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At least 1,099 records · Page 61

Study of the interaction of solutes with Σ5 (013) tilt grain boundaries in iron using density-functional theory

Substitutional alloying elements significantly affect the recrystallization and austenite-ferrite phase transformation rates in steels. The atomistic mechanisms of their interaction with the interfaces are still largely unexplored. Using density functional theory, we determine the segregation energies between commonly used alloying elements and the Σ5 (013) tilt grain boundary in bcc iron. We find a strong solute-grain boundary interaction for Nb, Mo, and Ti that is consistent with experimental observations of the effects of these alloying elements on delaying recrystallization and the austenite-to-ferrite transformation in low-carbon steels. In addition, we compute the solute-solute interactions as a function of solute pair distance in the grain boundary, which suggest co-segregation for these large solutes at intermediate distances in striking contrast to the bulk.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Solutes at the liquid:liquid phase boundary—Solubility and solvent conformational response alter interfacial microsolvation

A detailed understanding of solvent structure and dynamics at liquid:liquid interfaces is a necessary precursor for control and manipulation of these phase boundaries. Experimentally, amphiphilic solutes are often used to alter transport properties across water:organic interfaces; yet, a fundamental model for the mechanism of this action has not been determined. Our study compares the solvation profiles of ampiphilic solutes that traverse the phase boundary in binary water:n-hexane, and the individual microsolvation processes for interfacial water and hexane molecules therein. Microsolvation is defined as the rare event where one solvent molecule temporarily penetrates the co-solvent phases and is fully solvated therein. The solutes tri-butyl phosphate (TBP), hydrogen di-butyl phosphate, and di-hydrogen mono-butyl phosphate have been examined as they exhibit a systematic increase in aqueous solubility and selectively partition to the interfacial region at the infinite dilution limit. The relationship between adopted configurations of the solute, orientation of the solvent, and the ability of the solute to enhance microsolvation, specifically the ability of n-hexane to penetrate the aqueous phase, is observed within a 20 Å radius of TBP.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulation of macromolecule self-assembly in solution: A multiscale approach

One of the most common processes to produce polymer nanoparticles is to induce self-assembly by using the solvent-displacement method, in which the polymer is dissolved in a “good” solvent and the solution is then mixed with an “anti-solvent”. The polymer ability to self-assemble in solution is therefore determined by its structural and transport properties in solutions of the pure solvents and at the intermediate compositions. In this work, we focus on poly-ε-caprolactone (PCL) which is a biocompatible polymer that finds widespread application in the pharmaceutical and biomedical fields, performing simulation at three different scales using three different computational tools: full atomistic molecular dynamics (MD), population balance modeling (PBM) and computational fluid dynamics (CFD). Simulations consider PCL chains of different molecular weight in solution of pure acetone (good solvent), of pure water (anti-solvent) and their mixtures, and mixing at different rates and initial concentrations in a confined impinging jets mixer (CIJM). Our MD simulations reveal that the nano-structuring of one of the solvents in the mixture leads to an unexpected identical polymer structure irrespectively of the concentration of the two solvents. In particular, although in pure solvents the behavior of the polymer is, as expected, very different, at intermediate compositions, the PCL chain shows properties very similar to those found in pure acetone as a result of the clustering of the acetone molecules in the vicinity of the polymer chain. We derive an analytical expression to predict the polymer structural properties in solution at different solvent compositions and use it to formulate an aggregation kernel to describe the self-assembly in the CIJM via PBM and CFD. Simulations are eventually validated against experiments.

36 MATERIALS SCIENCE↗

Investigation on nanoscale processes on the BaF{sub 2}(111) surface in various solutions by frequency modulation atomic force microscopy

In this study, we have directly observed nanoscale processes that occur on BaF{sub 2}(111) surfaces in various solutions using liquid-environment frequency modulation atomic force microscopy (FM-AFM) with a true atomic resolution. In addition, to investigate atomic-scale mechanisms of crystal growth process of BaF{sub 2}, we determined a suitable solution for atomic-resolution FM-AFM imaging of the BaF{sub 2}(111) surface. For undersaturated solutions, the surface is roughened by barium hydroxo complexes in the case of high pH, whereas by dissolution and proton or water molecule adsorption throughout the surface in the case of low pH. On the other hand, for supersaturated solutions, the surface shows two-dimensional nucleation and growth (σ = 0.1) and three-dimensional crystal growth with tetrahedral structures (σ = 1), where σ is the degree of supersaturation. The atomic-resolution imaging of the BaF{sub 2}(111) surface has been demonstrated in potassium fluoride (KF) and the supersaturated (σ = 0.1 and 1) solutions, wherein atomically flat terraces are shown at least for about 30 min.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindrical probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Asymptotic solutions and convergence studies of the resistive inner region equations

A recent publication presents a detailed prescription for constructing global eigenfunctions and complex growth rates for resistive instabilities in axisymmetric toroidal systems, using the method of matched asymptotic expansions. At each singular surface in the plasma, the small-x asymptotic solutions of the ideal MHD outer-region equations are matched to the large-x asymptotic solutions of the resistive inner-region equations, with x being the distance from the singular surface. The success of this method depends upon accurate asymptotic solutions of the resistive inner region equations. Extensive studies have shown that there are not only regimes of excellent agreement with straight-through methods, without asymptotic matching, but also regimes of strong disagreement. As such, in an effort to find the cause of this discrepancy, we present here a different method of constructing asymptotic solutions of the inner region equations and we study the convergence properties of the new and old solutions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multiscale modeling of solute diffusion in triblock copolymer membranes

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model’s predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Furthermore, our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

36 MATERIALS SCIENCE↗

On the number of stable solutions in the Kuramoto model

We consider a system of n coupled oscillators described by the Kuramoto model with the dynamics given by θ˙=ω+Kf(θ). In this system, an equilibrium solution θ∗ is considered stable when ω+Kf(θ∗)=0, and the Jacobian matrix Df(θ∗) has a simple eigenvalue of zero, indicating the presence of a direction in which the oscillators can adjust their phases. Additionally, the remaining eigenvalues of Df(θ∗) are negative, indicating stability in orthogonal directions. A crucial constraint imposed on the equilibrium solution is that |Γ(θ∗)|≤π, where |Γ(θ∗)| represents the length of the shortest arc on the unit circle that contains the equilibrium solution θ∗. We provide a proof that there exists a unique solution satisfying the aforementioned stability criteria. This analysis enhances our understanding of the stability and uniqueness of these solutions, offering valuable insights into the dynamics of coupled oscillators in this system.

Arenas, Alex (ORCID:0000000309370334)↗

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Chemical Solution Derived Planarization Layers for Highly Aligned IBAD MgO Templates

The main goal of this research is to develop a chemical solution derived planarization layer to fabricate highly aligned IBAD-MgO templates for the development of high temperature superconductor (HTS) based coated conductors. The standard IBAD-MgO template needs an additional electrochemical polishing step of the mechanically polished 50- m-thick Hastelloy C-276 substrates to ensure a flat and smooth surface for subsequent growth of multi-layer buffer architectures, which include: sputtered 80-nm Al2O3; sputtered 7-nm Y2O3; IBAD 10-nm MgO; sputtered 30-nm homo-epi MgO; and sputtered 30-nm LaMnO3 (LMO) layers. We have successfully developed a solution planarization layer that removes the electrochemical polishing step and also acts as a barrier layer. Crack-free, smooth Al2O3 layers were prepared on mechanically polished Hastelloy substrates using a chemical solution process. A nearly 10-15-nm thick Al2O3 layer was formed with each coating and the coating was repeated several times to achieve the desired film thickness with intermediate heat-treatments after each coating. The Al2O3 planarization layer significantly reduced the surface roughness of the substrate. The average surface roughness value, Ra for a starting substrate was 9-10 nm. After 8 coatings of Al2O3 layer, the Ra was reduced to 2 nm. Highly aligned IBAD-MgO layers with out-of-plane and in-plane textures comparable to the standard IBAD-MgO layers were successfully deposited on top of the solution planarization Al2O3 layers with an Y2O3 nucleation layer using a reel-to-reel ion-beam sputtering system. Both homo-epi MgO and LMO layers were subsequently deposited on the IBAD-MgO layers using rf sputtering to complete the buffer stack required for the growth of HTS films. YBa2Cu3O7- (YBCO) films with a thickness of 0.8 m deposited on these IBAD-MgO templates by pulsed laser deposition showed a high self-field critical current density, Jc of 3.04 MA/cm2 at 77 K and 6.05 MA/cm2 at 65 K. These results demonstrate that a low-cost chemical-solution-based, high-throughput Al2O3 planarization layer can remove the electro-polishing step and replace sputtered Al2O3 layers for the production of high Jc YBCO-coated conductors.

Paranthaman, Mariappan Parans↗

Stability of exact solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the 'mass' (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. Here we observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M*(κ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick's theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M*(κ) versus κ lies below the two curves found by Derrick's theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the 'frustrated' blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Stability of exact solutions of the nonlinear Schrödinger equation in an external potential having supersymmetry and parity-time symmetry

We discuss the stability properties of the solutions of the general nonlinear Schrödinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time (${ \mathcal P }{ \mathcal T }$) symmetric superpotential $W(x)$ that we considered earlier, Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation $\{{\rm{i}}\,{\partial }_{t}+{\partial }_{x}^{2}-{V}^{-}(x)+| \psi (x,t){| }^{2\kappa }\}\,\psi (x,t)=0,$ for arbitrary nonlinearity parameter κ. We study the bound state solutions when ${V}^{-}(x)\,=(1/4-{b}^{2}){\text{sech}}^{2}(x)$, which can be derived from two different superpotentials $W(x)$, one of which is complex and ${ \mathcal P }{ \mathcal T }$ symmetric. Using Derrick's theorem, as well as a time dependent variational approximation, we derive exact analytic results for the domain of stability of the trapped solution as a function of the depth b 2 of the external potential. We compare the regime of stability found from these analytic approaches with a numerical linear stability analysis using a variant of the Vakhitov–Kolokolov (V–K) stability criterion. The numerical results of applying the V–K condition give the same answer for the domain of stability as the analytic result obtained from applying Derrick's theorem. Our main result is that for $\kappa \gt 2$ a new regime of stability for the exact solutions appears as long as $b\gt {b}_{{\rm{crit}}}$, where ${b}_{{\rm{crit}}}$ is a function of the nonlinearity parameter κ. In the absence of the potential the related solitary wave solutions of the NLSE are unstable for $\kappa \gt 2$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Global centroid moment tensor solutions in a heterogeneous earth: the CMT3D catalogue

SUMMARY For over 40 yr, the global centroid-moment tensor (GCMT) project has determined location and source parameters for globally recorded earthquakes larger than magnitude 5.0. The GCMT database remains a trusted staple for the geophysical community. Its point-source moment-tensor solutions are the result of inversions that model long-period observed seismic waveforms via normal-mode summation for a 1-D reference earth model, augmented by path corrections to capture 3-D variations in surface wave phase speeds, and to account for crustal structure. While this methodology remains essentially unchanged for the ongoing GCMT catalogue, source inversions based on waveform modelling in low-resolution 3-D earth models have revealed small but persistent biases in the standard modelling approach. Keeping pace with the increased capacity and demands of global tomography requires a revised catalogue of centroid-moment tensors (CMT), automatically and reproducibly computed using Green's functions from a state-of-the-art 3-D earth model. In this paper, we modify the current procedure for the full-waveform inversion of seismic traces for the six moment-tensor parameters, centroid latitude, longitude, depth and centroid time of global earthquakes. We take the GCMT solutions as a point of departure but update them to account for the effects of a heterogeneous earth, using the global 3-D wave speed model GLAD-M25. We generate synthetic seismograms from Green's functions computed by the spectral-element method in the 3-D model, select observed seismic data and remove their instrument response, process synthetic and observed data, select segments of observed and synthetic data based on similarity, and invert for new model parameters of the earthquake’s centroid location, time and moment tensor. The events in our new, preliminary database containing 9382 global event solutions, called CMT3D for ‘3-D centroid-moment tensors’, are on average 4 km shallower, about 1 s earlier, about 5 per cent larger in scalar moment, and more double-couple in nature than in the GCMT catalogue. We discuss in detail the geographical and statistical distributions of the updated solutions, and place them in the context of earlier work. We plan to disseminate our CMT3D solutions via the online ShakeMovie platform.

58 GEOSCIENCES↗

Exact general solutions for cosmological scalar field evolution in a background-dominated expansion

We derive exact general solutions (as opposed to attractor particular solutions) and corresponding first integrals for the evolution of a scalar field $\phi$ in a universe dominated by a background fluid with equation of state parameter wB. In addition to the previously examined linear [V($\phi$)=V 0 $\phi$] and quadratic [V($\phi$)=V 0 $\phi$ 2 ] potentials, we show that exact solutions exist for the power-law potential V($\phi$)=V 0 $\phi$ n with n=4(1+w B )/(1-w B )+2 and n=2(1+w B )/(1-w B ). These correspond to the potentials V($\phi$)=V 0 $\phi$ 6 and V($\phi$)=V 0 $\phi$ 2 for matter domination and V($\phi$)=V 0 $\phi$ 10 and V($\phi$)=V 0 $\phi$ 4 for radiation domination. The $\phi$ 6 and $\phi$ 10 potentials can yield either oscillatory or nonoscillatory evolution, and we use the first integrals to determine how the initial conditions map onto each form of evolution. The exponential potential yields an exact solution for a stiff/kination (w B =1) background. We use this exact solution to derive an analytic expression for the evolution of the equation of state parameter, $w_\phi$, for this case.

79 ASTRONOMY AND ASTROPHYSICS↗

Triple junction solute segregation in Al-based polycrystals

Solute segregation is a crucial means of stabilizing nanostructured alloys, and at very small grain sizes, this requires consideration of triple junctions (TJs), which attain a meaningful volume fraction and thus become relevant for bulk material behavior. Here, in this study, the solute segregation spectra for grain boundary (GB) and TJ sites are calculated for a large number of dilute Al-based binary systems with available interatomic potentials. A defect-identifying algorithm is applied to quantify the average GB thickness and classify the intergranular site spectra into GB and junction subspectra. The algorithm is also applied to a hybrid electronic-level database for GB segregation of various solutes in Al, yielding polycrystalline TJ solute segregation spectra from first principles. The results suggest that TJ segregation is alloy or interatomic potential dependent and can exhibit either boundary or junction preference. With these spectra as inputs, the spectral GB segregation model gives quantitative predictions of segregation as a function of grain size, temperature, and total solute concentration, suitable for alloy screening and design.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Successive Procedure for Solution Verification Based on User Needs

This paper discusses a revised solution verification procedure for computational fluid dynamics simulations to estimate the uncertainties in the quantities of interest based on discretization error models. This proposed procedure builds upon current procedures described in ASME V&V 20 but provides more guidance in determining the necessary number of mesh levels to build reliable discretization error models. Such guidance is particularly useful for practicing engineers without prior experience in solution verification. The key features of this proposed solution verification procedure are the ability to determine the need for additional mesh levels iteratively and the seamless treatment for underdetermined, exact, and overdetermined solutions of the power series approximation to the discretization error models. This study applies the proposed procedure to a set of synthetic examples to demonstrate the revised procedure’s clarity in determining the number of mesh solutions required for a reliable estimate of the discretization error in computational fluid dynamics settings. Additionally, this proposed procedure prevents a potential pathway in the current procedure in ASME V&V 20 that may lead to unreasonably small discretization errors.

Weinmeister, Justin↗

SU-E-T-588: Characterization and Clinical Validation of the Varian Pivotal™ Treatment Solution for Prone Breast Care

Purpose: To report on the clinical validation of the Varian Pivotal™ Treatment Solution for Prone Breast Care: a platform for prone breast radiation therapy. Methods: Patients treated using Breast Conserving Radiation Therapy may benefit from treatment in the prone position with the breast tissue falling freely away from the body. This geometry allows the breast tissue to be treated while avoiding the lung and heart tissue. Eighteen patients simulated and treated using the Varian Medical Systems Pivotal™ Treatment Solution for Prone Breast Care were monitored over the course of treatment for positioning integrity and reproducibility. As this carbon-fiber platform actually replaces a portion of the couch top, indexing is inherent to its design. Patients were positioned on the couch and aligned using fiducial markers and lateral SSD to the breast fiducial point. The daily couch coordinates then serves as indicators for positioning variability with this system. Results: The variations in couch vertical, longitudinal and lateral positions were centered on a mean value of zero with standard deviations of 0.44cm, 0.75cm and 0.79cm respectively. Other factors explored were variations in distance of mid-sternum to table edge and patient rotation into the opening. The median rotation of the chest wall was found to be 11.5 degrees at CT-Simulation with a median distance of 2.5cm from midsternum to support opening. Patient rotation was not associated with either breast size or distance from edge of platform. Conclusion: The Pivotal™ Treatment solution consists of a couch top that replaces the standard top and as such is open from beneath without obstruction. This is a distinction from all other solutions which rely on a platform positioned above and indexed to the treatment couch. We found the reproducibility to be consistent with our historical measures while offering benefits of an integrated solution as stated above. supported by Professional Services Agreeement with Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗

Designing and defining dynamic protein cage nanoassemblies in solution

Central challenges in the design of large and dynamic macromolecular assemblies for synthetic biology lie in developing effective methods for testing design strategies and their outcomes, including comprehensive assessments of solution behavior. Here, we created and validated an advanced design of a 600-kDa protein homododecamer that self-assembles into a symmetric tetrahedral cage. The monomeric unit is composed of a trimerizing apex-forming domain genetically linked to an edge-forming dimerizing domain. Enhancing the crystallographic results, high-throughput small-angle x-ray scattering (SAXS) comprehensively contrasted our modifications under diverse solution conditions. To generate a phase diagram associating structure and assembly, we developed force plots that measure dissimilarity among multiple SAXS data sets. These new tools, which provided effective feedback on experimental constructs relative to design, have general applicability in analyzing the solution behavior of heterogeneous nanosystems and have been made available as a web-based application. Specifically, our results probed the influence of solution conditions and symmetry on stability and structural adaptability, identifying the dimeric interface as the weak point in the assembly. Force plots comparing SAXS data sets further reveal more complex and controllable behavior in solution than captured by our crystal structures. Lastly, these methods for objectively and comprehensively comparing SAXS profiles for systems critically affected by solvent conditions and structural heterogeneity provide an enabling technology for advancing the design and bioengineering of nanoscale biological materials.

59 BASIC BIOLOGICAL SCIENCES↗