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Compression behavior of delaminated composite plates

The response of delaminated composite plates to compressive in-plane loads was investigated. The delaminated region may be either circular or elliptical, and may be located between any two plies of the laminate. For elliptical delaminations, the axes of the ellipse may be arbitrarily oriented with respect to the applied loads. A model was developed that describes the stresses, strains, and deformation of the sublaminate created by the delamination. The mathematical model is based on a two dimensional nonlinear plate theory that includes the effects of transverse shear deformation. The model takes into account thermal and moisture induced strains, transverse pressures acting on the sublaminate, and contact between the sublaminate and plate. The solution technique used is the Ritz method. A computationally efficient computer implementation of the model was developed. The code can be used to predict the nonlinear-load-strain behavior of the sublaminate including the buckling load, postbuckling behavior, and the onset of delamination growth. The accuracy of the code was evaluated by comparing the model results to benchmark analytical solutions. A series of experiments was conducted on Fiberite T300/976 graphite/epoxy laminates bonded to an aluminum honeycomb core forming a sandwich panel. Either circles or ellipses made from Teflon film were embedded in the laminates, simulating the presence of a delamination. Each specimen was loaded in compression and the strain history of the sublaminate was recorded far into the postbuckling regime. The extent of delamination growth was evaluated by C-scan examination of each specimen. The experimental data were compared to code predictions. The code was found to describe the data with reasonable accuracy. A sensitivity study examined the relative importance of various material properties, the delamination dimensions, the contact model, the transverse pressure differential, the critical strain energy release rate, and the relative growth direction on the buckling load, the postbuckling behavior, and the growth load of the sublaminate.

Peck, Scott O.↗

Backscatter model for the unusual radar properties of the Greenland Ice Sheet

A number of planetary objects exhibit large radar reflectivity and polarization ratios, and more recently, a similar behavior has been observed over a vast portion of the Earth's surface: the percolation facies of the Greenland Ice Sheet. Surface-based ranging radar data and snow stratigraphy studies demonstrated that the radar properties of that portion of Greenland are caused by enhanced scattering from massive, large, solid-ice bodies buried in the top few meters of the dry, cold, clean snowy surface of the ice sheet and created by seasonal melting and refreezing events. Here, we model the icy inclusions as randomly oriented, discrete, noninteracting, dielectric cylinders embedded in a transparent snow medium. An exact analytical solution is used to compute the scattered field from the cylinders. Using this model, we correctly predict the polarimetric radar observations gathered by an airborne imaging system at three wavelengths (5.6, 24, and 68 cm), between 19 deg and 65 deg incidence angle. The diameter and number density of the cylinders that are inferred from the radar data using the model are consistent with in situ observations of the icy inclusions. The large radar reflectivity and polarization ratios are interpreted as arising internal reflections of the radar signals in the icy inclusions that first-order external reflection models fail to predict. The results compare favorably with predictions from the coherent backscatter or weak localization theory and may provide a complementary framework for interpreting exotic radar echoes from other planetary objects.

Rignot, Eric↗

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

displacement transfer functions↗

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

Berger, Marsha↗

Interstellar and cometary dust

Aspects of interstellar dust which are known from direct observation will be discussed. Some specific difficulties that various theories have in explaining the observations will be presented. Several theoretical interpretations which have been advanced will be discussed, highlighting first their similarities and then their differences. Also discussed will be the author's ideas about the conditions of interstellar dust throughout its life cycle, from origin to incorporation in pre-cometary ices. Dust is primarily observed by its effects on the spectra of background stars, so observations at optical and ultraviolet (UV) wavelengths are confined to the diffuse interstellar medium (ISM) or to the outer regions of dense clouds. Within this somewhat limited range of environments there are very few lines of sight which show any evidence for icy mantles, but there are major variations in the wavelength dependence of the extinction. In the infrared region of the spectrum, it is possible to observe a few stellar sources deeply embedded within molecular clouds.

Mathis, John S.↗

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

displacement theory↗

Thermodynamic Behavior of Nano-sized Gold Clusters on the (001) Surface

We have studied thermal expansion of the surface layers of the hexagonally reconstructed Au (001) surface using a classical Molecular Dynamics (MD) simulation technique with an Embedded Atomic Method (EAM) type many-body potential. We find that the top-most hexagonal layer contracts as temperature increases, whereas the second layer expands or contracts depending on the system size. The magnitude of expansion coefficient of the top layer is much larger than that of the other layers. The calculated thermal expansion coefficients of the top-most layer are about -4.93 x 10(exp -5)Angstroms/Kelvin for the (262 x 227)Angstrom cluster and -3.05 x 10(exp -5)Angstroms/Kelvin for (101 x 87)Angstrom cluster. The Fast Fourier Transform (FFT) image of the atomic density shows that there exists a rotated domain of the top-most hexagonal cluster with rotation angle close to 1 degree at temperature T less than 1000Kelvin. As the temperature increases this domain undergoes a surface orientational phase transition. These predictions are in good agreement with previous phenomenological theories and experimental studies.

Paik, Sun M.↗

An Approach to V&V of Embedded Adaptive Systems

Rigorous Verification and Validation (V&V) techniques are essential for high assurance systems. Lately, the performance of some of these systems is enhanced by embedded adaptive components in order to cope with environmental changes. Although the ability of adapting is appealing, it actually poses a problem in terms of V&V. Since uncertainties induced by environmental changes have a significant impact on system behavior, the applicability of conventional V&V techniques is limited. In safety-critical applications such as flight control system, the mechanisms of change must be observed, diagnosed, accommodated and well understood prior to deployment. In this paper, we propose a non-conventional V&V approach suitable for online adaptive systems. We apply our approach to an intelligent flight control system that employs a particular type of Neural Networks (NN) as the adaptive learning paradigm. Presented methodology consists of a novelty detection technique and online stability monitoring tools. The novelty detection technique is based on Support Vector Data Description that detects novel (abnormal) data patterns. The Online Stability Monitoring tools based on Lyapunov's Stability Theory detect unstable learning behavior in neural networks. Cases studies based on a high fidelity simulator of NASA's Intelligent Flight Control System demonstrate a successful application of the presented V&V methodology. ,

Liu, Yan↗

Extension of Ko Straight-Beam Displacement Theory to Deformed Shape Predictions of Slender Curved Structures

The Ko displacement theory originally developed for shape predictions of straight beams is extended to shape predictions of curved beams. The surface strains needed for shape predictions were analytically generated from finite-element nodal stress outputs. With the aid of finite-element displacement outputs, mathematical functional forms for curvature-effect correction terms are established and incorporated into straight-beam deflection equations for shape predictions of both cantilever and two-point supported curved beams. The newly established deflection equations for cantilever curved beams could provide quite accurate shape predictions for different cantilever curved beams, including the quarter-circle cantilever beam. Furthermore, the newly formulated deflection equations for two-point supported curved beams could provide accurate shape predictions for a range of two-point supported curved beams, including the full-circular ring. Accuracy of the newly developed curved-beam deflection equations is validated through shape prediction analysis of curved beams embedded in the windward shallow spherical shell of a generic crew exploration vehicle. A single-point collocation method for optimization of shape predictions is discussed in detail

Ko, William L.↗

Proceedings of the Second NASA Formal Methods Symposium

This publication contains the proceedings of the Second NASA Formal Methods Symposium sponsored by the National Aeronautics and Space Administration and held in Washington D.C. April 13-15, 2010. Topics covered include: Decision Engines for Software Analysis using Satisfiability Modulo Theories Solvers; Verification and Validation of Flight-Critical Systems; Formal Methods at Intel -- An Overview; Automatic Review of Abstract State Machines by Meta Property Verification; Hardware-independent Proofs of Numerical Programs; Slice-based Formal Specification Measures -- Mapping Coupling and Cohesion Measures to Formal Z; How Formal Methods Impels Discovery: A Short History of an Air Traffic Management Project; A Machine-Checked Proof of A State-Space Construction Algorithm; Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications; Modeling Regular Replacement for String Constraint Solving; Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol; Can Regulatory Bodies Expect Efficient Help from Formal Methods?; Synthesis of Greedy Algorithms Using Dominance Relations; A New Method for Incremental Testing of Finite State Machines; Verification of Faulty Message Passing Systems with Continuous State Space in PVS; Phase Two Feasibility Study for Software Safety Requirements Analysis Using Model Checking; A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover; SimCheck: An Expressive Type System for Simulink; Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness; Software Model Checking of ARINC-653 Flight Code with MCP; Evaluation of a Guideline by Formal Modelling of Cruise Control System in Event-B; Formal Verification of Large Software Systems; Symbolic Computation of Strongly Connected Components Using Saturation; Towards the Formal Verification of a Distributed Real-Time Automotive System; Slicing AADL Specifications for Model Checking; Model Checking with Edge-valued Decision Diagrams; and Data-flow based Model Analysis.

Munoz, Cesar↗

Analysis of Graphite-Reinforced Cementitious Composites

Strategically embedding graphite meshes in a compliant cementitious matrix produces a composite material with relatively high tension and compressive properties as compared to steel-reinforced structures fabricated from a standard concrete mix. Although these composite systems are somewhat similar, the methods used to analyze steel-reinforced composites often fail to characterize the behavior of their more advanced graphite-reinforced counterparts. This Technical Memorandum describes some of the analytical methods being developed to determine the deflections and stresses in graphite-reinforced cementitious composites. It is initially demonstrated that the standard transform section method fails to provide accurate results when the elastic moduli ratio exceeds 20. An alternate approach is formulated by using the rule of mixtures to determine a set of effective material properties for the composite. Tensile tests are conducted on composite samples to verify this approach. When the effective material properties are used to characterize the deflections of composite beams subjected to pure bending, an excellent agreement is obtained. Laminated composite plate theory is investigated as a means for analyzing even more complex composites, consisting of multiple graphite layers oriented in different directions. In this case, composite beams are analyzed using the laminated composite plate theory with material properties established from tensile tests. Then, finite element modeling is used to verify the results. Considering the complexity of the samples, a very good agreement is obtained.

Vaughan, R. E.↗

Chandra Observations of a Young Embedded Magnetic B Star in the p Ophiuchus Cloud

This paper reports the analysis of two Chandra X-ray observations of the young magnetic B star rho Ophiuchus S1. X-ray emission from the star was detected in both observations. The average flux is almost the same in both, but during each observation the flux shows significant time variations by a factor of two on timescales of 20-40 ksec. Each spectrum can be fit by either an absorbed power law model with a photon index of approx. -3 or a thin-thermal plasma model with a temperature of approx. 2 keV and an extremely low metal abundance (approx. less than 0.1 solar). The spectrum of the first observation has an apparent line feature at about 6.8 keV, which likely corresponds to highly ionized iron K alpha. In contrast, the spectrum of the second observation shows an anomalous edge absorption component at E approx. 1 keV. The continuum emission and log (L(sub X)/L(sub bol)) approx. -6 are similar to those of young intermediate-mass stars (Herbig Ae/Be stars) although the presence of the magnetic field inferred from the detection of non-thermal radio emission has drawn an analogy between rho Ophiuchus S1 and magnetic chemically peculiar (MCP) stars. If the X-ray emission is thermal, the highest plasma temperature observed is too high to be explained by the conventional theories of magnetic stars, and favors some kind of magnetic dynamo activity, while if the emission is nonthermal, it might be related to mass infall. The 6.8 keV line and 4 keV edge features are marginal but they give important information near the stellar body if they are real. Their physical interpretation is discussed.

Hamaguchi, Kenji↗

Limits to Creation of Oxygen-Rich Atmospheres on Planets in the Outer Reaches of the Conventional Habitable Zone

Abundant free oxygen appears to be a requirement for macroflora and macrofauna. To the best of our knowledge, a general discussion of which habitable planets are conducive to oxygen has not taken place. Theories for the rise of oxygen fall into 4 categories: (i) It is governed by an intrinsic rate of biological innovation, independent of environmental factors. (ii) It is caused by mantle evolution, probably consequent to secular cooling. (iii) It is caused by hydrogen escape, which irreversibly oxidizes the Earth. (iv) It is Gaia's response to the brightening Sun, its rise prevented until reduced greenhouse gases were no longer needed to maintain a clement climate. All but the first of these make implicit astronomical predictions that can be quantified and made explicit. Here we address the third hypothesis. In this hypothesis hydrogen escape acts like an hourglass that continues until all relevant reduced mineral buffers have been oxidized (titrated, as it were) and the surface made safe for O2. The hypothesis predicts that abundant free O2 will be absent from habitable planets that have not experienced significant hydrogen escape. Where hydrogen escape is modest or insignificant, the atmosphere can be approximated as hydrostatic, which makes assessing radiative cooling by embedded molecules, atoms, and ions such as CO2 and H3+ straightforward. In particular, H2 is efficient at exciting non-LTE CO2 15 micron emission, which makes radiative cooling very effective when H2 is abundant. We can therefore map out the region of phase space in which habitable planets do not lose hydrogen, and therefore do not develop O2 atmospheres. A related matter is the power of radiative cooling by embedded molecules to enforce the diffusion limit to hydrogen escape. This matter in particular is relevant to addressing the empirical observation that rocky planets with thin or negligible atmospheres are rarely or never bigger than approx.1.6 Earth radii.

Zahnle, Kevin↗

An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells

The inverse Finite Element Method (iFEM) is a revolutionary methodology for real-time reconstruction of full-field structural displacements and stresses in structures that are instrumented with strain sensors. This inverse problem is commonly referred to as shape and stress sensing, which is well-recognized as an enabling technology for structural health monitoring systems. In this study, an improved iFEM formulation is proposed for shape and stress sensing of laminated composite and sandwich plates and shells. The formulation includes the kinematics of a shear deformation plate theory known as Refined Zigzag Theory (RZT) as its baseline. The present iFEM formulation is based upon the minimization of a weighted-least-squares functional that uses the complete set of section strains of RZT. The improved iFEM methodology is applicable for shape and stress sensing of thin and moderately thick plate and shell structures involving a relatively small number of strain gauges. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. A three-node inverseshell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. For both problems, the experimental strain data are generated numerically by the direct finite element analysis using high-fidelity discretizations. These strains are then regarded as the experimental strains obtained from surface mounted strain gauges or embedded fiber Bragg grating (FBG) sensors. The numerical results demonstrate the superior capability and potential applicability of the i3- RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures.

Kefal, Adnan↗

Ly(alpha) Photolysis in the Primitive Solar Nebula

This is the final report for the third year of work on this project. Our proposal was to quantitatively investigate the importance of photochemistry in the solar nebula. In the generally accepted theory for the chemical evolution of the primitive solar nebula, Prinn and Fegley argued that photochemistry is unimportant, and that thermochemistry controls the relative abundances of molecular species throughout the planet-forming region. They provided useful estimates of the chemical energy available to the solar nebula from a variety of sources, and established that even the small photolysis rate due to starlight is more important than the photolysis rate from direct sunlight (although small, the UV flux from starlight could have processed a non-negligible fraction of the solar nebula. The reason for this is that the opacity of the disk was so large that direct sunlight could only penetrate to 0.1 AU or so, despite the expectation that the protosun, if comparable to a T-Tauri star, would be emitting up to 10(exp 4) more H I Ly(alpha) photons than the current sun. We developed a Monte Carlo resonance fine radiative transfer code, capable of accurately calculating the radiation field of H I Ly(alpha), He I 584 A, and He II 304 A emissions throughout the nebula and the nearby interstellar medium in which it is embedded. We applied the code to two appropriate models of the primitive solar nebula. Our model provided the photolysis rates of various species over the entire surface layer of the nebula, and from this we evaluated the importance of UV photochemistry due to backscattered solar UV resonance line emissions on different parts of the nebula. The results discussed below were presented.

Gladstone, G. Randall↗

The TSO Logic and G2 Software Product

This internship assignment for spring 2014 was at John F. Kennedy Space Center (KSC), in NASAs Engineering and Technology (NE) group in support of the Control and Data Systems Division (NE-C) within the Systems Hardware Engineering Branch. (NEC-4) The primary focus was in system integration and benchmarking utilizing two separate computer software products. The first half of this 2014 internship is spent in assisting NE-C4s Electronics and Embedded Systems Engineer, Kelvin Ruiz and fellow intern Scott Ditto with the evaluation of a newly piece of software, called G2. Its developed by the Gensym Corporation and introduced to the group as a tool used in monitoring launch environments. All fellow interns and employees of the G2 group have been working together in order to better understand the significance of the G2 application and how KSC can benefit from its capabilities. The second stage of this Spring project is to assist with an ongoing integration of a benchmarking tool, developed by a group of engineers from a Canadian based organization known as TSO Logic. Guided by NE-C4s Computer Engineer, Allen Villorin, NASA 2014 interns put forth great effort in helping to integrate TSOs software into the Spaceport Processing Systems Development Laboratory (SPSDL) for further testing and evaluating. The TSO Logic group claims that their software is designed for, monitoring and reducing energy consumption at in-house server farms and large data centers, allows data centers to control the power state of servers, without impacting availability or performance and without changes to infrastructure and the focus of the assignment is to test this theory. TSOs Aaron Rallo Founder and CEO, and Chris Tivel CTO, both came to KSC to assist with the installation of their software in the SPSDL laboratory. TSOs software is installed onto 24 individual workstations running three different operating systems. The workstations were divided into three groups of 8 with each group having its own operating system. The first group is comprised of Ubuntus Debian -based Linux the second group is windows 7 Professional and the third group ran Red Hat Linux. The highlight of this portion of the assignment is to compose documentation expressing the overall impression of the software and its capabilities.

TSO Logic↗

The new organization: Rethinking work in the age of virtuality

Like two enormous steam engines, throttles wide-open, bells clanging and whistles screeching, careening toward each other down the same track, two powerful forces are about to collide and the point of collision will be smack in the middle of the white-collar workplace. Moreover, once the dust has settled, it is quite likely that we will never be able to think about the white-collar workplace in quite the same way again. The forces couldn't be more different. One force, the theory of complex adaptive systems, has its roots in the radical new sciences of chaos and complexity. The other force, the notion of organizations being learning systems, more like living organisms than 'information factories,' is an outgrowth of the new management thinking of leading organizational theorists like the Claremont Graduate School's Peter Drucker, MIT's Peter Senge, and Hitotsubashi University's Ikujiro Nonaka. Nevertheless, both the new science and the new management thinking seem to point to a similar and perhaps even startling conclusion: the business organization of the 21st century will look nothing like the bureaucratic organizational model that prevails in most companies today, a model that has remained largely unchanged since the manufacturing heydays of 1950s. While the details of the new organization remain sketchy, its rough outline is already beginning to take shape. Rather than simply being flatter through the elimination of layer upon layer of 'middle management,' the new organization is likely to be made up of networks of specialists who will be, for all practical purposes, self-managing. Rather than focusing on issues like re-engineering business processes, a holdover from Taylorism, the focus will be on supporting the continuous learning of an organization's specialists, the sharing of this learning with other specialists, and the embedding of this learning in the organization's physical structure. Finally, rather than viewing themselves as going through relatively long periods of stability punctuated by shorts bursts of 'reorganization,' business enterprises will come to realize that their very survival depends upon their being in a state of continuous organization. The implications of the new organization with respect to how companies approach the planning, design, and management of the technology infrastructure that enables individual learning, self-management, and continuous orgsnization, are both numerous and far-reaching. As part of this technology infrastructure, the white-collar workplace exists in the form it does today as a direct result of management's beliefs about how time, space, and tools ought to be organized and managed in order to accomplish useful intellectual work. Obviously, if these beliefs change radically, as both the new science and the new management thinking suggest is about to happen, then it is almost inevitable that the form and function of the white-collar workplace will change radically, as well. Will there even be a white-collar workplace in the 21st century, in the sense of purpose-built facilities designed to support the co-location of large numbers of white-collar workers? Only time will tell. However, the leading indicators seem to suggest that, as the old saying goes, 'We ain't seen nothin' yet!'

Sutherland, Duncan B., Jr.↗