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Full-Text Articles in Mechanical Engineering

A Computational Investigation Of Wood Selection For Acoustic Guitar, Jonah Osterhus May 2024

A Computational Investigation Of Wood Selection For Acoustic Guitar, Jonah Osterhus

Senior Honors Theses

The acoustic guitar is a stringed instrument, often made of wood, that transduces vibrational energy of steel strings into coupled vibrations of the wood and acoustic pressure waves in the air. Variations in wood selection and instrument geometry have been shown to affect the timbre of the acoustic guitar. Computational methods were utilized to investigate the impact of material properties on acoustic performance. Sitka spruce was deemed the most suitable wood for guitar soundboards due to its acoustic characteristics, strength, and uniform aesthetic. Mahogany was deemed to be the best wood for the back and sides of the guitar body …


Characterization Of Interlayer Laser Shock Peening During Fused Filament Fabrication Of Polylactic Acid (Pla), Fabien Denise Dec 2023

Characterization Of Interlayer Laser Shock Peening During Fused Filament Fabrication Of Polylactic Acid (Pla), Fabien Denise

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

The field of additive manufacturing (AM) has gained a significant amount of popularity due to the increasing need for more sustainable manufacturing techniques and the adaptive development of complex product geometries. The problem is that AM parts routinely exhibit flaws or weaknesses that affect functionality or performance. Over the years, surface treatments have been developed to compensate certain flaws or weaknesses in manufactured products. Combining surface treatments with the modularity of additive manufacturing could lead to more adaptable and creative improvements of product functions in the future. The current work evaluates the feasibility of pursuing a new research axis in …


Impact Of Silicon Ion Irradiation On Aluminum Nitride-Transduced Microelectromechanical Resonators, David D. Lynes, Joshua Young, Eric Lang, Hengky Chandrahalim Nov 2023

Impact Of Silicon Ion Irradiation On Aluminum Nitride-Transduced Microelectromechanical Resonators, David D. Lynes, Joshua Young, Eric Lang, Hengky Chandrahalim

Faculty Publications

Microelectromechanical systems (MEMS) resonators use is widespread, from electronic filters and oscillators to physical sensors such as accelerometers and gyroscopes. These devices' ubiquity, small size, and low power consumption make them ideal for use in systems such as CubeSats, micro aerial vehicles, autonomous underwater vehicles, and micro-robots operating in radiation environments. Radiation's interaction with materials manifests as atomic displacement and ionization, resulting in mechanical and electronic property changes, photocurrents, and charge buildup. This study examines silicon (Si) ion irradiation's interaction with piezoelectrically transduced MEMS resonators. Furthermore, the effect of adding a dielectric silicon oxide (SiO2) thin film is …


Trumpet Directivity From A Rotating Semicircular Array, Samuel D. Bellows, Joseph E. Avila, Timothy W. Leishman Sep 2023

Trumpet Directivity From A Rotating Semicircular Array, Samuel D. Bellows, Joseph E. Avila, Timothy W. Leishman

Directivity

The directivity function of a played musical instrument describes the angular dependence of its acoustic radiation and diffraction about the instrument, musician, and musician’s chair. Directivity influences sound in rehearsal, performance, and recording environments and signals in audio systems. Because high-resolution, spherically comprehensive measurements of played musical instruments have been unavailable in the past, the authors have undertaken research to produce and share such data for studies of musical instruments, simulations of acoustical environments, optimizations of microphone placements, and other applications. The authors acquired the data from repeated chromatic scales produced by a trumpet played at mezzo-forte in an anechoic …


Gamelan Gong Directivity Dataset, Samuel D. Bellows, Dallin T. Harwood, Kent L. Gee, Micah R. Shepherd Jan 2023

Gamelan Gong Directivity Dataset, Samuel D. Bellows, Dallin T. Harwood, Kent L. Gee, Micah R. Shepherd

Directivity

No abstract provided.


Kemar Hats Head Orientation Directivity, Samuel D. Bellows, Timothy W. Leishman Mar 2022

Kemar Hats Head Orientation Directivity, Samuel D. Bellows, Timothy W. Leishman

Directivity

This directivity data set for a KEMAR head head-and-torso simulator (HATS) includes head orientations in 14 directions in 5° steps starting from 0° to 40° and then in 10° steps from 40° to 90°. The full spherical measurements followed at an a = 0.97 m radius with the mouth aperture at the spherical center. The sampling density and distribution followed the AES 5° dual-equiangular sampling standard, omitting the south pole (θ = 180°). Thus, each spherical directivity assessment included 36 polar-angle θ samples and 72 azimuthal-angle ϕ samples. The presented data include 22 1/3-octave bands, ranging from 80 Hz …


Development And Characterization Of Nb₃N/Al₂0₃ Superconducting Multilayers For Particle Accelerators, Chris Sundahl, Junki Makita, Paul B. Welander, Yi-Feng Su, Fumitake Kametani, Lin Xie, Huimin Zhang, Lian Li, Alex Gurevich, Chang-Beom Eom Jan 2021

Development And Characterization Of Nb₃N/Al₂0₃ Superconducting Multilayers For Particle Accelerators, Chris Sundahl, Junki Makita, Paul B. Welander, Yi-Feng Su, Fumitake Kametani, Lin Xie, Huimin Zhang, Lian Li, Alex Gurevich, Chang-Beom Eom

Physics Faculty Publications

Superconducting radio-frequency (SRF) resonator cavities provide extremely high quality factors > 1010 at 1-2 GHz and 2 K in large linear accelerators of high-energy particles. The maximum accelerating field of SRF cavities is limited by penetration of vortices into the superconductor. Present state-of-the-art Nb cavities can withstand up to 50 MV/m accelerating gradients and magnetic fields of 200-240 mT which destroy the low-dissipative Meissner state. Achieving higher accelerating gradients requires superconductors with higher thermodynamic critical fields, of which Nb3Sn has emerged as a leading material for the next generation accelerators. To overcome the problem of low vortex penetration …


Average Speech Directivity, Samuel D. Bellows, Claire M. Pincock, Jennifer K. Whiting, Timothy W. Leishman Nov 2019

Average Speech Directivity, Samuel D. Bellows, Claire M. Pincock, Jennifer K. Whiting, Timothy W. Leishman

Directivity

Speech directivity describes the angular dependence of acoustic radiation from a talker’s mouth and nostrils and diffraction about his or her body and chair (if seated). It is an essential physical aspect of communication affecting sounds and signals in acoustical environments, audio, and telecommunication systems. Because high-resolution, spherically comprehensive measurements of live, phonetically balanced speech have been unavailable in the past, the authors have undertaken research to produce and share such data for simulations of acoustical environments, optimizations of microphone placements, speech studies, and other applications. The measurements included three male and three female talkers who repeated phonetically balanced passages …


Spin Response Function For Spin Transparency Mode Of Rhic, V. S. Morozov, P. Adams, Y. S. Derbenev, Y. Filatov, H. Huang, A. M. Kondratenko, M. A. Kondratenko, F. Lin, F. Méot, V. Ptitsyn, W. B. Schmidke, Y. Zhang Jan 2019

Spin Response Function For Spin Transparency Mode Of Rhic, V. S. Morozov, P. Adams, Y. S. Derbenev, Y. Filatov, H. Huang, A. M. Kondratenko, M. A. Kondratenko, F. Lin, F. Méot, V. Ptitsyn, W. B. Schmidke, Y. Zhang

Engineering Technology Faculty Publications

In the Spin Transparency (ST) mode of RHIC, the axes of its Siberian snakes are parallel. The spin tune in the ST mode is zero and the spin motion becomes degenerate: any spin direction repeats every particle turn. In contrast, the lattice of a conventional collider determines a unique stable periodic spin direction, so that the collider operates in the Preferred Spin (PS) mode. Contributions of perturbing magnetic fields to the spin resonance strengths in the PS mode are usually calculated using the spin response function. However, in that form, it is not applicable in the ST mode. This paper …


Investigation Of Toppling Ball Flight In American Football With A Mechanical Field-Goal Kicker, Chase M Pfeifer, Timothy J. Gay, Jeff A. Hawks, Shane Farritor, Judith M. Burnfield Jan 2018

Investigation Of Toppling Ball Flight In American Football With A Mechanical Field-Goal Kicker, Chase M Pfeifer, Timothy J. Gay, Jeff A. Hawks, Shane Farritor, Judith M. Burnfield

Department of Mechanical and Materials Engineering: Faculty Publications

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded …


Resilient And Real-Time Control For The Optimum Management Of Hybrid Energy Storage Systems With Distributed Dynamic Demands, Christopher R. Lashway Oct 2017

Resilient And Real-Time Control For The Optimum Management Of Hybrid Energy Storage Systems With Distributed Dynamic Demands, Christopher R. Lashway

FIU Electronic Theses and Dissertations

A continuous increase in demands from the utility grid and traction applications have steered public attention toward the integration of energy storage (ES) and hybrid ES (HESS) solutions. Modern technologies are no longer limited to batteries, but can include supercapacitors (SC) and flywheel electromechanical ES well. However, insufficient control and algorithms to monitor these devices can result in a wide range of operational issues. A modern day control platform must have a deep understanding of the source. In this dissertation, specialized modular Energy Storage Management Controllers (ESMC) were developed to interface with a variety of ES devices. The EMSC provides …


Formation Of Mound-Like Multiscale Surface Structures On Titanium By Femtosecond Laser Processing, Edwin Peng, Alfred Tsubaki, Craig A. Zuhlke, Ryan Bell, Meiyu Wang, Dennis R. Alexander, George Gogos, Jeffrey E. Shield Mar 2017

Formation Of Mound-Like Multiscale Surface Structures On Titanium By Femtosecond Laser Processing, Edwin Peng, Alfred Tsubaki, Craig A. Zuhlke, Ryan Bell, Meiyu Wang, Dennis R. Alexander, George Gogos, Jeffrey E. Shield

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Surface Functionalization Technique • Femtosecond Laser Surface Processing (FLSP) • Utilize high power, femtosecond (10-15 s) laser pulses • Produce self-organized, multiscale surface micro/nanostructures • Diverse range of applicable substrates: semiconductors, metals, polymers, & composites

Why? • What are the different types of FLSP structures on Ti? • Physical evidence needed for FLSP formation models • Optimize FLSP of Ti for biomedical & other applications

How? • Obtain evidence of mound growth processes by examining underlying microstructure • Utilize dual beam Scanning Electron Microscope-Focused Ion Beam instrument to cross section surface structures & fabricate transmission electron microscopy samples


Available Work Rate Of A Reversible System Bounded By Constant Thermal Resistances Linked To Isothermal Reservoirs, Jim Mcgovern May 2015

Available Work Rate Of A Reversible System Bounded By Constant Thermal Resistances Linked To Isothermal Reservoirs, Jim Mcgovern

Conference Papers

Exergy analysis is based on the concept of an idealized, all-enclosing reference environment that has infinite heat capacity and thermal conductivity, and is in equilibrium. The actual surroundings of a real plant such as a heat engine, a heat pump or a refrigerator may differ significantly from the ideal. First law performance parameters and second law rational efficiency are examined. The concepts of finite time thermodynamics are applied in an attempt to refine the concept of T0, the environmental reference temperature, thereby making exergy analysis more reflective of reality.


Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr. May 2015

Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr.

Senior Honors Projects

Putting may appear to be the easiest but is actually the most technically challenging part of the game of golf. The ideal putting stroke will remain parallel to its desired trajectory both in the reverse and forward direction when the putter head is within six inches of the ball. Deviation from this concept will cause a cut or sidespin on the ball that will affect the path the ball will travel.

Club design plays a large part in how well a player will be able to achieve a straight back and straight through club head path near impact; specifically the …


Near-Infrared Surface-Enhanced Fluorescence Using Silver Nanoparticles In Solution, Michael D. Furtaw Dec 2013

Near-Infrared Surface-Enhanced Fluorescence Using Silver Nanoparticles In Solution, Michael D. Furtaw

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Fluorescence spectroscopy is a widely used detection technology in many research and clinical assays. Further improvement to assay sensitivity may enable earlier diagnosis of disease, novel biomarker discovery, and ultimately, improved outcomes of clinical care along with reduction in costs. Near-infrared, surface-enhanced fluorescence (NIR-SEF) is a promising approach to improve assay sensitivity via simultaneous increase in signal with a reduction in background. This dissertation describes research conducted with the overall goal to determine the extent to which fluorescence in solution may be enhanced by altering specific variables involved in the formation of plasmonactive nanostructures of dye-labeled protein and silver nanoparticles …


Universal Scaling And Intrinsic Classification Of Electro-Mechanical Actuators, Sambit Palit, Ankit Jain, Muhammad A. Alam Apr 2013

Universal Scaling And Intrinsic Classification Of Electro-Mechanical Actuators, Sambit Palit, Ankit Jain, Muhammad A. Alam

Birck and NCN Publications

Actuation characteristics of electromechanical (EM) actuators have traditionally been studied for a few specific regular electrode geometries and support (anchor) configurations. The ability to predict actuation characteristics of electrodes of arbitrary geometries and complex support configurations relevant for broad range of applications in switching, displays, and varactors, however, remains an open problem. In this article, we provide four universal scaling relationships for EM actuation characteristics that depend only on the mechanical support configuration and the corresponding electrode geometries, but are independent of the specific geometrical dimensions and material properties of these actuators. These scaling relationships offer an intrinsic classification for …


Propagation Of Ultrasound Through Freshly Excised Human Calvarium, Armando Garcia Noguera Jul 2012

Propagation Of Ultrasound Through Freshly Excised Human Calvarium, Armando Garcia Noguera

Department of Engineering Mechanics: Dissertations, Theses, and Student Research

The propagation of ultrasound through complex biological media, such as the human calvarium, poses a great challenge for modern medicine. Several ultrasonic techniques commonly used for treatment and diagnosis in most of the human body are still difficult to apply to the human brain, in part, because of the properties of the skull. Moreover, an understanding of the biomechanics of transcranial ultrasound may provide needed insight into the problem of blast wave induced traumatic brain injury (TBI). In the present study, the spatial variability of ultrasonic properties was evaluated for relevant frequencies of 0.5, 1, and 2.25 MHz. A total …


Quantifying Multiple Types Of Damping Acting On Bronze-Wound Guitar Strings, Jonathan Christian Jun 2011

Quantifying Multiple Types Of Damping Acting On Bronze-Wound Guitar Strings, Jonathan Christian

Purdue Polytechnic Masters Theses

The goal of this study was to quantify the contributions of multiple damping types acting on guitar strings for each mode over a wide frequency range so that design variables could be identified to one day create frequency based damping in guitar strings. Structural dynamic testing was used to obtain the time-response of a vibrating string in open air and in a vacuum. From this signal, each harmonic was filtered and the decay envelope was curve-fitted with a function that was a linear summation of decay functions. From the curve-fits, the damping coefficients for aerodynamic, friction, and material damping were …


Optical Cell For Combinatorial In Situ Raman Spectroscopic Measurements Of Hydrogen Storage Materials At High Pressures And Temperatures, Jason R. Hattrick-Simpers, Wilbur S. Hurst, Sesha S. Srinivasan, James E. Maslar Jan 2011

Optical Cell For Combinatorial In Situ Raman Spectroscopic Measurements Of Hydrogen Storage Materials At High Pressures And Temperatures, Jason R. Hattrick-Simpers, Wilbur S. Hurst, Sesha S. Srinivasan, James E. Maslar

Faculty Publications

An optical cell is described for high-throughput backscattering Raman spectroscopic measurements of hydrogen storagematerials at pressures up to 10 MPa and temperatures up to 823 K. High throughput is obtained by employing a 60 mm diameter × 9 mm thick sapphire window, with a corresponding 50 mm diameter unobstructed optical aperture. To reproducibly seal this relatively large window to the cell body at elevated temperatures and pressures, a gold o-ring is employed. The sample holder-to-window distance is adjustable, making this cell design compatible with optical measurement systems incorporating lenses of significantly different focal lengths, e.g., microscope objectives and single element …


Strain Energy And Lateral Friction Force Distributions Of Carbon Nanotubes Manipulated Into Shapes By Atomic Force Microscopy, Mark C. Strus, Roya R. Lahiji, Pablo Ares, Vincente Lopez, Arvind Raman, Ron R. Reifenberger Aug 2009

Strain Energy And Lateral Friction Force Distributions Of Carbon Nanotubes Manipulated Into Shapes By Atomic Force Microscopy, Mark C. Strus, Roya R. Lahiji, Pablo Ares, Vincente Lopez, Arvind Raman, Ron R. Reifenberger

Other Nanotechnology Publications

The interplay between local mechanical strain energy and lateral frictional forces determines the shape of carbon nanotubes on substrates. In turn, because of its nanometer-size diameter, the shape of a carbon nanotube strongly influences its local electronic, chemical, and mechanical properties. Few, if any, methods exist for resolving the strain energy and static frictional forces along the length of a deformed nanotube supported on a substrate. We present a method using nonlinear elastic rod theory in which we compute the flexural strain energy and static frictional forces along the length of single walled carbon nanotubes (SWCNTs) manipulated into various shapes …


Pressure-Driven Transport Of Particles Through A Converging-Diverging Microchannel, Ye Ai, Sang W. Joo, Yingtao Jiang, Xiangchun Xuan, Shizhi Qian Jun 2009

Pressure-Driven Transport Of Particles Through A Converging-Diverging Microchannel, Ye Ai, Sang W. Joo, Yingtao Jiang, Xiangchun Xuan, Shizhi Qian

Mechanical Engineering Faculty Research

Pressure-driven transport of particles through a symmetric converging-diverging microchannel is studied by solving a coupled nonlinear system, which is composed of the Navier–Stokes and continuity equations using the arbitrary Lagrangian–Eulerian finite-element technique. The predicted particle translation is in good agreement with existing experimental observations. The effects of pressure gradient, particle size, channel geometry, and a particle’s initial location on the particle transport are investigated. The pressure gradient has no effect on the ratio of the translational velocity of particles through a converging-diverging channel to that in the upstream straight channel. Particles are generally accelerated in the converging region and then …


Predicting The Hydrogen Pressure To Achieve Ultralow Friction And Diamondlike Carbon Surfaces From First Principles, Haibo Guo, Yue Qi, Xiaodong Li Jun 2008

Predicting The Hydrogen Pressure To Achieve Ultralow Friction And Diamondlike Carbon Surfaces From First Principles, Haibo Guo, Yue Qi, Xiaodong Li

Faculty Publications

Hydrogen atmosphere can significantly change the tribological behavior at diamond and diamondlike carbon (DLC) surfaces and the friction-reducing effect depends on the partial pressure of hydrogen. We combined density functional theory modeling and thermodynamic quantities to predict the equilibrium partial pressures of hydrogen at temperature T, PH2 (T), for a fully atomic hydrogen passivated diamondsurface. Above the equilibrium PH2 (T), ultralow friction can be achieved at diamond and DLC surfaces. The calculation agrees well with friction tests at various testing conditions. We also show that PH2 (T) …


Performance Comparison Of Pb(Zr0.52Ti0.48)O3-Only And Pb(Zr0.52Ti0.48)O3-On-Silicon Resonators, Hengky Chandrahalim, Sunil A. Bhave, Ronald G. Polcawich, Jeff Pulskamp, Dan Judy, Roger Kaul, Madan Dubey Jan 2008

Performance Comparison Of Pb(Zr0.52Ti0.48)O3-Only And Pb(Zr0.52Ti0.48)O3-On-Silicon Resonators, Hengky Chandrahalim, Sunil A. Bhave, Ronald G. Polcawich, Jeff Pulskamp, Dan Judy, Roger Kaul, Madan Dubey

Faculty Publications

This paper provides a quantitative comparison and explores the design space of lead zirconium titanate (PZT)–only and PZT-on-silicon length-extensional mode resonators for incorporation into radio frequency microelectromechanical system filters and oscillators. We experimentally measured the correlation of motional impedance (RX) and quality factor (Q) with the resonators’ silicon layer thickness (tSi). For identical lateral dimensions and PZT-layer thicknesses (tPZT), the PZT-on-silicon resonator has higher resonant frequency (fC), higher Q (5100 versus 140), lower RX (51 Ω versus 205 Ω), and better linearity [third-order input intercept …


). Size Dependency Of The Elastic Modulus Of Zno Nanowires: Surface Stress Effect, Guofeng Wang, Xiaodong Li Dec 2007

). Size Dependency Of The Elastic Modulus Of Zno Nanowires: Surface Stress Effect, Guofeng Wang, Xiaodong Li

Faculty Publications

Relation between the elastic modulus and the diameter (D) of ZnOnanowires was elucidated using a model with the calculated ZnOsurface stresses as input. We predict for ZnOnanowires due to surface stress effect: (1) when D>20nm, the elastic modulus would be lower than the bulk modulus and decrease with the decreasing diameter, (2) when 20nm>D>2nm, the nanowires with a longer length and a wurtzite crystal structure could be mechanically unstable, and (3) when D<2nm, the elastic modulus would be higher than that of the bulk value and increase with a decrease in nanowire diameter.


Nanoindentation Of The A And C Domains In A Tetragonal Batio3 Single Crystal, Young-Bae Park, Matthew J. Dicken, Zhi-Hui Xu, Xiaodong Li Oct 2007

Nanoindentation Of The A And C Domains In A Tetragonal Batio3 Single Crystal, Young-Bae Park, Matthew J. Dicken, Zhi-Hui Xu, Xiaodong Li

Faculty Publications

Nanoindentation in conjunction with piezoresponse force microscopy was used to study domain switching and to measure the mechanical properties of individual ferroelectric domains in a tetragonal BaTiO3 single crystal. It was found that nanoindentation has induced local domain switching; the a and c domains of BaTiO3 have different elastic moduli but similar hardness.Nanoindentationmodulus mapping on the a and c domains further confirmed such difference in elasticity. Finite element modeling was used to simulate the von Mises stress and plastic strain profiles of the indentations on both a and c domains, which introduces a much higher stress level than …


Self-Assembled Composite Nano-/Micronecklaces With Sio2 Beads In Boron Strings, Hai Ni, Xiaodong Li Jul 2006

Self-Assembled Composite Nano-/Micronecklaces With Sio2 Beads In Boron Strings, Hai Ni, Xiaodong Li

Faculty Publications

Nano-/micronecklaces with SiO2 beads in boron strings were synthesized by simply sublimating the desired powders in a sealed quartz tube at high temperature. The boron strings have a rectangular cross section with width varying from 80to1000nm while the SiO2 beads bear either spindle or spherical shape with a size ranging from 100nmto5μm. The spacing between the SiO2 beads is uniform in each boron string. Both the boron strings and the SiO2 beads are amorphous and free of defects. The supersaturated vapors of silicon and oxygen induced the SiO2 bead formation.


A Magnetic Suspension System With A Large Angular Range, Colin P. Britcher, Mehran Ghofrani Jan 1993

A Magnetic Suspension System With A Large Angular Range, Colin P. Britcher, Mehran Ghofrani

Mechanical & Aerospace Engineering Faculty Publications

In order to explore and develop technology required for the magnetic suspension of objects over large ranges of orientation, a small-scale laboratory system, the large-angle magnetic suspension test fixture (LAMSTF) has been constructed at NASA Langley Research Center. This apparatus falls into the category of large-gap, actively stabilized magnetic levitation systems. The hardware comprises five conventional electromagnets in a circular arrangement, each driven from a separate bipolar power amplifier. Electromagnet currents are commanded by a digital control system, implemented on a microcomputer, which in turn derives the position and attitude of the suspended element from an infrared optical system. The …


An Apparatus For Measuring The Thermal Conductivity Of Cast Insulation Materials, Christine A. Wilkins, Robert L. Ash Jul 1980

An Apparatus For Measuring The Thermal Conductivity Of Cast Insulation Materials, Christine A. Wilkins, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

A steady-state apparatus has been developed for measuring the thermal conductivity of cast materials. The design has employed a novel thermal symmetry arrangement which can permit total electrical isolation of the test material from its surroundings. © 1980 American Institute of Physics