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At least 1,549 records · Page 86

Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength

Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO{sub 3} crystal is experimentally investigated. Possibility of output beam control at changing of wavelength and using of a diffraction axicon is shown. Full transformation of beams at changing of wavelength Δλ=1.5 nanometers is received at initial wavelength λ=637.5 nanometers for a crystal of CaCO{sub 3} with 15 mm long and a diffraction axicon with period of 2 microns. The theoretical value of necessary wavelength changing is Δλ=1.7 nanometers that is according with experimental results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Shock wave induced martensitic transformations and morphology changes in Fe-Pd ferromagnetic shape memory alloy thin films

Combining experimental methods and classical molecular dynamics (MD) computer simulations, we explore the martensitic transformation in Fe{sub 70}Pd{sub 30} ferromagnetic shape memory alloy thin films induced by laser shock peening. X-ray diffraction and scanning electron microscope measurements at shock wave pressures of up to 2.5 GPa reveal formation of martensitic variants with preferred orientation of the shorter c-axis of the tetragonal unit cell perpendicular to the surface plane. Moreover, consequential merging of growth islands on the film surface is observed. MD simulations unveil the underlying physics that are characterized by an austenite-martensite transformation with a preferential alignment of the c-axis along the propagation direction of the shock wave, resulting in flattening and in-plane expansion of surface features.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Conformal array design on arbitrary polygon surface with transformation optics

A transformation-optics based method to design a conformal antenna array on an arbitrary polygon surface is proposed and demonstrated in this paper. This conformal antenna array can be adjusted to behave equivalently as a uniformly spaced linear array by applying an appropriate transformation medium. An typical example of general arbitrary polygon conformal arrays, not limited to circular array, is presented, verifying the proposed approach. In summary, the novel arbitrary polygon surface conformal array can be utilized in array synthesis and beam-forming, maintaining all benefits of linear array.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Laplace-transformed atomic orbital-based Møller–Plesset perturbation theory for relativistic two-component Hamiltonians

We present a formulation of Laplace-transformed atomic orbital-based second-order Møller–Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Digital holographic interferometry employing Fresnel transform reconstruction for the study of flow shear stabilized Z-pinch plasmas

The ZaP-HD Flow Z-Pinch project provides a platform to explore how shear flow stabilized Z-pinches could scale to high-energy-density plasma (HEDP) and fusion reactor conditions. ZaP-HD generates shear stabilized, axisymmetric Z-pinches with stable lifetimes approaching $60$$\mu$s. The goal of the project is to increase the plasma density and temperature compared to the previous ZaP project by compressing the plasma to smaller radii ($\approx 1$ mm). Radial and axial plasma electron density structure is measured using digital holographic interferometry (DHI), which provides the necessary fine spatial resolution. ZaP-HD's DHI system uses a 2 ns Nd:YAG laser pulse with a second harmonic generator ($\lambda = 532$ nm) to produce holograms recorded by a Nikon D3200 digital camera. The holograms are numerically reconstructed with the Fresnel transform reconstruction method to obtain the phase shift caused by the interaction of the laser beam with the plasma. This provides a two-dimensional map of line-integrated electron density, which can be Abel inverted to determine the local number density. The DHI resolves line-integrated densities down to $3\times 10^{20}$ m$^{-2}$ with spatial resolution near $10 \mu$m. This work presents the first application of Fresnel transform reconstruction as an analysis technique for a plasma diagnostic, and it analyzes the method's accuracy through study of synthetic data. It then presents an Abel inversion procedure that utilizes data on both sides of a Z-pinch local number density profile to maximize profile symmetry. Error estimation and Abel inversion are applied to measured data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Bi-invariant functions on the group of transformations leaving a measure quasi-invariant

Let Gms be the group of transformations of a Lebesgue space leaving the measure quasi-invariant. Let Ams be a subgroup of it consisting of transformations preserving the measure. We describe canonical forms of double cosets of Gms by the subgroup Ams and show that all continuous Ams-bi-invariant functions on Gms are functionals of the distribution of a Radon-Nikodym derivative. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗

Broadband surface-wave transformation cloak

Guiding surface electromagnetic waves around disorder without disturbing the wave amplitude or phase is in great demand for modern photonic and plasmonic devices, but is fundamentally difficult to realize because light momentum must be conserved in a scattering event. A partial realization has been achieved by exploiting topological electromagnetic surface states, but this approach is limited to narrow-band light transmission and subject to phase disturbances in the presence of disorder. Recent advances in transformation optics apply principles of general relativity to curve the space for light, allowing one to match the momentum and phase of light around any disorder as if that disorder were not there. This feature has been exploited in the development of invisibility cloaks. An ideal invisibility cloak, however, would require the phase velocity of light being guided around the cloaked object to exceed the vacuum speed of light—a feat potentially achievable only over an extremely narrow band. In this paper, we theoretically and experimentally show that the bottlenecks encountered in previous studies can be overcome. We introduce a class of cloaks capable of remarkable broadband surface electromagnetic waves guidance around ultrasharp corners and bumps with no perceptible changes in amplitude and phase. These cloaks consist of specifically designed nonmagnetic metamaterials and achieve nearly ideal transmission efficiency over a broadband frequency range from 0 + to 6 GHz. Finally, this work provides strong support for the application of transformation optics to plasmonic circuits and could pave the way toward high-performance, large-scale integrated photonic circuits.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Mesoscale martensitic transformation in single crystals of topological defects

Liquid-crystal blue phases (BPs) are highly ordered at two levels. Molecules exhibit orientational order at nanometer length scales, while chirality leads to ordered arrays of double-twisted cylinders over micrometer scales. Past studies of polycrystalline BPs were challenged by the existence of grain boundaries between randomly oriented crystalline nanodomains. Here, the nucleation of BPs is controlled with precision by relying on chemically nanopatterned surfaces, leading to macroscopic single-crystal BP specimens where the dynamics of mesocrystal formation can be directly observed. Theory and experiments show that transitions between two BPs having a different network structure proceed through local reorganization of the crystalline array, without diffusion of the double-twisted cylinders. In solid crystals, martensitic transformations between crystal structures involve the concerted motion of a few atoms, without diffusion. The transformation between BPs, where crystal features arise in the submicron regime, is found to be martensitic in nature when one considers the collective behavior of the double-twist cylinders. Single-crystal BPs are shown to offer fertile grounds for the study of directed crystal nucleation and the controlled growth of soft matter.

36 MATERIALS SCIENCE↗

A simple variant selection in stress-driven martensitic transformation

Significance Variant selection plays an important role during martensitic transformations in both metals and oxides. Due to its great effects on the crystallographic texture, it has received a great deal of attention in fields of physics, material science, and even Earth science. Previously, most studies focused on transitions in metals induced by temperature. Here, we investigate more complex oxides structures during the pressure/stress-driven martensitic transformation and find a very simple variant selection in cubic/orthorhombic Mn 2 O 3 . The high-pressure orthorhombic phase inherits texture from the low-pressure cubic phase. Only one of the six cubic {110} planes becomes the orthorhombic (100) plane: the one perpendicular to the compression direction. This will become a reference to demonstrate the variant selection behavior under high pressure.

42 ENGINEERING↗

Origin for electrochemically driven phase transformation in the oxygen electrode for a solid oxide cell

The next generation of fuel cells, electrolyzers, and batteries requires higher power, faster kinetics, and larger energy density, which necessitate the use of compositionally complex oxides to achieve multifunctionalities and activity. These compositionally complex oxides may change their phases and structures during an electrochemical process—a so-called “electrochemically driven phase transformation.” The origin for such a phase change has remained obscure. The aim of this paper is to present an experimental study and a theoretical analysis of phase evolution in praseodymium nickelates. Nickelate-based electrodes show up to 60 times greater phase transformation during operation when compared with thermally annealed ones. Theoretical analysis suggests that the presence of a reduced oxygen partial pressure at the interface between the oxygen electrode and the electrolyte is the origin for the phase change in an oxygen electrode. Guided by the theory, the addition of the electronic conduction in the interface layer leads to the significant suppression of phase change while improving cell performance and performance stability.

25 ENERGY STORAGE↗

Demonstration of the Advanced Dynamic System Modeling Tool TRANSFORM in a Molten Salt Reactor Application via a Model of the Molten Salt Demonstration Reactor

Liquid-fueled nuclear reactors, particularly molten salt reactors (MSRs), have recently gained significant interest in the advanced reactor community. As with all reactors, modeling and simulation are critical to advanced reactor design and licensing and will be required for MSR deployment. However, there are significant gaps in existing simulation capabilities for MSRs, particularly with the unique challenges of liquid-fueled systems (e.g., fission product transport). Furthermore, advanced reactor designers require near-term tools that are readily modifiable to perform design and analysis, including the ability to extend their analysis beyond the primary system to auxiliary systems. Transient Simulation Framework of Reconfigurable Models (TRANSFORM), a Modelica-based, system modeling library developed at Oak Ridge National Laboratory, is an advanced tool that can help meet some of the near-term needs of the advanced reactor community. Here, this paper describes advanced system modeling criteria and presents TRANSFORM to the advanced reactor community by demonstration of system modeling capabilities and support of advanced analysis workflows, i.e., the Risk Analysis Virtual Environment (RAVEN) framework from Idaho National Laboratory, using the liquid-fueled Molten Salt Demonstration Reactor (MSDR) as a reference design.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A Monte Carlo Laplace Transform Estimator for Radiation Transport

This work formulates and implements a Laplace transform estimator in a simple Monte Carlo radiation transport code. The estimator maps flux-based quantities of interest, like reaction rates, from a desired phase-space dimension to the complex Laplace domain. This on-the-fly Monte Carlo integration technique enables the spectral analysis of arbitrary nuclear systems via the Laplace transform. A simple code tests the estimator in neutron slowing-down problems across various infinite media, and the results compare well with Ganapol’s uninverted analytical solution of the neutron slowing-down equation.

97 MATHEMATICS AND COMPUTING↗

A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

79 ASTRONOMY AND ASTROPHYSICS↗

Swift heavy ion irradiation of Pt nanocrystals: I. shape transformation and dissolution

We report on the effects of swift heavy ion irradiation of embedded Pt nanocrystals (NCs), which change from spheres to prolate spheroids to rods upon irradiation. Using a broad range of ion irradiation energies and NC mean sizes we demonstrate that the elongation and dissolution processes are energy and size dependent, attaining comparable levels of shape transformation and dissolution upon a given energy density deposited in the matrix. The NC shape transformation remains operative despite discontinuous ion tracks in the matrix and exhibits a constant threshold size for elongation. In contrast, for ion irradiations in which the ion tracks are continuous, the threshold size for elongation is clearly energy dependent.

74 ATOMIC AND MOLECULAR PHYSICS↗

Transformer coupled toroidal wave-heated remote plasma sources operating in Ar/NF 3 mixtures

Remote plasmas are used in semiconductor device manufacturing as sources of radicals for chamber cleaning and isotropic etching. In these applications, large fluxes of neutral radicals (e.g. F, O, Cl, H) are desired with there being negligible fluxes of potentially damaging ions and photons. One remote plasma source (RPS) design employs toroidal, transformer coupling using ferrite cores to dissociate high flows of moderately high pressure (up to several Torr) electronegative gases. In this paper, results are discussed from a computational investigation of moderate pressure, toroidal transformer coupled RPS sustained in Ar and Ar/NF 3 mixtures. Operation of the RPS in 1 Torr (133 Pa) of argon with a power of 1.0 kW at 0.5 MHz and a single core produces a continuous toroidal plasma loop with current continuity being maintained dominantly by conduction current. Operation with dual cores introduces azimuthal asymmetries with local maxima in plasma density. Current continuity is maintained by a mix of conduction and displacement current. Operation in NF 3 for the same conditions produces essentially complete NF 3 dissociation. Electron depletion as a result of dissociative attachment of NF 3 and NF x fragments significantly alters the discharge topology, confining the electron density to the downstream portion of the source where the NFx density has been lowered by this dissociation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A FOURIER-TRANSFORMED BREMSSTRAHLUNG FLASH MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS IN ACCRETING BLACK HOLE SOURCES

Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resulting Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Faster Johnson–Lindenstrauss transforms via Kronecker products

The Kronecker product is an important matrix operation with a wide range of applications in signal processing, graph theory, quantum computing and deep learning. In this work, we introduce a generalization of the fast Johnson–Lindenstrauss projection for embedding vectors with Kronecker product structure, the Kronecker fast Johnson–Lindenstrauss transform (KFJLT). The KFJLT reduces the embedding cost by an exponential factor of the standard fast Johnson–Lindenstrauss transform’s cost when applied to vectors with Kronecker structure, by avoiding explicitly forming the full Kronecker products. Here, we prove that this computational gain comes with only a small price in embedding power: consider a finite set of $p$ points in a tensor product of $d$ constituent Euclidean spaces $\bigotimes _{k=d}^{1}{\mathbb{R}}^{n_k}$, and let $N = \prod _{k=1}^{d}n_k$. With high probability, a random KFJLT matrix of dimension $m \times N$ embeds the set of points up to multiplicative distortion $(1\pm \varepsilon )$ provided $m \gtrsim \varepsilon ^{-2} \, \log ^{2d - 1} (p) \, \log N$. We conclude by describing a direct application of the KFJLT to the efficient solution of large-scale Kronecker-structured least squares problems for fitting the CP tensor decomposition.

Kronecker structure↗

Complex coordinates in transformation optics

We show that complex coordinates used in conjunction with transformation optics offer an extra degree of freedom that allows control over not only the propagation direction of electromagnetic waves but also their amplitude. We illustrate this idea in two applications. First, we show that in an n-dimensional space one can manipulate the field amplitude for up to n different amplitude distributions in regions that are critical to the performance of the device under consideration, and thus reduce the device's sensitivity to design imperfections in these regions. Second, we expand previous work on reflectionless perfectly matched layers and show how complex coordinates and transformation optics are a natural choice for designing perfectly matched layers of arbitrary shape.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗