si. O Chiral STFs Seto et al. , J. Vacuum Sci. Technol. B 17, 2172 (1999)

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Si. O Chiral STFs Simple Theory: Chiral STF

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Si. O Chiral STFs Simple Theory: Chiral STF is a bed of parallel (macroscopic) springs Seto et al. , J. Vacuum Sci. Technol. B 17, 2172 (1999)

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Si. O Chiral STFs s l i a

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Si. O Chiral STFs s l i a F Simple Theory: Chiral STF is a bed of parallel (macroscopic) springs e l p m i S y r o e h T Seto et al. , J. Vacuum Sci. Technol. B 17, 2172 (1999)

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Chromium Zigzag STFs Simple Theory: STF is a

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Chromium Zigzag STFs Simple Theory: STF is a bed of parallel (macroscopic) springs Better continuum model of each spring. Lintymer et al. , Thin Solid Films 503, 177 (2006)

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Chromium Zigzag STFs Simple Theory: STF is a

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Chromium Zigzag STFs Simple Theory: STF is a bed of parallel (macroscopic) springs Better continuum model of each spring. Experimental Models Lintymer et al. , Thin Solid Films 503, 177 (2006)

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Chromium Zigzag STFs Simple Theory: STF is a

STRUCTURAL INTEGRITY A. Lakhtakia Nanoindentation of Chromium Zigzag STFs Simple Theory: STF is a bed of parallel (macroscopic) springs Better continuum model of each spring. Experimental Models Lintymer et al. , Thin Solid Films 503, 177 (2006)

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia Chiral STF is a circular-polarization Bragg filter

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia Chiral STF is a circular-polarization Bragg filter Center wavelength ~ Period x Effective RI FWHM ~ Period x Linear Birefringence Wang et al. , J. Modern Opt. 50, 239 (2003)

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia Chiral STF is a circular-polarization Bragg filter

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia Chiral STF is a circular-polarization Bragg filter Center wavelength ~ Period x Effective RI FWHM ~ Period x Linear Birefringence Wang et al. , J. Modern Opt. 50, 239 (2003)

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia Shift of center wavelength ~ DC Voltage

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia Shift of center wavelength ~ DC Voltage Wang et al. , J. Modern Opt. 50, 239 (2003)

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia FWHM does not change Wang et al.

MECHANICAL TUNABILITY OF OPTICAL FILTERS A. Lakhtakia FWHM does not change Wang et al. , J. Modern Opt. 50, 239 (2003)

MECHANICAL TUNABILITY OF LIGHT-EMITTERS A. Lakhtakia Dye-doped polymer chiral STF Light-emitters Wang et al.

MECHANICAL TUNABILITY OF LIGHT-EMITTERS A. Lakhtakia Dye-doped polymer chiral STF Light-emitters Wang et al. , Sens. Actuat. A 102, 31 (2002)

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Hooke’s Law Kelvin notation Compliance

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Hooke’s Law Kelvin notation Compliance Lakhtakia, J. Compos. Mater. 36, 1277 (2002)

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Hooke’s Law Kelvin notation Compliance

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Hooke’s Law Kelvin notation Compliance Lakhtakia, J. Compos. Mater. 36, 1277 (2002)

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Compliance Lakhtakia, J. Compos. Mater.

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Compliance Lakhtakia, J. Compos. Mater. 36, 1277 (2002)

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Compliance Homogenize a collection of

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Compliance Homogenize a collection of parallel ellipsoids to get Lakhtakia, J. Compos. Mater. 36, 1277 (2002)

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Compliance Homogenize a collection of

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Compliance Homogenize a collection of parallel ellipsoids to get Lakhtakia, J. Compos. Mater. 36, 1277 (2002) Mori-Tanaka formalism

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Solve Navier’s equation

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Solve Navier’s equation

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Solve Navier’s equation

A. Lakhtakia LINEAR ELASTODYNAMIC MODEL Of a CHIRAL STF Solve Navier’s equation

 • Nanotechnology • Metamaterials • Sculptured Thin Films

• Nanotechnology • Metamaterials • Sculptured Thin Films

A. Lakhtakia

A. Lakhtakia