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A perturbative method, using Lie transforms, is given for calculating the Hannay angle for slow, cyclic evolutions of a classical system, taking into account the finite rate of change of the Hamiltonian. The method is applied to the generalized harmonic oscillator. The classical Aharonov-Anandan angle is also calculated. The interpretational ambiguity in the definitions of geometrical angles is discussed.
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.
We investigate mismatch strain driven programmable shape transformation of spherical domes and report the effects of different geometric and structural characteristics on dome behavior in response to applied mismatch strain. We envision a bilayer dome design where the differential swelling of the inner layer with respect to the passive outer layer in response to changes in dome surroundings (such as the introduction of an organic solvent) introduces mismatch strain within the bilayer system and causes dome shape transformation. Finite element analysis reveals that, in addition to snap-through, spherical domes undergo bifurcation buckling and eventually gradual bending to morph into cylinders with increasing mismatch strain. Besides demonstrating how the snap-through energy barrier depends on the spherical dome shape, our analysis identifies three distinct groups of dome geometries based on their mismatch strain-transformed configuration relationships. Our experiments with polymer-based elastic bilayer domes that exhibit differential swelling in organic solvents qualitatively confirm the finite element predictions. We establish that, in addition to externally applied stimuli (mismatch strain), bilayer spherical dome morphing can be tuned and hence programmed through its geometry and structural characteristics. Incorporation of an elastic instability mechanism such as snap-through within the framework of stimuli-responsive functional devices can improve their response time which is otherwise controlled by diffusion. Furthermore, our proposed design guidelines can be used to realize deployable, multi-functional, reconfigurable, and therefore, adaptive structures responsive to a diverse set of stimuli across multiple length scales.
Highlights: • Grain fragmentation and steady-state stages occur during HPT processing. • A gradual transformation of LAGBs to HAGBs is characterized in both regimes. • During plastic deformation, dislocations gather collectively as geometrical walls. • The presence of GNDs is more pronounced in the vicinity of already existing HAGBs. • The density of GNDs is greater in the fragmentation stage. - Abstract: In this paper, severe plastic deformation (SPD) is applied to commercially pure aluminum. Monotonic high pressure torsion (HPT) processing is employed at room temperature, and the microstructure of samples deformed up to an equivalent strain of 50 is investigated by electron backscatter diffraction (EBSD). The distribution pattern and the density of geometrically necessary dislocations (GNDs) are evaluated by examination of transmission Kikuchi diffraction (TKD) maps. Three different methodologies are utilized for assessment of the GND density. It was observed that two distinct stages of grain fragmentation and steady-state occur during processing. During the first stage, a severe grain refinement was observed as the average grain size decreased from ~85 μm to ~1 μm at an equivalent strain of 10. Quantification of the density of dislocations in both deformation regimes showed that, independent of the choice of model, the GND density is greater in the fragmentation stage than in the steady-state stage. This observation was linked with the prevalence of the continuous dynamic recrystallization (CDRX) phenomenon in each stage. Furthermore, a significant presence of GNDs in the steady-state stage was characterized. Formation of microstructure, grain refinement and saturation of grain size are discussed in the light of statistics of GNDs.
The microstructure and the dislocation density in as-quenched ferrous lath martensite were studied by different methods. The blocks, packets and variants formed due to martensitic transformation were identified and their sizes were determined by electron backscatter diffraction (EBSD). Concomitant transmission electron microscopy (TEM) investigation revealed that the laths contain subgrains with the size between 50 and 100 nm. A novel evaluation procedure of EBSD images was elaborated for the determination of the density and the space distribution of geometrically necessary dislocations from the misorientation distribution. The total dislocation density obtained by X-ray diffraction line profile analysis was in good agreement with the value determined by EBSD, indicating that the majority of dislocations formed due to martensitic transformation during quenching are geometrically necessary dislocations.
Constructing a chemically diverse dataset while avoiding sampling bias is critical to training efficient and generalizable force fields. However, in computational chemistry and materials science, many common dataset generation techniques are prone to oversampling regions of the potential energy surface. Furthermore, these regions can be difficult to identify and isolate from each other or may not align well with human intuition, making it challenging to systematically remove bias in the dataset. While traditional clustering and pruning (down-sampling) approaches can be useful for this, they can often lead to information loss or a failure to properly identify distinct regions of the potential energy surface due to difficulties associated with the high dimensionality of atomic descriptors. In this work, we introduce the Multi-kernel Edge Attention-based Graph Autoencoder (MEAGraph) model, an unsupervised approach for analyzing atomic datasets. MEAGraph combines multiple linear kernel transformations with attention-based message passing to capture geometric sensitivity and enable effective dataset pruning without relying on labels or extensive training. Demonstrated applications on niobium, tantalum, and iron datasets show that MEAGraph efficiently groups similar atomic environments, allowing for the use of basic pruning techniques for removing sampling bias. This approach provides an effective method for representation learning and clustering that can be used for data analysis, outlier detection, and dataset optimization.
We apply the methodology developed in Li et al. to BOSS DR12 galaxies and derive cosmological constraints from the redshift dependence of the Alcock–Paczynski (AP) effect. The apparent anisotropy in the distribution of observed galaxies arise from two main sources, the redshift-space distortion (RSD) effect due to the galaxy peculiar velocities, and the geometric distortion when incorrect cosmological models are assumed for transforming redshift to comoving distance, known as the AP effect. Anisotropies produced by the RSD effect are, although large, maintaining a nearly uniform magnitude over a large range of redshift, while the degree of anisotropies from the AP effect varies with redshift by a much larger magnitude. We split the DR12 galaxies into six redshift bins, measure the two-point correlation function in each bin, and assess the redshift evolution of anisotropies. We obtain constraints of Ω{sub m}=0.290±0.053,w=−1.07±0.15, which are comparable with the current constraints from other cosmological probes such as SNe Ia, cosmic microwave background, and baryon acoustic oscillation (BAO). Combining these cosmological probes with our method yield tight constraints of Ω{sub m}=0.301±0.006,w=−1.054±0.025. Our method is complementary to the other large-scale structure (LSS) probes like BAO and topology. We expect this technique will play an important role in deriving cosmological constraints from LSS surveys.
Structural transformations in crystalline solids are increasingly the basis of the functional behavior of materials. Both low hysteresis and reversibility of phase transformations have been linked to the satisfaction of the nongeneric conditions of compatibility between phases in diverse alloy systems. According to the Cauchy–Born rule, these conditions are expressed as properties of transformation stretch tensor. The transformation stretch tensor is difficult to measure directly due to the lack of knowledge about the exact transforming pathway during the structural change, and the complicating effects of microstructure. In this paper we give a rigorous algorithmic approach for determining the transformation stretch tensor from X-ray measurements of structure and lattice parameters. For some traditional and emerging phase transformations, the results given by the algorithm suggest unexpected transformation mechanisms.
We consider a quantum system subjected to a controlled phase transformation and interaction with the environment in between the acts of selection, which leads to the emergence of interference effects. It is shown that the shift of the dependence of the statistics of contacts’ information with the environement on the controlled phase shift can be interpreted as a geometric phase. This interpretation is consistent with the known operational approach to the geometric phase. As a result, we suggest generalising the operational approach to the realm of pre- and post-selected quantum states. (paper)
The mechanism of ethanol upgrading to higher products is still under debate, especially regarding intermediate species and hydrogenation and dehydrogenation steps. In this work, we conducted a combined theoretical and experimental approach to contribute to this discussion. For such, detailed electronic structure density functional theory calculations (aiming at probing density of states, infrared spectra, geometric parameters, charge densities, and reaction energetics) and diffuse reflectance infrared Fourier transform spectroscopy experiments were carried out revealing the relevance of an appropriate combination of reactive surface sites to support the formation of several intermediates that are formed in the C-C coupling over MgO. The roles of Mg and O sites were also studied under an electronic perspective and different geometrical arrangements. We found that a kink configuration was the most adequate for ethanol to 1-butanol upgrading. Our calculations also gave us arguments to propose distinct reaction routes, whose mutual predominance would depend upon reaction temperature. At temperatures up to 573 K, the so-called β-route, which goes through scission of a Cβ-H bond and formation of an oxametallacycle-like intermediate, would dominate the coupling, whereas at higher temperatures, up to 673 K, a more usual Guerbet mechanism, via an aldol coupling step and then consecutive hydrogenations, would be expected. Here, the theoretical conclusions were followed by a careful experimental strategy using sequential experimental planning techniques in order to estimate accurate parameters with the lowest possible experimental load. Information from these different sources were coupled to develop a mathematical model for the rate of the ethanol upgrading reaction, using a Langmuir-Hinshelwood-Hougen-Watson approach. The developed and statistically validated model adequately described the experimental data at 673 K and 1.1 bar total pressure for ethanol partial pressures in the range from 0 to 20 kPa.
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.
Here we describe the Fourier Transform Spectrometer (FTS) used for in-field testing of the POLARBEAR receiver, an experiment located in the Atacama Desert of Chile which measures the cosmic microwave background (CMB) polarization. The POLARBEAR-FTS (PB-FTS) is a Martin-Puplett interferometer designed to couple to the Huan Tran Telescope (HTT) on which the POLARBEAR receiver is installed. The PB-FTS measured the spectral response of the POLARBEAR receiver with signal-to-noise ratio >20 for ~69% of the focal plane detectors due to three features: a high throughput of 15.1 sr cm 2 , optimized optical coupling to the POLARBEAR optics using a custom designed output parabolic mirror, and a continuously modulated output polarizer. The PB-FTS parabolic mirror is designed to mimic the shape of the 2.5 m-diameter HTT primary reflector, which allows for optimum optical coupling to the POLARBEAR receiver, reducing aberrations and systematics. One polarizing grid is placed at the output of the PB-FTS and modulated via continuous rotation. This modulation allows for decomposition of the signal into different harmonics that can be used to probe potentially pernicious sources of systematic error in a polarization-sensitive instrument. The high throughput and continuous output polarizer modulation features are unique compared to other FTS calibrators used in the CMB field. In-field characterization of the POLARBEAR receiver was accomplished using the PB-FTS in April 2014. We discuss the design, construction, and operation of the PB-FTS and present the spectral characterization of the POLARBEAR receiver. We introduce future applications for the PB-FTS in the next-generation CMB experiment, the Simons Array.
The maximum capacity of a block-oriented, random-access memory is determined primarily by the geometrical parameters of the lenses required to create a Fourier transform of a spatial bit pattern and to image the reconstructed bits onto a photodetector array. Furthermore, the maximum packing density is determined primarily by the same parameters. Several important relationships are developed that are useful in the preliminary design of holographic memories.
The utility of numerical methods for predicting transonic flows over wings and bodies is well established. The computer program FLO22, based on a method presented earlier, has actually been widely used to calculate the aerodynamic performance of wings of transport aircraft. Provided that a correction is made for the displacement effect of the viscous boundary layer, this code has been found to give predictions which are accurate enough to serve as a useful design guide. The main disadvantages of the scheme used in FLO22 are the use of nonconservative difference formulas, which result in a failure to satisfy conservation of mass across shock waves, and the difficulty of finding suitable transformations of coordinates to permit the treatment of more complex geometric configurations. The method described here is an attempt to overcome these shortcomings, while retaining the successful features of the previous method. The basic idea is to use a discrete approximation which directly represents a balance of the mass flow through small volume elements. This leads to a relatively simple treatment of the potential flow equation in conservation form.
Many pieces of existing and proposed space hardware that would be targets of interest for a telerobot can be represented as planar or near-planar surfaces. Examples include the biostack modules on the Long Duration Exposure Facility, the panels on Solar Max, large diameter struts, and refueling receptacles. Robust and temporally efficient methods for locating such objects with sufficient accuracy are therefore worth developing. Two techniques that derive the orientation and location of an object from its monocular image are discussed and the results of experiments performed to determine translational and rotational accuracy are presented. Both the quadrangle projection and elastic matching techniques extract three-space information using a minimum of four identifiable target points and the principles of the perspective transformation. The selected points must describe a convex polygon whose geometric characteristics are prespecified in a data base. The rotational and translational accuracy of both techniques was tested at various ranges. This experiment is representative of the sensing requirements involved in a typical telerobot target acquisition task. Both techniques determined target location to an accuracy sufficient for consistent and efficient acquisition by the telerobot.
Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.
Fusion-based additive manufacturing technologies enable the fabrication of geometrically and compositionally complex parts unachievable by conventional manufacturing methods. However, the non-uniform and far-from-equilibrium heating/cooling conditions pose a significant challenge to consistently obtaining desirable phases in the as-printed parts. Here, in this study, we report a martensite stainless steel development guided by phase transformation dynamics revealed by in-situ high-speed, high-energy, high-resolution X-ray diffraction. This developed stainless steel consistently forms desired fully martensitic structure across a wide range of cooling rates (10 2 –10 7 °C/s), which enables direct printing of parts with fully martensitic structure. The as-printed material exhibits a yield strength of 1157 ± 23 MPa, comparable to its wrought counterpart after precipitation-hardening heat-treatment. The as-printed property is attributed to the fully martensitic structure and the fine precipitates formed during the intrinsic heat treatment in additive manufacturing. The phase transformation dynamics guided alloy development strategy demonstrated here opens the path for developing reliable, high-performance alloys specific for additive manufacturing.
This paper explores potential methods for characterizing the meshing complexity of solid geometry. While numerous metrics exist to measure the quality of the finite element, there are currently no metrics that measure the quality of a solid with respect to its meshing complexity. The meshing complexity of a solid is defined by how difficult it is to generate a valid finite element mesh for a given solid. There are many variables that affect meshing complexity. This paper seeks to discuss methods that are decoupled from more subjective variables such as user expertise and software maturity, and it will focus on methods that describe the topological and geometric aspects of a solid. It will present techniques based on: medial axis transformation, wavelets, curvature, proximity, intersection, heuristic topology search, and the measurement of space (volume/area/length) and will analyze their suitability as meshing complexity metrics.