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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics

We present a new multiscale simulation methodology for coupling a region with atomistic detail simulated via molecular dynamics (MD) to a numerical solution of the fluctuating Navier-Stokes equations obtained from smoothed dissipative particle dynamics (SDPD). In this approach, chemical potential gradients emerge due to differences in resolution within the total system and are reduced by introducing a pairwise thermodynamic force inside the buffer region between the two domains where particles change from MD to SDPD types. When combined with a multi-resolution SDPD approach, such as the one proposed by Kulkarni et al. [J. Chem. Phys. 138, 234105 (2013)], this method makes it possible to systematically couple atomistic models to arbitrarily coarse continuum domains modeled as SDPD fluids with varying resolution. We test this technique by showing that it correctly reproduces thermodynamic properties across the entire simulation domain for a simple Lennard-Jones fluid. Furthermore, we demonstrate that this approach is also suitable for non-equilibrium problems by applying it to simulations of the start up of shear flow. The robustness of the method is illustrated with two different flow scenarios in which shear forces act in directions parallel and perpendicular to the interface separating the continuum and atomistic domains. In both cases, we obtain the correct transient velocity profile. We also perform a triple-scale shear flow simulation where we include two SDPD regions with different resolutions in addition to a MD domain, illustrating the feasibility of a three-scale coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Laser-induced forces on atoms during ultrafast demagnetization

Laser-induced femtosecond demagnetization has attracted a broad attention as a possible candidate for information storage technology. However, whether or not lattice vibration directly participates in demagnetization has been highly controversial over a decade. A recent electron diffraction experiment attributed the demagnetization to the polarized phonon effect, but a similar x-ray diffraction experiment attributed it to the Einstein–de Haas effect. Common to both experiments is that neither the angular momentum of the lattice nor the rotation of the sample was directly probed. Here, we report our first first-principles calculation of forces on atoms induced by an ultrafast laser during ultrafast demagnetization. We employ two complementary methods: (i) the frozen lattice with electronic excitation and (ii) frozen excitation but moving the lattice. We find that the forces on atoms start at –50 fs and peak around 30 fs. The magnitude of the force is far smaller than the empirical estimates. Within the limit of our theory, our results suggest that the polarized phonon effect and the Einstein–de Haas effect are unlikely to be the main course of demagnetization. As a result, we expect that our finding has a profound impact on the future direction of laser-induced dynamics in magnetic and quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Realistic Ion Dynamics through Charge Renormalization in Nonaqueous Electrolytes

While many practically important electrolytes contain lithium ions, interactions of these ions are particularly difficult to probe experimentally because of their small X-ray and neutron scattering cross sections and large neutron absorption cross sections. Molecular dynamics (MD) is a powerful tool for understanding the properties of nonaqueous electrolyte solutions from the atomic level, but the accuracy of this computational method crucially depends on the physics built into the classical force field. In this study, we demonstrate that several force fields for lithium bistriflimide (LiTFSI) in acetonitrile yield a solution structure that is consistent with the neutron scattering experiments, yet these models produce dramatically different ion dynamics in solution. Such glaring discrepancies indicate that inadequate representation of long-range interactions leads to excessive ionic association and ion-pair clustering. We show that reasonable agreement with the experimental observations can be achieved by renormalization of the ion charges using a “titration” method suggested herewith. This simple modification produces realistic concentration dependencies for ionic diffusion and conductivity in <2 M solutions, without loss in quality for simulation of the structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

On the validity of cosmological Fisher matrix forecasts

We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage-IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters w{sub 0} and w{sub a}. For purely geometrical probes, and especially when marginalising over w{sub a}, we find considerable disagreement between the two methods, since in this case the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function. More quantitatively, the Fisher method underestimates the marginalized errors for purely geometrical probes between 30%-70%. For cases including structure formation such as weak lensing, we find that the posterior probability contours from the Fisher matrix estimation are in good agreement with the MCMC contours and the forecasted errors only changing on the 5% level. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that for the purely geometrical probes and, more generally, in cases where it is not known whether the likelihood is close to Gaussian, the Fisher matrix is not the appropriate tool to produce reliable forecasts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Understanding Biases in Sample Preparation Techniques for Coupled Scanning Electron Microscopy and MAMA PuO 2 Morphological Analysis

In this project, the scanning electron microscopy (SEM) sampling method used during the statistical design study (SDS) was investigated to determine if any sampling biases were present in the analyzed data. Using standard particle size distribution powders from the National Institute of Standards and Technology (NIST 1984 standard reference material) with the origin wet dispersion method, it was determined that a bias to smaller particles was present. This was supported by theoretical calculations using Stokes’ law to determine the settling rate of spherical particles of roughly the same size and mass as those found in the SDS. Based on the theoretical calculations, it was determined that the settling rate for each of the 76 powder sets in the SDS could be unique based on specific particle shape and mass distributions, making a universal correction factor/formula not applicable. Therefore, priority shifted to developing an improved wet dispersion method that significantly reduced the particle settling rate for all particle size and shapes. This was achieved by replacing the original solvent (isopropyl alcohol) with a heavy liquid (lithium heteropolytungstates), which dramatically slowed the settling rate and allowed for the capture of a suitable homogeneous aliquot. SEM imaging and Morphological Analysis for Material Attribution (MAMA) software analysis were conducted on the NIST standard, and the SEM/MAMA data were compared to data captured by a dynamic image analysis particle size analyzer. The resulting data confirmed that the new wet dispersion method does indeed deliver an improved representative aliquot to the SEM stub. For instance, in the NIST certificate, the average particle size is ~17.1 µm ± 2.2 µm with a normal distribution. The initial wet dispersion method resulted in a drastically reduced average particle size of 6.1 µm in addition to a non-representative heavy bi-modal distribution whereas the improved LST wet dispersion method resulting in an average particle size that was much closer to the NIST certificate (12.7 µm) with a similar normal distribution. Although the improved method was still short of the NIST certificate average, atomic force microscopy analysis determined that the resulting ~20-25% reduction in size was due to particles sinking into the carbon sticky tape used for SEM imaging. It is believed that that this bias can be calibrated in a much more predicable manner than the original settling rate bias. In addition, the matching normal distribution curves between the NIST certificate and the heavy liquid method indicate a much-improved representative aliquot has been sampled and imaged. A surrogate CeO 2 powder was used to reflect PuO 2 more accurately and to aid in implementing radiological controls and shielding. The resulting data sets from the SEM/MAMA method and the particle size analyzer give almost identical average particle sizes and particle distribution statistics. Future work will re-analyze several select runs from the SDS to determine if morphological signatures can be found with the improved sampling method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Novel method for accurately estimating membrane transport properties and mass transfer coefficients in reverse osmosis

Here, we present a simple and robust method to simultaneously characterize the water and salt permeability (A, B) of reverse osmosis (RO) membranes and mass transfer coefficient (k) in membrane modules. The proposed methodology comprises a set of RO experiments performed at different operating pressures or stages. The measured water and salt fluxes in each stage are simultaneously fitted to the RO transport equations by performing a non-linear regression, using A, B, and k as regression parameters. We first perform a systematic accuracy analysis of the proposed method across the full operational range of RO. The assessment shows that the method accuracy is substantially higher than current methods and increases with number of experimental stages and driving forces. This assessment is used to inform the design of an experimental protocol that minimizes errors in estimated A, B, and k. We then evaluate two commercial RO membranes following the new protocol. For both membranes, A and B parameters decrease by 17% and 15% from the dilute solution to seawater concentrations, whereas the k parameter remains constant. Our study demonstrates that the proposed method, informed by data-driven experimental designs, provides a new approach for accurately characterizing transport phenomenon in membrane processes with feeds of less than 100 g/L total dissolved solids.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Dynamic simulation of powder packing structure for powder bed additive manufacturing

Here, powder packing structure is a critical parameter of powder bed-based additive manufacturing (AM). Experimental characterization of powder is typically limited to measuring bulk properties, whereas many numerical models of AM powder packing are based on geometrical consideration without accounting for particle-to-particle interactions. In the present paper, the powder packing dynamics is simulated using a discrete element method (DEM)-based model that solves the mechanical contact forces and moments between individual particles. As DEM uses explicit time integration, a main challenge in modeling dynamics of metallic powder packing is the need for extremely fine time increment size (e.g., in the order of 1 ns for a 10-μm-diameter particle). The effect of mass scaling, employed for speeding up the calculation, on the simulation results is examined in a test case of powder particles packed inside a box container. The calculated packing density for two different particle size distributions is validated against independent literature data for laser powder bed AM with AISI 316L stainless steel powder. The sensitivity of key input parameters (e.g., friction coefficient) is further evaluated in this test case. The powder packing model is then applied to a practical situation of binder jet AM involving rolling of multiple layers of IN718 powder particles onto a powder bed, for which the calculated packing density is also validated with independent literature data.

42 ENGINEERING↗
DOE OSTI2022

Evaluation of Physical Security Risk for Potential Implementation of FLEX using Dynamic Simulation Methods

The requirements for United States nuclear power plants to maintain a large onsite physical security force contribute to their large operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability Program Physical Security Pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. This pathway will analyze and minimize the conservatisms built into current security postures in order to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within this pathway has successfully developed a dynamic force-on-force (FOF) modeling framework using various computer simulation tools and integrated them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This document provides an overview of lessons learned in applying a dynamic computational framework that links results from a commercially available FOF simulation tool, a commercially available thermal-hydraulic tool, and EMRALD to an operating commercial nuclear power plant. This process of including plant procedures and multiple analysis results is being called Modeling and Analysis for Safety Security using Dynamic EMRALD Framework. Previous reports described how a user could integrate their plant-specific FOF models with the dynamic simulation tool EMRALD, model operator actions, integrate with probabilistic risk assessment tools, such as Computer Aided Fault Tree Analysis System or Systems Analysis Programs for Hands-on Integrated Reliability Evaluations, and with thermal-hydraulic tools, such as RELAP-5. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report documents the results of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. The purpose of this study was to verify that results achieved using generic models are similar to actual plant results and to refine our guidance of the use of the framework. Such an assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants. NOTE: The work performed in this report is based on a generic EMRALD model with actual plant data used for the analysis. However, only the generic model and general results of the analysis are in the report. No plant’s sensitive information is discussed in this report. The discussion shows examples of insights that can be obtained from the MASS-DEF methodology.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Thermal fluctuations of pair interaction forces in liquid Yukawa systems

The dynamics of charged particles in two- and three-dimensional Yukawa systems is studied using numerical methods. Nonideal systems are simulated in a wide range of their parameters. The density of thermal fluctuations of pair interaction forces in liquid structures is obtained and compared with the internal energy density of the systems under study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). In this study, we implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Lastly, various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Atomic charges for modeling metal–organic frameworks: Why and how

Atomic partial charges are parameters of key importance in the simulation of Metal–Organic Frameworks (MOFs), since Coulombic interactions decrease with the distance more slowly than van der Waals interactions. But despite its relevance, there is no method to unambiguously assign charges to each atom, since atomic charges are not quantum observables. There are several methods that allow the calculation of atomic charges, most of them starting from the electronic wavefunction or the electronic density or the system, as obtained with quantum mechanics calculations. In this work, we describe the most common methods employed to calculate atomic charges in MOFs. In order to show the influence that even small variations of structure have on atomic charges, we present the results that we obtained for DMOF-1. We also discuss the effect that small variations of atomic charges have on the predicted structural properties of IRMOF-1. - Graphical abstract: We review the different method with which to calculate atomic partial charges that can be used in force field-based calculations. We also present two examples that illustrate the influence of the geometry on the calculated charges and the influence of the charges on structural properties. - Highlights: • The choice of atomic charges is crucial in modeling adsorption and diffusion in MOFs. • Methods for calculating atomic charges in MOFs are reviewed. • We discuss the influence of the framework geometry on the calculated charges. • We discuss the influence of the framework charges on structural the properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods

In this work, we report an implementation of non-adiabatic coupling (NAC) forces within the equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) framework via the summed-state approach. Using illustrative examples, we compare NAC forces computed with EOM-CCSD and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC vectors, we analyze their direction, which is important for the calculations of the rate of non-adiabatic transitions. Our benchmark set comprises three doublet radical-cations (hexatriene, cyclohexadiene, and uracil), neutral uracil, and sodium-doped ammonia clusters. When the characters of the states agree among different methods, we observe good agreement between the respective NAC vectors, both in the Franck-Condon region and away. In the cases of large discrepancies between the methods, the disagreement can be attributed to the difference in the states’ character, which, in some cases, is very sensitive to electron correlation, both within single-reference and multi-reference frameworks. Finally, the numeric results confirm that the accuracy of NAC vectors depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC methods provide a viable alternative to MR approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Modeling Salt-Material Interactions in Molten Salt Reactors: Opportunities and Path Forward

A revitalized interest in molten salt reactor technology has resulted in a concerted effort across US based national laboratories and universities to investigate and overcome the remaining scientific and engineering questions facing the industry. This report provides a detailed description of the atomistic modelling techniques that could be employed to investigate the atomic-level forces and behaviors governing salt chemistry and thermodynamics, and the corrosion of container materials in these systems. The molten salt environment is broken down into three unique regions in which atomic behaviors are governed by separate processes and forces. A discussion is given on how each region can be modelled using different computational methods. The objective of the models presented for each region is to understand and quantify the individual atom-to-atom forces driving corrosion processes and changes in salt chemistry. Once these fundamental mechanisms are better understood, larger models, which connect the regions, can be designed to investigate the long-term non-equilibrium behaviors exhibited by these molten salt systems. With a large enough computational effort, employing the modeling techniques discussed in this report to supplement experimental investigations, a greater understanding of the degradation of salt-facing structural materials can be gained, enabling more accurate lifetime prediction, greater safety and regulatory compliance, and faster material innovation.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Development of reactive force fields using ab initio molecular dynamics simulation minimally biased to experimental data

Incorporation of quantum mechanical electronic structure data is necessary to properly capture the physics of many chemical processes. Proton hopping in water, which involves rearrangement of chemical and hydrogen bonds, is one such example of an inherently quantum mechanical process. Standard ab initio molecular dynamics (AIMD) methods, however, do not yet accurately predict the structure of water and are therefore less than optimal for developing force fields. We have instead utilized here a recently developed method which minimally biases AIMD simulations to match limited experimental data to develop novel multiscale reactive molecular dynamics (MS-RMD) force fields by using relative entropy minimization. In this paper, we present two new MS-RMD models using such a parameterization: one which employs water with harmonic internal vibrations and another which uses anharmonic water. We show that the newly developed MS-RMD models very closely reproduce the solvation structure of the hydrated excess proton in the target AIMD data. We also find that the use of anharmonic water increases proton hopping, thereby increasing the proton diffusion constant.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Tailoring the Weight of Surface and Intralayer Edge States to Control LUMO Energies

Abstract The energies of the frontier molecular orbitals determine the optoelectronic properties in organic films, which are crucial for their application, and strongly depend on the morphology and supramolecular structure. The impact of the latter two properties on the electronic energy levels relies primarily on nearest‐neighbor interactions, which are difficult to study due to their nanoscale nature and heterogeneity. Here, an automated method is presented for fabricating thin films with a tailored ratio of surface to bulk sites and a controlled extension of domain edges, both of which are used to control nearest‐neighbor interactions. This method uses a Langmuir–Schaefer‐type rolling transfer of Langmuir layers (rtLL) to minimize flow during the deposition of rigid Langmuir layers composed of π‐conjugated molecules. Using UV–vis absorption spectroscopy, atomic force microscopy, and transmission electron microscopy, it is shown that the rtLL method advances the deposition of multi‐Langmuir layers and enables the production of films with defined morphology. The variation in nearest‐neighbor interactions is thus achieved and the resulting systematically tuned lowest unoccupied molecular orbital (LUMO) energies (determined via square‐wave voltammetry) enable the establishment of a model that functionally relates the LUMO energies to a morphological descriptor, allowing for the prediction of the range of accessible LUMO energies.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Intersublattice magnetocrystalline anisotropy using a realistic tight-binding method based on maximally localized Wannier functions

Using a realistic tight-binding Hamiltonian based on maximally localized Wannier functions, we investigate the two-ion magnetocrystalline anisotropy energy (MAE) in L 1 0 transition metal compounds. MAE contributions from throughout the Brillouin zone are obtained using magnetic force theorem calculations with and without perturbation theory. The results from both methods agree with each other, and both reflect features of the Fermi surface. The intrasublattice and intersublattice contributions to MAE are evaluated using a Green's function method. We find that the sign of the intersublattice contribution varies among compounds, and that its amplitude may be significant, suggesting MAE can not be resolved accurately in a single-ion manner. The results are further validated by scaling spin-orbit-coupling strength in density functional theory. Altogether, this realistic tight-binding method provides an effective approach to evaluate and analyze MAE while retaining the accuracy of corresponding first-principles methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Advancing density functional tight-binding method for large organic molecules through equivariant neural networks

Semi-empirical quantum-mechanical (QM) methods have become valuable tools for studying complex (bio)molecular systems due to their balance between computational efficiency and accuracy. A key aspect of these methods is their parameterization, which not only governs the reliability of the results but also provides an opportunity to enhance their overall performance. In our previous work [J. Phys. Chem. Lett., 2021, 11, 16], we advanced the third-order semi-empirical density functional tight-binding (DFTB3) method for computing multiple properties of small molecules by developing the machine learning (ML) potential NN rep to bridge the gap between DFTB3 electronic components and those of the hybrid DFT-PBE0 functional. To overcome the limitations of NN rep , we introduce the EquiDTB framework, which leverages physics-inspired equivariant neural networks (NN) to parameterize scalable and transferable many-body Δ TB potentials, replacing the standard pairwise DFTB repulsive potential. This advancement extends the applicability of our ML-corrected DFTB approach to larger molecules and non-covalent systems (including only C, N, O, and H atoms), going beyond the chemical space represented in the training QM datasets. The enhanced performance of EquiDTB over the standard TB methods is demonstrated by the accurate computation of the atomic forces of S66x8 molecular dimers, as well as their interaction energies. Moreover, EquiDTB can be effectively employed to explore the potential energy surfaces of large and flexible drug-like molecules—for example, to determine the minimum energy path between isomers, analyze structural transitions during dynamical simulations, compute vibrational modes, and investigate energetic rankings. The performance for single molecules slightly decreases when the DFTB electronic energy is reduced to first-order but remains superior to standard TB methods. Our work thus demonstrates that an optimal integration of an equivariant NN with QM datasets can advance the DFTB method while maintaining high efficiency, paving the way for reliable (bio)molecular simulations.

Medrano Sandonas, Leonardo [Technische Universität↗
DOE OSTI2012

Online Image-based Monitoring of Soft-tissue Displacements for Radiation Therapy of the Prostate

Purpose: Emerging prolonged, hypofractionated radiotherapy regimens rely on high-dose conformality to minimize toxicity and thus can benefit from image guidance systems that continuously monitor target position during beam delivery. To address this need we previously developed, as a potential add-on device for existing linear accelerators, a novel telerobotic ultrasound system capable of real-time, soft-tissue imaging. Expanding on this capability, the aim of this work was to develop and characterize an image-based technique for real-time detection of prostate displacements. Methods and Materials: Image processing techniques were implemented on spatially localized ultrasound images to generate two parameters representing prostate displacements in real time. In a phantom and five volunteers, soft-tissue targets were continuously imaged with a customized robotic manipulator while recording the two tissue displacement parameters (TDPs). Variations of the TDPs in the absence of tissue displacements were evaluated, as was the sensitivity of the TDPs to prostate translations and rotations. Robustness of the approach to probe force was also investigated. Results: With 95% confidence, the proposed method detected in vivo prostate displacements before they exceeded 2.3, 2.5, and 2.8 mm in anteroposterior, superoinferior, and mediolateral directions. Prostate pitch was detected before exceeding 4.7 Degree-Sign at 95% confidence. Total system time lag averaged 173 ms, mostly limited by ultrasound acquisition rate. False positives (FPs) (FP) in the absence of displacements did not exceed 1.5 FP events per 10 min of continuous in vivo imaging time. Conclusions: The feasibility of using telerobotic ultrasound for real-time, soft-tissue-based monitoring of target displacements was confirmed in vivo. Such monitoring has the potential to detect small clinically relevant intrafractional variations of the prostate position during beam delivery.

62 RADIOLOGY AND NUCLEAR MEDICINE↗