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Computer program performs transformations in the order S-to W-to Z to allow arithmetic to be completed in the W-plane. The method is based on a direct transformation from the S-plane to the W-plane. The W-plane poles and zeros are transformed into Z-plane poles and zeros using the bilinear transformation algorithm.
Blocked algorithms have much better properties of data locality and therefore can be much more efficient than ordinary algorithms when a memory hierarchy is involved. On the other hand, they are very difficult to write and to tune for particular machines. The reorganization is considered of nested loops through the use of known program transformations in order to create blocked algorithms automatically. The program transformations used are strip mining, loop interchange, and a variant of loop skewing in which invertible linear transformations (with integer coordinates) of the loop indices are allowed. Some problems are solved concerning the optimal application of these transformations. It is shown, in a very general setting, how to choose a nearly optimal set of transformed indices. It is then shown, in one particular but rather frequently occurring situation, how to choose an optimal set of block sizes.
In this study, local chemical and structural changes along superlattice intrinsic stacking faults combine to represent an atomic-scale phase transformation. In order to elicit stacking fault shear, creep tests of two different single crystal Ni-base superalloys, ME501 and CMSX-4, were performed near 750 degrees Centigrade using stresses of 552 megapascals and 750 megapascals, respectively. Through high resolution Scanning Transmission Electron Microscopy (STEM) and state-of-the-art energy dispersive x-ray spectroscopy, ordered compositional changes were measured along SISFs (Superlattice Intrinsic Stacking Faults) in both alloys. For both instances, the elemental segregation and local crystal structure present along the SISFs are consistent with a nanoscale to D019 (ordering of a hexagonal close-packed crystal) phase transformation. Another notable observation is prominent Cr- and Co-rich Cottrell atmospheres and new evidence of more complex reordering processes responsible for the formation of these faults. These findings are further supported using density functional theory calculations and High Angle Annular Dark Field (HAADF) STEM image simulations.
Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.
Phase transitions are omnipresent in modern condensed matter physics and its applications. In solids, first-order phase transformations typically occur by nucleation and growth under nonequilibrium conditions. Under constant external conditions, e.g., constant annealing temperature and pressure, the nucleation and growth dynamics are often thought of as spatially and temporally independent. Here, in situ Bragg X-ray photon correlation spectroscopy (XPCS) reveals nanoscale spatial and dynamical heterogeneity in the perovskite-to-brownmillerite topotactic phase transformation in La 0.7 Sr 0.3 CoO 3 thin films annealed under constant reducing conditions over a time span of multiple hours. Specifically, a time scale associated with domain growth remains stable, with a corresponding domain wall speed of v d = 6 ± 0.5 × 10 –4 nm/s (2 ± 0.2 nm/h), while a slower time scale, associated with temperature-driven depinning of domains, leads to accelerating dynamics with time scales following an aging power law with exponent −2.2 ± 0.5. This experiment demonstrates that Bragg XPCS is a powerful tool to study nanoscale dynamics in structural phase transformations, with the ability to extract quantitative average values related to nanodomain motion in situ. Furthermore, the results are relevant for phase engineering of phase-change devices, as they show that nanoscale dynamics, linked to domain and domain-wall motion, can continuously evolve and speed up with time, even hours after the initiation of the phase transformation, with potential repercussions on electrical performance.
This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.
The effectiveness of using currently available computer techniques for interpretation of MSS data to interpret SAR imagery for forest monitoring was assessed. Data were gathered with NASA's airborne APQ-102 dual-polarized, X-band SAR in a flight at 60,000 ft. Microdensitometry was employed to digitize the HH- and HV-polarized imagery. A ground spatial resolution of 15 m was obtained, control points were identified, a second order biquadratic transformation was applied to compensate for orientation, and rms errors were calculated. A second data set was taken with 30 m resolution in order to simulate thematic mapper operation. Classification was performed with pixel-by-pixel and textural classification algorithms. A statistical analysis was also carried out to find any significant differences between classifiers in a data set for a given classifier. Each polarization featured an independent distortion which required appropriate preprocessing to correct. Further studies are recommended with multiple frequencies viewing and multiple polarizations and look angles to define the actual forest classifications that can be made with the SAR imagery.
Soot formation rates measured in fuel-rich premixed flat flames are frequently used to calibrate or validate chemical kinetic models of soot formation. Unfortunately, these flames feature an extended region of soot precursor particle inception and carbonization that complicates interpretation of soot measurements and leads to a fundamental inconsistency in the nature of the soot material that is modeled versus what is being measured when using non-intrusive, optical techniques. In the work presented here, previously reported data on two canonical sooting ethylene-air premixed flames at 1 atm pressure are interpreted via a new analysis approach that combines soot optical dispersion coefficient measurements with soot carbonization kinetics. This analytical approach explicitly accounts for the production of poorly ordered soot precursor particle mass and its carbonization over time in the flames, providing a clear distinction between the formation rate of precursor particles and their transformation into ordered, solid soot particulate mass. In particular, the results of the analysis show that the precursor particles form much earlier in the flame than the majority of the carbonized soot and their formation rate is two to three times faster than that of ordered soot. The results also show that particle agglomeration begins when the particles are at an intermediate state of carbonization. In conclusion, these results offer a valuable new interpretation of these important datasets and should lead to substantial improvements in the development and calibration of quantitative soot models.
Three methods for performing Hankel transforms with optical or digital processors are described. The first method is applicable when the input data is available in Cartesian (x-y) format and uses the close connection between generalized Hankel transform and the two dimensional Fourier transform in Cartesian coordinates. The second method is useful when the input data is in polar (r - theta) format and uses change of variables to perform the nth order Hankel transform as a correlation integral. The third method utilizes the von Neumann addition theorem for Bessel functions to extract the Hankel coefficients from a correlation between the radial part of the input and a Bessel function. Initial experimental results obtained for optical implementation of the first two methods are presented.
A method of transferring digital image data over a communication link transforms and orders the data so that, as data is received by a receiving station, a low detail version of the image is immediately generated with later transmissions of data providing progressively greater detail in this image. User instructions are accepted, limiting the ultimate resolution of the image or suspending enhancement of the image except in certain user defined regions. When a low detail image is requested followed by a request for a high detailed version of the same image, the originally transmitted data of the low resolution image is not discarded or retransmitted but used with later data to improve the originally transmitted image. Only a single copy of the transformed image need be retained by the transmitting device in order to satisfy requests for different amounts of image detail.
Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to an external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here, in this study, we use neutron scattering to show that the application of a large external magnetic field to Ce 2 Zr 2 O 7 , an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wave vectors in Ce 2 Sn 2 O 7 pyrochlore, and its absence in Ce 2 Zr 2 O 7 . Therefore, our results identify Ce 2 Zr 2 O 7 as a strong candidate for an octupolar U(1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.
In this work, a ferroelectric BaTiO 3 thin film grown on a NdScO 3 substrate was studied using x-ray photon correlation spectroscopy (XPCS) to characterize thermal fluctuations near the a/b to a/c domain structure transformation present in this low-strain material, which is absent in the bulk. XPCS studies provide a direct comparison of the role of domain fluctuations in first- and second-order phase transformations. The a/b to a/c domain transformation is accompanied by a decrease in fluctuation timescales, and an increase in intensity and correlation length. Surprisingly, domain fluctuations are observed up to 25 °C above the transformation, concomitant with the growth of a/c domains and coexistence of both domain types. After a small window of stability, as the Curie temperature is approached, a/c domain fluctuations are observed, albeit slower, potentially due to the structural transformation associated with the ferroelectric to paraelectric transformation. The observed time evolution and reconfiguration of domain patterns highlight the role played by phase coexistence and elastic boundary conditions in altering fluctuation timescales in ferroelectric thin films.
Superelasticity associated with martensitic transformation has found a broad range of engineering applications, such as in low-temperature devices in the aerospace industry. Nevertheless, the narrow working temperature range and strong temperature sensitivity of the first-order phase transformation significantly hinder the usage of smart metallic components in many critical areas. Here, we scrutinized the phase transformation behavior and mechanical properties of multicomponent B2-structured intermetallic compounds. Strikingly, the (TiZrHfCuNi) 83.3 Co 16.7 high-entropy intermetallics (HEIs) show superelasticity with high critical stress over 500 MPa, high fracture strength of over 2700 MPa, and small temperature sensitivity in a wide range of temperatures over 220 K. The complex sublattice occupation in these HEIs facilitates formation of nano-scaled local chemical fluctuation and then elastic confinement, which leads to an ultra-sluggish martensitic transformation. The thermal activation of the martensitic transformation was fully suppressed while the stress activation is severely retarded with an enhanced threshold stress over a wide temperature range. Moreover, the high configurational entropy also results in a small entropy change during phase transformation, consequently giving rise to the low temperature sensitivity of the superelasticity stress. Furthermore, our findings may provide a new paradigm for the development of advanced superelastic alloys, and shed new insights into understanding of martensitic transformation in general.
Matric generalization of polar coordinate transformation to second order matrix differential system
Under high pressures, many crystalline metals undergo solid–solid phase transformations. In order to accurately model the behavior of materials under extreme loading conditions, it is essential to understand the kinetics of phase transition. Using molecular dynamics simulations, this work demonstrates the feasibility of characterizing the speeds of a moving phase boundary using atomistic simulations employing a suitable empirical potential for single-crystal magnesium. The model can provide temperature- and tensorial stress-dependent velocity of a moving phase boundary as a rate-limiting contribution to the kinetics of phase transformation in continuum codes. Results demonstrate that a nonlinear interaction exists between plasticity and phase transition, facilitating a jump in the velocity of a moving phase boundary, facilitated by activated plastic deformation mechanisms.
In-depth investigation of metal–metal oxide interactions and their corresponding evolution is of paramount importance to heterogeneous catalysis as it allows the understanding and maneuvering of the structure of catalytic motifs. Herein, using a series of core/shell metal/iron oxide (M/FeO x , M = Pd, Pt, Au) nanoparticles and through a combination of in situ and ex situ electron and X-ray investigations, we revealed anomalous and dissimilar M–FeO x interactions among different systems under reducing conditions. Further, Pd interacts strongly with FeO x after high-temperature reductive treatment, featured by the formation of Pd single atoms in the FeO x matrix and increased Pd–Fe bonding, while Pt transforms into ordered PtFe intermetallics and Pt single atoms immediately upon the coating of FeO x . In contrast, Au does not manifest strong bonding with FeO x . As a proof of concept of tailoring metal–metal oxide interactions for catalysis, optimized Pd/FeO x demonstrates 100% conversion and 86.5% selectivity at 60 °C for acetylene semihydrogenation.
Abstract Eliminating cobalt from high‐nickel layered oxide cathodes lowers the cost of lithium‐ion batteries for electric vehicles. However, cobalt‐free cathodes with high Mn 4+ and Ni 2+ contents are prone to Li/Ni mixing after synthesis, potentially compromising battery energy density, rate capability, and cycling stability. Without cobalt facilitating cation ordering in the layered structure, the degree of Li/Ni mixing in cobalt‐free cathodes depends heavily on the calcination conditions. In this study, a systematic exploration of calcination temperatures and LiOH ratio for LiNi 0.9 Mn 0.1 O 2 (NM‐90) provides detailed insights into the optimal synthesis conditions for high‐capacity cobalt‐free cathodes with extended cycle life. Surprisingly, high Li/Ni mixing does not necessarily lead to poor cycling stability whereas low Li/Ni mixing does not guarantee a long cycle life. More importantly, although excessive calcination temperature can further decrease Li/Ni mixing, it does not necessarily enhance capacity. Instead, the pernicious effects from the H2 → H3 phase transition are amplified due to a pronounced two‐phase reaction. An extensive suite of chemical and structural characterization methods uncovers a correlation between elevated calcination temperature, phase transformation, cation ordering, and capacity fading behavior: “overcooking” high‐nickel, cobalt‐free cathodes induce structural arrangement toward that of LiNiO 2 , with exacerbated lattice distortion and surface instability accelerating capacity fade.
The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.